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Virtual Muscle 3.1.5 Documentation

1. The actual SIMULINK block for the motor units of a single fiber type is depicted above and is based on a structure provided by Jiping He personal communication Those properites e g FL which are the same for all of these motor units are calculated only once Those properties which are unit specific are calculated separately as shown below in an example of a motor unit block sf Leftist ele a TOMA 2 Wr fet Oy x iue Ib 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 41 Equations and coefficients for the muscle model The equations and their coefficients that are used in this model are drawn from Brown et al 1996 1999 Brown and Loeb 2000 and Cheng et al 2000 A summary of the equations is listed below as well as their coefficients in feline slow and fast twitch fibers from experiments in feline soleus and caudofemoralis muscles respectively Curve Fast twitch muscle constants Slow twitch muscle constants Tendon elasticity cT kT E T T 27 8 0047 40047 0 964 FE 2 cen fox EY T Parallel elastic element L L L L c k In je Thick filament compression c fexp k L L 1 Fe Force length pee FL L a abs s Force velocity V 5 88 V lt V
2. This results from the method used to determine rise and fall times for the effective activation of the muscle While exact solutions for Ar would not produce these errors numerical solutions can be inaccurate If this warning arises check the lengths for the muscle indicated by SIMULINK Simulation running too slowly While the use of multiple motor units allows a combination of muscle fiber types and serves to increase accuracy of muscle force production an inherent drawback is the increased computational time required for your simulation Depending on the level of accuracy desired the use of multiple motor units may not be necessary to replicate relatively realistic muscle behavior Additionally for the purposes of familiarizing yourself with the muscle model software and to first set up your model it may be desirable to use single motor unit muscles which can later be replaced with muscles that have multiple units and fiber types using the Rebuild Existing Muscle Model option in the BuildMuscles function To facilitate a simple but effective single motor unit muscle you should modify the minimal firing frequency fmin of the fiber type to be used in your muscle to be zero in BuildFiberTypes function and specify U in the BuildMuscles function for that muscle to be zero 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 32 Interfacing with non MATLAB applications Provisions are provided in many si
3. 10 12 oc niei ions f os ff oo W Muscle 2 Bicep Shor 5 we 1157 J uo d 00 3 2515 so 2 ps oo 03 2 07 4 SER IS wen _ ve ws ES wen vo dur d vo Mudess fa LLL E ooo o NON BON i 010 Muscle 27 Muscle 8 Ee ovo 00 f wo Muscle 9 805 E NE os f QU Musde 210 0 d a 0 0 0 0 no 0 Comments Sampla Detabesel W Mosel Ned 10 Muscles b Jed 5 Abe The main descriptor window allows users to load save and edit a Muscle_Database each of which is constructed of a combination of fiber types as described in the fiber type database Each muscle from the database can be created as a SIMULINK block for use in a biomechanical model Loading and saving If you choose to Load an existing database from the File menu a dialog will open asking for the name of the existing database file Note that the Fiber Type Database mat file you used in the creation of this muscle database must either be in the current directory or in the MATLAB path If the expected Fiber Type Database mat file cannot be found you will be prompted to select one This database must contain at least as many fiber types
4. Interactions with Neural and Skeletal Elements Each SIMULINK block representing a muscle must be joined to an appropriate model of the segment dynamics which is not provided here The interaction between the muscle model and dynamics model is two way The muscle blocks produce output force which is used by the dynamics model to produce changes in kinematics These kinematic changes are then passed back to the muscle model as changes in muscle length which in turn result in changes in muscle force Concurrent with this data exchange must be a source of neural activation for the muscles This presumably will arise either from a data file of pre recorded or pre generated activations possibly from EMG data or from a control model built in SIMULINK or MATLAB that will generate the activation for each muscle As discussed later it may be necessary or appropriate to create a nonlinear scaling function between the source data and the activation applied to the model see Appendix C The dynamics model can be created either within MATLAB or SIMULINK or it can be linked to an external application via MATLAB s DDE interface A sample implementation of this function between MATLAB and the WORKING MODEL 2D package is described later in this document WORKING MODEL 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 13 Creating the muscle model Overview Muscle Morphometry Fiber Type Descriptor Muscle Model Descriptor M
5. SIMULINK block variables Sensor imotor 4 control muscle 4mdl Out SIMULINK block 25 1 muscle 5mdl Out 5j 1 SIMULINK block Mus cle NOE Muscle 4 xd morpho metr y 1 mechanics 4 Muscle E Via out ports 1 SimDDE m SUID MATLAB function E DDE Link DDE Link 1 Dyanmics System wm Working Model 2D document m mus ce 2 m uscle 3 mus ce 4 muscle 5 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 33 A sample application using WORKING MODEL 2D Getting started The software packages required to run this demonstration are MATLAB 5 2 or higher SIMULINK 2 2 or higher WORKING MODEL 2D 4 0 1 or higher The files required for the use of this sample function are SimDDE m MATLAB wrapper function Dynamics System wm WORKING MODEL 2D simulation template using SimDDE Muscle System mdl SIMULINK muscle block The combination of the first three files listed are required to run the SIMULINK driven model First ensure that MATLAB is already open and that the required files are in the current working directory or are part of your path Next open WORKING MODEL 2D and open the Dyanmics System wm file A simple skeletal system in WORKING MODEL 2D WORKING MODEL 2D provides an easy to use graphical interface for building dynamic systems It allows the user to specify many important details of a simulation i
6. in addition to the force N output These have been added because some of them may be necessary to provide as feedback to a neural circuit The current choices are activation fascicle length Lo fascicle velocity Lo s and Force Fo Creating a SIMULINK block of one muscle Once all details have been finalized to your satisfaction a SIMULINK block which has been assigned the name of your muscle can then be created by selecting the create SIMULINK Muscle Block item from the Model menu This will launch SIMULINK and create a block that can be drag and dropped into your working SIMULINK figure A SIMULINK block can be created as many times as desired and for as many different defined muscles as desired If you wish to utilize the Rebuild Existing SIMULINK Model function described below it is necessary that the SIMULINK block name be kept the same The use of these blocks is explained in the subsequent section Rebuilding an existing SIMULINK model After you have used the SIMULINK muscle blocks in a model you may wish to modify the parameters for each muscle or for the fiber types comprising the muscle blocks The Rebuild existing SIMULINK model option from the Model menu allows you to select an existing SIMULINK model and will replace each muscle block in that model This function works by searching the SIMULINK model for any blocks with names that match the muscle names in the currently open Muscle_Database Any blocks with matching names
7. or Next S Fibers buttons near the top of the window In the example of Figure 7 Muscle 1 Brachialis is composed of 5096 S type fibers and 5096 FF type fibers with the names being taken from the fiber type database the user has loaded Of these fiber types 2 motor units are allocated to the S fibers and 3 to the FF fibers Size of motor units Each real motor unit innervates a fraction of the muscle s total PCSA Realistic recruitment of biological motor units during activation occurs in a fixed sequence with smaller and slower motor units being recruited first according to Henneman s size principle For example motor units innervating slow twitch muscle fibers are typically smallest while motor units for the larger fast twitch fibers are recruited later To reproduce this orderly recruitment based on fiber type the Recruitment Rank parameter in the BuildFiberTypes function determines the order of recruitment of motor units composed of different fiber types if the Natural recruitment strategy is selected as described below Within motor units of the same muscle fiber type Henneman s size principle still applies in real biology for example motor units that innervate a smaller number slow twitch fibers will tend to be recruited before motor units that innervate a larger number of slow twitch fibers However in the muscle model motor units within a fiber type are recruited in the order in which they are listed e g Unit 1
8. Muscle 3 1 5 Documentation doc Page 35 Controlling muscle activation Muscle_System Edi View Simulation Format 1 amp ET gt activation Activation 1 Force N 1 PH path length Force 1 Muscle 1 1 9 M Activation Activation 2 Force N Musculo tendon path length cm Force 2 Muscle 2 Activation Activation 3 Force N T U path length Force 3 From Muscle 3 Workspace Fetivation Activation 4 Force N j path length cm Muscle 4 Petivation Activation 5 Force N Musculo tendon path length cm Muscle 5 1002 45 Z Muscle activation levels are controlled within the SIMULINK layer The muscles can be examined by running SIMULINK and then opening the m5 ma1 file Five muscles will be displayed each with two inputs and one output The elliptical out ports are the handles through which information is passed from SIMULINK to MATLAB and then to the DDE The square inputs for Activation 1through Activation 5 are local input values for activation of each muscle and should be between and 1 These can be set at fixed levels directly or replaced with other SIMULINK blocks to simulate a neural controller mechanism Note that lengths are not passed into the SIMULINK model directly via the elliptical 1n port
9. e nr ee rav re sau ee re uoa 14 COVER VIEW 14 THE BUILDFIBERTYPES FUNCTION ee sese esso eese sees sese 15 STARTING UP THE FUNCTION eorr ee EE Tee tete eee lote 15 CREATING AND EDITING FIBER TYPES IN THE MAIN DESCRIPTOR WINDOW 15 EDITING BIBERS TYPES Cour ode seda cime tka Mats alld hae dh 16 LOADING AND SAVING YOUR DATABASE csscccssceccsecensccccuscecsesceusccceescensececuscecsecceucceeesseuseceeusceeaeess 17 CREATING FIBER TYPES IN YOUR OWN FIBER TYPE DATABASE FILE c cscccsccssccesccesccsccesccssccessesceuscens 17 EDEFLHNG EIBER COEFEICIENTS ven cerea EET 18 EDITING GENERIC COEFFICIENTS cssccsccscosccscescescescescessessesceseesceseessessescaseescasseecaseescasseesaseescaveneees 18 5 c C EE E 18 THE BUILDMUSCLES FUNCTION iosita Pese ope iee e OUR ER ONE 19 STARTING UP THE FUNCT ION vesewscs re exon erase oc bes eene sese cedro oL Eee o Dan 19 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 2 CREATING NEW MUSCLE MODEL DATABASE cscccssccssccscessccesccusceusceusceeccusceusceueceuccusceusceusceuscenscees 19 EDITING MUSCLE TYPES IN T
10. eee eee eene eere e eene tree norte e nete eoo 7 CHANGES TO THE FIBER DATABASES esee eese sees eee eee 7 CHANGES TO THE BUILDFIBERT YPES FUNCTION eee ee eeee esee eoe ee tese eee sete eese sees eee eee 7 CHANGES TO THE BUILDMUSCLES FUNCTION e eee eese eese etes ree so eese sttes eese sese ee eese sees eee 7 INTRODUCTION e eese e pee eu ov ae ene ae uo aues on be e no Savas a Ves vv eaae ae ee vo sue ra aene Ie e rU ona 9 WHY A MUSCLE MODEL e eee oe PUn iue o eoe e oo Pa Vae e rssi ron have eere Fa deae oo oro ran 9 SYSTEM REQUIREMENTS 5 eee eure ae eae oo Gee esee ie po Gene s UNE ee ee P Pea ee 9 THE STRUCTURE OF THE MUSCLE MODEL eee eese eoo etes eoe 11 FIBER TYPE LEVEEt 11 WHOLE MUS CEE EVEL eee cete Woe 12 INTERACTIONS WITH NEURAL AND SKELETAL ELEMENTS s0ccesccesccescceccesceesccsscesccesceeceussescenscens 13 CREATING THE MUSCLE MODPBEL e a e e aora Peau
11. fiber types can be combined in varying proportions to produce SIMULINK blocks that model muscle force output complete with sequentially recruited motor units of varying size and fiber type and intra muscle interactions between active contractile elements and parallel and series elastic elements The function allows muscle data to be stored in two representations The first is as a Muscle Database mat data file in MATLAB This stores the current configuration of each muscle and can be loaded into the BuildMuscles function to be edited again This database file is only used by this function and will not constitute part of your simulation In order to use the muscles you must generate the second representation as a SIMULINK block Starting up the function From within MATLAB this function is invoked by typing gt gt BuildMuscles Creating a new muscle model database If you wish to create a new muscle model database you should select a Fiber Type Database mat file to use from the Select Fiber Type Database item from the File menu If you have not yet created one return to the previous section and create one using the BuildFiberTypes function The Fiber Type Database mat file selected at this point is permanently associated with the created muscle database and any changes made to the fiber type database will be reflected in the muscle model so long as the fiber type names remain consistent Once a Fiber Type Database file has been sele
