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1. exegesis Version 2 Methods Ecol Evol 2 229 232 Semendeferi K Teffer K Buxhoeveden D P Park M S Bludau S Amunts K et al 2011 Spatial organization of neurons in the frontal pole sets humans apart from great apes Cereb Cortex 21 1485 1497 Smith S J 2007 Circuit recon struction tools today Curr Opin Neurobiol 17 601 608 Wearne S L Rodriguez A Ehlenberger D B Rocher A B Henderson S C and Hof P R 2005 New techniques for imaging digitization and analysis of three dimensional neural morphol ogy on multiple scales Neuroscience 136 661 680 White E L and Peters A 1993 Cortical modules in the postero medial barrel subfield Sml of the mouse J Comp Neurol 334 86 96 Yanez I B Munoz A Contreras J Gonzalez J Rodriguez Veiga E and Defelipe J 2005 Double bouquet cell in the human cere bral cortex and a comparison with other mammals J Comp Neurol 486 344 360 Zubler F and Douglas R 2009 A framework for modeling the growth and development of neurons and networks Front Comput Neurosci 3 25 doi 10 3389 neuro 10 025 2009 Conflict of Interest Statement The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest Received 16 December 2012 accepted 21 March 2013 published online 09 April
2. under the null hypothesis solid black line Thus the probabil ity that the BTSS value based on the actual samples belongs to the bootstrapped distribution is less than 5 and the two sets are significantly different at 5 significance level The aim of this analysis was to show how RipleyGUI can be used to compare two experimental distributions the statistical test that can be used and how the results can be interpreted The results show that the structural organization ofa given population of genetically labeled neurons can differ in two sensory cortices This difference in spatial soma distribution in combination with the differences in neuron morphology Groh et al 2010 could indicate that these neuron types are organized according to differ ent structure function relationship principles in the two different sensory cortices Larger degrees of aggregation thus means in this case that etv pyramids in visual cortex are more packed within a sphere with a radius of 20 um than expected from a CSR distri bution whereas for etv pyramids in barrel cortex this is the case only for a bigger sphere with radius 30 um How these changes influence connectivity remains to be investigated combining both experiments and modeling DISCUSSION We describe a MATLAB based software for analyzing the spatial distribution of neurons in 3D The program has a graphical user interface making it easy to use without any MATLAB programing experience The sof
3. 2013 Citation Hansson K Jafari Mamaghani M and Krieger P 2013 RipleyGUI soft ware for analyzing spatial patterns in 3D cell distributions Front Neuroinform 7 5 doi 10 3389 fninf 2013 00005 Copyright 2013 Hansson Jafari Mamaghani and Krieger This is an open access article distributed under the terms of the Creative Commons Attribution License which permits use distribution and reproduction in other forums provided the original authors and source are credited and subject to any copyright notices concerning any third party graphics etc Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 9
4. RipleyGUI edge correction terms Baddeley et al 1993 is based on the exact evaluation of volumes rather than calculations of surface areas Examples of software for spatial analysis of 2D and 3D data respectively is PAST and SpPACK which has an impressive num ber of functions Hammer et al 2001 Perry 2004 and SA3D and PASSaGE Eglen et al 2008 Rosenberg and Anderson 2011 that evaluates Voronoi tessellations nearest neighbor dis tance and estimates Ripley s K function The software presented in this paper RipleyGUI focuses on using Ripley s K function and in contrast to existing software includes statistical tools that allow the user to easily compare cell distributions thus providing methods for a more thorough analysis of the data Furthermore RipleyGUI handles sets of data for analyzing the mean and vari ance of the estimated K function within a data set and through comparison with distributions following complete spatial ran domness CSR the statistical significance level of all findings can be calculated An important complement and improvement to existing software are thus the statistical tools implemented in RipleyGUI to determine statistically significant differences RipleyGUI is written in MATLAB which is commonly used by experimental scientists and can thus easily be integrated with other analysis plugins IMPLEMENTATION COMPUTING ENVIRONMENT RipleyGUI has been developed using MATLAB 7 1 The only
