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EFFECTS OF MICRO- AND NANO-SCALE SURFACE

1. Name N6 1 Wavelength 0 79031 Amplitude 98 0172 Accuracy 0 99679 Figure 2 4 AFM image of a buckled patterned produced by plasma oxidation This is a particularly nice section confirmed by the thinness of the side view in the lower portion of the figure which indicated low roughness and high uniformity 50r The parameters affecting the dimensions of the wavy patterns are the oxidation time the oxidation power the ratio of base crosslinker of the PDMS substrate the curing conditions and the pre strain Additionally the distance of the sample surface from the electrode during oxidation has a significant impact on the degree of surface oxidation and thus the pattern The parameter space can be narrowed by considering the theoretical equation increasing the oxidation via time power or distance will increase the thickness and hardness of the film layer while changing the substrate properties affects the Q value Section 2 3 1 addresses the variation of stiffness by altering the PDMS properties 31 A number of different cases were studied with each of the described parameters varied To simplify the results data is only displayed from samples cured at room temperature for 36 hours where wavelength and amplitude were both measured using AFM This data is listed in Table 6 1 in the Appendix as a list of results and process conditions In practice one can use the knowledge of the underlying mechanics as discussed in the th
2. Figure 3 4 Verification of alignment algorithm Each row contains three images that were analyzed then the histogram of energy by orientation one curve per image and then the average alignment one value per image The first row demonstrates invariance to scale and frequency The second row demonstrates invariance to number of objects and contrast The third row demonstrates that reduced alignment in a simulated population reduces the output value of the algorithm 3 1 4 Response to Feature Size We conducted a systematic study of cell responses to patterned surfaces by culturing C2C12 cells on surfaces with a range of different pattern sizes Three distinct responses were observed i On the large patterns tested cells immediately and strongly align with the wavy pattern Frames from the time lapse video M1 in the Appendix Figure 6 5 show cell behavior on a wavy surface with A 1670 nm and d 410 56 nm over 42 hours A high degree of cell alignment in this video is clearly visible and confirmed by the values measured with our alignment algorithm Such cell behavior is in agreement with observations by other researchers for features of similar size and geometry ii On the very small patterns tested cells do not show any global alignment and cell behavior is indistinguishable from that of cells grown on flat control surfaces This is shown in frames from video M2 in Figure 3 5 an experiment on a wavy surface with A 420nm and d
3. 3 Stafford C M et al A buckling based metrology for measuring the elastic moduli of polymeric thin films Nat Mater 3 545 50 2004 Kemkemer R Jungbauer S Kaufmann D amp Gruler H Cell orientation by a microgrooved substrate can be predicted by automatic control theory Biophys J 90 4701 4711 2006 Van Delft F C M J M et al Manufacturing substrate nano grooves for studying cell alignment and adhesion Microelectron Eng 85 1362 1366 2008 Teixeira A I Nealey P F amp Murphy C J Responses of human keratocytes to micro and nanostructured substrates J Biomed Mater Res A 71 369 76 2004 Dunn G A amp Heath J P A New Hypothesis of Contact in Tissue Cells Exp Cell Res 101 1 14 1976 Jiang X et al Controlling Mammalian Cell Spreading and Cytoskeletal Arrangement with Conveniently Fabricated Continuous Wavy Features on Poly dimethylsiloxane Langmuir 18 3273 3280 2002 Mathur A Moore S W Sheetz M P amp Hone J The role of feature curvature in contact guidance Acta Biomater 8 2595 2601 2012 James J Goluch E D Hu H Liu C amp Mrksich M Subcellular curvature at the perimeter of micropatterned cells influences lamellipodial distribution and cell polarity Cell Motil Cytoskeleton 65 841 852 2008 Wang L Sun B Ziemer K S Barabino G a amp Carrier R L Chemical and physical modifications to poly dimethylsiloxane surfaces affec
4. Figure 1 14 Extraction of spring constant slope and energy stored integral for a force data set The width of the translucent bands indicate the region of the measurement and the band height is the value Top image is the entire force curve for the test Left are the extracted slopes from every interval where it remains consistent and positive Right image shows a closer view of the area considered as part of the stored energy Regardless of the arrangement of the pillars the slope of the force increases as area fraction decreases This is interesting in that it might be opposite what we expect since lower area fraction is associated with a more hydrophobic droplet in this situation Such an observation is not in agreement with prior work addressing pinning on dilute pillar surfaces where such a spring constant is found to decrease as the spacing of pillars increases or the size of pillars decreases However the slope of the force is less well defined for high densities of pillars as there is less space between adjacent pillar edges The average force for experiments on dilute pillars is still much lower than on high density pillars but the fluctuations are more significant when area fraction is low Relatively dense pillar arrays here may also void the dilute pillar assumption in The capability of measuring the forces during the entire process of droplet deformation and advancement is unique to this experimental platform The topic is further
5. X bi t ih UT TA A 1 4 j Ned d i dile n j LAA j l D Ari IN m mi i PEA I nM HR E AY aM nie yt NA ae ay TENN A PEVAI i d hu JA m m 119 Figure A 5 Additional examples of alignment and confluence metrics Figure A 6 Wire diagram for automatic stage motor controller 121 Figure A 7 Optogenetics software usage instructions H ot Ke S Select the Camera window and press any of these buttons Type Press Once Press Once Press Once Toggle Toggle Toggle Toggle Toggle Toggle Toggle Toggle Toggle Increment Decrement Increment Decrement Increment Decrement Key C Esc W Description Clear Gets rid of all the illuminated spots Exit Exits the program Calibrate Starts the auto calibrations sequence Point and Click Toggles between clicking a spot to illuminate a predefined shape once and selecting a shape of arbitrary size to illuminate Tracking Toggles between tracking and stationary illumination illuminated areas will either move to follow their selection or stay at the selected location Saving Toggles between saving selections for repeated illumination blinking or just illuminating the selection once Black When Off switches between projecting black regions between illuminations while blinking and not Effective when background is not black Projection Plane Rotation switches between projecting spots to the plane imaged by
6. 24nm over 72 hours This result is also in agreement with previous studies defining a limit for sensitivity to patterns 7 iii Within a range of intermediate pattern sizes the cells are initially randomly oriented but undergo a transition to alignment as the cell population becomes confluent This phenomena is discussed in detail in the following section c 4 Ar A ber gael LN t T yy 7 QN M L D NN g Al cK VW Ves eec Ui n i 7 ett VIA DUET mi fa M I yyy i f j I i dy CA 7 M i m if 13 JA i R a TU AMATA H TA Aa tA b I f i Ri ve K Mrd ht M VA Hy 7 ils TIU PA TR LENA igh ENA AROAN YA j TEN i Pea tf iip CLE A SUN AS iy y i iM i i LM ETEA E j i M AVR BR NEC E i SUN n 20 7 y N No N S Py if T un M 1 wu t in IN Tw CNW e V AN O CZ n IY SAARI A H At S T fj thaw fl LN 98 RV Ass Ais Y Tw ds SFO u LOW A DNA NS cv sn a Wb eX d 1 EUREN EA TERRAE nm eil WA SN a ELIS CL MUN not a Uh OIN LPECPN Figure 3 5 Select frames from a time lapse sequence on a pattern with A 830nm and d 100nm Alignment increases as cell density increases Cells were seeded at an initial density of 1 0x10 cells cm and imaged over the course of 4 days Grooves run vertically in all images Scale bare is 200um 57 3 1 5 Response to Confluence and Cell Cell Interaction For patterns of intermediate size that do not immediately align we observe an interesting
7. 4 2 Optogenetics System Optogenetics is a recently popularized technique used to selectively stimulate cells using light 7 It has been predominantly used in the study of neural networks where it allows for stimulation of individual neurons to probe their function This technique has the advantages of high spatial and temporal resolution while being noninvasive and noncontact Recently the field of optogenetics has expanded to include other types of cells such as muscle cells and allowed for the control of movement in small invertebrates with light In this study the technique is utilized in an effort to improve upon a previously designed biobot to allow for more precise control rather than the spontaneous contraction in the original design A stimulation system was created to generate patterned illumination sequences that would allow a light sensitive biobot to move in a controlled manner 4 2 1 Cells To sensitize cells to light they are first genetically altered to express ion channels that activate when exposed to a particular wavelength Cells are transduced with two proteins forming light activated ion channels one to activate the cell and another to inactivate it The first protein channelrhodopsin 2 is the cation channel that opens when exposed to blue light near 470nm wavelength 7 which stimulates the cell causing it to contract The second protein is halorhodopsin which drives a chloride pump causing
8. A Lh A Ga A cen it215min E Eo ee S ee d el e e Microconstruct Width 50 um oo e 60 Qa c i et LL LL Normalized Cell Count 0 10 20 30 40 50 60 70 80 90 Cell Nuclei Orientation degrees Figure 3 2 Alignment metrics A B Manual selection of an ellipse bounding the cell C D FFT with original image in C and transformed image in D Intensity is summed along radial slices passing through the center of the image E DAPI stains the nucleus so the image is easily thresholded and an ellipse is automatically fit F Results from FFT method in C D showing that the peaks increase with increasing confluence even though cell alignment is constant Frequency based approaches have also been used to measure alignment for example in fibrous samples One example is a tutorial on how to quantify alignment by summing radial slices of a Fourier transformed image along different angles The method has been successfully applied for measuring alignment in dense cell cultures However this approach is not consistent for different cell population densities which we observe by noting that the peaks in the frequency spectrum increase as cells become confluent Additional problems for frequency methods may arise when the pattern itself is visible More flexible Gabor filters have been used to identify the local orientation in confluent cultures 7e but this approach does not specify how to quantify alignme
9. constraints are applied to all vertices on each pillar where the bounds are unique to each pillar Droplet facets are unconstrained The propagation of constraints during refinement is handled internally by SE Only one quarter of the droplet is modeled with symmetry conditions at the boundaries as seen in Figure 1 2A For symmetry in a surface model we need only apply an equality constraint to ensure boundary edges stay on the plane of the boundary Choosing to model a fourth of the droplet rather than an eighth or half gives a balance between computational efficiency difficulty of generating the model and presence of asymmetric shapes The quarter is mirrored about the center axis to produce the images of the full droplets in Figure 1 2B C Figure 1 2A also reveals the bare area near the center of the droplet which is not meshed These unmeshed facets are not included in the energy functional for gradient descent for computational efficiency because they do not change although they still contribute a constant value when reporting the total energy of the system The appropriate size of the bare area is estimated during model generation by a complex empirical function of all the system parameters In general at least one row of pillars is meshed between the bare area and the pillars on the contact line to ensure the simulation is not affected by leaving out the innermost pillars 1 1 2 Dewetting The model starts in a non equilibrium state la
10. having to tune the parameters in most cases The maximum focus is then chosen for each pixel across all images To prevent ghosting effects from blending images where individual features may look different common in phase contrast microscopy a single image is designated as the most focused for each point Blending is only performed at the interfaces between patches from the z stack images For this a novel method of blending is employed such that the low resolution component is blended over a larger scale than the high resolution components This is accomplished naturally with the pyramid approach as a constant blending kernel applied at each level of the pyramid blends coarser levels over a larger region The individual levels are thus blended alone then each level is up sampled to the final resolution and added to produce a single image The output is also slightly enhanced by weighting the low resolution contribution less than the high resolution contribution and also by increasing the weight on the high resolution component based on the focus measurement such that low focus areas have a higher weight on the high resolution component An example z stack and result is given in Figure 4 5 This algorithm is not currently integrated with the stage control software although it would not be difficult if needed the program is implemented in standard C as a single class As a standalone application it will automatically process all the image in
11. mo NOME NT P rm E Lad DX nd ad ha Figure 3 14 Co culture of RMF and MCF10a displaying typical response to the meniscus The entire image is 11mm by 11mm comprising the entire square culture well Day 6 after plating We are interested in quantifying the locations of tube formations in relation to the surface geometry The highly branched sample in Figure 3 14 is quite difficult to analyze so a less developed sample without fibroblasts was used for measuring the topography Figure 3 15 The method used to measure the topography was a best in focus technique where a microscope with a motorized stage having 1um resolution in the X and Y axes and 0 1um resolution in the Z direction was moved to bring points on the surface into focus The sample was clamped to the stage and drained of media to minimize optical distortion at the liquid air interface The stage was then maneuvered to focus on points at the center of the field of view and the location of the stage at each focused point was recorded The gel surface itself 69 is generally transparent so the points were recorded where acini were present at the location where the topmost portion of the spheroid was in focus The uncertainty in the best focused location was typically 10um while the total variation in the surface height was 1mm We are interested in height relative to the bottom of the well and the acini form very near the surface Thus this measurement was a reasonable
12. 1 by bolding the alignment value for aligned cells Table 3 1 also includes several geometric parameters that have or could be used to quantitatively characterize the patterns Each parameter is defined in terms of the pitch and depth of the pattern where size is Ad aspect ratio is d A and effective curvature is d A The effective curvature is proportional to the maximum curvature of a sinusoidal wave Additionally a parameter of our own definition Q is listed which we refer to as the sensitivity parameter The relation of these parameters to cell alignment and the merit of the sensitivity parameter are addressed in the following sections As shown in Figure 3 6 when the surface waviness is very large sparsely distributed cells align with the patterns immediately upon seeding whereas when the waviness is very small cells do not align with patterns at all For patterns within a range of intermediate dimensions cells align with the patterns as they become confluent an emergent phenomenon of high density cell populations Although alignment increases with time as well as confluence we find that confluence is the determining factor based on the observation that alignment on a single pattern varies within a culture in relation to the local cell density This phenomenon can be seen in the individual frames of the time lapse sequence in Figure 3 5 and has been indicated on the two images in Figure 3 8 These observations agree with prior work in
13. 12 hours Afterward the mold can be cured in an over at 60 80 C for gt 2 hours 40 The pattern can then be removed from the mold and cut out into the desired shape for use in culture After cutting to size apply TDFS to the patterned PDMS and allow to sit in a fume hood gt 12 hours Rinse with methanol and dry to remove excess TDFS The pattern should now be non stick and unreactive so it may be used to imprint the surface pattern onto other material The suggested use is to pour PDMS into the desired culture container then drop the nonstick pattern on top degas and allow to cure After removing the nonstick PDMS the pattern remaining may be coated with ECM proteins or gel and used in place It may be necessary to briefly oxidize the surface for 30 seconds in order to allow the gel or protein to wet and adhere to the surface The final product before adding protein or gel should look like Figure 2 14 Figure 2 14 Patterns in 35mm l dishes ready for culturing cells cro fj Left 330um buckled pattern enu Y copy Right 1 6um commercial diffraction grating copy Mr ENG lt ad 1 f i N An alternative replication method particularly useful for PDMS on PDMS buckled patterns where the pattern is stable in the strained state is to produce a stamp that can be immersed and replicated in culture dishes This is done by bonding the buckled pattern to a glass slide so that the glass slide rests on the lip of a culture dish
14. Brittain S Evans A Hutchinson J amp Whitesides G Spontaneous formation of ordered structures in thin Nature 393 146 148 1998 Lam M T Sim S Zhu X amp Takayama S The effect of continuous wavy micropatterns on silicone substrates on the alignment of skeletal muscle myoblasts and myotubes Biomaterials 27 4340 4347 2006 Harrison C Stafford C M Zhang W amp Karim A Sinusoidal phase grating created by a tunably buckled surface Appl Phys Lett 85 4016 2004 Kim D H Ghaffari R Lu N amp Rogers J a Flexible and stretchable electronics for biointegrated devices Annu Rev Biomed Eng 14 113 28 2012 Groenewold J Wrinkling of plates coupled with soft elastic media Phys A Stat Mech its Appl 298 32 45 2001 Bowden N Huck W T S Paul K E amp Whitesides G M The controlled formation of ordered sinusoidal structures by plasma oxidation of an elastomeric polymer Appl Phys Lett 75 2557 1999 Mora T amp Boudaoud a Buckling of swelling gels Eur Phys J E Soft Matter 20 119 24 2006 105 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Volynskii A L Bazhenov S Lebedeva O V amp Bakeev N F Mechanical buckling instability of thin coatings deposited on soft polymer substrates J Mater Sci 5 547 554 2000 Choi W M et al Biaxially stretchable wavy silicon nanomembranes Nano Let
15. PDMS Silicone sealant stamp mounted on a 3 x 1 glass slide with some additional black electrical tape The pattern is inverted and the taped area is placed on the rim of a 35mm culture dish PDMS is added to submerge the patterned top of the stamp To make a pattern at the bottom of a divot pour PDMS into a 35mm culture dish and then place the stamp inverted so that the glass slide rests on the lip of the 35mm culture dish and the patterned top of the stamp is slightly submerged in the uncured PDMS It is important to submerge the patterned side of the stamp at an angle as if peeling from the surface in reverse so air is not trapped at the pattern surface Degas the PDMS and the construct can be immediately cured at 60 C for 4 hours An X acto knife will be required to gently separate the stamp and the printed pattern without damaging the stamp The final product should look like Figure 2 16 Figure 2 16 Result of copying the stamp in the figure above The embossed pattern is convenient for filling with hydrogels 42 Patterns may also be replicated as and used as thin films This is particularly relevant for submicron wavelength patterns because they may be viewed with high numerical aperture objectives The focal length of such an objective can be lt 200um This short distance can be accommodated by mounting the pattern directly on a piece of cover glass Following the same procedures outlined above the final step is replac
16. all ScrnSz get 0 ScreenSize saveType png or emf or eps if exist dirName var dirName uigetdir end dirFiles dir dirName for ii 1 length dirFiles gt Import data oo fName dirName dirFiles ii name if exist fName file strcmpi fName end 3 end txt 1 continue end afmDat importdata fName img afmDat data ptDim size img 2 img 1LO O img Ls pcDim 3 66 Extract sample info samplufo strsplit dirriles 11 name a if length sampInfo 5 sampLbl sampInfo 1 d sampNo sampInfo 2 trueDim sscant samplinfo 3 d ScanNo sscanf sampinfo 4 d else disp Incorrect name um u scan number gt txt sampLbl dirFiles ii name SampNo L trueDim 1000 scanNo 1 end 5 Get approximate rotation angle ft abs fft2 img ft2 ft 1 floor ptDim 8 1 floor ptDim 8 ftMaxLoc max ft2 naxY maxX ind2sub floor ptDim 8 floor ptDim 8 ft2 padarray ft2 1 1 replicate ft2NearMax t2 maxY maxY 2 maxX maxX 2 2 112 strcempi fName end 3 end dat 1 amp amp use format sample label sample number dimension in ftMaxLoc Figure A 2 continued Matlab script to extract wavelength and amplitude from AFM data WoOLY i eL le Qo 0 OX 1 1 dg meaxy lL WOLX ehe d 1 s1 U 1 aiiax 1 maxY2 sum sum wgtY ft2NearMax sum f
17. and causes fracture This could be prevented by applying biaxial strain to counteract the lateral contraction during pre strain One way this can be done is to heat the sample during pre strain or film deposition PDMS has a very high thermal expansion coefficient so lateral strains exceeding 596 can be negated by heating the sample within the working temperature range of the material Efforts to accomplish this so far have been unsuccessful but a renewed effort may prove fruitful Eliminating the lateral stresses in the film may also help decrease dislocation defects and variation in the wavelength throughout the buckled surface 49 3 Cell Response to Physical Features Tissues in biological systems are formed by complex but highly organized cells Extra cellular cues that cause cells to organize themselves is a topic of tremendous importance Among other factors the in vivo environment of a cell includes a wide variety of mechanical signals which may originate from the extracellular matrix or other cells It is well known that cells respond to these mechanical signals by potentially altering many aspects of their behavior This response is termed mechanotransduction A better understanding of mechanotransduction will have an impact in fields ranging from developmental biology to tissue engineering A variety of techniques have been used to study mechanotransduction one of which is to observe cellular responses to topographic features Res
18. and the pattern extends into the dish The dish is then filled with the replication material PDMS as described here but a hydrogel could also be directly printed patterned Depending on the desired thickness of the replica in the culture dish a layer of PDMS could be built up on top of the glass slide so the stamp will extend the necessary distance into the culture container This can be done by cutting out several slabs of PDMS in the shape of the buckled pattern and then bonding them to each other and to the glass slide The bonding can be done via plasma oxidizing both faces for 30 seconds at 100W or by using 100 silicone adhesive sealant Dow Corning Either way the bonded parts should be left in an oven at 60 C for 24 hours after bonding The edges of the stack of PDMS strips will likely be rough and irregular at this point so they must be cut into a tapered shape like a pyramid 41 Starting at the top the patterned face with a razor blade cut down to the base of the stamp the glass slide tapered slightly so that the stamp is wider near the glass slide than it is at the buckled face Repeat the cutting for each side of the stamp Once the pyramid shaped stamp is cut and each side is tapered one may wish to apply another layer of silicone sealant or PDMS if the edges are not smooth and flat Apply TDFS to the finished stamp as described above to make it nonstick Figure 2 15 shows a picture of a completed stamp Figure 2 15
19. as practical methods that allow such tuning The wide range of length scales also results in a number of techniques to measure the waves One additional topic that is rarely discussed in the context of buckled wavy patterns is the quality of the pattern which may vary significantly depending on the technique and processing conditions Thus attention is given to improving the quality of these buckled patterns 26 2 1 Theory The equations governing the buckling of a thin rigid film on a compliant substrate can be solved analytically If the substrate is assumed infinitely thick this is a classical mechanics problem Considering the context of the buckling we are working with here one of the earliest formulations is given in where strain is assumed to be small In fact most of the samples used for buckling herein have polydimethylsiloxane PDMS Sylgard 184 as the substrate which is a highly stretchable elastomer Thus a more accurate set of equations has been derived for large strains in It should be noted that the only difference in the finite deformation model is the addition of the terms containing y which are derived from equations for the shape of accordion bellows The factor y tends to O for small strains The values we are most concerned with are the critical strain above which buckling occurs the wavelength and the amplitude These are given in the following set of equations Ratio of Plain Strain Moduli Q I E EET E
20. cause some confusion if regions overlap the order of selection might change behavior A toggle will be available soon Pressing V will start recording the contents of the Camera window exactly as it appears on the computer The file should have some name like date time avi The file is saved in the same folder as the executable and config dat which is something like Optogenetics Release If you re using a shortcut right click the shortcut and select Open File Location When you exit the program all your settings should be saved in a file called config dat If available the settings are loaded when the program starts The config dat file will be created and loaded from the same folder as the executable so you can load transfer a saved configuration by putting config dat in this folder See Recording Video for finding the folder The preferred way to exit the program is to select any window and press Esc If the program freezes it s usually best to just use End Task and restart It won t hurt anything 125
21. cells are found to be 44 confluent with alignment of 0 09 B D F The same cells that have grown to confluence their area coverage and the orientation energy histogram respectively The cells are now 97 confluent with alignment of 0 61 In 45 90 135 45 90 135 Orientation Angle Orientation Angle 55 Figure 3 3 shows the visual output from the confluence and alignment algorithms for two example images with low and high confluence cells The binarized images show the area covered by the cells and the plots show the spectral energy histogram from the alignment measurement This demonstrates that the method described here provides a consistent measurement of cell alignment for a wide range of cell distributions Additional characterization of the alignment algorithm demonstrating the invariance to changes in cell density and contrast is given in Figure 3 4 where a number of test images have been generated with varying contrast spacing and alignment The Matlab script performing the confluence and alignment measurements is available in the Appendix Figure 6 3 along with additional example images showing the measured values in Appendix Figure 6 4 Alignment 135 45 90 2 Orientation Angle Image Number 135 t o 2 x 45 90 2 Orientation Angle Image Number Alignment 135 45 90 2 Orientation Angle Image Number
22. dependence of alignment on the confluence of the cell population For certain patterns cells that do not align as sparsely seeded individuals may begin to align as the population increases and cells interact with one another The phenomenon is most striking when viewed in a time lapse movie for example Figure 3 5 shows select frames in a time lapse sequence for a pattern with 420nm pitch and 52nm depth demonstrating the typical alignment on an intermediate sized pattern The trend can be captured quantitatively by using the previously discussed image analysis algorithms to measure alignment and confluence Alignment data from three time lapse recordings showing three distinct types of alignment behavior are given in Figure 3 6 as a function of time and confluence Immediately aligning and non aligning cells show nearly constant alignment values as the culture grows from very sparse lt 15 confluent to very dense nearly 100 confluent while the cell cultures exhibiting delayed alignment tend to show a relatively sharp transition from low to high alignment at high confluence From the data and visual observations it is clear the effect of confluence on alignment is non linear and the transition li li edes 9 Ls Figure 3 6 Normalized alignment and S7 confluence data from three separate time Repeal e j T 4 e lapse video sequences Each sequence shows Cj APerod 420nm eee a distinct trend Blue squares very small E Bd dE a pattern