12. for each compartment each such compartment should be treated as a separate muscle within the model For simplicity throughout this document the term muscle will be used to denote a single neuromuscular entity with a unidimensional command signal and a homogeneous mechanical action 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 12 Modified Hill type model EA contracte element muscle mass series elastic 1 element active contractile paulelysq elgsis a 2 os motoruniti motor unit 3 A given muscle consists of three interacting elements the contractile element a series elastic element and a muscle mass The contractile element and series elastic element both act on the muscle mass which has inertial properties to prevent instabilities from arising within the muscle The contractile element in effect consists of as many smaller contractile elements as are defined by the number of motor units each of which has a passive parallel elastic element an individually defined firing frequency and force length velocity relationships as determined by the fiber type properties The parallel elastic element includes a small viscosity for the purposes of stability These active sub compartments sum together to produce the total contractile element force Muscles are created using a GUI designed in MATLAB called BuiidMuscles which outputs those muscles as SIMULINK blocks as described below
13. function creates and saves a database file also containing two structures Muscle Morph and Muscle Model Parameters The former variable tracks the values that independently assigned to each muscle in the database such as the muscle names masses and compartment PCSA distributions The latter variable stores the variables that remain constant for all muscles in that database such as the tendon properties the filename of the associated Fiber Type Database and the names of the fiber types used in the Muscle Database Both these variables are structures and are described at the beginning of the BuildMuscles nrfile Upon loading an existing BuildMuscles database file BuildMuscles function searches for and attempts to load BuildFiberTypes database file associated with BuildMuscles database file so ensure that this file can be found in the current directory or in the MATLAB search path 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 39 Appendix B Structure of Model and SIMULINK Blocks Representations of muscle properties and components Our general approach to modeling is to create a set of functions and terms that have a one to one correspondence with known anatomical structures and physiological processes that occur in muscle and tendon The experiments on which this model is based were designed to dentify the specific structures and processes within muscle that give rise to complex phenomena e
14. g frequency length interactions yield sag etc The functions that describe those structures and processes or their input parameters were then modified to reflect the mechanisms underlying the phenomena This strategy improves the likelihood that the model will extrapolate accurately to deal with ranges and combinations of input conditions that have not been tested explicitly in the source experiments The resulting model has three representations providing increasing levels of detail as described in the following sections Schematic diagram of functions Activation delay Rise and fall time Sag Yield at iL Af fer Paralel elastic Thick filament T mut element Con asco Force Length Force Vel ocity 4 Fpg Fpg1 Af F pE2 Total parallel elastic force etive contractile force FTotal FpE FCE Total contractile element force Each of the blocks represents a physiological process whereby input parameters are converted into output parameters according to that process as described by a mathematical function The output parameters of one process represent input parameters to other processes contained in other blocks of the hierarchy which ends at the bottom with total force output of the contractile element The label associated with each block is a short hand name for the physiological process which often reflects the experimental phenomenon whereby that process was first revealed or quantified The corresponding SIMULINK com
15. is initially calculated from the detailed FV coefficients however changing this value will automatically rescale the related FV coefficients in the muscle coefficients level The terms that are specifically affected are by and Vmax As an option if you change Vos you will be prompted as to whether or not you wish to also scale 6 5 and related rise and fall time constants in proportion because in normal muscles these values appear to scale proportionally to each other fo s pps The frequency in pulses per second at which the fibers in the compartment produce half of maximal isometric tetanic force at 1 0 Lo see Brown et al 1999 Similar to Vo 5 field described above you will be prompted as to whether or not to allow automatic rescaling of any related coefficients for rise and fall times see Brown and Loeb MS IV and also if you wish to scale Vo s in proportion Again the default is to allow automatic rescaling The terms specifically affected are and fo5 The minimal frequency at which a given recruitment compartment is activated upon threshold activation relative to f s frequency A default value of 0 5 is provided 105 The maximal frequency at which a given recruitment compartment is activated upon maximal activation relative to the 6 5 frequency A default value of 2 is provided Comments Entry into this field is optional It is a user field that can contain any informati
16. muscles typically function at lengths slightly below Similarly it is inaccurate to assume that 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 48 Lo is the length at which peak twitch force is evoked as that length is typically 10 30 longer than Lo Close 1972 Roszek et al 1994 Brown and Loeb 1998 Short of using actual tetanic stimulation and force recordings from the subject muscles we use the following technique to obtain Lo Fix the muscle in situ and measure its fascicle length Next excise bundles of a few muscle fibers mount them with glycerol and coverslip them and examine them under a light microscope at approximately 400x magnification Using a calibrated measuring graticule it is possible to obtain measures of sarcomere lengths in the fixed muscle This value can then be compared with literature values for optimal sarcomere lengths For example if average sarcomere length from your muscle was 2 0 um and optimal sarcomere length for skeletal muscle in the same species is 2 4 um then you would have to multiply your in situ fascicle length by 1 2 to obtain Lo Tendon length Lo This is the sum of any external tendon plus all in series aponeurosis as this has been shown to have similar mechanical properties to external tendon Scott and Loeb 1995 This value scales the length of the tendon for the purposes of series elastic force production This parameter differs from Zajac s 1989 model whic
17. non linearity in frequency response remains 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 45 The figure above on the left depicts the mean frequency driving the total PCSA for the entire muscle when two yellow five magenta and ten cyan motor units are modeled To linearize the response of the muscle one method is to take the square root of activation input before applying it to the muscle The figure above on the right depicts the effects of using a square root adjustment on the activation input With fewer than 10 compartments a lower exponent might be desired such as However uw fits relatively well for 5 or more compartments The relationship between recorded EMG and effective muscle activation is complex and probably depends on the recording method If all regions and fiber types in the muscle are sampled without bias then it should be possible to estimate this relationship from first principles A single action potential in a single motor unit should produce a unitary potential whose amplitude corresponds approximately to the total physiological cross sectional area of its muscle fibers This assumes that the recorded action potential reflects the total action current which is the sum of the synchronous action currents in each muscle fiber e The action current generated by a spike in a simple cylindrical conductor such as an unmyelinated axon tends to depend on diameter i e surface area r
18. of fiber type parameters that match the subject you are trying to model the next step is to provide information on the muscle you are attempting to model A brief description of the function of and methods to obtain the parameters required by BuildMuscles function follow Muscle mass In the muscle model this value serves two purposes The first is to provide the volume of the muscle in conjunction with the density of muscle which is fixed at 1 06 g cm Mendez and Keyes 1960 which is then used to calculate physiological cross sectional area PCSA PCSA relates to Fo or maximal tetanic force which in turn scales all of the force output of the muscle The specific tension of muscle is effectively constant across different fiber types see Brown et al 1998 so it is set as a single value for each Muscle Database The second purpose of muscle mass is to provide stability in the simulation for the interaction between the visco elastic contractile element and the elastic tendon element see Loeb and Levine 1990 In our model half of this value is incorporated to provide inertial damping i e the muscle mass 15 assumed to centered halfway along the length of the fascicles The stability of the model proved relatively insensitive to the amount of muscle mass used a change in the stabilizing mass by an order of magnitude only changed rise and fall times of force production by a few milliseconds The only stipulation for collecting this v
19. significant passive force at the start of a simulation the system will have to be allowed to reach equilibrium After the first time step the positions of all the internal muscle masses are stored in a state vector that is continuously updated by SIMULINK These state values are important so that SIMULINK can remember the lengths and velocities of each contractile and elastic element If your simulation is run uninterrupted this state vector is completely transparent to the user and does not need to be considered However if you plan on stopping your simulation and restarting it at different times this state vector will have to be stored on stop and reloaded on restart to avoid going through a new settling period Doing this may be necessary if you are interfacing with an external simulation package such as to model system dynamics An explanation of this procedure is given in the following section describing a sample implementation of this model Common problems Using experimental data One typical use of muscle models is to predict muscle force from experimentally recorded data for activation and length Kinematic data often have noise or quantization errors that are magnified when the length data are differentiated to produce velocities of muscle stretch as shown below Note that while the position signal appears smooth when differentiated in the SIMULINK model the velocity is not smooth Because muscle fiber velocity has such a large effec
20. thirty coefficients for each fiber type this method is both tedious and prone to data entry errors Most users will wish to avoid building their fiber types this way 2 Another method is to start with an existing Fiber Type Database such as the included database containing fe line fiber properties make whatever minor changes are desired to the existing fiber types and then save it under a new file name 3 If you wish to use more fiber types than are provided in an existing database you may wish to add new fibers based on other fibers already in the database This can be done by selecting the Copy Or Cut items from the Edit menu Either action will open a dialog thatlists the names of the fibers in the current database Selecting a fiber type will put the fiber type along with its parameters and coefficients into the clipboard which will be reflected in the clipboard contains text string near the top of the window Note that the cuc option will delete the selected fiber subsequent to storing it in the clipboard At this point selecting the Paste command will copy whatever fiber type is in the clipboard into the target column You will be prompted for a column number to copy the clipboard fiber type in to The Paste function will overwrite any contents in the destination fiber type Note that the clipboard is not a standard Windows clipboard thus fiber type data can not be pasted into other Windows applications using this function Note also th
21. ATLAB function muscle 1 mdl Sensorimotor MATLAB function vealed SIMUL INK block gt control Save Refers to 1 gt SMULINK Load muscle 2 mdl Fiber Type Database muscles 7 MATLAB mat data file muscle4 idual muscle5 1 SIMULNK block Muscle mo m mig mechanics Skeletal dynamics 5 7 Musc Morph Database MATLAB mat data file Existing Database MATLAB mat data file This software package provides a means to simulate the middle layer of the hierarchical model that is the muscle structure and the underlying mechanical function The steps to use this software are relatively straightforward l Use BuiidFiberTypes function to define the necessary muscle fiber types in MATLAB This function is a GUI that allows the user to define fiber types either from scratch or to import existing fiber types from file Once all fiber types to be used in a given muscle model are defined they are saved to a Fiber Type Database file This database can be loaded and edited again or can have its fiber types imported into other databases Use BuildMuscles function to specify a set of muscles composed of varying proportions of the fiber types defined in steps 1 and 2 Once the desired muscles have been defined they may be saved as a Muscle Model Database file As before this file can be opened and edited later Create muscle SIMULINK blocks using the create function i