5. brain through neuroinfor matics Front Neurosci 2 22 doi 10 3389 neuro 01 022 2008 Costa L D F Bonci D M Saito C A Rocha F A Silveira L C and Ventura D F 2007 Voronoi anal ysis uncovers relationship between mosaics of normally placed and displaced amacrine cells in the thraira retina Neuroinformatics 5 59 78 Defelipe J 2010 From the connec tome to the synaptome an epic love story Science 330 1198 1201 Diggle P J 2003 Statistical Analysis of Spatial Point Patterns London Arnold Eberhard J P Wanner A and Wittum G 2006 NeuGen a tool for the generation of realistic morphology of rons and neural networks in 3D Neurocomputing 70 327 342 Eglen S J Lofgreen D D Raven M A and Reese B E 2008 Analysis of spatial relationships in cortical neu three dimensions tools for the study of nerve cell patterning BMC Neurosci 9 68 doi 10 1186 1471 2202 9 68 Gleeson P Steuber V and Silver R A 2007 neuroConstruct a tool for modeling networks of neu rons in 3D Neuron 54 219 235 Groh A and Krieger P 2011 Structure function analysis of genetically defined neuronal pop ulations in Optical Imaging in Neuroscience A Laboratory Manual eds A K R Yuste and F Helmchen New York NY CSHL Peress 377 386 Groh A Meyer H S Schmidt E F Heintz N Sakmann B and Krieger P 2010 Cell type specific propertie
6. requirement to run RipleyGUI is to have MATLAB preferably ver sion 7 0 or later with the Statistics toolbox RipleyGUI has been tested on Windows XP Windows Vista Ubuntu and Mac OS X Nevertheless given the cross platform nature of MATLAB it can be used with any Unix Macintosh or Windows environment The software is distributed as an open source software with a user manual RipeyGUI requires only basic experience and knowledge of MATLAB The user should be familiar with the MATLAB envi ronment and MATLAB path definitions RipleyGUI is started by typing RipleyGUI in the MATLAB command window a detailed explanation is given in the accompanying manual The user can now interact with a graphical interface without the need of any implementation of MATLAB commands Further analysis can be done by embedding the generated data into MATLAB s workspace DATA INPUT OUTPUT The state of RipleyGUI including all calculated functions can be saved in native MATLAB format at any time to be retrieved later All figures can be opened in separate MATLAB windows from where they can be saved in all formats supported by MATLAB such as jpg png or fig RipleyGUI loads neuron distribu tions from single files or from folders with files When single files are loaded the defaults file format is ascii but selecting in the import dialog All files also txt and csv files can be imported If files are imported in the import
7. 10 Analyzing changes in connectivity can be much more painstaking than simply ana lyzing a re distribution in soma locations The changes that these alterations in soma distributions cause for the connectiv ity can subsequently be analyzed using computational model ing of large scale anatomical networks Eberhard et al 2006 Gleeson et al 2007 Koene et al 2009 Zubler and Douglas 2009 Lang et al 2011 On a larger scale it is known that the brain can be divided into different anatomical and func tional areas but less is known about the functional significance of ordered structures on a smaller scale such as for example the dendrite bundles from layer 5B cells Krieger et al 2007 or even cortical columns Horton and Adams 2005 Rockland 2010 To fully explore the potential of the large data sets which Abbreviations CSR Complete Spatial Randomness GUI Graphical User Interface BTSS Between Treatment Sum of Squares K estimated value of the K function E K t expected K function EGFP enhanced green fluorescent protein can be obtained using imaging and digitization techniques it is necessary to develop automatized analysis tools Wearne et al 2005 Bjaalie 2008 Oberlaender et al 2009 Meijering 2010 Meyer et al 2010 In this paper we describe such a software tool and exemplify its use for analyzing neuron distributions in neocortex A spatial point pattern is a set of locations or events within a s
8. I the estimated K function is often displayed as the difference between the estimated K function K t and the expected E K t K function to make deviations from the CSR pattern more noticeable When the esti mated K function value is similar to the expected value from a distribution following CSR ELK t the difference R t E K t is close to 0 and we cannot discard that the sample dis tribution is following CSR Figures 2A D when the difference is positive the values of the estimated K function are higher than the expected value from a distribution following CSR it indi cates aggregation Figures 2B E when the difference is negative Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 3 Hansson et al Analyzing cell patterns using RipleyGUI RipleyGUI File Set Help Create a new distribution Set4 Green Size x 100 Y 100 z 100 Poisson CSR lambda Poisson Cluster lambda Slambda Edistance lambda delta O Simple Inhibition Cluster Inhibition lambda Slambda Edistance 02 O04 06 delta Operations on this distribution tvalue step 14 max 20 Estimate K function Simulations 100 Compare with CSR View plot in new window FIGURE 1 Screenshot of the opening screen of RipleyGUI The upper left panel Create a new distribution is allo