23. depinning and advancement at the trailing edge of the droplet and also correlation to a second smaller decrease in force shortly afterward Even so multiple oscillations occur after the major depinning events that cannot be explained by the contact line alone The flat areas in the center of mass curve in Figure 1 16 indicate no change in contact line and yet the force oscillates strongly during this period There is certainly some relation between changes in 22 the contact line and changes in the force but the situation is more complex than can be captured with linear correlation prem Force oscillates while Data from force4 ee contact line is constant 4 Advancing event mE o o X s Je UV Adi x 11H ple a eee o a 54 X J o 2 O i i 1 u a 52 No change in 5 i contact line 2 50 5 lt 48 46 3000 3100 3200 3300 3400 3500 3600 frame number Figure 1 16 Plot of the change in contact area centroid above the smoothed force curve as a function of the frame number Spikes in the centroid curve indicate depinning events The circled purple areas are times when the contact line remains constant but force still oscillates 1 3 3 Anomalous Frequency and Droplet Oscillations The particular plot in Figure 1 16 makes it apparent that there is a higher frequency mode in addition to the main mode associated with the droplet advancing
24. discussed in 7 and the work is ongoing It would be interesting to suppress the higher frequencies in the force curve so the force curve can be more precisely analyzed without the need for a large smoothing kernel 20 1 3 2 Identifying Pillars Correlating changes in the contact line to trends in the force curve requires identifying the contact line over numerous frames in the video This is especially challenging because there are generally 5 000 10 000 frames from high speed video in a given experiment too many frames to analyze by hand A fast automated method is needed to process all these frames while maintaining perfect contact line detection accuracy so a correlation may be performed The task is complicated by the low signal to noise ratio of the wetted pillar tops distortion produced by lensing from the curved droplet and light flickering causing the image contrast to change each frame The successful process flow was to apply a Kalman stack filter to mitigate flickering effects then run a frequency band pass filter for a bandta factor of 2 around the repeat spacing of the pillars to enhance the pillars Finding the exact contact line is not possible manually or via image processing but identifying the outermost wet pillars can be done To identify wet pillars the exact location of all pillars must be known A subroutine accepts either automatically detected or manually selected pillar locations on the raw image and finds all cen
25. is similar to the others in the sequence and topography of the specimen is a smooth continuous surface While this case is relatively simple a fast and automated method of consistently processing hundreds of similar images is necessary for practical use This particular functionality is not well satisfied by existing work Given a set of images of a scene it is assumed that portions of the scene are best focused in only one image in the set and portions of each image that are not in focus are blurry The area in focus is expected to smoothly vary so that small changes in position lead to small changes in the quality of focus The algorithm borrows an idea from by decomposing the image into a Gaussian contrast pyramid storing the difference between each level of the Gaussian pyramid This quickly separates the features at different length scales in the image and allows efficiently blending features at each level of resolution The separation also aids in determining the level of focus where the highest layers of the pyramid correspond to the highest frequency details and increased detail corresponds to high focus After decomposing into a pyramid each image is processed to calculate a value for the focus as a function of space Focus is calculated in a simple manner similar to which has been implemented in ImageJ where the local variance in the intensity level is taken as a measure of sharpness High variance indicates the pres
26. measure and values above this threshold have been bolded The column is the parameter we propose to describe the sensitivity of cells to periodic pattern The list is sorted by 9 which shows there is a clear alignment threshold at 0 006 for individual cells and at 0 002 for confluent groups What distinguishes confluent and sparsely distributed cell populations is the presence of cell cell interaction Cell cell interaction has been shown to have a strong effect on cell behavior that may even override signaling from the ECM Cell cell interaction has also been shown to play a role in cell alignment It is well known that polarized cells tend to locally align with one another when in contact and it has been suggested that the mechanism causing this mutual alignment is contact inhibition occurring when the lamellipodia touch The interaction of mutually aligning objects has also been studied using integro differential equations 76 80 81 This mathematical approach lends some insight into how global alignment may arise from local interactions The critical parameters determining the stability of local or global alignment were found to be the rate at which cells move in culture their rate of mutual alignment and the likelihood that neighbors will mutually align Mathematical analysis of global alignment in the presence of a patterned bias is lacking however and experimental results are not in agreement In some cases ce
27. no alignment Red circles Large SD m Period 420nm Eus i T Depth 24nm A 0 5 pattern alignment is immediate and mostly E af aB constant Green triangles Medium pattern N E alignment increases sharply as cells become ry confluent O at Z a A aA MA AA A A I 3 Aba aan hA saat hA FE Im ld rd ri MN A 0 i Confluence Figure 3 7 A Unaligned cells after 1 day on a pattern with 420nm and d 52nm B The same cells after growing to confluence and culturing in differentiation media for 7 days The resulting myotubes align even though the individual myoblasts do not align until they become 3 confluent Scale bar is 200um in alignment appears to be most dramatic after cells have reached approximately 70 confluence Interestingly cultures that exhibit delayed alignment are nearly indistinguishable from cultures that immediately align once both are confluent Either pathway to alignment will also lead to well aligned myotubes after differentiation is induced in cultures of C2C12 myoblasts Figure 3 7 The dimensions of all patterns examined in this study are given in Table 3 1 along with a summary of the alignment results from the various patterns We observe a distinct cutoff at an alignment value of 0 3 that separates cultures that do not visibly align from cultures that do align to some degree Using this cutoff cultures were categorized in a binary fashion as either aligned or unaligned in Table 3
28. not occur often 85 4 1 4 Motor Controller The motor controller is the portion of the electrical system that allows the computer to control the movement of the motors To keep the system low cost the motor is controlled at a low level using off the shelf electronics components In the present implementation the computer outputs a digital signal via its parallel port the ability to output via a microcontroller or data acquisition system is built into the source code which is connected to a circuit board containing components that send the appropriate current to the motors The digital signal from the computer is translated to the stepper motors via three stepper driver carriers Pololu part 1182 The driver carrier chips provide an accessible interface to the A4988 chip which handles the logic of driving current to the motors A picture of the actual part is given in Figure 4 3 along with the camera and cooling fan More detailed information about how the electronics work troubleshooting and a circuit diagram are available in the Appendix Figure 6 6 NUT RS Jud Ste b TEA 7 SN Figure 4 3 Electronics controlling the system On the left is the Point Grey Flea 3 camera the center is the motor controller receiving parallel port input via the gray ribbon cable and on the right is a fan to keep the camera and controller circuitry cool i M VA iN I z 4 1 5 Environmental Control The environme
29. of the affine transformation between camera space and projector space In practice the components may be adjusted several times during an experiment to optimize the view so the procedure must be fast and simple to use in order to maintain workflow 99 A prior method of accomplishing this task was a manual approach where the projector displays a 5x5 grid of circles which the user must click in order on the camera window This technique is not sufficient in the current setup because some of the grid would typically not be visible on the camera or it may be rotated 90 or 180 relative to the user Instead the system adaptively projects a sequence of randomly located dots which the program attempts to automatically locate in the camera window One red one green and one blue dot are simultaneously displayed every 50ms because the colors are easily distinguished from the separate channels of the color image tripling throughput over a monochrome version Successfully detected dots are saved as a pair of coordinates in projector and camera space When enough points have been detected to reliably determine the correspondence a RANSAC algorithm is applied to robustly calculate the transformation Because only a small fraction of the projector s image has been visible to the camera at different times during the system s development the algorithm must adapt the size and location of the displayed dots to match the visible region To do this robust
30. one pillar This is generally not as clear in other portions of the force data A more precise analysis is performed by obtaining the discrete Fourier transform of the data series The spectral data is plotted as a period plot in Figure 1 17 where the period and amplitude are rescaled so the dominant frequency lies at 1 1 The plot confirms that there is unexpected spectral energy near 1 5 the primary frequency which matches the apparent trend in the smoothed force curve 23 FFT Data from force4 Late Steady State X 0 9988 Veal 1 m 0 8 z 4 Extraneous high frequency response not depinning 0 4 X 0 203 Y 0 2957 X 0 4994 Y 0 2423 X 0 3329 m Y 0 192 0 2 X 0 2497 Nu Y 0 1582 m 1 f Normalized 1 pillar advance 1 Figure 1 17 Period plot of the spectral data from a force time data set rescaled so the primary frequency is unity The large noise near 1 5 the primary period is too large and distributed to be a harmonic of the primary response indicating that an extraneous frequency is present during the experiment This phenomenon cannot be directly explained by any feature of the contact line Close inspection of raw video frames suggest the droplet may be oscillating or vibrating upon recoiling from advancing a row of pillars This may be inherent to the experiment or the result of resonance from the measurement apparatus or it may arise d
31. over several waves A slightly more accurate method averaging over the entire image is to apply a Fourier transform and pick out the dominant frequency This is preferred because the wavy patterns tend to have numerous dislocation defects where one buckled wave merges into another Any imperfection or non uniformity in the strain field will result in local variations in the wavelength so this value is best characterized by averaging over a large area The fast Fourier transform FFT over a reasonable area tends to be consistent across the entire sample for uniaxially buckled samples An interesting application of this same concept is to perform the frequency transform optically i e with laser light The buckled pattern forms a diffraction grating and the average wavelength can be directly calculated from the spacing between maxima in the diffraction pattern dsin mA Where d is the wavelength of the pattern A is the wavelength of the light and O is the spread angle from the pattern to the m maximum in the diffraction pattern This measurement technique allows fast determination of the wavelength and orientation of a pattern down to the wavelength of the laser source Handheld blue 405nm laser pointers are particularly useful for quick measurements and determining the orientation of patterns For the amplitude AFM is perhaps the best way to measure micron scale wavy patterns The topography was characterized using an Asylum
32. process similar to a groove fabrication method previously described Standardized gratings are made with pitches in the range of 200nm 2um wavelength a range relevant for inducing cell alignment Although the patterns come with a predetermined groove depth the surface is fragile and tends to wear down over time The wearing reduces the amplitude but leaves the wavelength unchanged which allowed us to generate several different aspect ratios using a few master molds Figure 2 11 Fused silica diffraction gratings from Edmund Optics The apparent color is due to white light diffracting off the surface and being separated into its component wavelengths Holographic patterns used for cell biology experiments were purchased from Thor Labs and Edmund Optics A picture of some of the gratings used to make patterns in PDMS is given in Figure 2 11 The patterns are sold by the number of lines per millimeter with the available line counts generally being 600 1200 1800 2400 and 3600 lines mm where 600 lines mm is 1 6671 m wavelength and 3600 lines mm is 278nm wavelength Information about the exact surface profile and depth are not available but gratings are typically sold with separate versions available for use in the visible light spectrum and the UV spectrum The depth of the visible spectrum patterns is larger than those for the UV patterns presumably due to the shorter wavelength in the UV spectrum Although most of the patterns used
33. same surface with higher area fraction due to pinning and contact angle hysteresis A common way to study moving droplets and contact angle hysteresis in the past has been to use an inclined plane and gravity to identify the leading and trailing angles at which droplets become unpinned 3 gt Here a novel experiment has been designed as described previously allowing continuous monitoring of a droplet sliding along a superhydrophobic surface while also recording the force applied to keep it in constant velocity motion and the contact area Briefly a fluorescein salt is dissolved in water to allow high speed imaging of the droplet contact area with an inverted microscope when the droplet is exposed to laser light A PDMS sphere is attached to a high sensitivity force sensor which is adhered to the droplet by surface tension to allow pulling the droplet while recording the force See for additional details The focus here is analyzing the data from the experiment in order to extract information about the droplet s resistance to motion on the pattern and to try and relate this to the behavior of the contact line 1 3 1 Force Data Analysis Initial experimental analysis addresses only the force portion of the data The data is highly smoothed to analyze the simple saw toothed variation in the force and ignore higher frequency details The force curve after the moving droplet reaches a steady state can then be roughly described as a pe
34. strainer with bolts used to apply force to the compression plates B Close up of one clamping mechanism The compression plate with the two holes can be turned sideways to switch between the bolt clamping and latch clamping C The latching mechanism allows quick loading and release while minimizing strain due to uneven clamping The arm locks into a notch at the bottom of the image like the lock on a suitcase or tool chest 29 2 2 1 Plasma Oxidation Plasma oxidation is a process where a material is exposed to high energy electrons in the presence of pure oxygen at low pressure The electron energies in the plasma may reach 20 000 30 000 C while the bulk of the sample remains close to the ambient temperature inducing a variety of oxidation reactions that would not chemically occur such as the cleavage of methyl groups attached to the silicon atoms in PDMS and replacement with oxygen This is a very common procedure applied to PDMS and a number of researchers have exploited the thin oxide layer not only as the thin film in this buckling process but also to increase wettability and functionalize the surface in other contexts Conflicting reports exist for the exact properties of the oxide layer which are difficult to directly measure The oxide layer has been reported to be from 6nm 500nm thick with an elastic modulus anywhere from that of silicon oxide 70GPa down to about an order of magnitude greater than bare PDMS 12MPa Rea
35. the camera or the plane rotation the projector naturally projects to Video Press once to start video and again to stop video Records each frame of the Camera window at the frame rate being displayed see X Frequency Now prints the refresh rate of the projector window Later the actual measured frequency of repeated illumination averaged over a few cycles Time prints the time between successive frames displayed For testing how fast slow the program is running usually depends on camera exposure time Debug toggles printing information about calculations like projection plane calculation Size increase decrease size of predefined shape Color Cycle through the predefined illumination colors Shape Cycle through the predefined illumination shapes 122 Figure A 7 continued Optogenetics software usage instructions Co ntrols Sliders Slide these bars on the Controls window to change values Label Description Duty Cycle The percentage of time illuminated spots will be on when they are blinking Frequency The frequency at which the illuminated spots blink in Hertz 100 Phase As a percentage of one period the time delay between the illumination of successive spots of Dots Maximum number of tracked spots Ex set to less than total spots temporarily turn off some spots or overwrite earlier spots Back Int Brightness of the background projected by the projector 0 is black no background the projector w
36. the same specimen and then merge the data into a single image video For 3D cultures and gel specimens these several locations may be at different depths in the gel as well as different points within the same focal plane These acquisition and data condensing techniques are also useful for single exposure non time lapse images where an extended field of focus or larger viewing window can reveal information not possible from a single image Each of these situations should be possible to handle using this custom system 83 4 1 2 Microscope and Camera The microscope used for the system is a Nikon Diaphot TMD that was generously donated by Professor Ann Narduli This is a relatively old microscope that uses Hoffman modulation contrast optics which requires a unique set of objective lenses and corresponding polarized filters It should be noted that these items are no longer in production so upgrading the optics would necessitate replacing all the Optics Several cameras have been used with this system and microscope but the current model is a Point Grey Research Flea 3 0 which offers a low cost small package design with 2 0MP resolution monochrome output The current software accesses the camera directly through the manufacturer s API for a high degree of control over the camera s setting Earlier versions of the software contain code using Microsoft s DirectShow to interface with the camera at a low level which has the benefit of bein
37. was identified as a problem in previous studies so it is expected that a successfully transfected population of C2C12 should be reactive in the current configuration After a working C2C12 biobot is demonstrated the next step will likely be to innervate the muscle strip with neurons and then stimulate the neurons to induce contraction The stimulation system should be a useful tool in testing the different components of an integrated biobot design in line with the long term goals of the EBICS NSF STC 103 References 10 11 12 13 14 15 16 17 Cassie A B D amp Baxter S Wettability of porous surfaces Trans Faraday Soc 40 546 551 1944 McHale G Cassie and Wenzel were they really so wrong Langmuir 23 8200 5 2007 Gao L amp McCarthy T J How Wenzel and cassie were wrong Langmuir 23 3762 5 2007 Gao L amp McCarthy T J An attempt to correct the faulty intuition perpetuated by the Wenzel and Cassie laws Langmuir 25 7249 55 2009 Marmur A amp Bittoun E When Wenzel and Cassie are right reconciling local and global considerations Langmuir 25 1277 81 2009 Whyman G Bormashenko E amp Stein T The rigorous derivation of Young Cassie Baxter and Wenzel equations and the analysis of the contact angle hysteresis phenomenon Chem Phys Lett 450 355 359 2008 Cubaud T amp Fermigier M Advancing contact lines on chemically patterned surfaces J Colloid I
38. 001 0 0001 0 01 Effective Curvature nm t Sutherland 2005 Fibroblasts Grooves xe x WEB xx 1 x Loesburg 2007 Fibroblasts Grooves Clark 1990 Fibroblasts Grooves Biela 2009 Fibroblasts x Grooves 0 5 Wang 2010 Myoblasts Grooves Our Data Myoblasts Waves A Jiang 2002 Endothelial x Waves 100000 1000000 Pitch nm Figure 3 9 Alignment data from a number of different groups and cell types 909771778285 plotted against various parameters characterizing periodic features Data was collected from tables and figures from prior work characterizing alignment on periodic features and original alignment measures were linearly rescaled between 0 and 1 A valid phenomenological pattern should capture all the data as a single curve and alignment should increase monotonically as the parameter increases Such a trend is not observed for these parameters None of these models however has been rigorously verified and the assumptions for each model are not alike In order to check if any previously defined parameter could generally describe alignment over a large range of length scales we plotted our data along with data from several other research groups against these parameters Figure 3 9 compares normalized alignment data from several groups against a number of parameters It is clear that no obvious pattern is observed when the normalized alignment is plotted against any of these
39. 2 3 7end 4 end 3 0 outlierImg ifft2 outlierFt symmetric outlierDifl img outlierImg outlierDif abs outlierDif1 img2 img img2 outlierDif gt mean outlierDif 2 std outlierDif NaN 6 Analysis waveLength trueDim sqrt maxX2 24maxY2 2 cos pi turnAng 180 meanAmp pi nanmean abs img2 rmsAmp 2 1 5 nanmesn img2 s 4 2 455 waveAmp meanAmpt rmsAmp 2 ampQual 1 4 abs meanAmp rmsAmp waveAmp surfPts linspace trueDim ptDim newSize ptDim 2 trueDim ptDim newSize ptDim 2 newSize xx yy meshgrid surfPts surfPts XXX xx outlierDif gt mean outlierDif 2 std outlierDif yyy yy utlierDif gt mean outlierDir Z std outlrierDif i imz 1mq outlierbit gt mean outlrerDif 2 std outlierDif sin2d fittype a sainiz pu x b 27a ye d dependent z independent x Tyt ooefficients a b Ten d 1 5 pFit rsq fit xxx yyy imz sin2d startpoint waveAmp 2 0 1 waveLength 0 Sp2 linspace min surfPts max surfPts 768 x2 y2 m shgrid sp2 sp2 Display and Save titleText lambda num2str 1 sqrt pFit b 2 pFit c 2 3 mum o gt Lnum2sStri 2 pETLt a 3 nm R 12 numZ2str rsq rsquare 3 1 close all mdf mean outlierDif sdf lo stdioutlrerDLr 3 img outlierDif gt mdf sdf img outlierDif gt mdf sd
40. 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 Courbin L et al Imbibition by polygonal spreading on microdecorated surfaces Nat Mater 6 661 4 2007 Cubaud T amp Fermigier M Faceted drops on heterogeneous surfaces Europhys Lett 55 239 245 2001 Ahuja a et al Nanonails a simple geometrical approach to electrically tunable superlyophobic surfaces Langmuir 24 9 14 2008 Boucher E Evans M amp Jones T The computation of interface shapes for capillary systems in a gravitational field Adv Colloid Interface Sci 27 43 79 1987 Dufour R et al Engineering sticky superomniphobic surfaces on transparent and flexible PDMS substrate Langmuir 26 17242 7 2010 Hao P Lv C Yao Z amp He F Sliding behavior of water droplet on superhydrophobic surface EPL Europhysics Lett 90 66003 2010 Mahadevan L amp Pomeau Y Rolling Droplets Phys Fluids 11 2449 2453 1999 Quere D Drops at Rest on a Tilted Plane Langmuir 14 2213 2216 1998 Li H Solid Liquid Interactions in Microscale Structures and Devices 1 137 2011 Reyssat M amp Qu r D Contact angle hysteresis generated by strong dilute defects J Phys Chem B 113 3906 9 2009 Hutchinson J W Thouless M D amp Liniger E G Growth and Configurational Stability of Circular Buckling Driven Film Delaminations Acta Met Mater 40 295 308 1992 Bowden N
41. 35852 2012 Guo C et al Long range mechanical force enables self assembly of epithelial tubular patterns 2012 doi 10 1073 pnas 1114781109 DCSupplemental www pnas org cgi doi 10 1073 pnas 1114781109 Lee G Y Kenny P A Lee E H amp Bissell M J Three dimensional culture models of normal and malignant breast epithelial cells 4 359 365 2007 Szeliski R Image Alignment and Stitching A Tutorial Found Trends Comput Graph Vis 2 1 104 2006 Preibisch S Saalfeld S amp Tomancak P Globally optimal stitching of tiled 3D microscopic image acquisitions Bioinformatics 25 1463 5 2009 109 103 104 105 106 107 108 109 110 111 112 113 114 115 116 Hovden R Xin H L amp Muller D a Extended depth of field for high resolution scanning transmission electron microscopy Microsc Microanal 17 75 80 2011 Toet A amp Ruyven V Merging thermal and visual images by a contrast pyramid 28 789 792 1989 Aguet F Member S Ville D Van De amp Unser M Model Based 2 5D Deconvolution for Extended Depth of Field in Brightfield Microscopy IEEE Trans image Process 17 1144 1153 2008 Forster B Van De Ville D Berent J Sage D amp Unser M Complex wavelets for extended depth of field a new method for the fusion of multichannel microscopy images Microsc Res Tech 65 33 42 2004 Zemelman B V Lee G A Ng M amp Mies
42. CL Ve a 5e 1 Finite Strain Factor y C 1 1 Critical Strain amp ale 2nh 3Q 3 Wavelength 2 1 14 y h RE 1 Amplitude A P V1 t 1 y 1 2 In these equations the f subscript is referring to the film and the s subscript refers to the substrate The mismatch in strain between the film and the substrate the film must be more strained is given by and the thickness of the film is given by h These equations give us all the information needed to understand how to design a system with a desired wavelength and amplitude Several observations should be made regarding these equations first only the ratio of plain strain moduli is relevant not the modulus of either material alone Second both wavelength and amplitude are linearly proportional to the thickness of the film Third the wavelength will increase as the film becomes harder relative to the 27 substrate but only slowly with the cube root of the ratio Fourth the amplitude is somewhat independent of the ratio of moduli This last point is important for understanding how to decouple the wavelength and amplitude to some degree Although the two are strongly coupled by the film thickness we may adjust the strain to change the aspect ratio This is plotted in Figure 2 1 where the ratio of moduli is scaled logarithmically 1000 AJA 0 0 Figure 2 1 Theoretical aspe
43. EFFECTS OF MICRO AND NANO SCALE SURFACE GEOMETRY ON BEHAVIORS OF LIVE CELLS AND LIQUID DROPLETS BY MICHAEL GRIGOLA THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering in the Graduate College of the University of Illinois at Urbana Champaign 2014 Urbana Illinois Adviser Professor K Jimmy Hsia Abstract As the scale of the surface texture responsible for superhydrophobicity becomes similar to the size of a droplet simple models based on homogeneity assumptions begin to break down In order to better understand these discrete phenomena we first create a unique model with the finite element software Surface Evolver which simulates a droplet atop the individual features that comprise a superhydrophobic surface We observe that the well known Cassie Baxter and spherical cap models give poor estimates of characteristics such as contact angle and wet area and also fail to capture the complex liquid surface geometry when features have discrete size Further exploring this theme we consider the influence of gravity on these theoretical models using analytical and simulation results and we find that the impact of gravity on droplet shape becomes non negligible as surfaces become very hydrophobic Motion is also significantly affected by discrete features for example increased hydrophobicity may actually hinder droplet motility due to pinning In light of this we ana