22. EFERENCES 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 4 What is new in Virtual Muscle 3 1 5 This section will explain the changes between version 3 1 4 and version 3 1 5 Changes to the BuildMuscles Function 1 Changes introduced in version 3 1 4 unfortunately induced errors in the Rebuild capabilities of the BuildMuscles function This bug has been fixed 2 Various incompatibility problems with Matlab 6 0 have been corrected What was new in Virtual Muscle 3 1 4 If you are not familiar with Virtual Muscle 3 0 skip this section as all information here has been updated in the following manual Otherwise this section will explain the changes between version 3 0 5 and version 3 1 4 Changes to the BuildMuscles Function 1 CreateSimulinkBlocks has been separated from the BuildMuscles function This change has no effect on the user interaction but when installing Virtual Muscle the user will now notice a third m file 2 When creating or rebuilding Simulink blocks the program now ensures that m Lo Lo and Whole muscle maximal length are greater than zero 3 Minor correction to the estimation of Lmax Previous calculations assumed that the tendon was stretched to Lo when in fact it should only be stretched by the passive forces present in the muscle 4 Changes to the PCSA allotted to a fibertype are now always reflected in the individual motor units PCSAs for that fibertype Previo
23. HE MAIN DESCRIPTOR WINDOW cssccccsecccscccescccnscccusccccsscenseccceceeaescs 20 LOADING AND SA VING o 3 52 25 c eta tien bat cda eis Mond lc nod Ra io Meli EOM c ddp E AL AMI De 20 COPYING CUTTING AND PASTING MUSCLES ccccseccseccscccscccsccssccsceuscensceeccueceueceecusccusceesseussesceuseens 20 IMPORTING MUSCLES FROM ANOTHER DATABASE ccssecccscecsecceusccccsscecsccceuscccaesceusccecssceasecceusceaueess 21 EDITINGMUSCIJES 2 5 2 0 ede de aere oc E 21 se tii ed rra Neil Do a 22 RECRUITMENT OF MOTOR 5 ense en eese see ense e sese sese se sense 24 AXNDDITIONAISOUTPUTS eerie tese eo ol ee coblived aces ve eee pe bot eo coeno eres vl 25 CREATING SIMULINK BLOCK OF ONE MUSCLE s ccsccscccsccssccsccusceusceecceeceusceseceuccesceusseesseusceseens 25 REBUILDING AN EXISTING SIMULINK 25 USING THE MUSCLE MODBLL ease eeu ae eee ee ee nouae a eee os eaa n e us oae o aa eo e ao cerno e eee ro 26 STRUCTURE OF THE SIMULINK BLOCK ecce eese ee eene eoe nee ee tese eese sete sese 26 USING THE MUSCLE BLOCKS 5 ee so eeu eo oe ee po orna eee eu so ee na pu eo oe aas e
24. Unit 42 Unit 3 etc and PCSA is assigned to each motor unit individually So to maintain Hennemann s size principle in a model motor units should be listed in order of size smallest to largest at least for Natural recruitment strategies In a perfect muscle model each motor unit would be represented individually and thus each slow twitch motor unit would have a smaller PCSA assigned to it than a fast twitch motor unit This would make the computations unnecessarily lengthy however The model allows the number of simulated motor units and hence resolution of the simulation to be specified by the user It then apportions the PCSA of the muscle among those units according to one of several 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 22 algorithms In a typical simulation with 10 motor units each motor unit would actually reflect the contribution of about 10 real motor units The allocation of the total PCSA of the muscle to each simulated motor unit can be viewed and edited by choosing the Manually distribute unit PCSAs item from the Muscles menu A dialog will allow you to select the muscle to modify A muscle specific window will open listing the proportion of the muscle s PCSA that is apportioned to each motor unit and each different fiber type By default assigning PCSA and number of motor units to a previously unassigned fiber type i e with a previous PCSA motor units of 0 0 will result in an a
25. Virtual Muscle 3 1 5 MUSCLE MODEL FOR MATLAB User s Manual Written by Ernest Cheng Ian Brown and Jerry Loeb For updates and program downloads http ami usc edu Projects Muscular_Modeling index asp Documentation last revised Feb 21 2001 WHAT IS NEW IN VIRTUAL MUSCLE 3 1 5 5 CHANGES TO THE BUILDMUSCLES FUNCTION cccossscosssscccsccccsscccsccccescccsccccesccccssccesccesesccessccsescoeeess 5 WHAT WAS NEW IN VIRTUAL MUSCLE 3 1 4 5 CHANGES TO THE BUILDMUSCLES FUNCTION ee eese ee eese tees eese sse ees sete sese see eee 5 WHAT WAS NEW IN VIRTUAL MUSCLE 3 0 5 4 ccce ee ee ee eene eren n eene eene een 5 CHANGES TO THE FIBER DATABASES eee ee eene eene onere e nn ee eese ees sete sees eee eese sese eese 6 CHANGES TO THE BUILDFIBERT YPES FUNCTION ee ee eese eee ee eene eese tete no eese see 6 CHANGES TO THE BUILDMUSCLES FUNCTION cccossscccsssccssccccssccscccccssccesscccescceecscccsccecesccecscccescceeess 6 WHAT WAS NEW IN VIRTUAL MUSCLE 2 0
26. acies in integration On the right the same conditions but with relative accuracy tolerance tightened to 1e 6 In both cases for the first 20 ms there are initial force transients relating to the settling of the contractile element and the tendon This is unrelated to the integrator tokrances and is discussed in a following section 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 31 Inappropriate initial conditions Muscles with a zero tendon length will not function properly To counteract this a minimum tendon length of 0 1 cm is attributed to muscles specified in the BuildMuscles function Scaling of activation inputs with multiple motor units A consequence of simulating multiple motor units is that the recruitment function used in this model produces a nor linear response in the conversion from input activation into effective muscle activation such as might be measured by EMG This arises because increasing activation linearly increases the frequency envelope of any currently recruited motor units and also recruits additional motor units Suggested solutions are described in Appendix C Unrealistic simulation conditions If muscles are stretched to extremely long lengths 1 if the contractile element of the muscle exceeds 1 85 Lo SIMULINK will likely return the following warning Warning Attempt to raise negative value to a non integer power in untitled Brachialis contractile element Fiber 1 Af
27. ackages hardware requirements are dictated by the level of detail desired In order for the simulation to run at an acceptable level of performance with more elements or levels of detail more powerful hardware is desirable The system is also designed to be scalable according to the desired accuracy of the model For reference the model was created and tested on the following hardware Pentium Pro 200 MHz PC e 64 MB RAM Instructions provided herein regarding using the MATLAB and SIMULINK software itself are directed towards the Windows based PC platform For other platforms use of the muscle package should be the same but details regarding file paths sequences of mouse clicks and so forth may differ slightly To ensure that you have the correct version number you can type the command ver at your MATLAB prompt gt gt 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 10 The structure of the muscle model Sensorimotor control Muscle DEM Muscle morphometry mechani cs Muscle model Skeletal dynamics Our muscle modeling system is intended for use in a hierarchical framework The mechanical dynamics of the skeletal segments comprise the lowest level and are acted on by a realistic representation of physiological muscle properties at the middle level At the top level the muscles are controlled by any arbitrary set of activation commands ranging from pre recorded EMG data to dyn
28. alue is entered The coefficients for the properties of the tendon can be modified from their defaults with the Edit tendon properties item from the Muscles menu The tendon is modeled on a log linear relationship Brown et al 1996 Lo is the length of the tendon when stretched with force Fo this is well up in the linear stiffness range As the tendon shortens by 3 6 from length Lo force drops linearly to about 20 of Fo followed by an exponential decrease to slack essentially zero tension at 95 of Lo While the total range of length of tendon is small it can exert large effects on muscle force because it changes the way in which velocity of the whole muscle length appears at the contractile elements which are very velocity sensitive This is particularly true in muscles that have substantially longer tendon aponeurosis than fascicle length Max whole muscle length cm Maximum length of the whole muscle entire musculotendon path length at the most extreme anatomical position This value is used to calculate the following Lmax parameter which controls passive tension Fascicle Lmax Lo The maximal length of the fascicles at extreme anatomical position of the skeleton measured in terms of the optimal fascicle length This value cannot be entered directly and is calculated from the difference of the Max whole muscle length and the 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 21 Tendon 19 scal
29. alue is that the wet weight be used not the weight of desiccated muscle If you already have a muscle volume multiply by the density of muscle 1 06 g cm to obtain a mass Fascicle length Lo Fascicle length not muscle belly length is important for three purposes As previously discussed it is important for determining PCSA and hence Fo Second it scales the velocity and length dependence of the contractile element of the muscle and thus changes the sensitivity of the contractile element to changes in total musculotendon path length Thus a shorter fascicle will show greater changes in force output with the same total length change Finally it is used in conjunction with optimal tendon length and maximal musculotendon path length Lmax b to determine fascicle Lmax This term scales the passive force produced by the contractile element which will be discussed later It is important that the actual fascicles for the muscle you are studying are measured and not simply the muscle belly length or the whole musculotendon path length Commonly muscle belly length is reported in literature but this is usually an inaccurate representation of fascicle length for muscles with even a minimal pennation angle An additional factor is that the fascicles must be at Lo the length that provides maximal tetanic force It is inaccurate to assume that Lo will occur when muscle is at the midpoint of its range of motion for example cat hindlimb
30. amic feedback driven reflex models to high level simulations of cortical commands Our software provides the middle level of the hierarchy It enables users who may have only minimal interest in the details of muscle physiology to create realistic mathematical representations of muscles At the same time it is possible for those who wish to delve into and modify the mathematics of the muscle model to do so The hierarchical database structure described below was designed to facilitate such modifications 1 Fiber type specific details 2 Whole muscle details including motor units tendon and 0 P overall morphometry wet 7 3 Joint level with multiple muscles acting simultaneously Fiber type level It has been shown that the behavior of the contractile element of the muscle scales well from the sarcomere level up to the whole muscle fiber level and again up to the level of an entire recruitment group of motor units Zajac 1989 There are two critical assumptions behind Jumping of individual sarcomeres into a single group the sarcomeres in such a group must operate homogeneously with similar activation length and velocity While some phenomena are believed to arise specifically because of intra fiber sarcomere heterogeneity and or damage e g persistent stretch induced force changes these changes are small or rare under physiological use conditions Brown and Loeb Ms 02 23 01 User s Manual Virtual Muscl
31. and Loeb G E 2000 Measured and Modeled Properties of Mammalian Skeletal Muscle IV Dynamics of Activation and Deactivation J Musc Res Cell Motil In press Brown LE Liinamaa T L and Loeb G E 1996 Relationships between range of motion Lo and passive force in five strap like muscles of the feline hindlimb J Morphol 230 69 77 Brown LE Scott S H and Loeb G E 1996 Mechanics of feline soleus II Design and validation of a mathematical model J Musc Res Cell Motil 17 221 233 Burke R E Levine D N Tsairis P and Zajac F E 1973 Physiological types and histochemical profiles in motor units of the cat gastrocnemius J Physiol 234 723 48 Cheng E J Brown LE and Loeb G E 2000 Virtual Muscle A computational approach to understanding the effects of muscle properties on motor control J Neurosci Methods In press Close R I 1972 The relations between sarcomere length and characteristics of isometric twitch contractions of frog sartorious muscle J Physiol 220 745 62 De Luca Foley P J and Erim Z 1996 Motor Unit Control Properties in Constant Force Isometric Contractions J Neurophysiol 76 1503 16 Henneman E 1968 Organization of the spinal cord In Mountcastle B ed Medical Physiology 12 ed St Louis C V Mosby Co p 1717 32 Hoffer J A Sugano N Loeb G E Marks W B O Donovan M J and Pratt Cat hindlimb motoneurons during locomotion II Normal activity patt