9. Novelli E Leone P Resta V and Galli Resta L 2007 A three dimensional analysis of the develop ment of the horizontal cell mosaic in the rat retina implications for the mechanisms controlling pat tern formation Vis Neurosci 24 91 98 Oberlaender M De Kock C P Bruno R M Ramirez A Meyer H S Dercksen V J et al 2012 Cell type specific three dimensional structure of thalamocortical circuits in a column of rat vibrissal cortex Cereb Cortex 22 2375 2391 Oberlaender M Dercksen V J Egger R Gensel M Sakmann B and Hege H C 2009 Automated three dimensional detection and Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 8 Hansson et al Analyzing cell patterns using RipleyGUI counting of neuron somata J Neurosci Methods 180 147 160 Perry G L W 2004 SpPack spatial point pattern analysis in excel using visual basic for applications VBA Environ Model Softw 19 559 569 Ripley B D 1979 Tests of random ness for spatial point patterns J R Stat Soc Ser B 41 368 374 Ripley B D 1988 Statistical Inference for Spatial Point Patterns Cambridge Cambridge University Press Rockland K S 2010 Five points on columns Front Neuroanat 4 22 doi 10 3389 fnana 2010 00022 Rosenberg M S and Anderson C D 2011 PASSaGE pattern analy sis spatial statistics and geographic
10. Set option the imported files must be in the ascii format This enables the user to keep comments in txt format in the same folder as the files that will be analyzed with RipleyGUI Necessary in both cases is that the file has no headings and three columns cor responding to the x y and z values separated by comma tab or space REFERENCE DISTRIBUTIONS To help the user get familiar with the K function and how it behaves for different types of distributions RipleyGUI contains functions for generating some basic distributions with a user defined volume and intensity The distributions are based on the intensity parameter and the underlying stochastic process The reference distributions include 1 the homogenous Poisson process 2 the simple Poisson inhibition process 3 the Poisson cluster process and 4 the Poisson inhibited cluster pro cess These processes are also elaborated on in the RipleyGUI User Manual The homogenous poisson process CSR In the Homogenous Poisson Process events are placed randomly and independently in a 3D region The distribution of the events is assumed to follow CSR They can be generated for different val ues of lambda the intensity of the process The total number of events depends on lambda and the size of the volume V number of events x V Simple poisson inhibition process In an inhibited or sparse distribution events are less likely to appear close to other eve
11. bc and visual cortex vc thus shows that they are all dis tributed with a more or less strong tendency to be aggregated Figures 4 5 Using RipleyGUI one can test if the K functions from two experimental distributions are different using the between treatments sum of squares BTSS see User Manual and below In Figure 5A the estimated K function of the etv pyramids in visual and barrel cortex are plotted In Figure 5B the average of R t E K t is displayed with a 95 con fidence interval The non overlapping confidence intervals after t 20 um mean that 95 of the bc etv population does not over lap with 95 of the vc etv population after t 20 um and vice versa A more rigorous test however of statistical significance between two sample groups can be performed by utilizing the between group statistics and the BTSS test In plots of between group comparisons Figure 5C the red square shows the BTSS value for the real sets and the black curve the accumulated probability distribution under the null hypothesis by bootstrap Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 5 Hansson et al Analyzing cell patterns using RipleyGUI Thickness um S FIGURE 3 Cell count data A Confocal image z projection of a brain slice showing neurons gray labeled with Neuronal Nuclei NeuN antibodies and genetically EGFP labeled layer 5a corticostriatal pyramidal cells gree