44. MFP 3D AFM in tapping mode The AFM tips used were single beam silicon cantilevers with resonant frequency of 325 kHz and force constant of 40 N m The tip radius was 10 nm with a tip cone angle of 40 degrees MikroMasch Samples were scanned over an area of approximately 10 x 10 wavelengths squared varying with the scale of the pattern using 256x256 points Two methods were used for extracting the amplitude from the AFM data For copies of diffraction gratings we can generally assume a consistent sinusoidal pattern so we may fit a function to the surface of the form 2nx Amy z Asin i P p 47 There are 4 unknowns A x Ay These are the amplitude wavelength in x wavelength in y and phase Wavelengths in both x and y are necessary because the sample is generally not perfectly aligned with the axes Amplitude is then extracted directly We can also accurately measure the pattern wavelength which is JA Pa due to the potential rotation of the pattern For buckled patterns the sinusoidal fit is typically not reliable The buckled pattern may have cracks defects variations in the wavelength and distortions Even if these are minor it will ruin the fit with a sine wave To account for this variation a more generalized approach using an FFT is taken Wavelength and wave orientation are readily calculated by finding the maximum in the FFT magnitude in both directions The data is then rotated using bilinear int
45. PDMS with a patterned surface on the coverslip The coverslip was glued to the bottom of a culture dish before cell culture 51 Wavy surface topography was characterized using an Asylum MFP 3D atomic force microscope AFM in tapping mode The AFM tips used were single beam silicon cantilevers with resonant frequency of 325 kHz and force constant of 40 N m The tip radius was 10 nm with a tip cone angle of 40 degrees MikroMasch Samples were scanned over an area of approximately 100um with 256x256 points Two randomly chosen regions on the sample surface were scanned for each pattern and the reported dimensions are the average of the two measurements Pitch and depth were determined by fitting the data to a sinusoidal function The pattern was compared to an ideal sinusoid and found to match well except for some small scale roughness The defining parameters of the patterns are taken to be pitch A and depth d as shown in Figure 3 1A and a typical AFM scan is given in Figure 3 1B Figure 3 1 A Feature parameter definitions where d is the depth and J is the pitch The same parameters can be used to describe grooves and waves a 29 B Typical AFM scan of a wavy pattern used for d 200 cell culture A 1 67um N and d 410nm o 3 1 2 Cell Culture To prepare the patterned PDMS for cell culture the sample surface was treated with oxygen plasma for 30 seconds at 100W and then coated with a
46. RY siesai ose cutus e cicubedraz una mido hd e eade Duce dir E eir tex ad qds dle Us boudus Dev catu cesa a bet E DR Forte tre el 66 4 MICROSCOPY TOOLS esed ot evus sueta vex dee eu vi nut enel vat eua o dove vexe ven ca deve eive as 82 4 1 AUTOMATED STAGE AND TIME LAPSE SYSTEM csceccccececceccccececceceacececcecscceceacececeecsaeecsaeeceaeesseecseesseececeeceaeeseaeess 82 4 2 OPITOGENETICS SYSTEM 5659 2255 poEDe tcs teu Ets EOrHO ee a disces top MPs PIS a CoU SD DL Ede E 95 REFERENCES onis vete eeu sus vela ass rues oto a wows a preda alge wows equ eEa TU vas Ie UEM ds Saisie wane peus ERI LVapI Oe rud QU S M Mee NE 104 APPENDIX ciuicviccicua teva seuss jun weuatauaderpveuescwatcuatcwaws ue bones sue Ve A E aUo UP E CE SUELE TI T S EE S VE VE Ue Ue E Va PU TETTE RUTd 111 1 Micro scale Droplets The classical Cassie Baxter model has long held as a reasonable simplification for understanding superhydrophobicity on rough surfaces In short this model assigns an equivalent contact angle to a composite surface by taking the average of the contributions from each material of the composite weighted by the area fraction encompassed by the material In the case that the surface is rough and composed partially of air void of solid features we may take the air portion to have a 180 contact angle Thus we can correctly predict that very high contact angles are possible when a surface is mostly composed of air and the area fraction understood to be th
47. Y AU QU Y Y Y good but there is distortion near the center Red Sin Fit Blue Connected Data Points 2 2 2 PDMS on PDMS Larger patterns can be made by using PDMS for both the film and substrate The film is made harder by either increasing the base crosslinker ratio and or increasing the curing temperature as discussed in section 2 3 1 Care must be taken to ensure that Q is sufficiently large to cause buckling as the stiffness ratio between different formulations of PDMS may be relatively small The critical strain is solely a function of Q as given in theory section above so this strain should be calculated and exceeded during 32 fabrication by a reasonable margin of error The necessary strain to induce buckling may be on the order of 10 50 The PDMS film component of this buckling system must be made much thinner than the substrate If the film is not sufficiently thinner than the substrate global buckling will occur rather than the local wavy buckling desired 7 The PDMS film is made thin by spin coating To do this a silicon wafer or square glass slide must be coated with a fluorinated silane to make it non stick see 2 2 5 for treatment details Here the silane may be rubbed directly onto the glass or silicon and the reaction will occur faster than for PDMS lt 30 minutes To spin coat uncured PDMS is poured to evenly cover the wafer or slide before mounting a spin coater the spin coater used here is Specialty Coatin
48. a time lapse set at nearly the rate at which the files can be opened and saved Additional possibilities include using the focus metering as a quasi quantitative measure of topography for a gel Presently the algorithm outputs a height map based on the focus to which the user may ascribe physical values of height based on the known stage position 92 where each image was captured see Figure 4 5 Combined with the multi image stitching algorithm this would quickly map the contour of a gel surface at least approximately Figure 4 5 Example of an extended depth of field image for typical cells Right The 10 original images Top The combined and focused image Bottom The height map produced by the algorithm roughly the depth of the cells within the gel 4 1 11 Adaptation to other Microscopes The hardware and especially the software from the imaging system can be easily integrated for other microscopes This has been done with an Olympus IX 51 microscope without an automated stage using the same software A motor was attached to the focus wheel to automate the z axis of the stage 93 without modifying the microscope itself The software allows time lapse imaging to be combined with extended field of depth and temperature recording without support from the Olympus control software Images can be post processed with the stand alone version of the extended field of depth algorithm as described above The schematics and instructions i
49. aces and droplets of 30uL volume the true contact area is 60 larger than one would assume with a naive spherical cap model Even in less extreme cases that researchers might use to study wetting the contact angle could be off by 20 30 if gravity is neglected Figure 1 12 Comparison of contact area with and without gravity from A l 1 6 E numerical solution to the gravity I I AA J Young Laplace Equation k PA 30 Ano gravity L 2 1 0 4 100 Volume uL 120 710 Effective Contact Angle 140 0 16 1 2 3 Surface Evolver Results The above results all rely on straightforward numerical analysis requiring a continuous and homogeneous wetted surface The SE model allows more realistic scenarios to be investigated in which the surface is discrete Previous results from the SE model all included normal 9 81m s gravity to compare to experimental results Now the gravity is removed and the results from equivalent models with and without gravity are compared The trends predicted by the numerical solution are confirmed in that the discrepancy between gravity and no gravity increases as droplet volume and contact angle related to the area fraction are increased Contact angle is also found to be relatively unaffected by gravity Interestingly the effect in the discrete model is even larger than that predicted by the numerical solution Two examples of output from typical large 20uL droplets are dis
50. al cells in an environment similar to that described above All of the experiments described in this section are based on the so called 3D on top protocol where a layer of gel is deposited and solidified before adding cells and additional gel is included in the media during culture 7 Cells will tend to migrate into the gel to some degree creating an effective 3D environment with most of the cells in the same plane for easy viewing with phase contrast optics The gel suggested for this protocol is Matrigel BD Biosciences 67 growth factor reduced phenol red free which is a liquid at 4 C but solidifies rapidly at room temperature To use this gel to make a reproducible 3D construct the gel pipet tips and container for the gel need to be chilled on ice prior to and during dispensing the gel The gel composition is not explicitly specified it is extracted from Engelbreth Holm Swarm mouse sarcoma cells and varies from lot to lot Results are best compared using the same batch of gel when possible Matrigel is a mimic for the basement membrane in vivo and consists mostly of collagen IV and laminin as well as entactin The Matrigel may be modified by changing the concentration or adding additional factors One addition common to several experiments is type collagen BD Biosciences rat tail which provides a fibrous element that the cells may organize making it more like native ECM Collagen for gel formation should come qualified
51. ance in human dermal fibroblasts is modulated by population pressure J Anat 206 581 587 2005 Dunn G a amp Brown a F Alignment of Fibroblasts on Grooved Surfaces Described by a Simple Geometric Transformation J Cell Sci 83 313 40 1986 Peterbauer T et al Dynamics of Spreading and Alignment of Cells Cultured In Vitro on a Grooved Polymer Surface J Nanomater 2011 1 10 2011 Ayres C E et al Measuring fiber alignment in electrospun scaffolds a user s guide to the 2D fast Fourier transform approach J Biomater Sci Polym Ed 19 603 621 2008 Bajaj P et al Patterning the differentiation of C2C12 skeletal myoblasts Integr Biol Camb 3 897 909 2011 Grote M J Palumberi V Wagner B Barbero A amp Martin Dynamic formation of oriented patches in chondrocyte cell cultures J Math Biol 63 757 777 2011 Biela S a Su Y Spatz J P amp Kemkemer R Different sensitivity of human endothelial cells smooth muscle cells and fibroblasts to topography in the nano micro range Acta Biomater 5 2460 2466 2009 Vogel V amp Sheetz M Local force and geometry sensing regulate cell functions Nat Rev Mol Cell Biol 7 265 275 2006 Erickson C A Analysis of the Formation of Parallel Arrays by BHK Cells In Vitro Exp Cell Res 115 303 315 1978 Kang K Perthame B Stevens A amp Vel zquez J J L An integro differential equation model for alignment and orientational a
52. and alignment metrics Using our experimental results for sparsely distributed and confluent cells the correlation between cell behavior and the sensitivity parameter reveals additional features Figure 3 11 compares our data for many experiments plotting individual and confluent cell alignment against The blue triangles represent the alignment measurement for sparsely distributed cells whereas the red circles at the same value of represent the corresponding alignment measurements for confluent cells The figure demonstrates that two critical values of the sensitivity parameter exist 1 and c For surface patterns with a sensitivity parameter smaller than c cells do not align with the patterns regardless of the confluence For a sensitivity parameter larger than c even sparsely distributed individual cells align with the patterns For surfaces between c and c individual cells do not align with the patterns but confluent cells do This trend is also clear in Table where the data are arranged in ascending order of the value of the sensitivity parameter Taking L to be 60um the thresholds are approximately 0 0015 and 0 0065 respectively The current results are particularly relevant in the context of muscle tissue engineering It has been shown that myoblast alignment is a critical step in the formation of functional muscle and myoblasts 64 are typically grown to or near confluence before differentiating into myotubes H
53. any packaged implementation is inherently separated from the live acquisition requiring a complete set of image files before the processing can begin When imaging live cells it is not reasonable to keep cells at room temperature for several minutes while each image is being composited Saving hundreds of individual images and post processing is invariably tedious and time consuming The custom integrated algorithm solves these problems there is no additional processing time after all the images are captured only the time needed to write the data to file This is accomplished by taking full advantage of all the known parameters of the acquisition as described below The algorithm uses normalized phase correlation in pyramids to calculate the overlap between adjacent images however only the region expected to overlap is used in the correlation to greatly speed up the correlation The correlation is carried out in the frequency space using fast Fourier transformations FFT which is equivalent to the spatial cross correlation but much more efficient for large matrices 1t The frequency space implementation also allows low frequency components of the correlation due to differences in lighting and shading to be readily disregarded by zeroing a few elements of the matrix Ideally a single sharp maxima occurs in the correlation indicating the offset for the overlap but in practice there are several maxima Knowledge about the expected layout is al
54. ary length in the typical case of 10uL droplets and thus gravity may be neglected and a spherical cap droplet shape can be assumed Implicitly it is done whenever a spherical cap assumption is invoked This is indeed generally accurate as the droplet radius for a spherical 10uL volume in air is 1 3mm which is less than the capillary length which is 2 7mm for water in air In fact the contact angle of a sessile drop is known to be invariant to the gravitational field as one might expect This gives further reason to ignore the effect of gravity when defining theoretical model in order to simplify a model However a more rigorous assessment is in order because the capillary length is at least on the same order of magnitude as the droplet size We also wish to quantify the impact of gravity and acceleration in general so we may determine if is truly negligible and at what point it ceases to be negligible While such things have been extensively studied before for example finding the shape of a pendant drop the topic has not been addressed in the context of superhydrophobic droplets and how gravity might affect modeling these systems With the introduction of equations dependent on the contact area of a droplet which might be exceedingly small for superhydrophobic surfaces we must be sure we are not introducing unnecessary error into our models This study seeks to quantify the impact of gravity on superhydrophobic droplets 1 2 1 Energy and Non d
55. cal cell response to the cylindrical geometry is given in Figure 3 22 This picture is of cells on a 15mm radius sample after 6 days of culture similar to the level of development of the cells in the figures above The axis of the cylinder is horizontal in the image The nascent ductal structures clearly lack a preferred direction for growth Although the curvature is an order of magnitude less than on the meniscus the experiments with smaller radii showed similar trends individual pictures of small radii gels are highly distorted Between these experiments and the measurements of the meniscus it seems unlikely that curvature alone is producing these results 75 nh ob a ees TERES Figure 3 22 Cells growing on constant thickness gel in a cylindrical annulus shape The axis of the cylinder is horizontal in the image and the radius is 15mm Image is a composite of 14 individual images tiled and at different focal planes 3 2 4 Thickness and Stiffness Stiffness is a well known regulator of epithelial cell behavior It has been observed previously that acini and ducts only form in gels soft enough that cells can deform the gel It has also been shown that culturing epithelial cells in a soft ECM can partially revert some cancerous phenotypes to normal 7 Of interest here is whether stiffness might be playing a role in the behavior of the epithelial cells near the meniscus The obvious question is can the cells sense the underlying
56. clear all the selected regions Hotkeys require one of the windows to be active When Tracking mode is OFF selected regions endlessly blink at their current location When tracking mode is turned ON current and new selected regions will be tracked this means a bunch of key points will be identified within the region and the program tries to follow them from one frame to the next Keep in mind it is contrast edge based and ignores color so the target area should ideally have some distinct contrast texture By default every selected region will blink with the same constant frequency measured in Hertz 100 i e frequency 100 means 1 00 Hz Use the slider bar on the Controls window to adjust the frequency it should snap to reasonable values Changing the frequency will affect existing regions To see the exact frequency the system is actually outputting press F and the average frequency is periodically printed in the command window The phase is the percentage of a full cycle slider needs integer delay between successive regions being illuminated Setting this to O will sync up all the regions Every time a new region is added the cycle restarts with the first region to ensure proper timing Duty cycle is the percentage of time the dot is illuminated To get constant illumination set Duty Cycle to 100 At the moment regions will actually project the same shape in black when they are blinking and off which could
57. constraints and added to the main droplet surface Vertex averaging is performed intermittently which helps spread the refinement near the surface towards the top of the droplet These procedures result in a smooth gradient of refinement from the top of the droplet to the pillar liquid interface The simulation process is not automated by surface evolver so the sequence of simulation steps is inputted by the user including iteration refinement vertex averaging step size selection and removal of unstable edges During the model generation process define the simulation sequence This is a single automated sequence of simulation steps refinements and selection of step sizes appropriate for the level of refinement The sequence first converges to the equilibrium shape then if desired for information about shape or curvature the model is globally refined and evolved to capture fine details Automating the process as a single execution keeps the refinement process impartial and repeatable which is necessary for parametric study Some key time points in a typical simulation sequence are given in Figure 1 4 The entire simulation is also readily captured as a movie Figure 1 4 Key frames from a recording of a simulated droplet 7 uL 0 25 evolving toward a minimum energy state Several rows of the initial pillars dewet and the mesh becomes progressively finer 1 1 4 Contact Area Numerous simulations were run for droplets in t
58. contributing to the mechanical cues experienced by the cells In this section an unusual observation of cell behavior spawns a series of experiments which are analyzed using tools from mechanics 3 2 1 Mammary Epithelial Cells One outstanding mystery related to cell mechanics in a 3D environment is the observation that epithelial cells appear to behave differently near edges of small culture containers when grown on a soft hydrogel Specifically when culturing mammary epithelial cells such as MCF10a on top of a layer of Matrigel cells will tend to form ductal structures in a region in the shape of an annulus near but not quite at the edge of the container This is in contrast to the acinar morphology observed elsewhere in the culture including the center area as well as the region high on the meniscus very close to the walls of the container There is no intentional biochemical cue to drive this behavior so a mechanical explanation is sought instead Better understanding of this behavior may be of interest to biologists studying epithelial cells wondering why cells form tubes in their culture but we might also gain more general insight into how cells organize into these ductal formations acinus Figure 3 12 Structure of epithelial cell formations in breast tissue 55 66 The epithelial cells studied here include MCF10a an immortalized cell line derived from human breast epithelium as well as HME496 which are a line of prima
59. crons by increasing the spin speed or mixing the PDMS with a suitable solvent before spinning For future work the film could be spun onto a flexible material than would allow handling to oxidize and transfer it to the substrate Brief tests with a few readily available flexible materials such as plastic transparency film either didn t yield an even film or did not properly transfer to the substrate These problems could be solved with better materials 34 2 2 3 Sputtering An alternative method of making a thin film on a PDMS substrate is to directly deposit it via sputtering This method is somewhat more involved than the other two methods discussed in that it requires fairly specialized equipment A similar effect can be produced by depositing metal in the vapor phase although we have not attempted this ourselves Sputtering has the advantage over the other techniques by being the most versatile in the dimensions of the waves The thickness of the deposited layer can be modulated from as little as bnm to over a um if the sputter time is significantly extended Exceptionally small waves however are not practical with PDMS as the metal will be significantly harder than the substrate Known suitable metals for sputtering onto PDMS are chromium and titanium which are often used as an intermediate layer for depositing other types of metal on PDMS Unfortunately these metals are particularly hard 280GPa 115GPa and brittle a problem di
60. ct ratio of buckled patterns as a function of the stiffness ratio and strain on the thin film High strain relative to the stiffness ratio yields sharper peaks 2 1 1 Tuning Elastic Properties of PDMS These properties can be exploited using PDMS Sylgard 184 PDMS comes as a 2 part kit of base and crosslinking agent While the standard mixing ratio is 10 1 base crosslinker the ratio can be varied to adjust the stiffness of the cured elastomer Increasing the proportion of crosslinker leads to a stiffer material while decreasing the proportion makes the PDMS softer For the standard mixture the elastic modulus is roughly 1 8MPa and Poisson s ratio is 0 45 As discussed in the following sections the elastic modulus can be varied over approximately two orders of magnitude PDMS is also known to be linear elastic up to 4096 strain which makes it ideal for reaching any point on the surface in Figure 2 1 28 2 2 Techniques Numerous methods are available for producing a thin hard film on a softer substrate One of the allures of the fabrication method is that it does not require a clean room to produce micron scale patterns in fact much smaller patterns can be made that would usually require special equipment with conventional fabrication methods The buckling technique also offers a way of producing surfaces without sharp edges at length scales where this could be very difficult or impossible Three different techniques are covered here for
61. d the reported confluence is the percentage of white pixels in the resulting binarized image Confluence was found to be consistent between images obtained using the same microscope and magnification which was the case for successive pictures in our time lapse sequences This method is similar to the methods used by several other groups However we have simplified the technique foregoing an attempt to identify individual cells In order to quantify alignment as cells grow we require an alignment metric that is consistent at different cell densities and can be applied to phase contrast images of live unstained cells Standard techniques to measure cell orientation involve fixing and staining cells so the shape of the cell 9997 the 62 70 nucleus or the polarity of the Golgi apparatus can be readily identified for individual cells Alternatively some researchers have identified cell major axes manually 46371 or semi automatically by converting images to binary gt from phase contrast images which generally requires cells to be separate and easily distinguished from one another In each case statistical data is gathered by sampling many individual cells in the population These methods are not feasible for our data because our cells are unfixed and unstained and the cells are in close contact with each other Additionally any manual technique is subject to bias and human error 53 Y 3
62. dentified and related to the topographical plot of the surface This has been done in Figure 3 16 where the center of each ductal structure is marked with a black dot The sample is the same as in the previous figures and the same color scale is used to indicate depth for the planar projection in Figure 3 16 Surprisingly most of the ductal structures were found near the outskirts of the relatively flat center area and not higher up on the surface where the meniscus induced more significant curvature Our own samples also seem to show a similar trend upon close inspection which is not obvious from the shading in the microscopy images alone The significance of this occurrence is discussed in the following sections 10000 3000 6000 4000 2000 2000 4000 6000 3000 10000 Figure 3 18 Example measurement of duct distance Figure 3 17 Locations of duct formations from Figures 3 14 from apparent meniscus boundary and 3 15 Same coloring to indicate surface height as Figure 3 15 The large black dots are the centers of small ducts elongated connections between several cells To further understand the distribution of duct structures the position of the cells relative to the beginning of the region affected by the meniscus was also investigated As seen in Figure 3 18 the distance from the meniscus is measured from the prominent shaded band visible in the DIC microscopy images This band is approximately the same as the blue ar
63. dicating that C2C12 and 3T3 fibroblasts tend to reach maximal alignment within 24 hours Our time lapse data typically span several days which suggests that delayed cell alignment is not a consequence of increasing exposure time on the patterns 59 Alignment Data Summary A d Size Aspect Ee Individual Confluent nm nm nm Ratio iode ds Alignment Alignment o nm 280 8 2 24E 03 2 86E 02 1 02E 04 0 00 0 01 6 78E 04 420 24 1 01E 04 5 71E 02 1 36E 04 0 09 0 02 1 49E 03 560 24 1 34E 04 4 29E 02 7 65E 05 0 10 0 48 1 59E 03 420 33 1 39E 04 7 86E 02 1 87E 04 0 11 0 49 1 80E 03 560 40 2 24E 04 7 14E 02 1 28E 04 0 23 0 53 2 21E 03 420 52 2 18E 04 1 24E 01 2 95E 04 0 04 0 71 2 33E 03 830 62 5 15E 04 7 47E 02 9 00E 05 0 08 0 36 3 19E 03 560 91 5 10E 04 1 63E 01 2 90E 04 0 00 0 35 3 56E 03 830 85 7 06E 04 1 02E 01 1 23E 04 0 30 0 76 3 90E 03 830 100 8 30E 04 1 20E 01 1 45E 04 0 00 0 56 4 31E 03 830 200 1 66E 05 2 41E 01 2 90E 04 0 11 0 70 6 42E 03 1000 190 1 90E 05 1 90E 01 1 90E 04 0 44 0 94 6 68E 03 1670 220 3 67E 05 1 32E 01 7 89E 05 0 37 0 62 8 34E 03 2000 240 4 80E 05 1 20E 01 6 00E 05 0 31 0 94 9 04E 03 1670 410 6 85E 05 2 46E 01 1 47E 04 0 41 0 93 1 24E 02 1670 440 7 35E 05 2 63E 01 1 58E 04 0 98 0 99 1 29E 02 2000 450 9 00E 05 2 25E 01 1 13E 04 0 80 0 82 1 38E 02 Table 3 1 List of each sample tested with several different parameters describing each pattern The threshold for alignment is taken to be 0 3 using our normalized alignment
64. ditions preclude manually defining the model Additionally in order to investigate effects of changing scale the model must be easily changed by adjusting the parameters of interest this requires an automatically generated model The target model consists of a liquid droplet on an array of pillars where the droplet volume pillar size pillar spacing anisotropy ratio and surface energy may all be adjusted All results presented here are for the PDMS water air interface where the liquid gas surface energy is 0 072 J m and the homogeneous contact angle is 114 as determined from experimental data Gravity has been included with a value 9 81m s except where otherwise indicated The model simulates a droplet receding on the pillars to determine its stable shape as discussed in detail below It should be noted that the resulting shape may not and generally will not be the absolute lowest energy configuration but rather the lowest local minimum in energy i e the stable configuration reached such that total energy is always decreasing during the simulation This is similar to the case of droplet being roughly deposited on the surface such that it reaches an equilibrium but does not continue receding to the optimal shape if the intermediate states present an energy barrier We are interested in the final contact area as well as the shape of the droplet particularly close to the surface where it might be distorted from a spherical cap a aa