32. ary its time step sizes to fit occasions when high accelerations are used In most simulation packages when high rates of change are detected time step sizes are reduced to ensure that instabilities are not generated However because SIMULINK essentially unaware of the segment dynamics it is not able to modify its time step size to match rapid changes in segment dynamics Conversely SIMULINK can not control the time step size of WORKING MODEL 2D should instabilities begin to arise in the muscle model Initially time steps must be kept conservatively small to prevent small instabilities in one layer from being magnified by phase lags in communication with another layer The figure below depicts the position of a simple model where two equal length musculotendon actuators act on an arm that has been perturbed from its equilibrium position All traces have been vertically offset to allow easier visualization The top black trace shows the position of the arm in radians over time with WORKING MODEL 2D set to run with a 1 ms time step Note that the arm is accelerated towards an equilibrium position overshoots somewhat and then eventually approaches its equilibrium position The following traces depict the same simulation but run with a 2 ms blue 5 ms red 7 ms green and 7 5 ms magenta time step As the time step increases beyond a critical point for this simple example it was 7 ms the simulation becomes unstable 02 23 01 User
33. as are used by the muscle database The program will prompt you to choose which fiber types to associate with which if the names do not match Ensure that a valid database file has been loaded before proceeding to edit your muscles or errors will result The save item in the File menu allows you to store your muscle parameters for later modification It is recommended that muscle model files be saved using a mat extension Copying cutting and pasting muscles It is possible to Copy cut and Paste muscles to and from the clipboard using the items from the Edit menu Contents of the clipboard will be reflected in the clipboard contents string at near the top of the window 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 20 Importing muscles from another database As with fiber types muscles can also be imported from other Muscle_Database mat files Selecting Import muscle from the Muscles menu will open a file selection dialog allowing you to select another muscle model database file and select a muscle from that file This muscle data will then be stored in the clipboard for pasting into the currently open database Editing muscles The main descriptor window allows ten rows of muscles to be viewed and edited simultaneously Scrolling through muscles if more than five are used is accomplished with the lest 10 Muscle buttons The muscle parameters that may be modified Muscle name A unique name
34. at the copy cut and paste operations include both the visible parameters and the hidden coefficients for a given fiber type 4 Should you wish to combine fiber types from more than one Fiber Type Database you start with an existing database and use the Import action from the Edit menu This will bring up a standard file selector dialog From here you should select the name of the database that you wish to import a fiber type from Next a list of fiber types in that file will be presented allowing you to copy one of those fiber types into the clipboard The fiber can then be pasted into your current database 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 17 Editing fiber coefficients For most purposes users should be able to obtain a reasonable approximation of the function of most mammalian muscle fiber types by modifying the and properties of the fiber types imported from two databases we provide and allowing BuildFiberTypes function to rescale any related coefficients However should you wish to access the details of each equation at a lower level selecting the Edit Coefficients item from the Fibers menu will bring up the fiber specifics window allowing modification of any of these coefficients The equations related to these coefficients are available in Appendix B of this document see Brown et al 1999 Brown and Loeb 2000 and Cheng et al 2000 for a detailed description of th
35. ately the complex mechanical properties of real muscles and tendons so that the user can understand the consequences of those properties for the control of musculoskeletal systems System requirements The muscle model has been implemented in SIMULINK to be platform independent and requires only that your platform be able to run the following software 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 9 MATLAB 5 2 or higher SIMULINK 2 2 or higher This muscle model can be customized to interface with a wide range of MATLAB or SIMULINK Mathworks http www mathworks com compatible packages which can be used to model other aspects of the hierarchical system An implementation of an interface with WORKING MODEL 2D software Knowledge Revolution http www krev com is provided as a functional example of this capability WORKING MODEL 2D is a motion simulation and kinetic analysis package that complements the mathematical model provided by this muscle model For example elements such as limb segments can be created easily in WORKING MODEL 2D attached at joints with pin elements and moved by actuators acting between the segments Our muscle model in SIMULINK then computes the force of each muscle actuator according to its level of activation and kinematic feedback from WORKING MODEL For this example the following software version is required WORKING MODEL 2D 4 0 or higher As with most computer simulation p
36. ather than cross sectional area but the action currents of muscle fibers may scale more closely to their cross sectional area because of active conduction down the transverse tubules Fortunately the range of muscle fiber diameters is relatively small with more of the range in motor unit size related to innervation ratio number of muscle fibers per motor unit Unfortunately the recorded EMG is not a simple linear summation of these unitary action potentials because of occlusion the tendency of biphasic action potentials to cancel each other when their opposite polarity phases happen to overlap The higher the aggregate rate of action potentials the more likely they are to be partially occluded before they can contribute to the recorded AC waveform whose area under the curve is taken to represent activation This would suggest that the recorded EMG should be squared to more accurately reflect the underlying total muscle activation Thus this effect might be expected to counteract the above noted suggestion that you should use the square root of a recorded EMG envelope in order to use it as an activation input There is one piece of evidence suggesting that the EMG envelope is in fact linearly related to the input signal to the motoneuron pool itself as currently structured in the model When such a recorded EMG envelope was scaled linearly and applied as an intracellularly injected depolarizing current to individual motoneurons those moto
37. cted or an existing Muscle Database has been loaded the name of the associated fiber type database file will be reflected in the Fiber Type Database text string near the top of the window It is possible to change the Fiber Type Database mat file associated with a Muscle Database by choosing the Select Fiber Type Database option when a muscle model database is already open The limitation is if existing fiber types present in the original muscle model database are not present in the new fiber type database there must be enough new or unused fiber types that can replace the old ones else an error will occur It is not recommended that you keep multiple copies of a single Fiber_Type_Database in different directories of the MATLAB path as this will make it difficult to track which file is being used at any given time As with the BuilaF iberTypes function the BuildMuscles m file must be either in the current directory or in the MATLAB path 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 19 Editing muscle types in the main descriptor window P BuildMuscles muse_morph in xil He Edt Medes Mode Hep Fiar Database human fibar Clipboard conterts Empty Fiber type distribution POSE Units F Musde Fasade Muscle Muscle Tendon Whole Fasade Ur rness q Lo cm PCSA Fo N muede iem 2
38. data such as EMG signals recorded over time via either a From Workspace block or a From File block Essentially the data must be in tabular form with time values as one column and any other values to be passed into SIMULINK as other columns Detailed instructions are given in the SIMULINK documentation External software that can exchange data with MATLAB can also be used as the controller model In Windows DDE is a common standard to facilitate inter software communication The SimDDE example given in the following section can be modified to suit this role Editing the muscle blocks Each SIMULINK muscle block contains fixed equations and constants as defined in the original Fiber Type Database mat and Muscle Database mat files at the time of the creation of the block Once the muscles have been created and linked into a SIMULINK model their parameters can be changed by modifying the information in the original Fiber Type Database mat and Muscle Database mat files and using the Rebuild Existing SIMULINK Model from the BuildMuscles functions In this way it is simple to observe the effects of different muscle and fiber type parameters on the behavior of your system As described previously the names of the 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 29 muscle blocks in your SIMULINK model should match the names of the muscles in your Muscle Database mat file should you wish to use the rebuild function To examin
39. del to activate each unit in turn according to its defined recruitment order Within each motor unit the frequency of motoneuronal firing is modulated in a realistic manner Normally a muscle has about 100 or more motor units While it is possible to create such a detailed muscle model with our software this resolution will make the model run very slowly and is not usually necessary For most uses it will be sufficient to create a small number of model motor units perhaps 3 5 for each fiber type where each unit represents a group of real motor units with a total physiological cross sectional area PCSA of around 10 of the muscle first recruited units should be smaller than later recruited ones as in real muscle This will generally produce an acceptably smooth force modulation because of two features built into the model 1 The model motor units always produce a smooth output force even at sub tetanic frequencies simulating the force that would have been produced by a large number of asynchronously active motor units all firing at the same sub tetanic frequency 2 The normal range of frequency modulation results in about a 4 1 range of force modulation so the force step contributed by a newly recruited motor unit is relatively low until it gradually increases its firing frequency as activation of the muscle increases further If a muscle is compartmentalized in its mechanical actions and or different neural activation is desired
40. e 3 1 5 Documentation doc Page 11 e The sarcomeres must all have the same contractile properties i e their force length velocity relationship parallel elasticity and so forth These characteristics have been shown to be homogenous within a single histochemical fiber type By defining the properties of each fiber type that will be used throughout the model in a single database the muscle model can reference these properties when these fiber types are later combined into typical mixed fiber type muscles The creation of the fiber type database is handled in a MATLAB function called BuilaFiberTypes which is a graphical user interface GUI described below Whole muscle level Muscles are organized into motor units each of which consists of a motoneuron and the several hundred muscle fibers that it controls All fibers in a unit are the same type Groups of similar motor unit types tend to be recruited together Different types of motor units tend to be recruited in a fixed order This fact provides an ideal way to simplify the model Each whole muscle is broken into motor units consisting of a single fiber type with each unit being defined by its fiber type its order of recruitment and its force producing capacity which is proportional to its total physiological cross sectional area It is assumed that the motor nucleus of the whole muscle receives a single time varying neural activation command signal which is the apportioned by the mo
41. e Manually Distribute PCSAs window of the BuildMuscles function A strict PCSA based recruitment order was not enforced at this level for two reasons 1 the user is able to simulate this behavior by apportioning smaller fractions of PCSA to the first motor units and larger PCSA to later motor units and 2 the simulated motor units are not necessarily intended to model individual motor units instead they represent groups of motor units to reduce computational time The auto distribution of PCSA in the BuildMuscles function actually replicates this behavior to an extent by apportioning less PCSA to the earlier recruited motor units this apportioning is detailed in the description of BuildMuscies earlier in the manual This also serves a practical purpose in that it makes the onset of force production more gradual by making the first recruited motor units of a given fiber type smaller than the later recruited ones The ideas behind the implementation of the natural recruitment function are described by Brown 1998 with some minor variations All the motor units in a given pool are driven by a common activation signal U Motor units are recruited sequentially based on two properties 1 the Recruitment Rank ofthe fiber type for that motor unit and then 2 the order determined in BuildMuscles function As U increases more motor units are recruited until U is reached this is the point at which all motor units have been recruited incr