12. cated for distribution simulations Each of the four reference distributions see section Reference distributions can be tuned with intensity and other parameters The simulated distributions are displayed in the upper center panel Name The lower left panel Operations on this distribution is designed for 0 8 mies 20 View plot in new window Station Divide gt gt lt lt Open lt lt Remove SSS v e Operations on all distribuitions in chosen set View set data t value step 4 Estimate K functions Bootstrap contidence intervals Simulations 100 Compare with CSR ma ae aa Compare sets analysis of the distribution on display in the upper central panel Name The right panel Operations on all distributions in a chosen set is designed for saving managing and analyzing single or multiple data sets The results of all the analysis can be viewed inside or outside of RipleyGUI depending on the user s preference All analysis related parameters are tunable in their corresponding panels it indicates inhibition Figures 2C F An estimation of R t or in general any stochastic quantity is based on sample observa tions under given assumptions that might not always be fulfilled The expectation E K t of a stochastic quantity is the mean value of the quantity under fulfilled assumptions over the entire population USING RipleyGUI ON EXPERIMENTAL DATA Cor
13. frontiers in NEUROINFORMATICS METHODS ARTICLE published 09 April 2013 doi 10 3389 fninf 2013 00005 RipleyGUI software for analyzing spatial patterns in 3D cell distributions Kristin Hansson Mehrdad Jafari Mamaghani and Patrik Krieger 1 Department of Neuroscience Karolinska Institutet Stockholm Sweden Mathematical Statistics Centre for Mathematical Sciences Lund University Lund Sweden 3 Department of Biosciences and Nutrition Karolinska Institutet Huddinge Sweden Department of Mathematics Stockholm University Stockholm Sweden Edited by Sean L Hill International Neuroinformatics Coordinating Facility Sweden Reviewed by Larry Millet University of Illinois at Urbana Champaign USA Marcel Oberlaender Max Planck Institute for Biological Cybernetics Germany Correspondence Patrik Krieger Department of Neuroscience Karolinska Institutet SE 171 77 Stockholm Sweden e mail patrik krieger ki se t These authors have contributed The true revolution in the age of digital neuroanatomy is the ability to extensively quantify anatomical structures and thus investigate structure function relationships in great detail To facilitate the quantification of neuronal cell patterns we have developed RipleyGUI a MATLAB based software that can be used to detect patterns in the 3D distribution of cells RipleyGU uses Ripley s K function to analyze spatial distributions In addition the software con
14. leyGUI is distributed free under the conditions that 1 it shall not be incorporated in software that is subsequently sold 2 the authorship of the software shall be acknowledged in any publication that uses results generated by the software 3 this notice shall remain in place in each source file AUTHOR CONTRIBUTIONS Kristin Hansson and Mehrdad Jafari Mamaghani wrote the mod eling code validated and tested the software Kristin Hansson designed the program and wrote the user guide Kristin Hansson analyzed the experimental data Patrik Krieger conceived the project and refined the software requirements Kristin Hansson Mehrdad Jafari Mamaghani and Patrik Krieger wrote the paper SUPPLEMENTARY MATERIAL The Supplementary Material for this article can be found online at http www frontiersin org Neuroinformatics 10 3389 fninf 2013 00005 abstract REFERENCES Armstrong R A 2010 Quantitative methods in neuropathology Folia Neuropathol 48 217 230 Baddeley A J Moyeed R A Howard C V and Boyde A 1993 Analysis of a three dimensional point pat tern with replication Appl Stat 42 641 668 Berlanga M L Phan S Bushong E A Wu S Kwon O Phung B S et al 2011 Three dimensional reconstruction of serial mouse brain sections solution for flat tening high resolution large scale mosaics Front Neuroanat 5 17 doi 10 3389 fnana 2011 00017 Bjaalie J G 2008 Understanding the
15. n Scale bar 50 um B 2D projection of manually placed markers indicating the position of NeuN labeled cell bodies in a brain slice of the somatosensory B 0 T T L1 200 L2 3 4 400 L4 E amp 600 A Q E g L5 S D 800 m f L6 1000 1200 gt L 200 400 Width um mouse cortex cut in the coronal plane Pia matter is at y 0 and the y axis is distance from pia matter xaxis is the width of the tissue slice The six cortical layers are labeled L1 Layer 1 etc The black box shows the approximate position of the image in A and the green box the approximate position of the EGFP labeled cells A sub section of the image is plotted in 3D in C 45x 10 K t Distance t um FIGURE 4 Comparing a test distribution with a CSR distribution Etv pyramid distributions in visual cortex vc are not randomly distributed The samples n 6 have been divided and rotated using Divide and Station to obtain stationarity 200 CSR distributions were generated and used to create a confidence interval for the CSR hypothesis A The estimated 10 20 30 40 50 Distance t um K function for etv pyramids blue lines compared to simulated CSR distributions red lines The K function is estimated for t values between 4 and 50 um with a 2 um step size B P values from the hypothesis test of CSR For t 18m the etv pyramid distributions differs from CSR with 95 significance These