65. done by using Delaunay triangulation to interpolate between the irregularly scattered surface measurements and then resampling the surface on a structured grid at equal intervals The structured sampling is then filtered with a Gaussian function giving a smooth and continuous data set From this point we could calculate the maximum and minimum principal curvatures throughout the domain although this has been simplified by taking a few section cuts perpendicular to the well walls at some well behaved areas of the surface The data is still rougher than the surface appears demonstrating the noise in the best focus measurement so a third degree B spline 73 function was fit to the section cut which can then be differentiated to obtain the curvature The result is in Figure 3 20 with one cut in X blue and another in Y red in the locations marked in the same figure The two sections are quite similar hinting that the surface should be fairly consistent throughout the culture as expected Gel Curvature 0 0015 2 Slicein X 3000 L Slicein Y i E 0 001 60068 H fe 2 S 0 0005 gU b 0 4 1000 2000 3000 Distance from Wall m o ee aie eer r ae a O 2000 4000 6000 86000 100090 Figure 3 20 Curvature along two representative slices in the gel surface Image on the right shows location of the cuts There is an un
66. e Appendix Figure 6 7 Point and Click Mode is toggled by pressing W When on an outline of the selection region is visible on the computer screen and clicking causes the region to be illuminated by the projector while the mouse is depressed The region can be moved around while remaining illuminated by moving the mouse When off the size and location of the shape is chosen by clicking and dragging in which case the location remains stationary and illuminated until clicking again If other regions are already saved and being illuminated they are not affected by this illumination 98 Save Mode is toggled with the letter S When off locations are only temporarily illuminated as per the Point and Click Mode state When on user selected regions are saved which means the regions are continuously illuminated using the pattern specified by the controls panel The pattern is defined by its frequency duty cycle and phase delay between regions Additional saved regions are added to the end of the sequence Pressing C clears the saved sequence Additional options allow for further control over the system The hue and intensity of the background or baseline projector image can be adjusted to stimulate the specimen or provide general illumination although even when displaying black the projector does emit some light which is usually enough to see the specimen For example the background can be set to red to produce generalized inhibiti
67. e Cassie Baxter does not accurately describe wetting behavior Specifically we look at surfaces where the composite is not homogenous and the size of the roughness features is finite Additionally we consider the correctness of the spherical cap model which also has built in assumptions regarding the size of the droplet The limitations of the spherical cap are identified in terms of droplet size as well as hydrophobicity of the surface Lastly a study related to contact angle hysteresis and pinning another aspect unaccounted for by the Cassie Baxter model is addressed by looking at the resistance to motion in moving droplets Each topic addresses the shortcomings of the generally accepted but simple models Figure 1 1 shows a typical contact surface at the interface between a pattern of pillars and a liquid droplet The key parameters describing the geometry and listed in the image droplet volume V area fraction the fraction of a unit cell on the pillar surface that is solid the spacing between pillars L and the pillar diameter d Additionally the contact angle O can be defined as a single value relating the surface interface energies of the three phases present in a liquid droplet on a solid surface the apparent or effective contact angle can be defined as the observed angle between droplet and a real surface which will generally be different than the energetic contact angle For the simulation work presented here t
68. e capture rate of the camera Most cheap USB cameras automatically choose their own frame rate based on the ambient light level with typical values between 8 and 60 fps In good light the actual object update rate is usually in the 50 60 fps range for a 102 640 x 480 image with multiple objects This high speed also helps improve the accuracy as the difference between successive frames is typically small making it easy to match points 4 2 7 Ongoing Work There is a great deal of potential work left for this project So far the best results were obtained by stimulating the flower in Figure 4 8 where it was not clear if the flower had a significant response due to spontaneous contraction A major advancement will be improving the responsiveness of cells to light at which point more interesting results may be obtained Until then the function of the stimulation system is in order and ready for manipulating cell cultures The ongoing issue is the weak and dilute response from the C2C12 cells upon light stimulation The original system was built with a single focusing lens for easy testing but a low portion of the projector output was guided to the target viewing area Arecent still untested improvement in the optics has been to add a series of lens to narrow the focus to a much smaller region while still minimizing dispersion The particular projector was chosen for its relatively high lumen output because the power of smaller projectors
69. e computer has the projector connected as an extension of the primary monitor required for operation the Projector window will automatically move to the projector and encompass the entire screen it outputs the illumination pattern The Camera window holds the input from the camera overlaid with information about the illuminated regions when applicable The Controls window allows access to all the variable parameters in the program such as region and timing parameters The command line prints information about the status of the program A picture of the interface is given in Figure 4 8 with a proof of concept flower shaped biobot being globally stimulated to gauge sensitivity to the light Figure 4 8 The control interface of the optogenetics system The specimen being viewed here is a flower coated with cardiomyocytes being illuminated Back Int 0 Back Hue 3 Cal Bright 77 Cal Size 3 Cal Thresh 190 E Proj Color 2 Proj Rad 10 Proj Shape 0 d 1628AM NE The system allows for the illumination of a number of predefined shapes with adjustable size color orientation timing and brightness There are several methods of choosing what areas are illuminated that are toggled using hotkeys the full user manual is available in th
70. e fraction of surface area where the solid is in contact with the droplet is low When coupled with the assumption that a small droplet takes ona perfectly spherical shape or a spherical cap when wetting a flat surface we can fully describe the system by simply knowing the relative surface free energies of each material and the area fraction of the surface For many applications the Cassie Baxter and spherical cap models are sufficient and accurate This is particularly true when the roughness is homogeneous and much smaller in scale than the droplet For the purposes here we assume the droplet remains sessile resting on top of the surface features and not descending and wetting the bulk of the features Recently the Cassie Baxter model has come under closer scrutiny and its efficacy has been hotly debated by a number of groups 7 A key point of contention lies in the assumption that the composite surface is homogenous and infinitesimal Several simple experiments show that when these assumptions are broken the resultant droplet shape can be vastly different than the models predict Additionally the Cassie Baxter model in assigning a single equilibrium contact angle fails to capture the observed existence of advancing and receding contact angles which bound the contact angle observed to within a range not a single value The present study of liquid droplets on superhydrophobic surfaces aims to better understand the cases when th
71. e microscope itself which was not altered If desired the resolution can be improved by taking fractional steps between each detent this is performed by the electronic controller by adjusting the current sent to each electromagnetic coil so the motor holds a position partway between two detents The fractional step size can be set to one of several values down to 1 16 giving approximate 1um linear resolution depending on the state of three pins on the controller For simplicity only the 1 16 step mode is available which can be toggled with full steps from the software by pressing the letter m Although the precision of these motors can be quite good it is important to understand the limitations of hobby grade stepper motors Unlike a servo motor the stepper motor has no built in feedback system to record the state and position of the motor Thus the position of the stage is only known relative to its position when powered on and the relative position is only known by counting the exact number of steps taken in each direction As long as the motor doesn t slip or get stuck the position is quite exact and very repeatable However if an external force prevents the motor from moving when it is commanded to take a step the recorded stage position is no longer accurate and will never recover the offset Consequently the motors were chosen to be significantly overpowered in an effort to prevent missed steps and in practice missed steps do
72. e of the resources already available from the time lapse system in place The system was designed to be simple and very low cost while maintaining the functionality of a high end commercial package 4 1 1 System Overview Several of the tools and techniques built into the system are individually adaptable to other microscopy systems or individual images but the complete package of the design is implemented in a single microscope The system consists of both hardware and software The hardware includes a 3 axis stage electronics motors environmental controls and periphery devices The software includes a program to control the stage and camera from a computer as well as image processing utilities integrated with the stage and camera control that can also be run independently The entire setup is shown in Figure 4 1 82 Figure 4 1 Automated microscopy system overview Above Side view The black tank at the far left is the humidifier In the upper left corner are the flow rate and temperature controllers Right Front view The shutter is visible at the top cener attached near the mercury arc lamp Several scenarios requiring this type of imaging system were in mind when the system was developed The first is the multi well or multi specimen time lapse where several wells in a standard multi well plate or several small petri dishes are simultaneously imaged over multiple days A variation of this would be to record several locations from
73. e the edges might be significantly thicker especially because the wells are relatively small 33mm area In each case including the control the media contained 296 Matrigel in addition to the standard growth media which seems to affect the behavior of cells grown on bare polystyrene polystyrene PTT Gel Thickness 100 um 200 um 400 um 800 um Figure 3 23 Experimental results for MCF10a on different nominal thicknesses of Matrigel There seems to be a threshold below which cells do not interact and form 3D structures and a threshold above which cells only form acini The results of the experiment are displayed in Figure 3 23 We do indeed observe differences between the different thicknesses of gel There are three types of behavior that summarize the observations For thin or no gel cells behave similarly to 2D cultures where they spread and perhaps aggregate but they remain mostly as a monolayer and do not form 3D structures For slightly thicker gels in the nominal range of 200 400um cells form a mixture of acini and tubules where the tubules tend to preferentially elongate parallel to the boundary of the well similar to the observations in the samples provided by 77 Yvonne For gels of 800um and thicker the culture contains almost exclusively acini that are of similar shape and size throughout the culture These results support the hypothesis that thickness and or stiffness are affecting the duct formation 3 2 5 Wavy Pa
74. e the sensitivity of cells to a periodic anisotropic pattern The numerator is related to the previously described barrier size and increases as either pitch or depth increase The denominator is related to the inverse of the relevant curvature k of the substrate or the effective radius of curvature compared to the length of the cell For a fixed d as A becomes increasingly large the curvature term in the denominator begins to dominate which reflects the fact that the surface appears locally flat to an individual cell when curvature is low 3 1 7 Parameter Application Figure 3 10 shows the normalized alignment plotted against the sensitivity parameter from measurements by us and several other groups on a few different cell types In Figure 3 10A a single cell length dimension L 60um is used to non dimensionalize the feature lengths for all data obtained by different groups Unlike the poor correlations between cell alignment and other feature parameters shown in Figure 3 9 Figure 3 10 shows a clear transition where cell behavior changes from non alignment to alignment as the values of increase over a range of a decade note the log scale for the horizontal axis It may be further argued that since each experiment uses a different cell line with different culture conditions and measurements the behavior should be characterized using a different L for each experiment The result given by varying L is shown in Figure 3 10B which show
75. ea in the surface plots where curvature and the change of gel depth become significant This measurement can be taken as approximate but it helps quantify the observations The result of this analysis combining data from the above sample and 72 an additional sample that was plated at the same time not shown is given as a histogram in Figure 3 19 where O is the location of the band and positive distances are gives to structures closer to the center of the well This histogram is weighted by the length of the duct which relates to the number of cells in the structure 1800 4 DAY 5 All Ducts Total length by distance from meniscus 1400 4 Figure 3 19 Histogram of duct distances from apparent meniscus boundary weighted by duct length Positive distances are toward the center of the well Apparent meniscus is a indicated in Figure 3 17 i n 100 200 300 500 600 400 300 200 100 0 700 Distance from meniscus bottom edge 120 Total Length 3 2 3 Curvature A first impression might be to consider the curvature of the gel surface as a factor affecting the location of the ductal structures Indeed the ducts seem to extend parallel to the boundary of the well along the direction of minimum curvature so we wonder if the cells may have also aggregated at a position of maximal curvature perpendicular to the edges To look into this possibility the curvature can be extracted from the surface data This is
76. earchers have observed that cells will align when grown on grooved patterns spanning a wide range of sizes but we still do not fully understand this phenomenon For example there is no accepted way to predict if a certain pattern will cause cells to align A common observation is that either increasing the depth or decreasing the spacing of a grooved pattern will lead to better alignment although this has generally not been formalized quantitatively At least one attempt has been made to formulate an equation to predict alignment on grooved features by using automatic control theory which led to the conclusion that the strength of the alignment signal is proportional to the square of the pattern aspect ratio depth divided by pitch This formulation is qualitatively in agreement with many observations but it is not clear if it is generally applicable In the context of very small patterns other parameters such as the barrier size defined as the square root of the product of pitch and width are used to define a threshold for eliciting contact guidance Others have also observed effects deviating from a pure aspect ratio dependence for small features gt Compared to the great deal of data addressing alignment on sharp edged grooves there is very little data for edgeless features Early studies of cells aligning on single fibers showed that curvature may have a direct effect on alignment and these observations have been extended to r
77. ed by printing the PDMS directly onto this cover slip with weight applied on top of the mold to keep the pattern thin and flat To use this pattern in culture a hole is drilled in the bottom of a culture dish with a drill press This is a convenient method for ensuring good optical properties of the sample with longer focal length objectives as well The process and outcome is illustrated below in Figure 2 17 Figure 2 17 Process of making a very thin PDMS pattern for cell culture From left to right first a hole is drilled in the bottom of a 35mm culture dish Then the pattern is compressed against and cured on a 1 glass cover slip Lastly the cover slip is glued to the bottom of the culture dish with PDMS replacing the drilled hole 43 2 3 Measurements 2 3 1 Tensile Testing Sylgard 184 PDMS is a very commonly used material and a great deal of literature is available on its various physical properties However less publicly available information is available on how the modulus of the PDMS varies with different curing conditions Not only does the ratio of base to crosslinker affect the modulus of the cured product the temperature and time of curing also play a nearly equally significant role The influence of the temperature on the modulus is not well documented and a naive researcher viewing the manufacturer s recommendations might assume any of the documented curing methods 48 hours at room temperature 10 minutes at 150 C 20
78. enbo G Selective Photostimulation of Genetically ChARGed Neurons Neuron 33 15 22 2002 Deisseroth K et al Next Generation Optical Technologies for Illuminating Genetically Targeted Brain Circuits J Neurosci 26 10380 10386 2006 Arrenberg A B Stainier D Y R Baier H amp Huisken J Optogenetic control of cardiac function Science 330 971 4 2010 Stirman J N Crane M M Husson S J Gottschalk A amp Lu H A multispectral optical illumination system with precise spatiotemporal control for the manipulation of optogenetic reagents Nat Protoc 7 207 20 2012 Chan V et al Development of miniaturized walking biological machines Sci Rep 2 857 2012 Neal D Sakar M S amp Asada H H Optogenetic Control of Live Skeletal Muscles Non Invasive Wireless and Precise Activation of Muscle Tissues 1513 1518 2013 Schobert B amp Lanyi J Halorhodopsin is a light driven chloride pump Annu Rev Biophys Biophys Chem 257 11 28 1982 The OpenCV Reference Manual 2012 Lucas B amp Kanade T An interative Image Registration Technique with an Application to Stereo Vision Proc DARPA Image Underst 674 679 1981 Bouguet J Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the algorithm 1 1 9 110 Appendix Figure A 1 CAD model of straining device 111 Figure A 2 Matlab script to extract wavelength and amplitude from AFM data close
79. ence in this case Moreover these duct like structures are much more defined on the wavy patterns than in the meniscus samples which might correspond to the more significant stiffness gradient present in the wavy samples Work to quantify the effect of stiffness on epithelial cell movement and aggregation using other dimensions of wavy patterns is currently ongoing It would seem that the same stiffness effect could explain the formations observed on the meniscus but a finite element model of both systems would be required to quantitatively compare the two 79 3 2 6 Seeding Density In addition to the previous findings it is also worth mentioning that seeding density has a significant effect on the formation of ducts and acini While a low seeding density leads to almost entirely acini high seeding densities are much more likely to yield networks of tubes In extreme cases of very high seeding densities HME496 cells are observed to coalesce into a single cluster consisting of almost every cell plated within the culture container Several images demonstrating this behavior are presented in Figure 3 27 For observing the formation of ducts in vitro with epithelial cells more interesting and complex interactions occur when cells are seeded at 5E4 1E5 cells cm compared to the 2 5E4 cells cm suggested in popular protocols Epithelial cells plated at 2 5E4 cells cm tend to form small acini which will not interact with one another over any
80. ence of sharp high contrast features while blurry regions have lower variance Similar to the statistical measure variance is defined as X Qu Xy XP Ai i Var N N Note that X is the average value of X However for an image we wish to calculate this value locally for a region centered about each pixel This can be calculated efficiently for an image as the mean of the square minus the square of the mean where the local mean is calculated with a Gaussian blur to 91 prevent edge effects from a square averaging matrix Element wise squaring and subtraction are fast so this method is significantly more efficient than popular wavelet based methods Because the topography is typically smooth focused regions should be continuous To enforce this variance is calculated at each level of the pyramid and then resampled to a coarse level where it is added to the cumulative variance for the image Contributions from each pyramid level are weighted with a larger weighting given to high resolution portions of the pyramid as these contain the features we wish to preserve The coarse focus measure is then blurred to further smooth local variations in focus and ensure that maximally focused regions are continuous Averaging over larger areas helps maintain continuity over regions devoid of features where focus is ambiguous This procedure gives a measure of sharpness matching well with the perceived sharpness for microscopy images without
81. eory section in order to predict the results of making small changes to one of the previously tested processes There is variability between tests with similar conditions so any prediction of wavy pattern properties will be an estimate It should be apparent from the image in Figure 2 4 that the quality of the buckled pattern can be very good although there is significant variation at a larger scale apparent in Figure 2 3 This behavior is typical for the technique There are primarily two types of defects in the samples The first defect type is the dislocation defect similar to the phenomenon in a crystal lattice with the same name The ridge of one wave ends and neighboring ridges displace around it A single line scan from AFM data of a buckled pattern near a dislocation defect is given in Figure 2 5 This shows that the pattern is very close to a perfect sine wave in many regions but also that the sine wave is distorted near the defects The other major defects are the cracks running axially that form due to lateral strains induced by the Poisson effect These defects are mentioned later in the section f if VAA IN d AAA MAN f Figure 2 5 Line scan of buckled pattern blue bU Jw FW HO HO HON HOS compared to an ideal sine wave red near a i7 Ww 1 i 1 1H E ji jj u N j j j Lu M Ww H H WH A Li WA j dislocation defect The overall match is quite j H M f i Jj AT A j j V VJ W
82. erpolation so the waves are aligned with the axes of the image this is also performed for display and presentation purposes Outliers must be removed or the various imperfections described above could interfere with the amplitude measurement Outliers are detected by generating an error image which is the difference between the original data and the filtered data after applying a frequency bandpass centered at the pattern wavelength Data where the error exceeds twice the standard deviation of the error image is not used when calculating the amplitude The amplitude is then calculated by finding the root mean square RMS and the mean absolute value MAV of the data and determining the amplitude of the sine wave that would give these values The difference between the amplitude calculated with RMS and the amplitude calculated with MAV 0 for a perfect sinusoid gives an indication of the quality of the wave reported in the pictures above as accuracy For good patterns the difference will be lt 1 of the total amplitude indicating a very close fit to a sine wave We can also inspect pattern quality visually by looking at the side views in the AFM data displayed earlier in this section which is a view of the surface looking along the axis of the wave This view would ideally be a thin line as the side projection of the sinusoidal pattern would be one dimensional The finite thickness indicates roughness variation in the phase or variation
83. es with the contact angle thus we may conclude that the effect of gravity on the energy of the system becomes more important for highly hydrophobic surfaces B A S 1 0 a S 0 15 E 0 9 E e gravity o 10 30 0 8 surface f 0 7 0 05 2 0 00 72 5b 0 6 i 7 lt a E 53 100 Volume uL RU 20 5 o 140 Effective Contact Angle L Contact Angle 60 180 Figure 1 10 Comparison of gravitational and surface energy potential A Pre factor contribution from the contact angle alone B Accounting for volume and contact angle 14 1 2 2 Numerical Solution The differential equation governing the shape of a liquid droplet due to surface tension is well known as the Laplace Young equation Numerical solutions to this equation in the case of a liquid droplet ona solid surface have been available for over a century There are several ways to approach this problem using different forms of the Laplace Young equation and different starting conditions In this case where contact angle and volume are known the simplest method to numerically solve for the shape of the droplet is borrowed from where the relevant differential equation takes the form r n 1 pgz 1 r 9 mr 1 r 2 y Where r the radius is solved for as a function of z the height above the solid surface The mass density and surface tension are p and y respectively This form is simple as there are no disc
84. estimate of the geometry the cells interact with Note that this best focus optical method requires an object that can be brought into focus so the bare curved regions very close to the walls of the square well were not measurable Figure 3 15 MCF10a cell culture used for surface measurements Day 5 after plating Several hundred points were recorded from each gel sample and the surface was plotted using the ListPointPlot3D function in Mathematica with the option of visibly smoothing the overlaid mesh applied The actual data points are also plotted as small black dots to show the sampled locations on 70 the surface An example of the surface that is generated by this method from the same sample as in Figure 3 15 is given in Figure 3 16 The surface as plotted has the lowest point at the surface of the gel set to O height After measuring points on the surface the gel was removed from the well so the bottom of the plate could be imaged this gave the depth of the gel which was 200um at its thinnest point in the center of this particular sample Day 3 Matrigel Surface p No Fibroblasts J 10 000 4000 2000 2000 10000 5000 um Figure 3 16 Surface plot of Matrigel surface in Figure 3 15 Bottom image is the same surface viewed from the side The black dots are the measurement points 71 Using the patched together image in Figure 3 15 the locations of the budding ductal structures can be i
85. every step Convergence and the accuracy of the final solution can be difficult to determine In this particular case there is added difficulty due to the multiple length scales the detail near the contact line is much finer than the detail near the top of the droplet and must be accounted for by maintaining a graded mesh as the shape of the droplet changes and contact line recedes In practice this is accounted for by starting with a coarse mesh and selectively refining facets combined with vertex averaging In SE any individual ll V r facet may be refined by issuing the refine command which divides each of the facet s edges in half and creates 4 facets from the original Vertex averaging V redistributes all vertices so they are at the weighted centroid of their adjacent facets making vertices more evenly spaced Facets are labeled during model generation in groups based on increasing distance from the origin so they can be selectively refined during the simulation pillars just above the liquid solid interface are refined first and as more pillars dewet the new facets closest to the interface are refined This is simply done after a fixed number of simulation iterations empirically determined by the rate the droplet dewets converges The wetted facets are kept smaller more refined because they contain the most intricate detail in the model so additional refinement is produced as the pillar facets are freed from their