42. e as a function of firing frequency past and present length and velocity e Passive elastic elements for passive muscle force e Passive elastic elements for series compliance of tendons and aponeuroses We have found it useful where possible to divide the model into components that have an obvious one to one correspondence with anatomical entities and physiological processes that occur in motoneurons muscle and tendon The experiments on which this model is based were designed to identify the specific structures and processes within muscle that give rise to complex phenomena e g passive vs active force series compliance recruitment and frequency modulation frequency length interactions yield sag etc The functions that comprise the model were chosen to describe those structures and processes explicitly and their coefficients were determined by best fit procedures using data from experiments that explored these processes under a wide range of physiological conditions This strategy improves the likelihood that the model will extrapolate accurately to deal with ranges and combinations of input conditions that may occur during normal use of muscles but may not have been tested explicitly in the source experiments It also makes it simpler to identify the terms and coefficients that must be changed to describe muscles with different morphologies or different fiber type properties such as from different species Our goal is to capture accur
43. e oe Pe Pone 27 INTERACTING WITH MODELS OF SEGMENT DYNAMICS ccecccseeccesccccsscecsccccuscecuscccusccccssceasececusceeueecs 28 INTERACTING WITH A CONTROLLER MODEL sscccssececsecccescecsecceuscccssscecsecceusceauscccuccecssceusecceusceaneess 29 EDITING THE MUSCLE BLOCKS 4 v es eo 29 RUNNING YOUR 30 INITIAL CONDITIONS FOR THE MUSCLE MASS BLOCK e hene rennes 30 COMMON PROBLEM desa bee evan e EDU AER 30 A SAMPLE APPLICATION USING WORKING MODEL 20 eene eene n eene ete 34 GETTING STARTED ertet ee esed se sce E E Dens Qe ete ede e deme bonis 34 A SIMPLE SKELETAL SYSTEM IN WORKING MODEL 2D eee RI 34 CONTROLLING MUSCLE ACTIVATION c ccccccsscscccsccsccscccscceccusscuscessseesseesceeceuscesecesccesceeseussenssenscens 36 THE SIMDDE WRAPPER IN MATLAB cssesese secs cece 36 OPTIMIZING SM AT 37 APPENDIX A MATLAB DATABASE DETALILS eee ee
44. e the structure of the muscle model double click on the whole muscle block This will reveal the SIMULINK blocks that make up the muscle model At this level editing the details directly is not recommended but is possible For conceptualization purposes the blocks are loosely grouped into a contractile element subsystem of blocks a series elastic element subsystem and a muscle mass subsystem The visible lines control the flow of data between the subsystems Running your simulation The muscle block that you have created behaves like any other standard SIMULINK block Inserting it into any existing system or mdl file will allow you to click on the P icon in SIMULINK to use the s m command from within MATLAB to start your simulation Initial conditions for the muscle mass block At the first time step of the simulation positions of all internal muscle masses and hence the starting lengths of each contractile and elastic element are chosen based on the initial conditions predefined by the model The initial fascicle length conditions can be modified within the muscle mass subsystem by changing the default conditions for the muscle mass position integrator By default the position is set to a position that is almost exactly in equilibrium if the passive force of the muscle is less than 5 of maximum this position will be accurate to better than 0 1 At extremely long lengths or if the passive force equations are changed such that there is
45. eases in activation beyond this point result only in frequency modulation of motor units Motor unit recruitment threshold is determined based on a combination of the cumulative fractional PCSA of all motor units recruited prior to the given motor unit with range of recruitment between 0 and U as depicted in the figure below As an example the first two compartments are slow twitch and are thus recruited first and the for the muscle is 0 8 Note that while it appears that both slow and fast twitch motor units have the same firing frequency range recall that fmin and fmax are in units of f s and that fo 5 has different values depending on fiber type 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 44 fmax p 5 cy quen fre ringn Fi PCSA PCSAp PCSAg Pes Ur 1 Ur Ur Ur Ur Activation U For each motor unit the frequency modulates from a predetermined fmin when the unit is first recruited up to fmax which occurs at a full activation for the muscle This linear change in firing frequency change relative to change in EMG has been demonstrated experimentally e g Milner Brown et al 1973 The common initial firing frequenc y for motor units of a given fiber type and the convergence of their firing frequencies to a single maximal firing frequency at maximal activation have been demonstrated experimentally De Luca et al 1996 There is some suggestion that the frequency modulation of earlier rec
46. ed fascicle Reasonable values of Lmax are typically greater than 1 but less than 1 3 U Fractional activation level at which all motor units for a given muscle are recruited i e it is the threshold of the last motor unit for the Natural Recruitment algorithm provided Once activation has reached U further increases in activation result only in frequency modulation up to fmax for each motor unit at U 1 A reasonable default value of 0 8 is provided Lower values are more appropriate for muscles with unusually homogenous fiber type composition e Fiber type distribution PCSA of motor units The fraction of total muscle PCSA and the number of motor units assigned to each fiber type The fiber types named at the top are determined by those present in the selected Fiber Type Database The two values are separated by a forward slash for each fiber type Note that the PCSA assigned to the fiber types for each muscle must total 1 0 otherwise an error will be reported when attempting to save your database Should this occur you will be presented with an opportunity to either 1 have the BuildMuscles function automatically redistribute the PCSA among the fiber types in the same proportions but such that they total 1 0 2 to save the muscle with the incorrect PCSA total or 3 to cancel the save and manually redistribute the PCSA Scrolling through more than the five visible fiber types is accomplished by clicking the Prev 5 Fibers
47. eene ee eene 39 FIBER TYPE DATABASE eee e eee ero eese so eene ooo Tao ro eee esee V Ve oco svo ees Oeo eese osos onse a eve ves eaae avere veo LR 39 MUSCLE DATABASE eee veo ee eo eU eo Pao vue Vo een n aevo SU ee Vo 39 APPENDIX B STRUCTURE OF MODEL AND SIMULINK BLOCKS eee eee 40 REPRESENTATIONS OF MUSCLE PROPERTIES AND COMPONENTS cccssssccssccccsscccsccccssccccssccssscossscoees 40 SCHEMATIC DIAGRAM OF FUNCTIONS cccssccsssccccssccsssccccscccscsccesccccescccsssccesccecssccsscccsesccescsccescceeesces 40 SIMULINK MUSCLE BLOGKS eise ocv on nee ee one eu eo ro ae so eue e aeos so bae eoo e uoo oe ua oe ee so eeu Sob ee eU uana 40 EQUATIONS AND COEFFICIENTS FOR THE MUSCLE MODEL ccccccssscccssscccsccccsscccsscccesccecssccssscessscoees 42 APPENDIX C NATURAL RECRUITMENT DETAILS e eee eee eene eren o eene nero eonun 44 MULTIPLE MOTOR UNIT RECRUITMENT BEHAVIOR ccsscccsssccsssccccscccccscccsccccescccsscccesccecssccsscccsescoees 45 APPENDIX D TIPS FOR BUILDING YOUR MODBL eee eee ee ee eene nore eere nero eoo 48 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 3 OBTAINING MORPHOMETRIC MEASURES eeee eee eee eene eene eee eee eese eese eese eese e eese eese sese sese eese eee R
48. erns J Neurophysiol 57 530 553 1987 Loeb G E and Levine W S 1990 Linking musculoskeletal mechanics to sensorimotor neurophysiology In Winters J M and Woo S L Y editors Multiple Muscle Systems Biomechanics and movement organization New York Springer Verlag p 165 81 Hill A V 1938 The heat of shortening and the dynamic constants of muscle Proc R Soc Lond Biol 126 136 95 Mendez J and Keyes A 1960 Density and composition of mammalian muscle Metabolism 9 184 8 Milner Brown H S Stein R B and Yemm R 1973 The orderly recruitment of human motor units during voluntary isometric contractions J Physiol 230 359 70 Monster A W and Chan H 1977 Isometric force production by motor units of extensor digitorum communis in man J Neurophysiol 40 1432 43 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 51 Roszek B Baan G C and Huijing P A 1994 Decreasing stimulation frequency dependent length force characteristics of rat muscle J Appl Physiol 77 2115 24 Scott S H and Loeb G E 1995 Mechanical properties of the aponeurosis and tendon of the cat soleus muscle during whole muscle isometric contractions J Morphol 224 73 86 Zajac F E 1989 Muscle and tendon Properties models scaling and application to biomechanics and motor control Crit Rev Biomed Engng 17 359 411 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 52
49. ese coefficients 4 Coefficients for Fiber 1 88 5 File Help FL omega FL beta FL rho FL L 11244 23 182 1 Vmax 0 394 ss 0 avo evi av2 bv 47 84 531 017468 af nfi AffetLetvS ose 21 5 Leff t 0 088 Tfl 58 5667 45 3333 feff tfintL 940567 504333 a52 TS 1 aS S tfeff 1 1 VY vY os 200 Edit Prev Edit Next Fiber Clicking the Edit Prev Fiber Edit Next Fiber buttons will allow you to modify the coefficients for the previous or next fibers respectively To return to the main window click on the Back to main page button Editing generic coefficients Specific tension tendon properties and passive force properties including viscosity have their own sub menu in the BuildFiberTypes function These properties are assumed to be constant for all fiber types in a given database Help Selecting the Help menu item will bring up a window describing the definition of each property listed in the current window For a more detailed explanation of the equations and their related coefficients used in the muscle model please see Brown et al 1999 Brown and Loeb 2000 Cheng et al 2000 or see Appendix B 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 18 The BuildMuscles function Once a Fiber Type Database mat file has been created these
50. for each muscle must be input here Muscle data for each row will be saved to the database file only if a name is entered Muscle mass g Mass of the muscle belly in grams Fascicle Lo cm Average length of the fascicles in the muscle belly when the muscle is at its optimal length for production of isometric tetanic force note that this value is typically 10 30 less than the length at which optimal twitch force is generated Close 1972 Roszek et al 1994 Brown and Loeb 1998 Muscle PCSA cn Physiological cross sectional area of the muscle This value cannot be input directly and is instead calculated from values input for muscle mass and fascicle length A muscle density of 1 06 g cm is assumed Mendez and Keys 1960 Muscle Fo N The maximal amount of force that the muscle can produce isometrically This value cannot be entered directly and is calculated from the muscle PCSA multiplied by a standard value for specific tension of muscle The default specific tension for mammalian muscle defaults to 31 8 Brown et al 1996 can be modified by selecting the change specific tension item from the Muscles menu Tendon cm Length of the tendon at the muscle s optimal force This term should consist of the total amount of connective tissue in series with the muscle fascicles including both internal aponeurosis and external tendon This value must be greater than zero this value will default to 0 1 cm if no v
51. h uses tendon slack length The length is a measure of tendon length when the tendon is stretched by the maximal tetanic force of the fascicles Brown et al 1996 As mentioned above this value is also used in the calculation of the fascicle Lmax The external tendon component of Lo can be measured directly from the tendon using a ruler in situ Unfortunately it is impossible to measure Lo from a typical dissection without a system to stimulate the fascicles and measure the length of the tendon when the fascicles are producing an isometric force of Fo In the absence of direct Lo measures it can be approximated by using 105 of tendon slack length The aponeurosis component of Lo is the mean amount of aponeurosis that is in series with each fascicle This can be approximated by halving the sum of the total aponeurosis length at the origin plus the insertion scaled by 10596 if measured when the muscle was slack If you have a measurement of musculotendon path length at the skeletal posture where the muscle produces optimal force then Ly Eo La Maximal musculotendon path length Lmax The sole purpose of this value for the muscle model is to calculate maximal fascicle length Maximal fascicle length Lmax is calculated as Ema 101 which is then divided by fascicle to provide a scaled value for Lmax It has been shown that a separate Lmax term is more appropriate than simply for scaling passive forces prod
52. iber type with a new one 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 7 2 Fiber types are now listed in the BuildMuscles window in order of their recruitment rank 3 Specific tension viscosity and tendon properties have been removed from this function to the BuildFiberTypes function and the required changes for building the Simulink blocks have been made 4 The starting position of the muscle mass is now almost exactly correct It is impossible to get an exact solution to the equations to provide this number but the approximation provided is correct to within less than 0 1 if passive forces are less than 5 of maximum 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 8 Introduction Why a muscle model The models presented here were designed to meet the needs of physiologists and biomechanists interested in the use of muscles to produce natural behaviors The model system provides a framework for constructing accurate muscle models that can be incorporated easily into complete neuromusculoskeletal systems The muscle model includes the following components which can be scaled according to commonly available morphometric data e Motor nuclei that accept a single command input e g net synaptic drive or EMG envelope and apportion it into recruitment and frequency modulation of subgroups of motor units with type specific properties Type specific contractile elements that produce forc