16. n for all the distributions in the experimental data set blue lines and all Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 4 Hansson et al Analyzing cell patterns using RipleyGUI K t E K t K t E K t 05 gt K t E K t 8 L i J 100 ne da i L i distance t FIGURE 2 Examples of simulated reference cell distributions A D The Homogenous Poisson Process Complete spatial randomness CSR The difference K t E K t is close to 0 and we cannot discard that the sample 5 15 25 5 15 distance t 25 5 5 25 distance t distribution is following CSR B E K t E K t is positive indicating aggregation C F K t E K t is negative indicating inhibition dispersion Data was generated using a t value step 2 and max 30 the simulated distributions following CSR red lines generated to compare with the experimental data From visual inspection one can infer that if the different colored lines are separated it is likely that one can discard the hypothesis that the target sample data is based on CSR The statistical analysis on the existence of any difference between the estimated K functions obtained from the sample data and the distributions following CSR is shown in Figure 4B This difference is calculated as the fraction of the K functions following CSR simulation that a
17. nts A simple inhibition distribution is created through generation of independent events where any event closer than a certain distance to an earlier event is discarded New events are generated until the desired intensity is reached This type of distribution can be used to take the cell size into account when mimicking a situation where cells are placed ran domly and independently and where events cannot be closer than the diameter of the cells The constraint on event proximity limits the maximum number of events see RipleyGUI Manual Poisson cluster process In a clustered or aggregated point pattern distribution most events are closer to their neighbors than expected comparing to a distribution under CSR A Poisson cluster distribution is created from randomly distributed parent events which independently from each other create offspring events Seeding locations of the offspring are independently and identically distributed according to an exponential family distribution Only the offspring are part of the final distribution Diggle 2003 Offspring with a position outside the volume are placed on the other side of the volume that is the distribution is wrapped along its diagonal Poisson inhibited cluster process This distribution combines the properties of the inhibited and clustered Poisson processes This can be a way to take the cell size into account when mimicking a situation where neurons are clustered STATIONARITY S
18. onfidence intervals around the estimated K function average The upper and lower intervals within which 95 of the K functions can be expected to fall are displayed Comparing with CSR To quantify the deviation of a distribution from CSR RipleyGUI creates a comparison set of distributions The comparison set has the same size and intensity as the distribution being tested but consists of distributions following CSR The sample distribution is compared to the distributions following CSR and RipleyGUI will test whether or not the hypothesis that the sample distribu tion follows CSR can be rejected for different values of distance t In calculations with a relatively low number of events the sim ulated CSR distribution can appear more inhibited than actually expected This occurs as a consequence of how the boundaries are defined Boundaries are defined as the maximum span between events in each dimension and that might be smaller than the region in which the cell data was acquired especially in distri butions that have few events This however affects the sample distribution and the simulated distributions following CSR both in the same direction Comparing between data sets To facilitate for the user to make comparisons between sample sets RipleyGUI displays the estimated K functions for up to three data sets in the same plot By visually inspecting the overlap between the estimated K functions the user will get an overview of for which t