86. f b outlierDifl outlierDif gt mdf sdf hFig figure Pesition Scrnsz Visable orfrfr surf surfPts surtPts imo LineStyle none FaceLighting phong shading interp view 110 65 colormap jet xlams get goa TALIM ylims get gca ylim if floor xLimsi2 7 5 ceil xlims 1 5 gt 3 xstep 10 else xstep 5 end 114 Figure A 2 continued Matlab script to extract wavelength and amplitude from AFM data set gca fontsize 26 set gca Xtick ceil xlims 1 xstep xstep xstep floor xlims 2 xstep xstep set gca Ytick ceil xlims 1 xstep xstep xstep floor xlims 2 xstep xstep zavg max img min img 2 iliz IO0 rloor Logl0 zavg set gca Ztick fltz floor zavg fltz fltz floor zavg fltz set qca alim 1 95 m ximax img mimirxmg p L eo max max amg 2 min img title titleText FontWeight bold FontSize 20 saveas hFig fName l end 4 a saveType close hFEig figure Position scrnSz Visaible orf surt surfPts surfPts img Line5tyle FaceLighting phong shading interp view 90 0 title titleText FontWeight bold FontSize 20 xlims get gca Xlim set gca fontsize 26 gca Xtick ceil xlims 1 xstep xstep xstep floor xlims 2 xstep xstep set gca Ytick ceil xlims 1 xstep xstep xstep floor xlims 2 xstep xs
87. ffects can be eliminated during processing There are no visible seams or glitches in the output image By integrating the algorithm into the acquisition procedure all of the heavy computation can be performed while the stage is moving between images No matter how many pictures are in the composite only the overlaps from the last image need to be calculated after all the images are acquired With images already processed and in memory the result need only be written to file However the time to capture a composite image is still quite significant generally 2sec per image to allow the sample to settle after accelerating the stage between imaging location This can add up to several minutes for a very large image although it s quite a bit faster than manually saving images to view the same area 90 4 1 10 Extended Depth of Field A method was also developed to merge images from a single location at multiple focal depths Non proprietary implementations of this function tend to be geared towards merging dozens of high detail photos a z stack of an object with complex depth profile to create an aesthetically pleasing image 9 A high quality output may be produced but it requires individual attention to each image and non trivial processing time For the present implementation the usage case is generally a large number of z stacks acquired during a time lapse sequence where the focused region is not quite planar Each frame
88. for quantitative cell experiments were of a high quality fused silica design diffraction gratings are also sold in bulk as a plastic sheet The plastic is not only cheaper but disposable and easier to work with The patterns have been observed to be slightly rougher but they are equal or better than the fused silica variety for inducing cell alignment Sheets of plastic grating are available commercially in 1000 and 2000 lines mm 38 Name 1000A 1 Wavelength 0 99448 Amplitude 185 3433 Accuracy 0 97713 1007 Figure 2 12 AFM scan of a 1000 lines mm plastic 100 i diffraction grating that has 0 been replicated with PDMS F The thicker appearance of the m side view lower part of image 19 indicates that the surface is rougher than the buckled 100 patterns 1007 0 5 10 2 2 5 Replication and Use for Biology The pattern generated by any of the above methods may be transferred to an epoxy mold rather than directly creating a stamp in order to make a reusable master pattern Most epoxies will not stick to silicone although there are exceptions one tested epoxy that works for this purpose is the Standard formulation of Loctite 5 Minute Epoxy which reproducibly molds wavy patterns down to 300nm wavelength Regardless of the buckling method if the surface of the pattern is hydrophilic the pattern should be fluorosilanized to make it non stick To do this tetrahydrooctyl 1 1 2 2 tridecafluoro dimethylchlorosi
89. for this purpose by the manufacturer Whether used alone or added to Matrigel it must be neutralized to 7 8pH for it to solidify which is done with concentrated NaOH Collagen is also chilled before use and allowed to gel for at least an hour in an incubator to ensure reproducible structure 3 2 2 Gel Meniscus Samples for meniscus measurement were generously prepared and donated by Yvonne Ziegler from Professor Anne Nardulli s lab at the University of Illinois These samples were produced following a variant of the 3D on top procedure where a fixed amount of Matrigel was deposited in a standardized manner Importantly the culture container is square in shape with a side length of 11mm Samples were either plated with MCF10a cells or MCF10a cells co cultured with reduction mammoplasty fibroblasts RMF The addition of fibroblasts greatly enhances the formation of tubular constructs although these structures form in the same region whether or not fibroblasts are present Figure 3 14 shows a well developed culture prepared with fibroblasts to highlight the common features of these cultures and the problem at hand This image and the following images were taken at 6 days after seeding and 5 days after seeding respectively using differential interference contrast DIC on an Olympus IX 81 upright microscope 68 e v oe 7 P s Aciniirfcenter Jedi Y 4 e Tubules atborder of meniscus SUME ED w
90. g compatible with most commercial cameras 4 1 3 3 Axis Stage and Motion To transform the stock stage for 3 axis automated control a set of custom made brackets and linear actuation assemblies were fabricated to attach to the stage An image of the CAD model used to design and manufacture the parts are given in Figure 4 2 The mechanics work similarly to the hand held straining devices described in earlier sections where the manual knobs are replaced by stepper motors Care was taken to build in the capability of fine tuning the alignment of components to allow for reasonable tolerances in the measurement and fabrication Adjusting the tightness of bolts connecting the brackets can help smooth operation of the actuators and ensure repeatable positioning without slip The stage movement is accomplished using bipolar stepper motors Pololu part 1208 These motors have a finite set of stable positions they can settle in called detents The precision of the motor is determined by the number of detents per revolution which is 200 for these motors The motors are directly connected to a threaded rod without any additional gearing to generate linear motion The rod has a 1 8 pitch moving the attached threaded nut 1 8 per revolution so the base positioning resolution of the system is 15 9um 84 Figure 4 2 CAD model of attachments to Nikon TMD microscope and stage to automated control in the X Y directions The blue gray region is th
91. g Systems P6700 Spin Coater The spinning speed will control the thickness of the film Figure 2 6 details the relation between spin speed and film thickness The data is compiled from previous students and the current work using the standard 10 1 mixture of PDMS note that increasing the proportion of base which is more viscous than the crosslinker will result in a thicker film than predicted The film thickness is well fit by a power law and is relatively independent of the spinning time 8 The spin time used here and suggested for future studies is 5 minutes which ensures an even coat across the surface PDMS Spincoating 800 700 600 E EGG Thickness 39845 rpm 9 Figure 2 6 Spin coating and thickness of prd PDMS film The curve relates the spin o 400 speed to the film thickness Samples are 10 1 PDMS spun for 5 minutes at the z 300 indicated spin speeds 200 100 0 0 500 1000 1500 2000 2500 3000 3500 RPM Once cured the PDMS film is manually peeled away from the wafer or glass slide surface and wrapped around the outside of a scintillation vial This will allow the film to be rolled onto the substrate surface 33 during bonding Figure 2 7 illustrates this process To bond the PDMS film to the PDMS substrate both sides of the interface are plasma oxidized in the same oxidizer used to generate smaller wavy patterns The substrate is pre strained and then both the scintillation vial film and substrate are oxidized us
92. ge J S Morphogenesis and oncogenesis of MCF 10A mammary epithelial acini grown in three dimensional basement membrane cultures Methods 30 256 268 2003 Paszek M J et al Tensional homeostasis and the malignant phenotype Cancer Cell 8 241 54 2005 Rao S S et al Inherent Interfacial Mechanical Gradients in 3D Hydrogels Influence Tumor Cell Behaviors PLoS One 7 e35852 2012 Silberstein G B Tumour stromal interactions Role of the stroma in mammary development Breast Cancer Res 3 218 23 2001 Lee G Y Kenny P A Lee E H amp Bissell M J Three dimensional culture models of normal and malignant breast epithelial cells 4 359 365 2007 Deserno M The shape of a straight fluid meniscus 2004 Wozniak M a Desai R Solski P a Der C J amp Keely P J ROCK generated contractility regulates breast epithelial cell differentiation in response to the physical properties of a three dimensional collagen matrix J Cell Biol 163 583 95 2003 Krause S Maffini M V Soto A M amp Sonnenschein C The microenvironment determines the breast cancer cells phenotype organization of MCF7 cells in 3D cultures 2010 Buxboim A Rajagopal K Brown A E X amp Discher D E How deeply cells feel methods for thin gels J Phys Condens matter 22 1 10 2010 Rao S S et al Inherent Interfacial Mechanical Gradients in 3D Hydrogels Influence Tumor Cell Behaviors PLoS One 7 e
93. ggregation J Differ Equ 246 1387 1421 2009 Mogilner A amp Edelstein keshet L Spatio angular order in populations of self aligning objects formation of oriented patches Phys D 89 346 367 1996 Wang P Y Yu H T amp Tsai W B Modulation of alignment and differentiation of skeletal myoblasts by submicron ridges grooves surface structure Biotechnol Bioeng 106 285 294 2010 Clark P Connolly P Curtis a S Dow J a amp Wilkinson C D Topographical control of cell behaviour II Multiple grooved substrata Development 108 635 44 1990 Gingras J et al Controlling the orientation and synaptic differentiation of myotubes with micropatterned substrates Biophys J 97 2771 2779 2009 108 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 Wakelam M J The fusion of myoblasts Biochem J 228 1 12 1985 Kamm R D R Nerem K J H Cells into Systems A new research center will work with the basics of life to build complex biological machines Mech Eng Mag 132 30 34 2010 Pedersen J a amp Swartz M a Mechanobiology in the third dimension Ann Biomed Eng 33 1469 90 2005 Dhimolea E Maffini M V Soto A M amp Sonnenschein C The role of collagen reorganization on mammary epithelial morphogenesis in a 3D culture model Biomaterials 31 3622 30 2010 Debnath J Muthuswamy S K amp Brug
94. h J Y amp Khan Malek C Surface modification and aging studies of addition curing silicone rubbers by oxygen plasma Eur Polym J 44 2130 2139 2008 Wang S Song J Kim D H Huang Y amp Rogers J a Local versus global buckling of thin films on elastomeric substrates Appl Phys Lett 93 023126 2008 Wang S Kallur A amp Goshu A Fabrication and characterization of PDMS thin film 7935 79350M 79350M 6 2011 Mata A Fleischman A J amp Roy S Characterization of polydimethylsiloxane PDMS properties for biomedical micro nanosystems Biomed Microdevices 7 281 293 2005 Koschwanez J H Carlson R H amp Meldrum D R Thin PDMS films using long spin times or tert butyl alcohol as a solvent PLoS One 4 e4572 2009 Clark P Dunn G a Knibbs A amp Peckham M Alignment of myoblasts on ultrafine gratings inhibits fusion in vitro Int J Biochem Cell Biol 34 816 825 2002 106 52 53 54 33 56 57 58 29 60 61 62 63 64 65 66 67 Clark P Connolly P Curtis a S Dow J a amp Wilkinson C D Cell guidance by ultrafine topography in vitro J Cell Sci 99 73 77 1991 Teixeira A l Abrams G A Bertics P J Murphy C J amp Nealey F Epithelial contact guidance on well defined micro and nanostructured substrates 116 1881 1892 2003 Corning D Product Information Sylgard 184 Silicone Elastomer 1
95. hard substrate from atop the gel Several studies have been done looking at how far cells can sense below the surface of a gel Although a region of stiffness gradient has been suggested as low as a few micrometers other studies observe effects at distances up to 50um and changes in the stress profile up to 200um for gels of 450Pa modulus 98 A related observation is that cell cell interaction may occur at distances up to 600um for hydrogels containing collagen The fact that this distance is much greater than would be expected from 76 isotropic mechanics alone suggests that the story may be more complex and cells may sense the boundaries of their container at a much greater distance than predicted This longer interaction distance more closely matches our observations from experiments than the shorter estimates To test if stiffness variation induced by the thickness of the gel was affecting the development of cells seeded atop 3D gels cultures of MCF10a cells were grown on gels of different thicknesses and compared The 3D on top protocol was again followed using a 1 1 mixture of Matrigel and 1 mg mL collagen deposited in 96 well polystyrene plates The amount of gel added to each well was chosen to give nominal thicknesses of 0 100 200 400 800 1600 and 3200um where Oum is the control without any gel layer It should be noted that we expect a meniscus to form thus the center of the well is thinner than the nominal thickness whil
96. he pillars Even more telling are the minimum and maximum principal curvatures in the same region as seen in Figure 1 9 These plots show that the apparently least stable regions are near the corner pillars where curvature magnitude is large The minimum curvature plot shows there is a large area of negative curvature concavity near the corner pillars These minutia are very difficult to capture experimentally and perhaps represent the greatest value of the SE model Figure 1 8 Height maps of the droplet profile near the solid interface A Contours at 10um increments starting at 10um 7uL drop B Color is related to the height showing finer detail Overlaid on the actual mesh 11 125 Minimum Principal Curvature color curvature low middle differences exaggerated lt 0 005 0 1 63 x 1078 4 16 x 1075 0 000107 0 00107 0 00635 0 0273 gt 1000 Maximum Principal Curvature color curvature no exaggeration 0 005 0 0 0416 0 0832 0 125 0 166 0 208 0 250 gt 2500 Figure 1 9 Plot of the refined mesh with color indicating the local curvature A Minimum curvature black is negative concave B Maximum curvature largest near the corners of the contact line 12 1 2 Gravity The capillary length defines a characteristic length scale for an interface between fluids subject to gravity Y Capillary Length T Many researchers are quick to assert that the droplets in question are smaller than the capill
97. he pillars are always square and evenly spaced in a square grid so V 4 y O and either L or d uniquely define the system Figure 1 1 Droplet configuration and relevant parameters V is the volume is the area fraction of the surface L is the pillar spacing d is the pillar diameter and O is the contact angle The liquid air surface energy will be designated y 1 1 Surface Evolver Surface Evolver SE is a finite element software package for studying objects shaped primarily by surface tension The program was written by Kenneth Brakke and is freely available for general use SE works by building a surface model with surface energy body force energy and user defined energy functionals in arbitrary dimensional space and evolves toward a lowest energy state via gradient descent Surfaces are always defined as triangular patches with oriented edges and an outward normal and bodies can be defined as the enclosure of multiple surfaces 9 SE has been used in a number of scientific endeavors notably including the determination of the shape of solder joints in electronics the formation of soap bubbles and relevant to this work the shape of liquid droplets The goal of the model presented here is to fully represent the 3D and discontinuous nature of a droplet resting atop discrete pillars Developing such a model allows probing aspects of the droplet that are difficult or impossible to accomplish experimentally such as
98. he ranges of V 1 20LL o 0 09 0 64 and L 50 200um Results were manually analyzed for contact area defined as the bounding polygon connecting the outmost edges of wet pillars via straight lines One question that arose from looking at experimental drops regards the seemingly un round polygonal nature of the contact line for small droplets and if this was indeed a minimum energy state Given the finite number of ways a droplet can wet a surface given a certain volume the droplet may be biased to hold an octagonal contact area rather than a smoother shape with higher edge count due to differing line energies of bridges between 8 wet pillars Combining data from all the simulations yielded some 42 different contact line patterns that were observed for increasing droplet size The result is displayed as one image in Figure 1 5 where each unique difference between successively larger droplets is given a separate color The results seem to refute the idea that a more octagonal contact area is preferred although it is possible the cause of the effect in experimental results is not captured by the SE model Liquid imbibing a patterned surface is 18 19 known to form such defined geometries Figure 1 5 The different equilibrium configurations of the contact line compressed into one image Each different color represents a unique shape of the contact line achieved as a result of running the simulation to completetion for increasing droplet
99. how to generate waves at different length scales using PDMS as the stretchable substrate Plasma oxidation of PDMS has been used to reliably make wavelengths from 300nm up to 5um Sputter coating metal onto PDMS can theoretically be used to generate waves from 1um up to 100s of um Varying the base crosslinker ratio to create PDMS with different stiffnesses has been used to make patterns of wavelength 150um up to 1 5mm Together these different techniques should be able to cover the entire spectrum from very small to very large patterns using only PDMS as the substrate For all the fabrication techniques described below the primary strain is applied with a uniaxial straining device The straining device simply clamps two ends of a sample and stretches the sample by separating the two clamps The device is shown in Figure 2 2 Two methods of clamping samples were built into the device both of which work by compressing the sample under the rectangular compression plates Figure 2 2A shows the bolt compression design while Figure 2 2B C show the latching design which is meant to minimize stresses during loading and unloading samples Separation motion is produced by turning the knob attached to a 3 8 diameter 1 8 pitch ACME threaded rod The clamp in the middle of the device has a corresponding nut to travel along the rod Images from the CAD model for the design are available in the Appendix Figure 6 1 Figure 2 2 A Full view of the
100. idge like features by considering the bending of actin fibers in the lamellipodium A study comparing wavy and grooved features found that there was little difference in the response 99 although only two geometries were compared Recently it has been shown that progressively rounding the edges of grooved features led to decreased stretching ratios compared to sharp edged grooves of the same dimensions t Cells are also known to respond to in plane curvature and it is believed the response is dependent on contractility 9 It is still unclear how and to what extent substrate curvature affects cell alignment 50 3 1 Reaction to Micro scale Wavy Features The non lithographic techniques described in chapter 2 are employed to make approximately sinusoidal patterns with pitches in the micron and submicron range The patterns are used to gain some additional insight into the general parameters that cells are sensitive to when aligning with anisotropic substrates Time lapse imaging along with a novel image processing technique are used to quantitatively analyze both dense and sparse cell cultures The quantitative characterization of cell alignment at different confluence levels helps establish the role of cell cell interaction in the cell response to wavy patterns We find a phenomenological parameter approximating a pattern s aligning potential that applies over a large range of length scales for both grooved and wavy patterns The data presen
101. ifferent locations The cut through the nearest pillar to the edge is drawn in gray which reveals that the local position of the pillar relative to the free surface has a significant impact We can try to quantify these curves with a simple angle by looking for a limit of where the bulk shape should intersect the surface similar to a goniometer reading as plotted in Figure 1 7 for several different droplet sizes but there is significantly more variation than is captured by the single number which itself might vary over 5 for a given droplet Figure 1 6 Longitudinal slices through a droplet For reference the droplet is 7uL and approximately 2mm tall A The location of the slices at 5 degree increments colorcoded to match the right B The slices The grayed area is the cut through the outermost wet pillar 10 V 20 a V 13 V 7 150 v Figure 1 7 Plot of observed contact gt 145 angle at 5 increments around the droplet for different droplet c volumes O QO 140 0 10 20 30 40 Slice Angle An in depth understanding of the behavior near the surface can be gained by looking at the curvature The simple section cuts at increments of 10um above the surface in Figure 1 8A show that there is significant distortion occurring near the liquid surface interface particularly near the pillars Figure 1 8B gives a slightly finer view of a similar height map emphasizing the surface height in the first 20um above t
102. ill show the background where there are no spots Back Hue Color hue of the background projected by the projector 0 is black no background the projector will show the background where there are no spots l Initial brightness 0 255 of calibration dots Adapts during calibration for Cal Bright calibrating i e determining the camera plane gt projector plane matrix transformation Cal Size Initial size of calibration dots Size adapts during calibration for calibrating i e determining the camera plane gt projector plane matrix transformation Proj Color Cycle through the predefined illumination colors Same as lt gt and lt gt hotkeys Proj Rad increase decrease size of predefined shape Same as lt gt and lt gt hotkeys Proj Shape Cycle through the predefined illumination shapes Same as lt and lt gt hotkeys Colors at the bottom If it fits on the screen lets you select the Proj Color Also shows the color order for Proj Color 123 Figure A 7 continued Optogenetics software usage instructions U Sage How to operate the system roughly chronological order Run Optogenetics ex e Setup Hardware Calibrate Projector Start with P Debugging Auto Calibration Point and Click Mode Toggle with W There should be a shortcut to the executable on the desktop If not you can run the program directly by finding Optogenetics Release Optogenetics e
103. imensional Value As a first approach to the problem consider a homogeneous solid surface and a spherical cap droplet We may directly calculate the total potential energy of the body and to keep things simple ignore the solid liquid interaction The ratio between the two components of energy as a function of droplet volume is 13 EGravity _ Pg tini Esurface 3y MT This demonstrates how the ratio varies with volume but the assumed configuration is essentially a droplet floating above the surface with a 180 contact angle A more complex ratio would include a finite contact angle and account for the actual center of mass of the droplet and the contribution from the liquid solid interaction Interestingly this can be done by completely factoring the liquid solid interface energy and the height of the mass center as functions purely of the contact angle The terms can be lumped together as a pre factor to the above equation to separate the contributions 1 3 3 cos 8 sinZ f 8 2 2 cos 0 5 3 Where O is the effective contact angle independent of any assumption as to how the contact angle is achieved Thus the complete ratio consists of a portion related to the volume multiplied by the portion related to the contact angle The pre factor is plotted over the range of hydrophobic contact angles in Figure 1 10A and the volume is also included in the 3D plot in figure 1 10B The key feature of this curve is that itis monotonic and increas
104. in amplitude 48 2 4 Concluding Remarks The process of producing wavy patterns with wavelengths lt 10um and gt 150um has been fairly well optimized however this leaves the region in between less well covered Wavy patterns in this intermediate range can be produced via sputtering but the technique has been performed only several times and requires fine tuning Another method of expanding the range of wavy pattern scales would be to use other materials PDMS is a very convenient material well understood and readily available but other stiffer elastomers could be used for the substrate such as latex rubber Other materials can also be used to deposit a film aside from metal Polystyrene has been used as the film layer E 3GPa deposited as a solution to generate patterns with wavelengths below 100um It is certainly possible to produce wavelengths at nearly any scale using this buckling technique it is only a matter of acquiring the proper materials and making suitable devices to apply the strain Another area to explore is the mitigation of defects in the pattern Researchers typically don t comment on the uniformity or quality of the buckled surface although it is clear from our results that the pattern quality could be improved The cracks forming along the axis of uniaxially strained specimens are due to the lateral contraction of the substrate from the Poisson effect Subsequent release of strain puts the film under tension
105. ing the conditions previously described The oxidation time can be very short such as 15 seconds at 100W When the oxidation is complete the film and substrate must be removed quickly from the oxidizer and bonded As seen in Figure 2 7 the film is aligned with the substrate and then slowly rolled to make smooth contact along the length of the film The film should be allowed to form a strong bond to the substrate for at least an hour before releasing the strain Figure 2 7 PDMS film to PDMS substrate transfer procedure From left to right the film is wrapped around a scintillation vial The substrate and film are then oxidized The film is then aligned with the substrate and rolled onto the surface to ensure even and strain free film transfer The film should look like the right most image smooth and not extending over the edges of the substrate Patterns produced by this method can be well predicted by the equations in the theory section if the elastic moduli and film thickness are known ahead of time Wavy patterns with wavelengths as low as 180um have been produced with this method There is no physical reason the patterns can t be made smaller than this The practical limitation imposed here is due to the method of manually peeling the film off of the wafer and placing it on the scintillation vial films thinner than 50um or so are very difficult to manipulate by hand The films themselves can be made much thinner on the order of mi
106. jacent pillar corresponds to a discrete edge in the contact line that can be used to characterize it 21 Visualizing Force Contact Line Correlation x 2 O pa c q O S272 eeee e e eee ot 2 2 211 Trailing Q Leading Depinning EN Depinning Events A f ER Af 5 Events Ea rrcrcclll IXIIIIILI e O ic O LL 100 frames Current Frame 100 frames Figure 1 15 Left One frame from the raw high speed video Right The processed frame and visual output from the pillar identification The information gathered from identifying the contact line includes a list of every edge at the boundary the center of mass and the wet pillars comprising the leading and trailing edges as two separate vectors This information can be visually rendered in a video along with the force for frame by frame comparison one frame of such a video is given in Figure 1 15 Viewed alone there is a very apparent dominant frequency in the video and the force falls after a majority of the trailing edge depins in near synchrony One intuitively expects this behavior to hold for smaller depinning events with corresponding small decreases in force However given the full analysis of the contact line this does not appear to be the case Evidence supporting the poor correlation between depinning events and force decrease is given in Figure 1 16 Notice that the major decreases in force correspond well to the major advancement of the center of mass indicating
107. kling relieves the excess strain energy and results in a nearly sinusoidal topography where the wavelength is proportional to the film thickness but may vary significantly with the applied strain and mismatch in stiffness The buckling is initiated by the compressive strain mismatch between the film and the substrate with the requirement that the film is more compressed than the substrate A variety of methods have been used to apply this compressive strain with popular methods being heating differential swelling and applying mechanical pre strain to the substrate Different types of surface patterns may be achieved by modulating the direction of the strain a quasi 1D sinusoid is formed under uniaxial strain while a herring bone pattern occurs when strain is biaxial or uniform Patterning the surface to relieve strain or add an underlying component to the wavy topography also has been done to create more complex patterns This portion of the text addresses the fabrication and characterization of these buckled patterns primarily intended for use in studying cell biology The method for compressing the film is primarily uniaxial pre strain of the substrate before depositing a film Several variations of this technique are described for generating patterns with pitch or wavelength in the range of 100 s of nanometers to several millimeters The theory that allows the structure of the waves to be tuned is addressed as well