53. imal sarcomere length If this value is changed the user will be prompted as to whether or not they would like the active and passive force length relationships scaled appropriately with changing optimal sarcomere length the assumption is that the thick filament length stays constant In addition the main descriptor window allows the user to define the following general parameters for the fiber type e Fiber type name Each fiber type must be given a unique name Other functions will search the names in the database for a space and case sensitive match so consistent naming is important f this field is left blank then no data from this column will be retained when the database is saved to disk e Recruitment rank The values in this row determine the order in which the fiber types are recruited within a given muscle Any numerical value is acceptable including non integers Those with lowest rank are recruited first only when all the fibers of this rank are recruited are the types with the next higher rank recruited The absolute values of the recruitment ranks have an effect on the algorithm for automatic apportioning PCSA among simulated motor units of different fiber types as discussed below For most simulations small integer values for recruitment rank will work best e g S 1 FR 2 FF 4 Lo s This is the shortening velocity velocity necessary to reduce force to 0 5 Fo during a maximal tetanic contraction This value
54. itment and frequency outputs for each motor unit For Natural recruitment the activation input is assumed to be the relative strength 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 24 of the net synaptic drive or EMG envelope The Natural recruitment strategy recruits all motor units of a lower Recruitment Ranked fiber type before recruiting any motor units of the next highest Recruitment Ranked fiber type Within each fiber type motor units are recruited in the order in which they were listed i e it assumes that the motor units were listed in order of size The frequency of each unit begins at fmin when that unit is first recruited and reaches a maximum of fmax When input activation equals 1 The Intramuscular FES strategy requires both an activation and a frequency input The frequency input is assumed to be the frequency of stimulation being applied to the muscles and is the same in units of pps for all motor units The activation is the relative strength of the stimulus Motor units within each fiber type are recruited in the order in which they were listed however no distinction is made between recruitment rank Instead the motor units are recruited so as to equalize the fraction of each fiber type recruited A linear relationship between the fractional PCSA recruited and activation is maintained Additional Outputs There is an option to add one or more of several outputs to each SIMULINK block
55. ment e Series elastic element subsystem This element represents the effective length of the internal and external tendons aponeurosis elements should be included The force produced by this element is dependent only on length and has been shown to have no significant velocity dependence at physiologically relevant frequencies For this reason changes in the musculotendon path length are made to act directly on the series elastic element A single function block provides all the calculations for this element Note that the length of this element is calculated by subtracting the length of the contractile element from the musculotendon path length Muscle mass subsystem The muscle mass was included to prevent the system from becoming unstable as the series elastic element and contractile element act on each other 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 26 Position of the muscle mass within the block is tracked by first converting the force produced by the contractile and series elastic elements into a net acceleration based on the size of the mass Acceleration is then integrated to give a velocity and integrated again to give the position of the mass Velocity and position of the mass are fed back into the contractile element and position is subtracted from the musculotendon length and fed back into the series elastic element muscle 1 SIMULINK bl od Pd E SMULINK implementation Modified Hill
56. mplementation depend on both the application software and the model being created on it Details on the changes necessary are outlined in the comments within the actual code Optimizing your simulation As a first step once all the desired segments have been created and linked the simulation should be run for several frames with zero activation to each muscle to ensure that muscles were inserted at reasonable lengths Actuator muscle elements that are being held at lengths much greater than optimal will generate large passive forces and will rapidly pull the system away from its starting position even without activation this should be checked and accounted for It may be useful to adjust slightly the origin and insertion points to get to a reasonable starting length of each actuator muscle Even in well initialized model small start up transients will likely occur at the intra muscle level The contractile element and series elastic element are specified with initial starting lengths that may not be in equilibrium depending on the initial musculotendon path length The default initial conditions set the tendon to be at D where it generates force Fo The whole model will likely need several time steps for the tendon to shorten by pulling on the internal mass and inactive contractile elements Therefore a run in period before any behavior is modeled should be included A caveat when using external applications it is harder for SIMULINK to v
57. mulation packages for dynamic data exchange DDE that allow MATLAB to control one aspect of the simulation In this case it is possible to use MATLAB s DDE interface to allow SIMULINK to pass data to and from another application SIMULINK cannot do this directly This can be affected by writing a MATLAB wrapper function that acts as an intermediary between your external application and the SIMULINK model The MATLAB wrapper must call SIMULINK to run over a time step that matches the time step of the external application Inputs to the MATLAB function will vary depending upon the specifics of the external application As mentioned previously for all time steps except the first one SIMULINK relies on a vector of saved state variables that allow the muscle model to resume its run with the lengths and velocities of the elements within the muscle being retained Data is passed out of the MATLAB wrapper in the form of variables which may be in vector or scalar form The way in which your application utilizes these will vary A sample implementation of this function is givenin the included SimDDE code This acts to pass muscle data from SIMULINK into WORKING MODEL 2D software which provides an easy to use system for modeling segment dynamics Muscle System SIMULINK system Wn uscle_1 mdl 5 p SIMULINK block ut 1 muscle 2 SIMULINK block Outs L Via global gt muscle 3mdl l
58. n the BuildMuscles Subsequent changes to an existing simulation can be effected by the Rebuild function which searches for and replaces all muscle blocks in a SIMULINK model file with blocks using updated parameters 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 14 The BuildFiberTypes function This function allows the user to create and modify the Fiber Type Database mat files required for the BuildMuscles function within a GUI Fiber types may be imported from existing databases and modified or created entirely from scratch Starting up the function This function is called within MATLAB so the first step is to run the MATLAB program The BuildFiberTypes function is invoked by typing gt gt BuildFiberTypes Creating and editing fiber types in the main descriptor window 4 BuildFiberTypes human fiber types mat Edit Fiber Properties Help Clipboard contents Optimal Sarcomere Length um 27 Type 1 Type 2 Type 3 Type 4 Type 5 Fibertypename ss s D o o Recuitmentrank 7 f 2 3 fg 0 V0 5 LO s aos 3 pm o pm vo 10 5 pps B 12 20 D 0 fmin 10 5 o5 os o os 05 fmax 0 5 D 2 p pp 2 2 f 2 Comments super slow generic fasttwitch e g soleus slow twitch fiber fibertype type Additional All three fiber types were presented in Cheng et al J Neurosci Meth 2000 They were created by Comments adap
59. nax CyL V lt ayi av2 FV V L 841 5 34 b ay ayL as L V b V Activation delay TERES OT Taa 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 42 Rise and fall time fin t fits gt L Pa fort T Tof t Ls t gt 0 Effective activation af ng ng 0 56 2 11 3 31 Af f Lopo Y S 21 exp eff 851 aso Ts asi gt f t 0 1 1 76 0 96 43 Ag f t 2 0 1 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 43 Appendix C Natural Recruitment details The idea central to almost all recruitment functions for multiple motor units driven by a common input is the Henneman 1968 size principle which states that smaller motor units are recruited before larger motor units In our natural recruitment function this is applied to motor units of different histochemical fiber types reflecting the normal tendency of slow twitch motor units to be smaller than fast twitch motor units and thus recruited first Recruitment order of different fiber types is tracked in BuildFiberTypes function with the Recruitment Rank parameter assigned individually to each fiber type Physiologically motor units of the same fiber type are also recruited according to their sizes In our model recruitment order within a fiber type is determined by the sequence of the motor units as they are entered into th
60. ncluding contact forces gravity and linkages without the need to write explicitly the equations of motion WORKING MODEL 2D provides useful tutorials and help files and we refer the user to those to learn how to build a system like the one shown here 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 34 Musde _ d an 2 D Legh of 3 Th 4 1 WE a Se i i The Dynamics System wnm file provides a simple skeletal system with five pre created muscles and two skeletal segments These muscles or in WORKING MODEL terminology actuator elements are linked to our SIMULINK muscle model engine via an application interface Because our SIMULINK model represents whole muscles the tendons are not explicitly represented here When the simulation is running at each time step information on the length of each actuator muscle is reflected in the meters at the top left side of the screen These meters then pass the information on the actuator length to the application interface which communicates this information to MATLAB via DDE Muscle forces are received from MATLAB and displayed in the muscle force input boxes on the bottom left corner of the screen The length meters and force inputs are essential to the operation of the link and should not be deleted although they may be moved or made invisible 02 23 01 User s Manual Virtual
61. neurons reproduced the frequency 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 46 modulation recorded from single motor axons recorded at the same time as the EMG envelope Hoffer et al 1987 The appropriate theoretical relationship probably lies somewhere between linear and square root of EMG envelope Practically the effects of electrode design and placement and underlying muscle architecture are likely to be much larger For example skin surface electrodes are highly biased toward large superficial motor units that are recruited only at high activation levels severely underestimating low levels of recruitment Such records would be better modeled by taking the square root of the recorded envelope 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 47 Appendix D Tips for building your model Obtaining morphometric measures The first step in using this package is to create a database of fiber properties For most purposes the included database of feline muscle fiber types will provide a good starting point By knowing a few key parameters it may be possible to estimate values for other species by scaling the coefficients provided for feline muscle If you wish to collect your own data and fit it to the equations provided this is beyond the scope of the present text see Brown et al 1999 and Brown and Loeb 2000 for a more detailed discussion Assuming you already have a satisfactory set
62. ngle This muscle model assumes that there is no pennation angle in the muscles This appears to be accurate when pennation angle is less than 10 15 e g Zajac 1989 In most such muscles the main effect of pennation is to provide a long aponeurosis for insertion of large numbers of relatively short muscle fibers whose forces combine in parallel This important feature is now well captured by the ability to set and independently In more highly pinnate muscles the angle changes with the length of the muscle This necessitates a dynamic pennation angle to modify both the length and the velocity of the fascicles as well as to compute the portion of the force vector that acts on the line of pull of the muscle For small ranges of motion the force output of the muscle can be adjusted with the cosine of a fixed pennation angle but with the current muscle model large ranges of motion may not be correctly modeled using this simple approximation This condition is beyond the scope of the current discussion 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 50 References Brown I E 1998 Measured and Modeled Properties of Mammalian Skeletal Muscle Ph D Thesis Queen s University Brown LE Cheng E J and Loeb G E 1999 Measured and Modeled Properties of Mammalian Skeletal Muscle II The effects of stimulus frequency on force length and force velocity relationships J Musc Res Cell Motil In press Brown LE