19. pecified region Diggle 2003 The events are irregularly placed and are modeled as the result of an unknown underlying stochas tic process referred to as a spatial point process We can think of the distribution of neurons as the result of one such pro cess Analysis of spatial point patterns is a mathematical tool that allows us to obtain a quantified readout of the organization of neurons When exploring the properties of an unknown spatial dis tribution the first step is to look at the intensity The inten sity lambda can be estimated as the average number of events per unit volume A spatial distribution is also characterized by its second order properties that is how events distribute in relation to each other Ripley s K function is a method for exploring second order properties in n dimensions Ripley 1979 1988 Baddeley et al 1993 Diggle 2003 Mattfeldt 2005 Eglen et al 2008 Jafari Mamaghani et al 2010 Millet et al 2011 The three dimensional case requires more elab orated methods for edge correction Baddeley et al 1993 Eglen et al 2008 Jafari Mamaghani et al 2010 We pro vide a MATLAB based software for various analytical uses of Ripley s K function using the 3D edge correction term developed in Jafari Mamaghani et al 2010 which in contrast to other Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 1 Hansson et al Analyzing cell patterns using
20. re further from E K t than the sample set s average K function When this is less than 0 05 the black line we can discard randomness on a significance level of 0 05 In general the experimental data has negative values for small t values lt 15 um when estimating K t E K t When this difference is negative it indicates inhibition but for these small t values the inhibition is caused by the cell size since no cells can be closer to each other than their diameter While ana lyzing the K function one must thus consider the diameter of the neurons under investigation It is important to keep in mind that the deviations from CSR might be caused by many different factors If different parts of the measured distribution have different densities this will result in an aggregated pattern although it is not caused by actual clusters Even when stationarity can be guaranteed we cannot know anything about the underlying process that causes the aggregation The only certain conclusion is that the sample distribution deviates from CSR A possible explanation to the aggregated pattern in this data is that it was sampled over col umn borders As the cell density is slightly higher in the barrel column than the septa for the etv pyramids Groh et al 2010 the assumption of stationarity is not entirely fulfilled in this area Comparing two experimental cell distributions The analysis of each data set etv pyramids in barrel cortex
21. ribution of cells in the retina Novelli et al 2007 The software is released with an extensive user manual Future developments of the program includes 1 re programming in C to increase the speed of the edge correction and 2 add the possibility to use Ripley s K function in 3D for a cross correlation analysis of two different populations thus investigating if cells from two different populations are attracted or repelled from each other APPLICATION We used RipleyGUI to analyze spatial properties of genetically labeled layer 5 pyramidal neurons in neocortex This section can be used as a guide to interpret the results from RipleyGUI RUN RipleyGUI To run RipleyGUI type RipleyGUI in your MATLAB command window this will open the window shown in Figure 1 It is now possible to load test distributions as explained in the User Manual As an introduction to spatial point patterns the user can first use the reference distributions section Reference dis tributions to study the K function Spatial point patterns can be divided into three main categories of patterns Diggle 2003 aggregation where events tend to attract other events cluster ing inhibition where events tend to repel other events and hence create a more regular pattern dispersion and CSR where events are distributed randomly A plot of these three different built in distributions and the K function analysis of these distributions are shown in Figure 2 In RipleyGU
22. s of pyramidal neurons in neocortex underlying a layout that is modifiable depending on the corti cal area Cereb Cortex 20 826 836 Hammer Harper D A T and Ryan P D 2001 Past paleon tological statistics software pack age for education and data analysis Palaeontol Electron 4 9 Heintz N 2004 Gene expression ner vous system atlas GENSAT Nat Neurosci 7 483 Helmstaedter M Briggman K L and Denk W 2008 3D struc tural imaging of the brain with photons and electrons Curr Opin Neurobiol 18 633 641 Horton J C and Adams D L 2005 The cortical column a structure space without a function Philos Trans R Soc Lond B Biol Sci 360 837 862 Jafari Mamaghani M Andersson M and Krieger P 2010 Spatial point pattern analysis of neurons using ripley s K function in 3D Front Neuroinform 4 9 doi 10 3389 fninf 2010 00009 Jones A R Overly C C and Sunkin S M 2009 The Allen Brain Atlas 5 years and beyond Nat Rev Neurosci 10 821 828 Koene R A Tijms B Van Hees P Postma F De Ridder A Ramakers G J et al 2009 NETMORPH a framework for the stochastic generation of large scale neuronal networks with morphologies Neuroinformatics 7 195 210 Krieger P Kuner T and Sakmann B 2007 Synaptic connections between layer 5B pyramidal neu rons in mouse somatosensory cor tex are independent of apical den dri