108. lf also serves as the culture dish As discussed in the following sections the gel geometry produced by the meniscus effect also introduces other mechanical cues such a change in gel depth resulting in a stiffness gradient To isolate the stiffness effect the gel geometry can be designed to present a constant curvature in one direction and a constant gel thickness This is simply achieved by producing a cylindrical annulus of gel using a mold with a defined radius as illustrated in Figure 3 21 The depicted molds are produced by curing PDMS around cylinders of slightly different radii where the gel thickness is defined by the difference in thickness of the two radii PDMS is used so it may be fluoro silanized as described in the previous section leaving it non stick so the gel is not disturbed when removing the mold Several radii were examined in the range of about 2 30mm The lower end of this range is comparable to the magnitude of the curvature at the gel meniscus although limitations are introduced by the difficulty of viewing such highly curved surfaces and maintaining the gel in such a shape If the theory that cells form ducts at a point of maximum curvature and that the ducts grow parallel to the direction of minimum curvature holds the result from growing cells on cylindrical surfaces should be for cells to form ducts throughout the culture elongating along the axis of the cylinder This is not the case A representative image of the typi
109. listically the oxide layer is a diffused gradient near the surface that may additionally change over time due to the well known hydrophobic recovery of oxidized PDMS 45 Plasma oxidation of PDMS to produce a buckled pattern is carried out by first cutting out a strip of PDMS then stretching it on the straining device The sample surface is kept clean by using the PDMS immediately after it finishes curing and then blowing nitrogen over the sample to remove dust before oxidizing The PDMS is oxidized in a Diener plasma oxidizer with a maximum power of 200W with the power common set between 100W and 200W for most experiments For all experiments the oxidation chamber is pumped down to 1mbar with oxygen flowing at a rate of 50sccm The oxidation time is varied from 12 seconds to 20 minutes depending on the desired thickness of the oxide layer with 1 5 minutes usually giving the best results After oxidation the sample is removed from the chamber and allowed to rest for 10 minutes before releasing strain Best results are achieved when strain is released very slowly and carefully by gently turning the knob on the strainer by hand in a smooth and controlled manner A differential interference contrast DIC image of a typical buckled surface is given in Figure 2 3 and an atomic force microscopy AFM scan of a particularly nice section is given in Figure 2 4 30 Figure 2 3 Optical DIC image of buckling pattern produced by plasma oxidizing PDMS
110. lls have been found to lose their alignment as they become confluent including myoblasts 7 Other reports show that adherent cells become more aligned as they interact For example fibroblasts have been shown to become more sensitive to patterned substrates when they become confluent Our data strongly support this latter case and the mathematical models showing that cell cell interaction will enhance alignment of high density cell populations on surface patterns Figure 3 8 Aligned and unaligned cells in the same image Green Marrows indicate densely populated and aligned patches and magenta arrows indicate sparsely populated and unaligned JAEN nd patches At a fixed point fur lis i jh N aed TN in time the alignment fl ry TEN WA VM ini depends on the local cell NA NOVAM density Scale bar is Wa 200um and grooves run vertically in both images 3 1 6 Sensitivity Parameter Several efforts have been made to identify the cues controlling cell alignment Researchers have suggested that the aligning potential of a periodic pattern can be described as proportional to the groove depth or inversely proportional to the periodicity Other groups have suggested parameters combining periodicity and depth such as the aspect ratio barrier size or fitting regressions 95 Attempts have also been made to relate possible mechanisms for alignment to a parameter of the pattern A geometric model based on the assumption
111. lower Cal Rad try 5 If dots are circled with the wrong color lower Cal Bright try 70 If dots aren t detected at all increase Cal Bright or Cal Rad Test the calibration try selecting a shape on Camera it should be exactly illuminated on the screen When ON the outline of a shape is visible in the Camera window and it will follow your mouse when it s over the window Click and the projector projects the filled shape until you release Use the Controls to adjust shape size color of the shape When OFF click and drag to make a selection then release to have it illuminate Click anywhere again to clear the selection The Point and Click behavior continues while other spots are blinking or being tracked 124 Figure A 7 continued Optogenetics software usage instructions Save Move Toggle with S Tracking Mode Toggle with T Using The Repetition and Timing Controls Recording Video Start stop V Saving Loading Settings Exiting Freezing When Save mode is ON regions you illuminate are saved and will remain illuminated blinking until cleared On mouse up after a selection the selected area should start blinking Depending on the Tracking setting the region will either stay in place or start moving about If you toggle Save mode OFF the selected regions remain and you can continue illuminating on click selection independently of the saved regions which continue to blink Press C to
112. loxane TDFS Gelest Labs is applied in a fume hood If the surface is oxidized PDMS the TDFS a liquid as purchased need not be placed directly on the surface and can instead be placed inside a sealed container with the pattern Some of the TDFS will vaporize and react with the oxide layer as a gas forming a monolayer of fluorinated carbon chains at the oxide surface This might be useful if there is any concern about swelling due to absorption of the silane by PDMS i e for very small patterns In other cases the TDFS can be placed directly on the surface being modified and it will yield a similarly non stick surface In either case 50uL of TDFS is sufficient to treat all the material in a standard 100mm culture dish and the reaction should be carried out for 1 hour for oxidized PDMS or 24 hours in all 39 other cases The volume may be adjusted from this reference to containers of different sizes Excess TDFS should be rinsed away with methanol and dried with flowing nitrogen to prevent exposure to harmful vapors If the patterned surface is not hydrophilic non oxidized PDMS then it won t adhere to the epoxy and need not be treated The epoxy is prepared as instructed being very careful to not introduce bubbles during mixing A thin layer of epoxy is applied to the PDMS on PDMS wavy pattern and also on a glass slide that will hold the epoxy replica The two epoxy surfaces are then pressed together again being careful not to introd
113. lso allow other components to be introduced around the muscle such as neurons or blood vessels This technique offers a good platform for further investigating cell mechanics in 3D cultures 81 4 Microscopy Tools 4 1 Automated Stage and Time lapse System One of the most significant hindrances when studying the development of cells over time is limited throughput This is especially true when if one wants to obtain a complete and continuous record of the development using time lapse microscopy In this case a microscope may be unusable for several days or more while one experiment is conducted examining cells in a limited field of view Worse it can be difficult to exactly replicate experimental conditions repeatedly if multiple time lapse sequences are to be compared This project aimed to address these issues by creating new tools for imaging more samples over larger areas in parallel The obvious solution to the problem would be to simply buy several microscopes and replicate the imaging system However this is a very expensive and inefficient solution that would also require additional lab space for housing more microscopes An alternative approach would be to obtain a single system capable of automated imaging of multiple samples Such systems are commercially available but again very costly and unrealistic for dedicated single purpose use The implemented solution is instead a custom designed automated imaging system taking advantag
114. lters elseif noOrientations 6 tilts sp5Filters else filts rm end threshd 15 Cc 02 m ones threshd threshd n threshd 2 input directory urigetdir rlist getriles2 liuput directory 999 1 3BD8 a3pg otii jy ABS name num length input directory FOfid fopen input directory RESULTS txt w fid fopen input directory DETAILS txt w hhh waitbar 0 for ii 1 length flist waitbar ii length flist hhh Tie name ilris CLL if strcmp tile name XExEExx fprintf FOfid Tirin fprintf fid Xrin continue end img single imread flist ii if length size img img rgb2gray img end oe img imresize img 9 j7 im2 im2 borionmg l 256 3 z201m im2 if isempty filts pyr pind buildSpyr im2 noLevels filts else pyr pind buildSFpyr im2 noLevels noOrientations 1 end Get the histogram h zeros spyrNumBands pind min 4 spyrHt pind For each band look at all scales for b 1 spyrNumBands pind for s l1 min 4 spyrHt pind band spyrBand pyr pind s b h b s norm band 117 Figure A 3 continued Matlab script to measure alignment and confluence of C2C12 cells on wavy patterns Requires the matlabPyrTools library to be installed available at http www cns nyu edu lcv software php end end Sum the energy in all scales We can also use maximum or something similar htotal su
115. ly the system chooses points from a Gaussian distribution centered at the current best guess of the center of the view range with decreasing variance as the window becomes more certain Meanwhile the set of regions previously illuminated is saved so that a particular spot is not duplicated which ensures the calibration points are all unique and approximately randomly distributed while improving the convergence rate Based on the first few detected dots the brightness and size of the dots is adjusted so they are not oversaturated and fit entirely on the screen respectively Dots straddling an edge of the camera window are discarded but the location is marked as an approximate boundary of the image for use in refining the guess for the window area The process is carried out automatically by pressing the hotkey P and typically completes in 1 2 seconds It has been tested successfully when the portion of the projection visible to the camera is as little as 296 as well as when the field of view is larger than the projection area The transformation matrix is saved to a file and loaded when the program initializes to save time if nothing is changed between experiments Once calibrated illuminated shapes are resized and rotated to exactly match what the user selects in the camera feed 100 4 2 6 Cell Tracking The most challenging requirement for the system is being able to follow a moving biobot while still illuminating the proper locations to
116. lyze data collected with a novel method of measuring forces in moving droplets to better understand the dynamics of pinning The results and methodology developed here will help other researchers better understand the relevant mechanics in micro scale droplets In a different setting surface geometry also affects biological cells by altering their mechanical environment In the case of cell mechanics we generally lack even a flawed model for describing the observed behavior so we seek to identify parameters that might simplify these cellular systems One method that allows us to investigate the effects of mechanics on cells is to expose the cells to uniform periodic patterns We first describe a unique procedure for generating approximately sinusoidal patterns at multiple length scales using thin film buckling These patterns are applied to study cells first with muscle cells at the nano to micro scale where the patterns help identify a trend of muscle alignment as a function of surface characteristics In the process we discover that cell cell interaction also plays a role in the alignment Next we investigate the effects of geometry on epithelial cells where the wavy patterns are used to ascertain the cause of unexpected ductal formations in a hydrogel culture The cause is apparently mechanical and a result of variation in stiffness due to the underlying geometry A final section also illustrates some of the techniques that were developed and used t
117. m h 2 energy in each diretion F directions x 1 array hs sum htotal sum htotal snormalize htotal so total energy in all directions TE 1 max ratio max hs sum min hs sum scalar ratio of energy between highest and lowest directions arbitrary units usually 4 is perfect alignment for C2C12 images fprintf fid sNt file name name num 2 end 4 for jj l noOrientations fprintf rid SS 9rfXr he sum 2g include the normalized indivaidual directions might want to check on them later end Iprimtf rrd fTXsium 55 img conv2 im2 m same im2 im2bw im2 1 2 img n c 0 im2 imclose im2 strel disk 7 im2 imopen im2 strel disk 2 im2 imdilate im2 strel disk 2 im2 imclose im2 strel disk 5 tprintf FOfid 8XE 5 3TXES5 3FirAn file name name numt2 end 4 min 1 02 sum im2 numel im2 1 max ratio print resulte TCO Tile ILEISL EWS columns are name and alignment value end close hhh fclose FOfid fclose fid 118 Figure A 4 Images of C2C12 cells from time lapse experiment on pitch 1 67um depth 410nm pattern Images are evenly spaced over 42 hours SS ui EL AY en u Tm if AL kee j MI 9 c Y M y p Hf i oy n SOY a One TY MA vin Z yN p 9 n boy Y my UE 4 o M l Oh A LY M E TAM in ls e A NL Aia o T i ihr au UU f Zane n IN ev F Li he ih He M ha My N Es Ny Ea W A R k a N TUN ii W WE
118. maging so blocking unnecessary light should attenuate the problem The other peripheral device available for use is a thermocouple array connected to a DAQ Measurement Computing USB TC If a DAQ is detected with thermocouples attached the temperature is automatically logged during time lapse The framework for the interface with the DAQ and the Arduino is in place so that the functionality may be expanded to include further integration with either of these devices as needed 4 1 7 Software A custom software package was developed to integrate the hardware components and allow for operation of the microscope system The user interfaces with the system mostly through a number of hotkeys and text input Motion control of the stage is accomplished with wasdqe and the arrow keys while common tasks like capturing an image changing camera exposure and building image sequences are done with one key stroke The basic operation of the software is simply to maneuver the microscope stage and capture single images via the camera however there is significantly more utility available as discussed below Additional functionality includes capturing real time and time lapse video capturing multi image photos and changing the variable parameters of the attached components 87 4 1 8 Time Lapse Imaging The primary purpose of this system is to capture complex time lapse video The automated stage allows various improvements over the standard time lapse
119. me technique described for the thickness and curvature experiments Microscopy images from this experiment are given in Figure 3 25 The first image is of cells grown on the pattern from Figure 3 23 and represents the most interesting result of growing cells on wavy 78 patterns For patterns with sufficiently large wavelength where the overlaid gel has thickness similar to the amplitude of the waves cells will respond dramatically to the pattern In this case cells tend to aggregate into long strips over the highest point of the wave and thinnest portion of the gel and cells form small acini between the strips where the gel is thickest When the gel is thicker or the waves are relatively small such as the 240um pitch and 50um depth in the right image of Figure 3 26 cells do not respond to the pattern and only form acini uniformly throughout the culture et u Figure 3 26 MCF10a cells on Matrigel over wavy patterns Left 850um pitch 200um depth Cells tend to aggregate and elongate over the peaks where the gel is thin and form acini over the troughs where the gel is thicker Right 240um pitch 50um depth Cells do not respond to the waves and only form acini throughout the culture These results are strong evidence supporting stiffness being the dominant driving force in the formation of duct like structures Because the surface of the gel is relatively flat due to the even coating of gel curvature should not have a significant influ
120. minutes at 125 C 35 minutes at 100 C will result in the same mechanical properties This is not quite the case and extending the curing time beyond this has significant effects This section documents a simple method of performing tensile tests with PDMS specimens with varied cure time and compiles the results Figure 2 18 Tensile testing equipment A The testing device with a sample mounted showing the hangar used to apply masses B An image used to measure calculate strain Images are taken in low light so the painted dots are clearly identified C The aluminum mold used to cast T bone samples in PDMS ome 27 344 4 amS n S 7m EN p LI eewintermationss Stress strain curves for PDMS samples were produced using a custom built straining device and an optical method of measuring strain The tensile testing device is simply a stand to allow unhindered application of weights to the specimen The device can be seen in Figure 2 18A The weights are labelled with a precise measure of their actual masses and stresses are calculated by dividing the mass 44 by the measured cross sectional area Samples used were fabricated in a T bone shape using the aluminum mold in Figure 2 18C This shape ensures a consistent cross section and no nonlinear effects from the sample geometry Strains were measured in the necked regions Data points are collected by adding weights to the hangar clamped to the bottom of the specimen and then usi
121. n annn annnnn ans nunn se ees n se een n n en see 8 8 zen E 8 Figure 1 2 Droplet model in SE A One quarter of the droplet is modeled The mesh on the bottom of the droplet eventually appears as in the image B Side view of the droplet and mesh C Rendered bottom view of a droplet after reaching equilibrium The unique feature of this model is the discrete nature of the pillars Each pillar is uniquely defined with individually named constraints This allows an approximate modeling of pinning and individual dewetting events which cannot be captured in a continuous model To model the discrete pillars two types of facts are defined pillar facets and droplet facets The droplet and pillars are defined as a single body where the pillar facets are incorporated into the bottom of the droplet but have different energy and constraints not applied to the droplet facets The pillar facets are given an energy density equal to the liquid surface interface energy while the free facets of the droplet are given the liquid air interface energy In practice the pillar facet energy is implemented as a line integral applied to edges of all pillar facets as suggested by Ken Brakke Vertices of pillar facets are constrained such that their z coordinate is O corresponding to the pillar surface The x and y coordinates are constrained to lie within the boundary of the pillar for square pillars this means 4 inequality greater less than
122. n excess of 50ug mL human fibronectin BD Biosciences This treatment was found to be the most effective surface modification for cell adhesion 9 Patterns were allowed to incubate at room temperature for 1 hour then rinsed 3 times with PBS and used immediately C2C12 cells ATCC were cultured using Dulbecco s Modified Eagle Medium DMEM Life Technology supplemented with 1096 Fetal Bovine Serum FBS Hyclone and 196 penicillin streptomycin BD Biosciences Media was changed every 1 3 days as needed C2C12 cells between passage 5 and 15 were used Experiments consisted of seeding cells on the wavy patterns at a density of 1 0x10 cells cm and allowing them to grow to confluence generally 2 4 days For observation cells were either kept in an incubator and imaged daily or grown in an environment controlled chamber 37 C 596 CO on a phase contrast microscope Olympus IX 51 for time lapse recording 52 3 1 3 Image Analysis To characterize cell responses two parameters the confluence and the cell alignment were measured quantitatively by analyzing still images and video frames taken during the experiments The confluence was measured as the percentage of the surface area covered by cells The algorithm to measure confluence utilized a Sobel filter to find edges roughly outlining cells and then applied morphological dilation and erosion to recover the interior area of the cells A local threshold was applied to binarize the image an
123. n the Appendix would also allow duplicating the electronics and wiring for another microscope stage or any multi axis movement device The simple one axis design can be duplicated in a couple hours with lt 40 in parts 4 1 12 Future and Ongoing Work The full capability of the system has yet to be exploited Some potential experiments that would highly benefit from time lapse recording with extended depth of field or mosaic stitching might include imaging the development of mammary tube structures around the meniscus of a small culture well observing the differentiation and growth of myotubes from a population of myoblasts imaging neuro muscular development in 3D matrix or capturing large data sets of cells grown on a gel on top of a large wavy pattern In practice it can be difficult to successfully set up such experiments prevent the sample from shifting or changing and to keep important areas consistently in focus Increased usage and familiarity with the system might mitigate those issues One of the key developments that will make the system easier to use would be completion of the environmental chamber specifically designed for the stage Earlier versions of the design using low quality parts were not reliable enough to improve ease of use Areliable chamber with a large clear and nonslip viewing area and with proper mounting to stage via the exposed threaded holes would make some of the aforementioned experiments doable 94
124. ng a camera mounted on a tripod and fitted with a macro lens to take a picture of the equilibrium displacement An example image of the strained specimen is given in Figure 2 18B Colored dots are painted on the surface of the specimen and serve as markers allowing determination of strain PDMS is linear elastic over a large range of strains so the applied strain can be very large such that it is easily optically visible Images are processed in ImageJ by isolating the color channel corresponding to the color of the painted dots which are easily detected by applying the Find Maxima function in ImageJ The separation of the centroids of the dots is calculated for each image giving the strain when divided by the original length Calibration is not necessary all length can be measured in pixels The accuracy of this method can be confirmed by inspecting the stress strain plots such as the typical plot in Figure 2 19 The curve is highly linear as expected with a good fit quality Further confirmation can be obtained by painting multiple dots along the length of the neck region and checking if the strain is consistent throughout the necked region which it is 500 y 2365 8x 4 3314 R 0 9998 400 4 Figure 2 19 Typical stress strain curve s a d produced by this tensile testing method Usually 15 data points are used to i ell calculate the elastic modulus The slope amp of the fitting function gives
125. ning if a pillar has been sufficiently unwet is to check if any corner of the pillar is displaced greater than a threshold distance from its original position with the threshold defined as 0 75d See Figure 1 3 This is admittedly imperfect but computationally efficient and easily applied to all pillars by measuring the displacement of the vertices that started at the corners Results seem to match the intuitive sense of when a pillar should dewet the outermost pillars are extremely unfavorable and condense to a point within a couple iterations before they are checked and freed However as the contact line approaches an equilibrium state the determination of when a droplet should dewet becomes more ambiguous Also for a large droplet the energy contribution from small changes in wetted facets is nearly negligible compared to the rearrangement of larger facets higher up near the top of the droplet The exact dynamics of the dewetting process for a receding droplet need to be further studied to determine a more precise dewetting metric Still it is worth noting that while a multiplying factor of 0 75 was typically chosen there seems to be a range of reasonable factors that yield the same contact area and even larger changes in the threshold only lead to small changes in the contact area This was not systematically tested 1 1 3 Meshing and Convergence Surface evolver is different from many finite element packages in that the mesh changes at
126. nning and depinning processes The anomalous forces must be fully understood and either accounted for or eliminated before a reliable correlation between individual depinning events and changes in the force curve can be made Changing the speed at which the droplet is pulled and minimizing the impact of the pulling apparatus may help isolate forces not originating from the contact line If a direct correlation between the contact line and measure forces is not possible we still gain a better understanding of the droplet dynamics by identifying that the entire 3D nature of the droplet contributes to the forces resisting motion In this case there may still be conclusions to make about the global shape of the force curve that relate to large scale changes in the droplet shape 25 2 Wavy Patterns Up until the late 1990 s buckling generally was considered a mode of failure that might occur in a beam or cause delamination in films 78 However it was recently noticed that fascinating patterns arise when a thin film is compressed on a soft substrate and that these patterns might be useful Since then a number of researchers have looked to make use of these wavy patterns The results have had applications from cell biology to optics t to stretchable electronics In each case the theory and basic technique is the same a relatively thin hard film bonded to a softer thicker substrate will buckle if it is sufficiently compressed The buc
127. nt of the whole culture Figure 3 2 depicts how some of these alignment measurements work 54 In order to render a single scalar parameter to characterize alignment for a wide range of cell densities the images were analyzed using a robust local frequency based method which calculated the image energy in a number of discrete directions summed over the entire image Specifically to measure cell alignment between 0 and 180 we used 8 directions at increments of 22 5 Every image was captured with the ridges of the wavy pattern running vertically so the energy in the O direction could be used as an indication of alignment The procedure was performed using the first three levels of the Gaussian image pyramid to account for potential changes in magnification or cell size Normalization can be done in a number of ways We chose to subtract the mean histogram value from the value in the vertical direction and divide by the peak value for a series of vertical lines This gives an alignment value of O for random orientation and 1 for perfect alignment VY NIV Dawa DEVZSIZ r 2x B P rH H c ri Ma i tel Fok te Lo TEN d C PAS 1 Ay ae y L A d d WATAN TAIRA NM V Figure 3 3 Example visual output from alignment and confluence Rt algorithms A C E Sparse gt A Ma RONDE CAN l unaligned cells their area coverage G a FEW IN o x O eos in white confluence and the orientation energy histogram respectively The
128. ntal control hardware although not strictly part of the automated microscope system is meant to be used in conjunction with the microscope Most of the control system was based off the previous system designed by Casey Dyck Briefly a heated cylindrical chamber with an embedded RTD temperature sensor is used to house a culture dish with cells while under observation on the microscope The chamber is maintained at 37 C with high humidity and 5 CO by means of a PID temperature controller McMaster 38615K71 linked to the chamber and a flow meter McMaster 86 4112K93 which regulates the flow of humidified pre mixed 5 CO Inlet CO2 is warmed and humidified in a PVC water tank heated with a 25 watt aquarium heater Top Fin Additionally a heated wrap was added around the gas inlet tube and the chamber lid was replaced by a lid with an encapsulated heating coil to improve environment stability Components are visible in the picture of the whole system Figure 4 1 4 1 6 Peripherals A couple extra peripheral devices were also installed that may be useful in some situations First a shutter was added for the condenser light on the microscope which is controlled by a servo motor connected to an Arduino communicating with the computer via the USB The shutter is automatically open shut during time lapse imaging via the software There is some concern that cells may be sensitive to continuous exposure to intense light during time lapse i
