Simulation Lab #1 - Neuromuscular Biomechanics Lab
Contents
1. action potential and the development of peak force has been observed to vary from as little as 5 milliseconds for fast ocular muscles to as much as 40 or 50 milliseconds for muscles comprised of higher percentages of slow twitch fibers The relaxation of muscle depends on the re uptake of calcium ions into the sarcoplasmic reticulum This re uptake is a slower process than the calcium ion release and so the time required for muscle force to fall can be considerably longer than the time for it to develop In the forward dynamic simulations you will conduct in this lab activation dynamics is modeled using a first order differential equation to relate the rate of change in activation i e the concentration of calcium ions within the muscle to excitation i e the firing of motor units Dios A x xa i x a Trise T fall 3 where a is the activation level of a muscle x is the excitation level of a muscle and T ise and T fa are the rise and fall time constants for activation respectively In the model activation is allowed to vary continuously between zero no contraction and one full contraction In the body the excitation level of a muscle is a function both of the number of motor units recruited and the firing frequency of the motor units Some models for excitation contraction coupling distinguish these two control mechanisms Hatze 1976 but it is often not computationally feasible to use such models when conducting c2. muscle Replace muscle in the name of the file with the abbreviation of the muscle you did not excite e g jcontrols best HAMS V Input Files l software nmbl tutorials me382 L1 jinit in A file which specifies the initial values for the generalized coordinates generalized velocities muscle forces and muscle activations for the jumping simulation 2 software nmbl tutorials me382 L1 jcontrols stat A muscle excitation file which will hold the jumping model in a static squat position 3 software nmbl tutorials me382 L1 jmodel gfrc opt A data file containing the ground reaction forces predicted by the dynamic optimization solution VI Getting Started Compute work All labs for the class will be hands on and require that you have your own user account on the UNIX workstations in the BME computer lab If you need an account contact the instructor Each lab will guide you through a series of exercises which may require you to execute certain commands The commands you will need to execute are in Courier typeface Interactive dynamic simulator and muscle excitation editor In this lab you will use an interactive dynamic simulation program that allows you to edit the excitation signals sent to the muscles Before starting the program you will need to copy two files to a directory which you make in your own home directory Then you can start the simulator by typing the command jump mkdir Ll cd Ll cp software nmbl tutorials me3
3. of the selected nodes upward with the left mouse increase the excitation of all nodes to maximum Then start a forward integration by clicking the right mouse in one of the blue excitation fields on the left hand side of 7 the ExcitationEditor Let the integration complete Briefly describe the effect of exciting VAS on the joint angles and the ground reaction force 2 Why does a force in VAS which is a uniarticular knee extensor accelerate joints it does not span Explain this dynamic coupling both physically and in terms of the inertia matrix of Eq 1 3 Quit the ExcitationEditor shift left mouse click on QUIT and restart the program to reload the static equilibrium controls Repeat exercise 1 above for SOL 4 for GAS 5 for GMAXM and GMAXL together 6 for HAMS 7 for ADM 8 By manually editing the muscle excitation histories find a set of muscle excitation patterns which produce a well coordinated jump Try to maximize overall performance which is jump height minus ligament force penalties Jump height for the model is defined as the height reached by the center of mass above the model s standing height in meters The ligament penalty is the integral of ligament joint torques over the duration of the simulation multiplied by a constant See Anderson and Pandy 1999 for details The performance numbers will print out in your command shell as an integration progresses Record your best performance numbe
4. 82 L1 jcontrols stat cp software nmbl tutorials me382 L1 jinit in cp jcontrols stat jcontrols jump The file jcontrols stat contains excitation histories for the 54 muscles which will hold the jumping model in a squat position The dynamic simulator always looks for a file called jcontrols so it is necessary to copy jcontrols stat to jcontrols The file jinit in contains the initial states for the jumping simulation The simulator has two windows the ExcitationEditor and the 3DView When you type jump the ExcitationEditor comes up Click the middle mouse inside the ExcitationEditor to initialize it After initialization to the right of each muscle you will see a series of nodes connected by lines Each line represents the excitation history for each muscle i e x t in Eq 3 The horizontal axis is time You can edit individual nodes or groups of nodes using the left mouse Clicking the left mouse on a node toggles the node back and forth from an unslected state white to a selected state red When nodes are in a selected state you can decrease or increase their excitation levels by left clicking on any selected node and dragging the mouse down or up You can select a group of nodes by clicking the left mouse in an open area i e not on a node and dragging the left mouse to form a rectangle All nodes within the rectangle will become selected You can deselect or clear all nodes by clicking the middle mouse button Excitatio
5. Simulation Lab 1 Dynamic Simulation of Jumping Laboratory Developers Clay Anderson Allison Arnold Silvia Blemker Darryl Thelen Scott Delp ME 382 Modeling and Simulation of Human Movement Professor Scott Delp Stanford University Spring 2001 l Introduction In the study of human movement experimental measurement is generally limited to the kinematics of the body segments external reaction forces and electromyographic EMG signals While these data are essential for characterizing movement important information is missing For example because the body is actuated by more muscles than it has degrees of freedom we cannot uniquely solve for the muscle forces that gave rise to an observed motion Yet knowledge of muscle force is essential for quantifying the stresses placed on bones and also for understanding the functional roles of muscles in normal and pathological movement Using dynamic models of the musculoskeletal system to simulate movement provides not only a means of estimating muscle forces but also a framework for investigating how the various components of the musculoskeletal system interact to produce movement The purpose of this lab is to introduce you to the components of a musculoskeletal model illustrate how these components can be integrated together and demonstrate the value of dynamic simulation You will use an interactive dynamic simulation program to manually edit the excitation histories for the muscles of the