63. o a larger number of smaller units such that the largest S unit was smaller than the smallest FF unit The sudden recruitment of a relatively large unit at the beginning of muscle activation will create an unphysiologically large step in force although the problem is not as severe as might be thought because of the ongoing frequency modulation of the units after their initial recruitment These numbers can be manually edited by typing new values into each field If you change the total PCSA allotted to a fiber type the individual unit PCSAs will be updated using the Apportioning method for that fiber type If one of the unit PCSAs is manually updated then the total PCSA for that unit will be updated automatically and the apportioning method for that fibertype will change to manual Different apportioning methods can be chosen by chosen under the Muscles menu If there are more than ten motor units of a given fiber type the Prev 10 Units and Next 10 Units can be used to scroll through them If more than five fiber types are used the Prev 5 Fibers or Next 5 Fibers buttons are used When changes are completed select the close option from the File menu Recruitment of motor units Currently two different recruitment strategies can be chosen from Natural and Intramuscular FES Each one results in the creation of a SIMULINK block within the muscle block that takes the appropriate activation input and divides it into the recru
64. ock This element represents the motor pool for natural recruitment or stimulators for FES A single activation input plus a frequency input for FES 15 transformed into frequency outputs for each motor unit of that muscle The combined vector is sent to the CE PE element to calculate active force e Contractile element Passive element subsystem This element represents the fascicles in the muscle belly Its output force is determined by three inputs activation fascicle length and fascicle velocity Note that the fascicle length input to this subsystem is different from the entire musculotendon path length value which is input to the whole muscle block It is assumed that pennation angle is negligible for this model Fascicle velocity is computed within the SIMULINK block by integrating the calculated acceleration Also note that this element calculate the active and passive forces for the fascicles The block representing the contractile element subsystem consists of one sub block for each fiber type within that muscle Each of those fiber type specific blocks then contains blocks that calculate those muscle properties which are the same for all motor units of that fiber type as well as one sub block for each motor unit as defined in the BuildMuscles function The force blocks for each motor unit sum together to produce a force output for each fiber type block which then sum to produce a single force output for the entire contractile ele
65. ol systems 10 We have added two new types of automatic Motor Unit PCSA distributions equal sizes and geometrically increasing sizes 11 The program now warns users when creating or re building Simulink blocks if there are any motor units with 0 PCSA 12 The user can now edit the PCSA and motor units allotted to each fiber type when manually editing motor unit PCSAs 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 6 What was new in Virtual Muscle 2 0 If you are not familiar with Virtual Muscle 1 0 skip this section as all information here has been updated in the following manual Otherwise this section will explain the changes between the first version and 2 0 Changes to the Fiber Type Databases 2 We have replaced the old feline fiber types database with a newer updated one The old version had 4 fiber types the new one has 3 fiber types only one fast twitch fiber type The new database more accurately reflects the scaling between different fiber types Furthermore the fast twitch FV relationship has been re fit to the original data to ensure a higher degree of accuracy at higher shortening velocities 3 We have included a human fiber types database Details on how this was generated from the feline fiber types database and existing data on human muscle properties can be found in Cheng et al submitted Changes to the BuildFiberTypes function 1 Vo has replaced Vmax as one of the inp
66. on the user desires 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 16 Underneath these parameters for each fiber type there is a hidden layer of fiber coefficients see below Loading and saving your database The Save Database and Open Database options under the File menu item allow you to store the contents of your Fiber Type Database atany time and then reload them for further editing Both bring up a standard dialog that prompts you to select a filename to load or save Files can have any name with any number of characters The name of the database you have saved or loaded will be reflected in the title bar of the main descriptor window The only caveat is that MATLAB may have difficulty identifying files which are not saved with a mat extension so this is automatically appended on to the save filename It is recommended that you leave this extension intact so that the save file is easily loaded during future use Just before saving the program will ensure that you have assigned unique fiber names to each of the fiber types and prompt you if this has been done incorrectly Creating fiber types in your Own Fiber Type Database file There are several methods that you can typically use when creating a Fiber Type Database file for your own use 1 The first method is to open the BuildFiberTypes function and type in all the parameters and coefficients for each fiber that you wish to use However as there are
67. orrected a small error in the implementation of the relationship This will only effect forces at lengths less than 0 6 Lo We have corrected an error in the implementation of the as vs a choice for Sag We have added a limiting function to ensure that 0 We have added an additional comments box which is database specific The Recruitment block has been moved from out of each motor unit and changed so that there is a single block for each muscle Thus it is now separate from CE PE SE and the muscle mass facilitating replacement with different recruitment strategies We have eliminated numerous redundant calculations For example certain calculations e g FL FV etc are identical for all motor units of a single fiber type within one muscle Previously these calculations were determined for each motor unit whereas now they are done once for each fiber type in each muscle Additionally we have removed Yielding and Sag calculations for those motor units of those fibertypes which do not have them Lastly we only calculate the passive forces once for each muscle The result is a significant improvement in simulation speed We have added a new option for different recruitment strategies Thus far the only new recruitment type is for intramuscular FES Additional Outputs can now be chosen for the muscle block e g activation fascicle length velocity facilitating the connection of these muscle blocks with feedback to contr
68. ponent blocks and mathematical equations described in the next two sections are identified by the same labels SIMULINK muscle blocks Each SIMULINK muscle block is composed of many individual blocks that perform the mathematical functions described above The connectivity between blocks reflects the dependencies described schematically above Each block contains a mathematical function 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 40 whose constants were set when the muscle block was created reflecting the muscle fiber type data and parameters used to create it A sample function equation is given below l exp u 1 u 4 u 3 0 56 u 2 u 2 These equations are somewhat unwieldy when manipulated directly Changes are best effected by modifying the parameters and coefficients in the BuildMuscles function and using the Rebuild existing SIMULINK model function LS untitled CE amp S Motor Units Fie Edt View Smutiton Format rrene Frat Ze 2371010467100 0789 11 790 04 911 Foe h 1 0 02 Genre 19 7710 07 90 1 M 1 ferre t FL 1 Motor Unt 1 POSA 1 ERLID ZINN 2611 52 B TT aY lem ES 1 fm prve Fa Motor Unt2 CSA all Urite ye FY Qenghieri Unit Sun all Unite 0 m y j LJ FY shonen
69. pplied to the motor pool A single required output is provided from the SIMULINK block e Force N The force is measured at the series elastic element If the muscle is to act at a joint to create a torque it is important that the moment arm which the muscle acts through is realistic The force produced by the muscle is positive in sign Thus the output may have to be multiplied by 1 depending on the implementation of the skeletal mechanics portion of your model e Force Fo Activation Fascicle Length Lo and Fascicle Velocity Lo s These outputs are optional and may be of use when providing feedback to a controller The activation is just a wire through of the activation input Force Length and Velocity are simply the normalized versions of these variables Interacting with models of segment dynamics As discussed previously a model of the segment dynamics is not included as this model was intended to provide only realistic muscle forces and the segment systems are typically so specific that a generic model would not be useful for most users This muscle model fits best with systems that have been designed hierarchically i e that have existing handles for muscles that would allow forces to act directly on segments Especially with SIMULINK based models incorporating this muscle model would be trivial as the force outputs from the desired muscles could easily be summed modified by any requisite moment arm or other scalar
70. ruited units is hyperbolic rather than linear Monster and Chan 1977 This can be approximated by setting Fmax artificially high for such fiber types and taking advantage of the sigmoidal shape of the force frequency relationship Multiple motor unit recruitment behavior As a consequence of the interaction between having both an increased recruitment of motor units and an increase in the firing frequency of each motor unit with increasing activation the relationship between activation and the frequency envelope driving the motor units becomes non linear As an example of why this occurs consider first the simplest case having a muscle modeled as a single motor unit When activation reaches U the motor unit is activated at a frequency of fmin and the frequency envelope for the whole muscle rises linearly until fmax is reached Next consider a case with two compartments When threshold for the first motor unit is reached the frequency envelop for the portion of the muscle s PCSA allocated to that motor unit increases linearly from fmin to fmax However when the second motor unit reaches threshold there is a jump in motor unit activation as the PCSA for the second motor unit becomes recruited and also frequency modulates from its own fin to fmax Thus the mean frequency driving the total muscle PCSA increases at a higher rate at this point With more than two compartments sudden transients in mean frequency are reduced in magnitude but the
71. s and are instead passed to the MATLAB workspace and then into SIMULINK via a From Workspace block This allows SIMULINK to interpolate lengths between time steps providing more accurate velocity effects The SimDDE wrapper in MATLAB The SimDDE m MATLAB function works simply by telling SIMULINK to run the desired model at a single time for the duration of one time step If the start time entered is 0 then the wrapper function assumes that it is the first step and calls the model with the initial conditions for various lengths and velocities of the elements in each muscle At the end of each SIMULINK time step run muscle force and other variables are passed out of MATLAB to the DDE Additionally SimDDE saves a state vector of the lengths and velocities of the elements within each muscle block to a global variable If the start time entered is greater than 0 then 51 will load the state vector from the global workspace and run the muscle model with these initial conditions SimDDE automatically adjusts its time step to match that of the linked application The global 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 36 variable called tempst ateStorage is transparent to the user and does not need to manipulated in any way Users who wish to program their own external application interfaces for this muscle model software should examine the code for SimDDE m function because the specifics of i
72. s Manual Virtual Muscle 3 1 5 Documentation doc Page 37 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 38 Appendix A MATLAB database details Fiber type database The fiber type database file created by BuildFiberTypes function contains two structures named BFT Fiber Type Database and BFT FTD General Parameters that are required by the BuildMuscles function their names change to BM Fiber Type Database and BM FTD General Parameters respectively in the BuildMuscles function The structure of these variables is pre defined and must be conserved in order for the system to function properly For most users all editing of these structures is done transparently using the BuildFiberTypes function i e the user never sees the structure explicitly However for users interested in the workings of the function an explanation of these structures is given at the beginning of the BuildFiberTypes m file The GUI for BuildFiberTypes relies on global variables including but not limited to the two structure mentioned above So while this function is running it is best to avoid modifying variables in the global workspace within MATLAB If you are not an experienced MATLAB user you will not have to be concerned with this detail as global variables cannot be modified unless you explicitly attempt to do so These global variables are cleared after closing the BuildFiberTypes function Muscle database The BuildMuscles