129. nterface Sci 269 171 177 2004 Courbin L Bird J C Reyssat M amp Stone H a Dynamics of wetting from inertial spreading to viscous imbibition J Phys Condens Matter 21 464127 2009 Emmer M amp Brakke K a Surface Evolver Exp Math 25 391 1992 Emmer M amp Brakke K a Surface Evolver Surf Evolver Doc 25 1 1999 Harsh K F Bright V M amp Lee Y C Solder self assembly for three dimensional microelectromechanical systems Sensors Actuators A Phys 77 237 244 1999 Brakke K A amp Sullivan J M Using Symmetry Features of the Surface Evolver to Study Foams Li W amp Amirfazli a Microtextured superhydrophobic surfaces a thermodynamic analysis Adv Colloid Interface Sci 132 51 68 2007 Brandon S Haimovich N Yeger E amp Marmur A Partial wetting of chemically patterned surfaces The effect of drop size J Colloid Interface Sci 263 237 243 2003 Chen Y He B Lee J amp Patankar N a Anisotropy in the wetting of rough surfaces J Colloid Interface Sci 281 458 64 2005 Choi W Tuteja A Mabry J M Cohen R E amp McKinley G H A modified Cassie Baxter relationship to explain contact angle hysteresis and anisotropy on non wetting textured surfaces J Colloid Interface Sci 339 208 16 2009 Mognetti B M amp Yeomans J M Modeling receding contact lines on superhydrophobic surfaces Langmuir 26 18162 8 2010 104 18 19
130. o investigate these phenomena and which may be used by other researchers to further study these topics These studies help better our understanding of mechanics at the micro and nano scale while the methods used herein may be applied to a number of similar systems TABLE OF CONTENTS 1 VICRO SCALE DRODPDEETS wescrccesscecacatauscectuscecacatetevecnvescnca naan cnet ne eas Pince TX RES QUISC Dar EN II veces sic PU RP QUIS TIR VERA UP DU P6 1 1 1 SURFACE EVOLVER XR T UU OE 3 1 2 Cnm mc 13 1 3 Bid irespieuisid E 18 1 4 CONCLUDING REMARKS coca attese tuus otquuteavictod a Dad out a end ae aa onde aeu Ee Ec a assent eaten eee 25 2 WAVY PATTERNS NEC a w 26 2 1 WE ORY tI MN Per 27 2 2 TE GHINIOUIES et E 29 2 3 IVIEASUREMENTS 52 5 aodsteloc aur eat EN doli ed edat ced ullisidtuento tote datis EE E E esses eut NEE E Doom adipi LO adus 44 2 4 CONCLUDING REMARKS ERN 49 3 CELL RESPONSE TO PHYSICAL FEATURES cccscccccsccccansccccanscccessccccensccccsccccacscccessccccessscccessccecssscccasoccess 50 321 REACTION TO IVIICROSSCAEDE WANY FEATURES viaiia cate tes omar oaa ee unie uitio tun m Cosa oe cesse a a a 51 3 2 CELESIN GELS AND 3D GEOMET
131. of a solid nucleus and maximizing contact area was used to correctly predict how cells would align on patterns of posts Early work on fibroblast alignment led to a hypothesis that alignment is the result of the high bending stiffness of actin filaments which was observed when cells failed to cross a slanted ridge when it was sharper than a critical angle gt The effect of actin bending stiffness might also be related to the curvature of the pattern Most 61 research to date has focused on patterns with sharp edges and features fabricated with lithography so the influence of curvature cannot be accounted for Recently it was shown that the curvature of the edges of periodic grooves can indeed affect alignment within a certain range of dimensions t Sutherland 2005 Fibroblasts Grooves Loesburg 2007 Fibroblasts x Grooves x t Clark 1990 Fibroblasts x 8x Grooves x x Biela 2009 Fibroblasts Grooves Wang 2010 Myoblasts e Grooves Our Data Myoblasts Waves Normalized Alignment x A Jiang 2002 Endothelial x Waves Depth nm t Sutherland 2005 Fibroblasts Grooves Loesburg 2007 Fibroblasts Grooves Clark 1990 Fibroblasts Grooves 3 Biela 2009 Fibroblasts Grooves x x Wang 2010 Myoblasts Grooves Normalized Alignment Our Data Myoblasts Waves A Jiang 2002 Endothelial x x Waves x X 0 0001 0 001 Aspect Ratio 1 t Su
132. olored squares identify individual cells their location and their orientation Several cells have moved closer to the largest cluster of cells in the center One of the advantages of this tracking technique over popular feature based tracking is its simplicity and generality Because cells or biobots may drastically change their shape or move into or out of the focal plane it can be difficult to identify consistent features of a particular body This can be partially avoided by not attempting to locate specific features and instead simply looking at the general movement of prominent pixels In testing with various common objects in several different background settings the point based tracking method was generally more robust to large changes than the common SURF and SIFT algorithms However if future developers wish to change the implementation of the point tracking it can be relatively easily done without affecting the downstream logic due to the modular nature of the source code The sparse optical flow also has the advantage of being very fast By aggregating the key points from all the tracked objects into one call to the optical flow function we eliminate the redundant and costly pre processing that would occur if the optical flow function were called once for each object This results in achieving the same performance for almost any number of tracked objects Even on a relatively old laptop the tracking algorithm is generally limited by th
133. on of contraction except in selectively illuminated regions Similarly the letter B toggles displaying a secondary color for the off state of flashing regions A recording of the camera feed can be captured by toggling recoding on off with V Because the projector output and camera input image processing are separated into their own threads the system is capable of maintaining very precise timing of the illumination sequencing up to about 30Hz which is the maximum the projector is capable of outputting 30 on off cycles is 60Hz frame rate the maximum for many devices 4 2 5 Camera Projector Calibration One of the key features of the illumination system is the calibration to match the projector output with the camera input This is necessary so that the exact regions to be illuminated on the specimen can be chosen by selecting the region on the camera image The task is made nontrivial because any of the camera projector or optics may warp the camera s view or the projectors image so that the components are not perfectly aligned along the same optical axis The system is adjustable for panning zooming and rotating all of which change the correspondence between the camera s view and the projector s image Also the camera may only be able to see a small portion of the projector s image or a small portion may fill the camera s entire field of view The solution is an automated calibration procedure that calculates the 6 unique components
134. ons if they can be identified as separate from the larger tooth they reside in To find slopes groups of data points were fitted with a linear regression and if the quality of the fit was above a threshold subsequent data points were added to the regression until the quality decreased by more than a second threshold due to adding the next point If enough points were gathered in this manner the segment was recorded along with the slope of the regression Short segments and negative sloped segments were discarded This extracted data can be weighted for averaging using the number of points included in the segment Assuming this approximately saw toothed curve the same technique can be used to identify area under the curve for a single period In this case there is a higher threshold on the number of points to be included in a segment and a lower threshold on the regression quality There is also the additional requirement that the starting point for the regression be a local minimum Once the period is identified the slope of the regression is ignored and Simpson s rule is used to integrate the actual data Finding clean segments for measuring energy is more restrictive as the full period should be linear The results of this analysis and the slope analysis for one typical data set are given in Figure 1 14 where the width of a white bar indicate a region identified for measurement and its height is the magnitude of the measurement 19
135. ontinuities in the solution and we can mirror the result around r O Theoretical Droplet Shape with Gravity Vii 100L 10 160 Figure 1 11 Numerical solution to Laplace Young equation with gravity No Gavity Cavity lytical Solution 15 20 25 um 15 The ODE is solved using a shooting method where the contact angle is prescribed and the contact radius is guessed The system is then solved yielding a volume which is compared to the target volume If the actual volume is within a tolerance 001 of the target volume the solution is found otherwise the initial guess of the radius is improved and procedure repeated The linear ODE was solved at each iteration using a 4 order Runge Kutta scheme and convergence was generally achieved in lt 5 iterations The result for one such droplet with volume 10uL and contact angle of 160 is given in Figure 1 11 Qualitatively the droplet is noticeably distorted although the exact impact on contact area is subtle To elucidate how the contact area changes as volume and contact angle increase the numerical solution was obtained for a number of droplets in the same range as the energy ratio plot from Figure 1 10B The plot in Figure 1 12 shows the ratio of contact area of a droplet distorted by normal gravity anda droplet free from gravity Here it is quite clear that gravity indeed affects the contact area significantly for some droplets For highly hydrophobic surf
136. owever most studies on myoblast alignment specifically look at individual cells that are not in contact with other cells and there is relatively little quantitative data on how anisotropic geometry and cell cell interaction together influence myoblast alignment Some research has partially addressed this issue by looking at cell seeding density as a variable in muscle formation protocol Yet a deeper understanding of how cell cell interaction can affect and improve myoblast alignment is lacking Our observation that confluent cultures align with smaller patterns than individual cells means that researchers can use smaller patterns to achieve useful muscle alignment This could be useful in applications where micro scale mechanics are important such as the building of cellular machines 5 Oca Oca A Individual a e 2 i m e Confluent Figure 3 11 Our data comparing e e individual and group alignment where ES eo individual alignment is assessed at 2596 a e 0 5 confluence and confluent alignment is E i A i assessed at gt 90 confluence for the same ee A pattern c1 is the threshold at which confluent cells will align 2 002 and c is O the threshold at which individual cells will ala i A align 2 006 The normalizing length scale e e E n 0 is 60um 0 0005 0 005 Sensitivity Parameter 3 1 8 Conclusion Despite a large body of research questions remain regarding the fundamental mechanics of such respon
137. parameters We expect a successful generalized parameter to represent all the alignment data as a single sigmoidal curve where low values give no alignment and high values give maximal alignment The results clearly show that none of these parameters can accurately capture the experimental trend in such a way Thus we attempt to define a phenomenological parameter to describe cell behavior on generalized anisotropic patterns for a variety of cell types Based on our results in Table 3 1 we find that cells tend to align more readily with surface features when d and A are large If either of these parameters is very small cells tend not to respond to the features Additionally we expect that when the pitch is very large 62 relative to the depth the cells will not sense the features This can be described by the curvature of the substrate or more specifically an effective curvature which we take to be proportional to the maximum curvature for sinusoidal patterns The relevance of such a term may relate to the bending stiffness of actin filaments as previously described To maintain generality all of these dimensional features should be compared to a length scale relevant to the dimension of a cell L which is on the order of tens of microns With these asymptotic conditions in mind and considering that cells may respond to any or all of pitch depth and curvature we propose the following non dimensional parameter Q to characteriz
138. played in Figure 1 13 V 20uL 0 150 49 V 20uL 02137 Gravity No Gravity Gravity No Gravity Accrav Acnograv 1 60 Accrav Acnograv 1 26 Figure 1 13 SE simulations with and without gravity The pillars highlighted in pink are wet when gravity is included but not when gravity is neglected The trend of greater increase in contact area for the discrete model is consistent although it is not clear why it occurs The effect could be physical due to additional factors introduced by the discrete pillars or possibly computational due to the added component in the energy functional hindering convergence or the ability of the droplet to overcome small energy barriers to reach a lower energy state In any case the influence of gravity for a pillared surface is at least as great as for a continuous surface if not more so Researchers should keep this in mind during experiments and modeling if the contact area is to play a significant role 17 1 3 Dynamic Droplets In addition to the static shape of a liquid droplet the dynamics of moving droplets on superhydrophobic surfaces present a rich opportunity to study wetting and pinning on a discrete surface Dynamic droplet studies allow determining not just how hydrophobic a surface is but how readily it wicks away fluids This is more closely related to contact angle hysteresis than the hydrophobicity itself In fact a highly hydrophobic surface may actually be stickier than the
139. produces a walking effect Each cycle of contraction should move the bot slightly and to produce sustained motion the illumination targets must also move to continue stimulating the same portions of the biobot Thus an algorithm is needed to track the motions of the biobot and autonomously update the illuminated regions This task is somewhat complicated by the fact that a successful optogenetic biobot has not yet been produced so there is not a definite template for its form It is not certain how the biobot will move or change in appearance as it contracts Currently the solution is a generalized tracking algorithm with no built in assumptions about how shape or texture of the biobot may change over time The heart of the algorithm is the OpenCV implementation of the optical flow algorithm developed by Lucas and Kanade with improvements to handle sparse feature sets and use image pyramids The algorithm approximates the local movement of points between two images of a similar scene Given two images and a set of points in the first image the output is the set of points in the second image corresponding to the new location of the input points Thus objects can be followed by assigning them a set of key points and following the collective motion of the key points in every frame The key points are identified by another OpenCV function which returns the locations of strong corners and edges Some additional work is necessary to make thi
140. putter coating chromium to a thickness of 10nm with 5 pre strain are given in Figures 2 9 and 2 10 The qualitative appearance of the pattern is very similar to oxidative buckling on PDMS Chromium is very brittle and the compliant nature of PDMS makes it very easy to bend the substrate and apply destructive stress to the film The chromium film cracks readily as in Figure 2 9 where the diagonal direction of most cracks indicate that these cracks formed in part due handling after the pattern had formed This cracking was common in optical images and perhaps due to loading the sample on the microscope 36 Figure 2 9 Optical DIC image of buckled pattern produced by sputter coating chromium onto PDMS Name CR1 1 Wavelength 2 1373 Amplitude 281 3639 Accuracy 0 98523 Figure 2 10 AFM image of the 1007 same sputtered chromium pattern 1007 as in the figure above 100 100 2 2 4 Diffraction Gratings Using commercial holographic diffraction gratings for their surface pattern has not been reported previously to the best of our knowledge This is the quickest and the easiest method of producing a wavy patterns with lt 2um wavelength Holographic diffraction gratings are typically used in optics to separate different wavelengths of light and thus have a very tightly controlled quality The surface is approximately sinusoidal and very uniform over larger areas Diffraction gratings are made with a laser 37 holography
141. r Ratio ze D Cure Time hrs Figure 2 20 Tensile testing results A Elastic modulus of samples cured for 36 hours at 60 C with varying ratios of base crosslinker B Elastic modulus of samples with varying curing conditions and fixed base crosslinker ratio of 15 The ratio of base to crosslinker has a more complex effect on the stiffness The plot in Figure 2 20 shows variation for samples cured for 36 hours at 60 C Increasing the amount of crosslinker generally increases the stiffness of the PDMS but there are limits Very low concentrations of the crosslinker yield sticky semi solid substrates that are not easily workable A sample with 50 1 base to crosslinker lacked the integrity to be properly tensile tested On the other end of the spectrum very high concentrations of crosslinker yield exceedingly brittle samples Ratios of 5 1 or below may fracture rather than stretch Adding additional crosslinker beyond the suggested 10 1 also yields diminishing increases in the stiffness especially when heating The maximum tested elastic modulus was 3 1MPa for 8 1 PDMS cured for 6 hours at 150C which was not much more than the 10 1 PDMS cured the same time with 3 0MPa modulus At the lower end the softest PDMS tested was 80kPa giving a sizable range to work with 46 2 3 2 Wavelength and Amplitude The wavelength of the patterns can be easily measured using optical microscopy One may directly measure the length per wave typically averaged
142. reasonable period of time for nonmalignant cells MCF10a cells will behavior similarly to the HME496 cells in that their interaction Figure 3 27 HME496 primary epithelial cells seeded at increasing density From left to right 32 64 128 256 x 1000 cells cm seeding density Top row is day 2 bottom is day 8 Higher seeding density yields fewer larger clusters of cells that also aggregate more quickly than in the sparsely seeded specimens 3 2 7 Future Work The work remaining to be done on this topic is to definitively link the observations with mechanics and biological processes The preponderance of evidence presented here indicates a strong link between the mechanical properties of the substrate and the morphology of the structures cells form but a full explanation including quantifiable effects and a biological mechanism is lacking Additionally a useful application of understanding these underlying mechanisms could be demonstrated One application of 80 the mechanics would be to control the alignment of muscle cells in the same manner that the formation of epithelial tubes has been directed Muscle alignment on a 2D pattern as addressed in the previous section is only useful for 2D muscle strip applications Alignment in 3D could be much more impactful The wavy patterns coated in gel used to study epithelial alignment could be applied to C2C12 myoblasts to form functional myotubes in 3D Forming muscle in the hydrogel would a
143. rger than the expected final size including more wetted pillars than equilibrium as estimated by an empirical formula during model generation During the course of simulation the contact line recedes and facets on pillars that are energetically unfavorable to remain wet will reduce in area To account for the discrete dewetting the simulation periodically checks all pillars to see if they are nearly unwet and if so the pillar is irreversibly and fully set to become unwet When this happens all constraints imposed by the pillar are removed the line integral is removed the surface energy is changed to the liquid gas surface energy and the color of the facet is changed from green to blue to visually indicate the pillar has been unwet Vertex averaging removal of tiny edges t and equiangulation u are performed after a pillar has been unwet to limit instabilities from a sudden change in constraints j A Figure 1 3 Method of determining dewetting If ABCD are B i the corners of the wet pillar before simulation and A B C D are the same vertices some time later in the simulation the pillar is considered unwet if any of the distances AA BB CC or DD is greater than a threshold defined as a multiplying factor usually 0 75 times d the diameter or side length of the pillar l e if the maximum displacement of any vertex from its undeformed position is greater than 75d the pillar is removed D C The method of determi
144. riodic combination of two linear portions first a gradual increase in force as the droplet is displaced then a sharp decrease as the droplet depins and advances a row of pillars Considering the displacement portion of the force curve there are two characteristics that have been theoretically investigated before 7 but can be more closely scrutinized with this experiment These are the effective spring constant of the droplet being displaced from an equilibrium pillar configuration and the energy stored by the effective spring before jumping to the next equilibrium configuration depinning On the force curve 18 these are the slope and the area under the curve respectively from the time the droplet settles after depinning until the next depinning event Algorithms were developed to extract this slope and area from the noisy saw tooth data In both cases the data was highly smoothed with a moving average kernel approximately 1 10 the length of a cycle The confounding factors involved were the high amount of noise and the irregular pattern of the force curve which is not a perfect saw tooth There are many pillars at the leading and trailing edge that may not all depin at the same time or the depinning sequence might change between cycles This manifests as multiple smaller teeth superimposed on the overall saw tooth pattern From observation the slope might be similar for all these smaller teeth so we can collect those smaller linear regi
145. ry mammary epithelial cells provided by Dr Susan Clare at Indiana University In vivo these cells take on a branched tubular structure terminating in round acini The acini are hollow spheroids formed by a single layered shell of cells and both the acini and ducts have a distinct lumen in healthy tissue Figure 3 12 shows a simplified graphic of the structure The environment surrounding these cells in vivo is primarily composed of collagen which has a fibrous structure The cells grow on sheets of basement membrane primarily composed of collagen IV and laminin which forms a mesh like morphology The elastic modulus of this environment is on the order of 150Pa 200Pa in healthy tissue although it is well known to be stiffer in cancerous tissue 7 Such tissue is often simplified as isotropic and linear elastic for simulation but it should be remembered that the material is actually viscoelastic and very anisotropic as cells reorganize the ECM around them Most breast cancers originate from the ductal structures in the breast so understanding the nature of duct formation in this environment is particularly important for cancer research as well as developmental biology Figure 3 13 Different standard in vitro cultures Top illustration of the setup Bottom healthy cells of the corresponding culture method observed under phase contrast 93 In vitro these same acini and ducts may self assemble from a uniform seeding of individu
146. s algorithm useful for tracking We should first expect some error in the tracked points and in practice any individual key point is very likely to be lost no longer following a point connected to the object during significant movement of its parent object To counteract this problem many key points are identified for each tracked object Each key point has a weight emphasizing points close to the center of the object points close to their original orientation relative to the object and points that are well matched from previous frames i e confidence that the point is the same point it was in previous frames The position of an object is determined using the weighted key points with a weighted least squares fit for the translation and rotation of the object between frames If the weight of a particular point falls below a threshold indicating the pixel has likely strayed from its original edge corner the point is permanently discarded Over time an object may lose many of its key points if the cumulative weight for an object falls below a threshold the key points are refreshed by using the current location of the object as a selection region Figure 4 9 shows an example of the tracking algorithm in use Without a biobot for testing these cells are from time lapse culture 101 Figure 4 9 Two frames from a time lapse video demonstrating the efficacy of the tracking algorithm for cells similar to what a biobot might look like The c
147. s that the 63 transition behaviors of cell alignment from many prior studies collapse onto a single sigmoidal shape when plotted against gt CO XX x 1 mgg 1 Too a aca x x x Sutherland 2005 L 50um pb x i Loesburg 2007 Fibroblasts x A 4 Wisosbure LEi xx A a Grooves x x a x S dei SES oe X A x x E x O Fibroblasts x 2 gt c Clark 1990 L 120um x 20 en x x bang Md S x x Biela 2009 L 40um x x 7 N Wang 2010 Myoblasts os N e Wang 2010 L 60m x mem a Grooves E x x x 9 Our Data Myoblasts z 5 Waves x 2 5 Our Data L 60um x x e A Jiang 2002 Endothelial x x x Waves X x A Jiang 2002 L 60um x x A xy exe x LOX S o x e x e x x xX X ao 0 x xot s x xao 0 0 00001 0 0001 0 001 0 01 0 1 0 00001 0 0001 0 001 0 01 0 1 Sensitivity Parameter Sensitivity Parameter Figure 3 10 Alignment data from a number of different groups and cell types 9057 17 8253 plotted against Data was collected from tables and figures from prior work characterizing alignment on periodic features and original alignment measures were linearly rescaled between 0 and 1 A Plot with the normalizing length scale fixed at 600m Individual data sets tend to follow a sigmoidal trend B Allowing the normalizing length to vary between different data sets leads to collapse of the data towards a single curve Some variability is present due to differing conditions
148. sary field of view and a custom design was used instead Figure 4 6 shows the physical setup The apparatus consists of a 2 axis stage elevated above the focusing optics and the projector used to generate the light stimulation Above the stage is a USB microscope camera Adafruit 2 0 Megapixel USB Microscope with adjustable zoom from 25x to 400x with internal optics The camera is fitted with 550nm dichroic filter to block light at the stimulation wavelengths similar to a fluorescent filter system The camera and the projector are both connected to a laptop which controls the system Figure 4 6 Overview of the optogenetics system The stage at the right holds the specimen The jack allows adjusting the alignment of the projector with the optical train 4 2 3 Optics A commercial projector ViewSonic PJD5533w is used for the stimulation light source This projector uses digital light processing DLP technology with a 6 section color wheel to output of 3000 lumens with a resolution of 1280 x 800 pixels The original optics on the projector are left intact to make fine adjustments to focus and magnification but several plano convex lenses were added near the projector outlet to focus light down to the viewing area The optical components are shown in Figure 4 7 96 The spectrum produced by the projector was analyzed with a HR4000 spectrometer Ocean Optics using SpectraSuite software It was found that the optimal output colors were p
149. scussed in the later sections Aluminum is softer 70GPa and more ductile than chromium It may be a more suitable material for future experiments although its effectiveness is not known The method of performing the sputter coating is similar to the previous methods where the uniaxial strainer is used to stretch a strip of PDMS The strainer cannot be directly fit in most sputtering machines so custom made plates were machined to replace the standard sputtering plates 3 diameter 4 thick while holding a pre strained sample The sample is strained clamped onto the plate and then cut to hold the strain during sputtering as seen in Figure 2 8 The sample is suspended between the camped points without contacting the disk to allow for expansion and contraction The machine used for the results presented below is the Cooke Dual Gun Sputter system The chamber is pumped down to 2 0 E 6 torr before flowing argon into the chamber and applying a 100W DC current to initiate the sputtering This sputterer also has a heating feature which might be used for future experiments 35 Figure 2 8 Custom disk used for sputtering on strained samples Right disk holding a strained sample before sputtering Left illustration of the straining and loading process The sample is strained and the disk slides between the threaded rod of the strainer and the bottom of the sample The plates are then screwed down and the excess sample is cut away Results from s