23. tains statistical tools to determine quantitative statistical differences and tools for spatial transformations that are useful for analyzing non stationary point patterns The software has a graphical user interface making it easy to use without programming experience and an extensive user manual explaining the basic concepts underlying the different statistical tools used to analyze spatial point patterns The described analysis tool can be used for determining the spatial organization of neurons that is important for a detailed study of structure function relationships For example neocortex that can be subdivided into six layers based on cell density and cell types can also be analyzed in terms of organizational principles distinguishing the layers equally to this work Keywords Ripley s K function spatial point pattern software cell distribution neuroanatomical method INTRODUCTION Determining the spatial distribution of cells is important for projects aiming at large scale re constructions of neuronal net works Heintz 2004 Markram 2006 Smith 2007 Helmstaedter et al 2008 Lichtman et al 2008 Defelipe 2010 Oberlaender et al 2012 If a certain neurological disorder can be correlated with a change in the cell distribution this data is of course not suf ficient to explain the disease but can rather help understand how connectivity might have been affected Landau et al 2004 Landau and Everall 2008 Armstrong 20
24. tation As an optional feature in RipleyGUI the Station routine rotates a sample distribution using a rotation matrix minimizing the Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 2 Hansson et al Analyzing cell patterns using RipleyGUI volume needed to contain the events in the distribution The rota tion is performed in 2D the thinnest dimension is ignored during rotation This is suitable for distribution regions where parts of the region are vacant Divide Another RipleyGUI routine Divide cuts a distribution in pieces along its longest side If the longest and second longest sides are equal Divide will have no effect This will help station to create stationary subsets and obtain a more uniformly shaped sample domain DATA ANALYSIS Ripley s K function RipleyGUI estimates the K function in three dimensions with edge correction and displays plots of how the sample domain distribution deviates from its expected value One strength of the program is that it also manages sets of distributions and allows the user to estimate the average K function of the set and compare it to the expected values of K functions for a set of distributions following CSR The average is weighted so that distributions with more events influence the average proportionally Bootstrapping confidence intervals When working with sets of distributions RipleyGUI uses a bootstrapping method to create c
25. te bundling J Neurosci 27 11473 11482 Landau S and Everall I P 2008 Nonparametric bootstrap for K functions arising from mixed effects models with applications in neuropathology Stat Sin 18 1375 1393 Landau S Rabe Hesketh S and Everall I P 2004 Nonparametric one way analysis of of replicated bivariate tial point patterns Biom J 46 19 34 Lang S Dercksen V J Sakmann B and Oberlaender M 2011 Simulation of signal flow in 3D reconstructions of an anatomically realistic neural network in rat vibrissal cortex Neural Netw 24 998 1011 Lichtman J W Livet J and Sanes J R 2008 A technicolour approach realistic neuron variance spa to the connectome Nat Rev Neurosci 9 417 422 Markram H 2006 The blue brain project Nat Rev Neurosci 7 153 160 Mattfeldt T 2005 Explorative sta tistical analysis of planar point processes in microscopy J Microsc 220 131 139 Meijering E 2010 Neuron trac ing in perspective Cytometry A 77 693 704 Meyer H S Wimmer V C Oberlaender M De Kock C P Sakmann B and Helmstaedter M 2010 Number and laminar distribution of neurons in a thala mocortical projection column of rat vibrissal cortex Cereb Cortex 20 2277 2286 Millet L J Collens M B Perry G L W and Bashir R 2011 Pattern analysis and spatial distribution of neurons in culture Integr Biol 3 1167 1178
26. ticostriatal cells in visual and somatosensory barrel cortex The mouse brain samples investigated in the present study were etv expressing layer 5A pyramidal neurons projecting to stria tum corticostriatal cells etv pyramids Groh et al 2010 sam pled from the somatosensory barrel cortex and visual cortex Confocal images were acquired from coronal slices 50 100 pm thick Figure 3 We chose to analyze for t values up to 50 um to get estimations for the K function on a varying scale However the most stable results for Ripley s K function are for t values smaller than 0 25 times the shortest side of the volume Ripley 1988 Diggle 2003 Costa et al 2007 The distributions of genet ically labeled cells etv pyramids were compared in two different sensory cortices One aim for such a comparison could be to investigate if local factors influence the structural arrangement and thus presumably the organization of these cell types in micro circuits The distribution of etv pyramids in both somatosensory barrel cortex Jafari Mamaghani et al 2010 and visual cortex Figures 4 5 differs significantly from CSR distributions with the same size and intensity In the somatosensory barrel cortex the sample volume was layer 5A and in the visual cortex it was layer 5 Groh et al 2010 The distribution of cells is thus only analyzed with respect to the organization within a specific layer Figure 3 Figure 4A shows the estimated K functio