73. s and connected to the segment dynamics model Model integration will work well with any hierarchically designed models in other packages that can interface with MATLAB an example being WORKING MODEL 2D a sample implementation using dynamic data exchange DDE is described in the following section 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 28 Muscle System SIMULINK system ut muscle 1 mdl m 1 SIMULINK block Out_ muscle 2 mdl 7 SIMULINK block Out Via gl obal u3 JM muscle 3mdl SIMULINK vanaBes Sensor imotor control muscle 4mdl SIMULINK block m Ouid i dones u5 muscle 5mdl 5j q SIMULINK block Mus cle m Muscle 4 nb morphometry 7 mechanics 1 Meck i Via out ports 1 Skeletal SimDDE m dynamics MATLAB function I DDE Link DDE Link 1 Any dynamics modeling package that supports DDE Interacting with a controller model A control block created within SIMULINK is well suited to providing the activation levels needed for each muscle block This controller can easily receive input from the segment dynamics model to provide feedback control of the muscles This control can be supplemented by or replaced with pre generated muscle activation levels such as those recorded from EMG signals SIMULINK allows simple access to
74. t on force output it is usually desirable to apply a modest smoothing function to your length data before sending it to the SIMULINK muscle model block 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 30 Digitized position signal 2 X VW i LE Derived velocity J VAM LN Insufficient accuracy The tolerances for inaccuracy that SIMULINK uses can be viewed in an open mdl document under SimulationParametersSolver menu The default relative tolerance for SIMULINK 3 0 is 1e 3 Any errors in integration detected when the simulation runs above this value will result in SIMULINK automatically reducing its time step sizes For most muscle models a relative accuracy of 1e 6 is sufficient to prevent instabilities from arising under physiological conditions If accuracy conditions are not stringent enough SIMULINK may not return any errors but the force output between time steps may be change drastically as opposed to gradually This may be reflected in the kinematics of the system you are modeling by instability or jerkiness Try tightening tolerances by an order of magnitude to see if this resolves the issue An example is depicted below On the left a muscle is given a constant level of activation and has a constant velocity ramp stretch applied using the default relative accuracy in SIMULINK of le 3 Note the spikes in the force trace corresponding to inaccur
75. ting the analogous feline fibertypes as described in that paper to fit data from triceps surae hamstrings forearm and hand muscles Note in our original publication cited above the parameters listed forthe slow twitch fibers had an error which was corrected in a subsequent corrigendum the correct values are used in this database ers Next5Fibers You must ensure that the Bui ldFiberTypes m file is in your current working directory or is in a directory that is part of your path the list of directories that MATLAB automatically searches for files You can do the former by using dir to obtain a list of the files in your working directory and cd to change your working directory at the gt gt MATLAB prompt You can check which directories are part of your path with MATLAB s path command 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 15 The main descriptor window allows you to load save and import from database files as well as edit the general parameters for each fiber type The fiber types are arranged into columns with up to five types being displayed on screen at once If more than five types are created the user can scroll to next and previous groups of five fibers using the PrevSFibers Next Fibers button Editing fiber types The main descriptor window allows the user to define optimal sarcomere length for the database i e we force all fiber types in a single database to have the same opt
76. tomatic distribution The user can also choose one of two other automatic apportioning schemes each of which can be applied to either a single muscle or multiple muscles The geometric one will ask the user for the fractional increase between one motor unit and the next and will then distribute the PCSAs appropriately for each fiber type The equal one simply makes all motor units of each fiber type equal in size to the other motor units of that fiber type 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 23 Fractional of each motor unit belonging to Muscle 1 Brachialis zl xj Musdes Help ss 5 F 5 3 PESA ws oo oso fi Apportioning Method Ure 1 021429 T 013223 Urs 2 0 29571 016667 Urs 3 02 nee oues EdiMe The above figure depicts the automatic default distribution of the PCSA in Muscle 1 Brachialis using 50 Type S in 2 motor units and 50 type FF in 3 groups Thus the two S units were sized to 21 4 and 28 6 of the total PCSA each and the three FR units were sized to between 13 3 and 20 each Note that consecutive FF motor units have a smaller change in proportion of PCSA because FF fibers have a higher Recruitment Rank This model would be more realistic particularly at low recruitment levels if the relatively large fraction of total PCSA occupied by S units were divided int
77. type model atie element muscle mass Jr Cg i 1 active catractile YW d series elastic 1 element parallel vsco elastic 77 motor unit 1 motor unita Using the muscle blocks Each SIMULINK whole muscle block has at least two inputs and at least one output A few common implementations are briefly discussed but these will vary based on the form of the segment and activation data provided in your simulation The two required inputs are e Length The musculotendon path length is required in units of cm Note that this value may have to be calculated from the available data in the skeletal dynamics model as often only segment coordinates or joint angles are provided e Neural activation This is a value for activation of the active part of the contractile element This value is clipped between 0 and 1 The recruitment element of the muscle converts this activation and possibly using other inputs e g frequency for the case of FES recruitment into an effective firing frequency of the motor units of the muscle Typical inputs for natural recruitment might be from EMG data scaled to the level of maximal voluntary contraction or a simulated amp motoneuron that is controlled by reflex feedback or a neural network 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 27 e Frequency This value is only required for FES recruitment and is the stimulus frequency pps being a
78. uced by muscle Brown et al 1996 The value Lmax is measured by moving the appropriate joints to the extreme anatomical positions that produce a maximal in situ musculotendon path length y The manner in which Lmax is calculated subtracting Lo and then dividing by Lo is based on two assumptions The first is that Lo will represent the length of the tendon when the muscle is fully stretched this is reasonable considering that Lo represents the tendon length when it is already stretched to a certain degree The second is that pennation angle is negligible this assumption will be discussed later If this value cannot be measured and is unavailable in literature reasonable values for Lmax have been shown to be between 1 1 and 1 42 in five cat hindlimb muscles Brown et al 1996 Maximum musculotendon path length values can be entered ad hoc so that the calculated Lmax 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 49 value equals any approximation that you wish to use This is the only function of the maximum musculotendon path length input value so it does not need to correspond to a physiological measure so long as the calculated Lmax is reasonable In fact if the range of motion used in your model is in the midrange of motion of the muscles involved passive force from the fascicles is minimal At Lmax it has been measured at typically less than 7 of Fo at Lo or shorter it is negligible Pennation a
79. usly individual unit PCSAs were only updated when a fibertype s PCSA first became nonzero The last method used to apportion a fibertype s PCSA is now stored so that changes which are made are appropriate 5 If a change is made to single unit s PCSA then the total PCSA for that fibertype is adjusted automatically in the Manual Distribute screen What was new in Virtual Muscle 3 0 5 If you are not familiar with Virtual Muscle 2 0 skip this section as all information here has been updated in the following manual Otherwise this section will explain the changes between version 2 0 and version 3 0 5 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 5 Changes to the Fiber Type Databases 1 A small error in the slow twitch fibertypes rise and fall time parameters both human and feline was corrected here originally corrected in version 2 0 1 Changes to the BuildFiberTypes Function 1 2 We have added an additional comments box which is database specific The parameters for passive forces have been made fiber type independent i e one set of parameters per database This was done because there is no evidence to suggest otherwise and because it results in fewer calculations muscle hence an increased simulation speed Changes to the BuildMuscles Function 1 2 3 4 5 6 7 8 9 We have corrected an error in the initialization of the S variable for sag calculations We have c
80. ut parameters for scaling velocity related parameters 2 Changing or fo 5 now includes the option to scale the other parameter by the same amount and also the fiber type properties associated with that other parameter 3 There is a new input on the main dialog window Optimal Sarcomere Length Changing Optimal Sarcomere input gives the user the option to scale the FL and PE2 relationships appropriately When a fiber is imported if its Optimal Sarcomere length is different from that of the current database the user is queried on whether or not to scale the FL and PE2 relationships 4 Specific Tension tendon properties and viscosity inputs have been moved to the BuildFiberTypes function These are now part of a new sub menu window in which you can edit these properties 5 Passive Viscosity is now an editable feature of Virtual Muscle 6 The help function is a wee bit more explanatory 7 Fixed a bug in the Delete Fiber Type command when deleting the last 1 or 2 fiber types the wrong one was deleted Changes to the BuildMuscles function 1 If a new fiber type database is chosen to replace one currently being used the BuildMuscles function looks to see if the fiber types already in use by the current Muscle Model database are present If not and if there are new fiber types or existing ones that are not used by any muscle currently the Muscle Model database then the program allows the user to replace the missing f
81. utomatic distribution of PCSA for the motor units of that muscle and fiber type using the default apportioning algorithm For the default apportioning scheme the proportion of PCSA automatically allocated to each motor unit is based on the Recruitment Rank parameter for the fiber type and on the total number of units of that type as in the following equation Recruitment Rank n PCSA ath PCSA assignedto fiber type X Recruit Rank 1 Recruit_Rank 2 Tet Recruit Rank totals motorunits Effectively this distribution scheme assigns a larger proportion of PCSA to later recruited motor units of a given type Increasing the absolute value of the Recruitment Rank parameter for the fiber type reduces the differences in PCSA between consecutively recruited motor units Because the Recruitment Rank values of late recruited fiber types must always be greater than those of early recruited types the distribution will always represent the physiological phenomenon whereby fast fatigable units which have a higher Recruitment Rank a smaller range of sizes than slow twitch units Burke et al 1973 Note that if you change the Recruitment Rank parameter to change the automatic redistribution properties you must ensure that the Recruitment Rank for all other fiber types still accurately reflects the order of their recruitment If a user wishes he she can manually enter in the PCSA of each motor unit to override the au
82. will be replaced with a newly created SIMULINK block of that muscle using the current parameters in the muscle model database and its associated fiber type database This facility allows you to easily modify the parameters for your muscles and test the effects of their changes on your simulation 02 23 01 User s Manual Virtual Muscle 3 1 5 Documentation doc Page 25 Using the muscle model Structure of the SIMULINK block Once you have created your Muscle Database you can create blocks of physiologically functioning muscle from the BuildMuscles function The SIMULINK blocks are based on a modified muscle model which is described in detail in Brown et al 1996 Although it is not necessary to understand the internal details of the muscle block they are summarized here briefly If you are not interested in the internal details proceed to the next section In summary each SIMULINK muscle block contains a contractile element which is composed of an active element and a parallel visco elastic element and a series elastic element For modeling purposes a muscle mass is interposed between the contractile and series elastic elements to prevent unrealistically large instantaneous accelerations and instabilities that occur if the velocity dependent contractile element is connected directly to the series elastic element Descriptions of SIMULINK subsystems used to model each of the elements are given below e Recruitment bl

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