150. sequence The user can save a series locations that the stage will automatically and repeatedly move to and image with the designated timing The locations can be further divided into groups that will be imaged and saved together These locations can be selected by moving the stage to the desired location using the software motors and then saving the spot or the location can be manually entered as a tuple of coordinates Predefined grids can also be added to the moving sequence to form a mosaic image as described in the next section that can be captured as part of a time lapse sequence A preview mode allows the user to cycle through all the saved locations and adjust them for focus and content before starting a time lapse Once started a time lapse may be paused and resumed or canceled without disrupting the timing Sequences are saved to disk once defined and can be edited with a text editor and loaded at the next start up Individual images are immediately accessible to view after capture and may be saved directly online to view remotely Additionally the shutter and thermocouple array if attached are integrated with the time lapse so that the shutter closes when images are not being captured and thermocouple readings are taken at the end of each frame There are several intended applications for this functionality One might image multiple locations within a single sample which may be at different focal planes Similarly such multiple loca
151. ses Our results suggest that cells are sensitive to pitch depth and curvature of periodic anisotropic patterns at the micron scale and we propose a non dimensional parameter that may predict the tendency for cells to align on a pattern based on these sensitivities We identify thresholds for the parameter that separate patterns that will align cells from patterns that will not for individual and confluent cells Additionally between these thresholds we observe that confluence significantly affects alignment and we conclude that cell cell interaction may enhance alignment in the presence of weak topographic cues We still do not fully understand the mechanisms by which cells respond to their mechanical environment Further work may be done to better explain why cells respond to the pattern features investigated here and how cell cell interaction can lead to changes in cell alignment 65 3 2 Cells in Gels and 3D Geometry Although topographically patterned cells interact with nano scale wavy patterns as a 2D surface Recently the cell biology community has placed increasing focus on the more relevant 3D world in which cells normally inhabit We now know that cells will look and behave very differently in 3D than when cultured on a flat surface 8 Additionally the 3D environment may be much softer than rigid PDMS patterns previously addressed 3D cell environments may consist of a hydrogel containing ECM proteins fibrils and other cells all
152. so used to narrow the search area for matches and disregard extraneous maxima corresponding to unlikely displacements To ensure robustness and account for noise the 3 best matches in each phase correlation are saved similar to the implementation in There is often significant noise and uncertainty in the correlations so the locations of all the images in the composite are iteratively searched until a global consensus is reached This process compares the 3 best correlation matches from each image pair with the consideration that the separation between any two images must be the same no matter what path of overlaps is traversed between the images i e Where the vectors indicate the offset between any pair of images similar to Kirchhoff s current law applied to the offset between images a closed loop must yield O offset for consistency When a consensus cannot be reached for some images the search area is expanded and different weighting schemes on the FFT are applied to try and find a consistent overlap If even this fails the specimen likely slipped or shifted too much during acquisition the stitching is abandoned and the individual images are saved instead An example of a 6x6 tiled image showing the wide field of view is given in Figure 4 4 Figure 4 4 II Demonstration of lI stitching algorithm A WU raw 6x6 tiled image of myotubes growing on a wavy pattern is Hh presented as W captured Large scale y shading e
153. t 7 1655 63 2007 Jiang H et al Finite deformation mechanics in buckled thin films on compliant supports Proc Natl Acad Sci USA 104 15607 15612 2007 Schneider F Draheim J Kamberger R amp Wallrabe U Process and material properties of polydimethylsiloxane PDMS for Optical MEMS Sensors Actuators A Phys 151 95 99 2009 Schneider F Fellner T Wilde J amp Wallrabe U Mechanical properties of silicones for MEMS J Micromechanics Microengineering 18 065008 2008 Chua D B H Ng H T amp Li S F Y Spontaneous formation of complex and ordered structures on oxygen plasma treated elastomeric polydimethylsiloxane Appl Phys Lett 76 721 2000 Wu C C Yuan C Y amp Ding S J Effect of polydimethylsiloxane surfaces silanized with different nitrogen containing groups on the adhesion progress of epithelial cells Surf Coatings Technol 205 3182 3189 2011 B fahy S et al Thickness and elastic modulus of plasma treated PDMS silica like surface layer Langmuir 26 3372 5 2010 Mills K L Zhu X Takayama S amp Thouless M D The mechanical properties of a surface modified layer on poly dimethylsiloxane J Mater Res 23 37 48 2008 Hillborg H Tomczak N Ol h A Sch nherr H amp Vancso G J Nanoscale hydrophobic recovery A chemical force microscopy study of UV ozone treated cross linked poly dimethylsiloxane Langmuir 20 785 94 2004 Bodas D Rauc
154. t adhesion of Caco 2 cells J Biomed Mater Res A 93 1260 1271 2009 Chou L Firth J D Uitto V J amp Brunette D M Substratum surface topography alters cell shape and regulates fibronectin mRNA level mRNA stability secretion and assembly in human fibroblasts J Cell Sci 108 Pt 4 1563 73 1995 Wigmore P M Maleki F Evans D J amp McErlain M After embryonic day 17 distribution of cells on surface of primary muscle fibres in mouse is non random Dev Dyn 207 215 221 1996 Fujita S Ohshima M amp Iwata H Time lapse observation of cell alignment on nanogrooved patterns J R Soc Interface 6 S269 S277 2009 Loesberg W a et al The threshold at which substrate nanogroove dimensions may influence fibroblast alignment and adhesion Biomaterials 28 3944 3951 2007 107 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 Aubin H et al Directed 3D cell alignment and elongation in microengineered hydrogels Biomaterials 31 6941 6951 2010 Luna J I Ciriza J Ph D Garcia ojeda M E amp Kong M Multiscale Biomimetic Topography for the Alignment of Neonatal and Embryonic Stem Cell Derived Heart Cells Tissue Eng Part C 17 579 588 2011 Magdalena J Microtubule involvement in NIH 3T3 Golgi and MTOC polarity establishment J Ce Sci 116 743 756 2003 Sutherland J Denyer M amp Britland S Contact guid
155. t2NearMax maxX2 sum sum wgtX ft2NearMax sum ft2NearMax turnAng 180 atan maxX2 maxY2 pi oo Check if rotation is CW or CCW temp abs fft2 imrotate img turnAng bilinear rotMax max temp 1 temp abs fft2 imrotate img turnAng bilinear tempMax max temp 1 if tempMax gt rotMax Lurnang LurnAng rotMax tempMax end 5 Get ideal rotation by rotating image slightly and finding fft peak bestAngChange 0 ter dling L d X 4 X abe temp abs fft2 imrotate img turnAng dAng bilinear tempMax max temp 1 if tempMax rotMax bestAngChange dAng rotMax tempMax end end turnAng turnAng bestAngChange tor dAng 15 402 215 temp abs fft2 imrotate img turnAng dAng bilinear tempMax max temp 1 if tempMax rotMax bestAngChange dAng rotMax tempMax end end turnAng turnAng bestAngChange 5 Crop off blank stuff introduced by the rotation img imrotate img turnAng bilinear newSize floor ptDim abs cos pi turnAng 180 abs sin pi turnAng 180 offset round length img newSize 2 img img offsett l offsettnewSize offsettl offset newSize Remove outliers for measurement and side view 113 Figure A 2 continued Matlab script to extract wavelength and amplitude from AFM data outlierFt fft2 img outlierFt 1 round maxY2 3 round maxY2 3 end round maxY2 3 end round maxY
156. ted here also fill a gap in results for patterns without sharp edges that previously contained little comprehensive data from a single source 3 1 1 Pattern Preparation Samples were fabricated by replicating commercially available holographic diffraction gratings Edmund Optics with a biocompatible material We used Polydimethylsiloxane PDMS to produce the biocompatible replicas Sylgard 184 PDMS was mixed at the standard base crosslinker ratio of 10 1 poured on the grating surface and degassed under vacuum for 30 minutes The grating was then placed pattern side down on another pre cured slab of PDMS and cured at 60 C for 4 hours to bond the replica to the slab The replica was then gently peeled away with the rest of the slab with minimum damage to the fragile diffraction grating To make samples of high optical quality we performed an additional copying step to obtain the pattern as a thin film on cover glass To do this we silanized the PDMS replica by treating it with oxygen plasma Diener Electronics for 30 seconds at 100W and placing the replica in a sealed chamber containing tetrahydrooctyl 1 1 2 2 tridecafluoro dimethylchlorosiloxane Gelest Labs for at least 1 hour 9 The silanization prevents PDMS from bonding to the replica The replicating procedure described above was then repeated using a 25mm diameter coverslip The silanized replica was easily peeled away from the coverslip leaving an approximately 100um thick layer of
157. tep set goa Etiesk fltz tloor zavg tltz fltz floor zavg tltz l s set gca Zlim 1l l max max img min uimg 5 max max img min img saveas hkig LrName l end 4 b savervpel close imwrite 10 img min img 65535 fName 1 end 4 png png BitDepth 16 end 115 Table A 1 Summary of plasma oxidation experiments Wavelengths and amplitudes for various process conditions Base Strain Power Sesion Wavelength Depth Ratio 96 pu Ane nm nm min 18 10 100 10 830 180 18 8 200 5 830 145 18 6 200 2 670 115 21 8 100 5 860 150 21 8 100 10 1720 150 21 5 100 10 1690 200 21 10 100 10 1980 200 8 10 100 4 480 60 8 10 100 3 420 20 8 10 100 3 420 12 8 10 100 3 410 24 8 10 100 4 550 65 20 10 100 7 1160 145 20 10 100 3 750 70 20 10 100 5 910 63 20 10 100 1 460 36 15 10 200 3 1150 80 15 10 200 7 1600 110 15 10 200 5 1450 90 15 10 200 9 2200 210 20 10 200 3 1150 120 8 10 200 5 750 55 8 10 200 7 1200 75 10 10 200 3 800 50 10 10 200 5 1150 90 10 10 200 7 1250 115 10 10 200 9 1600 135 10 10 200 7 1200 140 10 10 200 5 1070 30 116 Figure A 3 Matlab script to measure alignment and confluence of C2C12 cells on wavy patterns Requires the matlabPyrTools library to be installed available at http www cns nyu edu lcv software php noLevels 2 2 is best noOrientations 8 I like 8 if mod 360 noOrientations good else bad if noOrientations 4 filts spa3rFi
158. ters to sub pixel resolution assuming consistent spacing between pillars This is done by optimizing an affine transformation from the integer pillar spacing to the image pixel spacing using iterative least squares to minimize error while allowing for minute distortion and rotation of the pillar grid Once the exact pillar locations are known in the image an average is calculated about each pillar and the image is resampled from the average so that each pixel corresponds to the average intensity in the neighborhood of a single pillar The processing described above greatly enhances the appearance of wet pillars but additional logic must be applied to identify the exact contact line Simply applying filters and a threshold is not sufficient to detect the wet pillars The best method to extract the full contact line with few mistakes was to walk around the edge of the droplet following the pixel intensity gradient produced at the boundary between wet and unwet pillars Starting from the clearest pillar at the trailing edge the algorithm steps to one of the 8 adjacent pillars cardinal and ordinal directions that is most likely to be the next pillar along the contact line based on pixel intensities gradients contact lines in previous frames and the current position relative to the whole droplet maintaining convexity and approximate circularity The stepping continues until the contact line arrives back at the first pillar Each step to an ad
159. the cell to hyperpolarize and thus preventing contraction The halorhodopsin pump is triggered with orange light near 588nm Between the two proteins cells be induced to contract with blue light or inhibited with red light The response occurs at a time scale on the order of a millisecond offering excellent temporal control Two different cell types have been tested with the system The first cell type was a primary cardiomyocyte harvested from rat heart tissue This is an extension of the previous biobot design which also used a rat cardiomyocytes to drive actuation In this case a secondary cell line with the necessary transfections is co cultured with the myocytes to provide the light activated stimulus the cardiomyocytes are not active but are stimulated when the secondary cells fire due to the difficulty of genetically altering the primary cells This has the disadvantage of lower yield due to the presence of non contracting cells and potential difficulty inhibiting contraction The eventual goal is to use 95 transfected C2C12 cells that will directly respond to light As of the time this was written the available population of C2C12 is too weakly responsive to the light to achieve noticeable movement 4 2 2 Design The stimulation system is designed for relatively large biobots that may have lengths on the order of 1 10mm which also need to move around freely Thus a typical inverted microscope would not provide the neces
160. the modulus 2 366MPa for this sample adii D D 0 05 0 1 0 15 0 2 Samples were fabricated with base crosslinker ratio in the range of 8 40 curing time in the range of 0 48 hours and curing temperature in the range of 60 150 C The results can be summarized by the two plots in Figure 2 20 We can look at the impact of each parameter in isolation Increasing curing time will increase the stiffness up to a point and then no more For samples cured at 60 C a common temperature to use because it is the maximum polystyrene can withstand maximum stiffness is reached 45 after 36 hours with negligible gain thereafter The maximum stiffness time at higher temperatures appears to be shorter although this wasn t explicitly tested The plateau in stiffness with time seems to indicate that the crosslinking reaction has gone to completion Temperature has a more significant impact than the curing time Samples cured for an hour at 150 C are significantly stiffer than samples cured for 48 hours at 60 C PDMS begins to thermally degrade around 200 250 C so it is feasible that harder samples could be produced by further increasing the temperature o Temperature C A Stiffness Variation with Base Linker Ratio B Eo 120 2500 l m 100 2 r SO 2000 o E LY Uo 5 1500 5 x o 1 K E kPa 1000 k LY e T T o T uj 500 LU EUR __ e 0 0 10 20 30 40 50 game 58 Base Crosslinke
161. the total energy local curvature local variation in the contact angle and the effect of small changes to the shape or wetted pillars The full model presented here is unique compared to a number of earlier models of droplets on pillars that either simplified the case to 2 dimensions P or modeled pillars as a single surface with continuously varying surface energy Similarly several groups have modeled droplet evolution on a ridged pattern 1546 Each of these studies takes care to avoid discrete changes Others have simplified the array of posts to study the dewetting of a single post in quasi 3D however only the space local to the pillar was considered losing the complex interaction form neighboring pillars 1 1 1 Model Development While SE provides a powerful tool for simulating a model moving towards an ever lower energy state it does not provide tools to help design the model itself The user must define the model using a text file listing the nodes points in space edges directed connection between two nodes facets ordered collection of three edges and constraints This is often typed by hand which is perhaps why most models are relatively simple A common approach is to define the constraints and build a very basic surface such as a cube and then refine and evolve the model to until it more closely matches the desired geometry 9 This same technique is applied here to some degree although the numerous constraints and con
162. therland 2005 Fibroblasts A ve x Grooves x x 4 3 Loesburg 2007 Fibroblasts A x x 5 Grooves x m ex E xo Clark 1990 Fibroblasts Xx x x c 7 Grooves x TT 3 Biela 2009 Fibroblasts Grooves x x x 0 5 9 Wang 2010 Myoblasts x x e m Grooves z E Our Data Myoblasts x x e 6 Waves x x x x Jiang 2002 Endothelial x x x x Waves x x x Pal x sos 8 e xx x x X herve xxx o 0 0000001 0 00001 Feature Frequency nm Sutherland 2005 Fibroblasts Grooves 1 ben gi Re xx x x Loesburg 2007 Fibroblasts x A x Grooves x a x x Clark 1990 Fibroblasts xo x x Grooves x x x 3 Biela 2009 Fibroblasts Grooves x x x o e x e x x x x x A Jiang 2002 Endothelial x Waves x x Xx x x e e x xy X x xxo xx Ax x xx 0 1 100 10000 1000000 100000000 Size Pitch Depth nm 0 5 x Wang 2010 Myoblasts Grooves Our Data Myoblasts Waves Normalized Alignment Normalized Alignment Normalized Alignment t Sutherland 2005 Fibroblasts Grooves xx 3 1 n nro x e 3 Loesburg 2007 Fibroblasts x X x Grooves x AK e 3 Clark 1990 Fibroblasts x X 9 x Grooves x x Biela 2009 Fibroblasts Grooves x 0 5 Wang 2010 Myoblasts x x I rd Grooves e Our Data Myoblasts x x e Waves x x x A Jiang 2002 Endothelial x Waves x Xx x 0 x x x e X X oe _ x X x x eso ax 0 10 1E 08 0 000
163. tions can be saved as a mosaic which may be combined together as a single image A series of mosaics may can be registered aligned and corrected for shifting over time and converted into a single video to conveniently view a large area over time One might also collect several different specimens together in several culture dishes or a multi well plate and image all the specimens in parallel using time lapse 4 1 9 Integrated Mosaic Stitching In addition to the capability of capturing video of multiple wells the microscope system has the ability to take several images over a large area and merge them into a single image This utility can be used as a stand alone program to merge previously captured images but it is also integrated with the main system control such that a grid of images can be automatically acquired and merged by pressing a single 88 hotkey the numbers 2 0 indicating the side length of the grid in images O would be 10x10 100 images Similar functionality is available to capture such mosaic images in a time lapse sequence Although several implementations of the algorithm used to stitch the images together are freely available such as a popular plugin for ImageJ Microsoft s ICE and the stitching module in OpenCV these sources tend to be prohibitively slow This may be due in part to the generality of these implementations since they do not account for the a priori knowledge of the grid layout More importantly
164. tterns Thickness and stiffness can also be studied in a more controlled manner by patterning the thickness in a well defined shape The wavy patterns discussed in section 2 provide one such method of controlling the shape of a gel and most applicable is the PDMS on PDMS buckling method which can be used to produce a pattern with wavelength in the range of 150um to several millimeters For this explanation the desired form of the usable pattern is that displayed in Figure 3 24 where a large section of pattern is printed on the bottom of a 35mm culture dish The procedure for producing such a pattern is the stamping method detailed extensively in section 2 2 5 A section cut through the wavy pattern after applying gel and culturing is given in Figure 3 25 The thickness and shape of the gel and the locations of the epithelial structures that formed are visible in this side view Flat gel surface thin harder Gel hick sof thick softer Wavy PDMS T 2 Figure 3 25 Section cut of PDMS Matrigel interface on a wavy pattern after fixing with 1096 formalin Sigma and cutting through the culture area with a razor The surface has no curvature but the waves affect the stiffness making the surface effectively stiffer near the peaks Figure 3 24 Sample with a wavy pattern 850um pitch 200um depth imprinted in PDMS Gel can be overlaid on top of the pattern to form a periodic thickness gradient Cells were cultured using the sa
165. uce bubbles into the epoxy To cure the mold should be placed with glass slide facing up and buckled PDMS side down so air bubbles will rise away from the patterned surface Light pressure should then be applied by placing a weight on top of the glass slide which will ensure and even surface After at least an hour if using 5 minute epoxy the PDMS pattern can be peeled away and the epoxy should be further cured in an oven at 60 80 C for gt 8 hours After curing it is recommended to use hot glue to create a barrier around the boundary of the pattern such that PDMS poured on top of the epoxy will remain within the barrier allowing regulation of the thickness of the copy This mold should now be reusable indefinitely for making PDMS copies This mold with hot glue applied should look like Figure 2 13 Wig n T L 4 ALIT TOLOI TTTTIT TTT d ASE u ae bd 4 p Alum t Figure 2 13 Epoxy copies of buckled patterns with surrounding barrier of hot glue to contain PDMS on the pattern during replication Left 330um wavelength buckled pattern copy Right 1 64m commercial diffraction grating copy To prepare the pattern for culture more PDMS is used to make a copy of the epoxy mold The PDMS should be degassed until no bubbles remain and then poured on the epoxy mold or pour first and then degas Allow the uncured PDMS to evenly spread and begin to solidify by leaving it on a flat surface at room temperature for gt
166. ue to an unfortunate choice of stage motion speed Further work will aim to improve the experimental design to remove these anomalous frequencies it might allow a fuller understanding of how individual depinning events affect the dragging force exerted by the droplet 24 1 4 Concluding Remarks Work on the micro scale droplets is still progressing on both the simulation and experimental fronts For simulation of droplets with SE a method for analyzing a receding droplet has been developed but there is no analog for an expanding droplet In order to better understand contact angle hysteresis we must be able to compare the geometry of a droplet at equilibrium after expanding as well as after receding In this case the model is somewhat more complex as the droplet must grow adding facets and constraints when new pillars are wet Such a model has been demonstrated for several specific cases but a parametric version capable of automatically handling variety of geometries may be needed for a thorough comparison to the receding model Additionally this expanding droplet model combined with the receding method may allow simulating quasi static droplets in motion comparable to the dynamic droplet experimental work Modelling a moving droplet may help understand the changes in shape and energy occurring as the contact line of the droplet makes a discrete jump to new pillars For the experimental work more data is needed to better understand the pi
167. ure blue and pure red RGB 0 0 255 and RGB 255 O 0 for activating the channelrhodopsin and halorhodopsin respectively Despite the absorption spectrum not quite matching these pure colors it was found that due to the nature of the DLP and color wheel any deviation from pure color adds significant noise over the entire visible spectrum though it is not detectable with the naked eye The pure colors do give sharp peaks near their respective wavelengths so the excitation should be reliable and specific Figure 4 7 Optical components to the optogenetics system Left Above the stage the camera and filters Top Below the stage 4 plano convex lenses are sandwiched into the housing at the left side of the image A mirror center redirects the light from the projector far left upwards toward the stage and camera Projector light is focused at the plane of the stage top 4 2 4 Software Custom software to control the light stimulation system was designed using C and the open source computer vision library OpenCV The main functionality provided by the software is to be able to view the specimen and quickly select regions on the image of the specimen for illumination with a desired wavelength of light There is also the option to produce time sequenced illumination patterns and to track and illuminate moving objects over time There are 4 main panels to the program Projector 97 Controls Camera and the command line If th
168. usual spike to the curvature with the peak 1500 1700um from the walls It can be first noted that there does appear to be a distinct region of maximum curvature However the peak seems to lie closer to the walls of the culture dish than where most of the ducts began forming This could potentially be due to the smoothing required to obtain a continuous curve so it might be worth repeating the procedure to further investigate the results It is also interesting to note that this surface and measured curvature do not follow the behavior we expect from fluid mechanics the curvature should steadily increase moving further up the meniscus towards the wall It is not clear if this is a result of the measurement technique or due to the nature of the hydrogel culture Shrinking or swelling of the gel could occur from the liquid flux with the media the high protein content might affect the surface differently than a pure liquid or the cells themselves might reorganize the gel and change the shape of the surface Optical observation of the surface also becomes more difficult on the severely curved surface close to the walls which degrades the accuracy away from the flat center region in the culture 74 Gel formed into cylindrical shell Mold to force Figure 3 21 Molding gel into cylindrical curvature and shell shape The top of the mold green is thickness fluorosilanized to prevent the gel from sticking Both halves are PDMS Bottom ha
169. volumes Fora given number of wet pillars the equilibrium wetted pattern tends to be the same across different droplet volumes and pillar spacings 1 1 5 Droplet Shape More difficult to assess experimentally is the nuanced 3D shape of the droplet near the contact surface Goniometer measurements may allow measurement of an effective contact angle at multiple orientations but they cannot give a precise shape or account for concavity if present One experimental solution to getting precise 3D data on the droplet shape is to use SEM however this will generally not work for liquid as it will evaporate under vacuum Some researchers have used curable polymers such as PDMS to freeze the droplet in place and view it 2 The alternative is to directly simulate and view the full mesh with information on curvature and contact angle A simple method to extract information about the surface shape is to take section cuts along the longitude and latitude of the droplet The built in rendering engine from SE is used to smooth the sharp edged facets and then cross sections of the droplet surface contours are captured at fixed locations The result is Figure 1 6 These images are taken from a 7uL droplet with o 0 25 and L 100um In Figure 1 6 longitudinal slices are taken at 5 increments comprising the 10 unique angles at this spacing The section view is near the interface with the surface showing the very different contact angles observed at d
170. xe Connect the projector and the camera to the computer and turn the projector on Make sure the camera has the proper field of view and focus by placing your specimen or equivalent on the stage Adjust the height of the camera above the stage to change the field of view then adjust the focus on the camera with the plastic cog in its midsection Set your focus before calibrating If the program has been run before the previous calibration is automatically loaded To make a new calibration the projector will project random points on the projector and try to find them with the camera You will need to place a piece of computer paper on the stage where the specimen will go so there is a surface on which the projector can form an image Press P and the program will attempt to threshold binarize the camera s view of the dots You ll see the result in the Camera window while it s working If successful you should see the transform matrix printed in the command window when it s done Once successfully calibrated remove the computer paper and replace with your specimen The calibration is not particularly robust so you might not be successful on the first attempt regions won t project where they should No problem change the calibration options and repeat the previous step On the Controls window see Slider Bars chart you can adjust the options Here s how to go about making it work If dots stop blinking on screen or you get RNG failed

EFFECTS OF MICRO- AND NANO-SCALE SURFACE

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