27. tware is an important addition to a growing arsenal of computer aided programs http www spatstat org Perry 2004 Wearne et al 2005 Eglen et al 2008 Rosenberg and Anderson 2011 for the analysis of large quantities of structural data that is becoming available Heintz 2004 Jones et al 2009 Berlanga et al 2011 The use of the method is exemplified by Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 7 Hansson et al Analyzing cell patterns using RipleyGUI analyzing the distribution of genetically labeled layer 5 corti costriatal cells We show how this data can be interpreted to indicate differences in the spatial organization of layer 5 pyra midal cells in visual compared to barrel cortex Conclusive evidence for these differences would however require data from large sample regions to overcome possible confound ing factors such as non stationarity and non uniform sample regions The developed software tool in combination with exper imental techniques that enables physiological measurements from genetically identified neurons Groh and Krieger 2011 ensures that structure function relationships can be examined in great detail AVAILABILITY AND REQUIREMENTS Operating system s Platform independent tested on Windows XP and VISTA Linux Ubuntu Mac OS X 10 4 10 8 Programing language MATLAB Other requirements MATLAB 7 or higher Statistics toolbox License Rip
28. types of graphs can be generated with the RipleyGUI Frontiers in Neuroinformatics www frontiersin org April 2013 Volume 7 Article 5 6 Hansson et al Analyzing cell patterns using RipleyGUI A 5 is lt lt Distance t um c P value 0 Accumulated probability 10 Bis x10 Bootstrapped BTSS values FIGURE 5 Example of how RipleyGUI can be used to compare two different cell distributions Etv pyramids in visual cortex red lines and etv pyramids in barrel cortex blue lines A The estimated K function for etv pyramids in visual vc etv and barrel cortex bc etv B Average of estimated K function with 95 confidence interval for etv pyramids in visual 0 10 20 30 40 50 0 10 20 30 40 50 Distance t um and barrel cortex C The BTSS value for the experimental data red square is larger than the BTSS value at the 0 95 quantile of the accumulated probability distribution The probability that the compared test distributions are from the same underlying distribution is thus less than 5 These types of graphs can be generated with the RipleyGUI resampling The BTSS value for the between group compari son is calculated over the entire range of t values for the null hypothesis that the two sets stem from the same underlying spa tial distribution This BTSS value the red square is beyond the 0 95 quantile of the BTSS distribution based on the BTSS values
29. values the K functions differ To confirm the dif ference between sets RipleyGUI is able to perform between group comparisons Figures 4 5 The between group comparison is based on the hypothesis that two sets are based on identical point pattern distributions Under this hypothesis replacing a distribution in a set with a distribution from the other set should not affect the weighted average K functions To verify this hypothesis sets with the same number of samples as the original data set chosen randomly from both sets are created using replacement This procedure is done 5000 times A score using a function of sum of squares is calcu lated for each of the 5000 re samplings and the real sets Diggle 2003 The verification of the hypothesis is then reduced to inves tigating whether or not the score based on the real sets is likely to have been produced by the scores under the hypothesis Diggle 2003 Jafari Mamaghani et al 2010 INTENDED USE AND FUTURE DIRECTIONS OF THE SOFTWARE This paper accompanies the first release of RipleyGUI show ing how it can be used to analyze the 3D distribution of cells Examples from neuroanatomy where this type of analysis can be used includes the analysis of the spatial distribution of neocortical layer 5B cell clusters White and Peters 1993 Krieger et al 2007 and interneurons Yanez et al 2005 the vertical alignment of neurons in frontal cortex Semendeferi et al 2011 and the dis t
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