6. a passive elastic element top Muscle force is dependent on muscle fiber length middle plot and velocity right plot Muscle is in series with tendon which is represented by a nonlinear elastic element left plot Pennation angle is the angle between the muscle fibers and the tendon The forces in muscle and tendon are normalized by peak isometric muscle force F Muscle fiber length a and tendon length a are normalized by optimal fiber length Tendon slack length 7 is the length at which tendons begin to transmit force when stretched Velocities are normalized by the maximum contraction velocity of muscle v For a given muscle tendon length v velocity and activation level the model computes muscle force F and tendon force F7 Activation dynamics A muscle is not capable of generating force or relaxing instantaneously The development of force is a complex sequence of events which begins with the firing of motor units and culminates in the formation of actin myosin cross bridges within the myofibrils of the muscle When the motor units of a muscle depolarize action potentials are elicited in the fibers of the muscle and cause calcium ions to be released from the sarcoplasmic reticulum The increase in calcium ion concentrations then initiates the cross bridge formation between the actin and myosin filaments See Guyton 1986 for review In isolated muscle twitch experiments the delay between a motor unit
7. able of representing a range of muscles with different architectures are most commonly used in dynamic simulation of movement Zajac 1989 In this lab the jumping model is actuated by 54 musculotendinous units each of which is represented as a Hill type contractile element in series with tendon The parameters used to characterize each muscle are maximum isometric force Fy optimal muscle fiber length lo tendon slack length Is Maximum shortening velocity vM and pennation angle a For a table of the muscle tendon parameters consult Anderson and Pandy 1999 During a forward dynamic simulation muscle force is treated as a state and integrated forward in time using a first order differential equation of the form fur D fe MyM a 2 MT MT MT where f L and v are the force length and velocity of the muscle tendon actuator respectively and is a non linear function Zajac 1989 In Lab 4 you will concentrate specifically on modeling muscle MT lt lt 1 IMcos a Cy RRR Wad F Famn normalized tendon force normalized f muscle force normalized muscle force T_T normalized jy normalized M tendon L r muscle fiber Wy muscle fiber EVEA Strain qe length velocity v 1 Figure 3 Dimensionless model of muscle and tendon used in our simulations Muscle properties are represented by an active contractile element CE in parallel with
8. are for Interactive Musculoskeletal Modeling with its Dynamics Pipeline to generate equations of motion for models you develop Delp et al 1990 Musculoskeletal geometry Accurately representing the path of a muscle from its origin to its insertion is one of the more challenging aspects of modeling the musculoskeletal system Sometimes a muscle can be represented as a straight line path between its origin and insertion Other times it is adequate to approximate the path as a series of straight line segments which pass through a series of via points Delp et al 1990 When modeling muscle paths in three dimensions it is often necessary to simulate how muscles wrap over underlying bone or musculature Cylinders spheres and ellipsoids have been used as wrapping surfaces Van der Helm et al 1992 Garner and Pandy 2000 Arnold et al 2000 The jumping model used in this lab uses cylindrical wrapping surfaces to model the wrapping of gastrocnemius and hamstrings around the femoral condyles iliopsoas over the rim Figure 3 Path geometry of psoas of the pubic ramus and gluteus maximus over underlying bone and musculature In Lab 2 you will use SIMM to specify alter and visualize musculoskeletal geometry for a kinematic model you develop Muscle tendon mechanics The force producing properties of muscle are complex and nonlinear See McMahon 1984 for review Fig 3 For simplicity lumped parameter dimensionless muscle models cap
9. e debugger which will be useful when you build your own dynamic models Note that before this lab is due there will be a lecture in which the structure of the code is reviewed At your discretion you can wait until after that lecture to step through the code However you are encouraged to take at least a short look at the code and the debugger before that lecture so that you know what the code looks like and so that you might formulate some questions The cvd debugger The SGI debugger is called cvd If you are familiar with dbx a standard debugger on most UNIX systems you will already be familiar with the basic workings of cvd cva is a more capable graphical version of dbx To use cvd on an executable named myexe enter the following command cvd myexe The cvd user interface will come up displaying the text code for the entry point of myexe To step through the code successfully myexe needs to have been compiled with the g option CC g o myexe myexe c The g option preserves the symbols of myexe c and prevents the compiler from performing optimization and reordering execution steps You can find help for cva in the Irix man pages type man cva at the Unix shell command prompt Since the commands in cva are based on dbx the dbx man pages will also be useful type man dbx For this lab Step through the simulation code by typing the command jumpDataDebug The cva debugger will start and show the main program for the jumping c
10. h FORTRAN 77 Addison Wesley Publishing Company Menlo Park Delp SL Loan JP Hoy MG Zajac FE Topp ET Rosen JM 1990 An interactive graphics based model of the lower extremity to study orthopaedic surgical procedures IEEE Transactions in Biomedical Engineering BME 37 757 767 Garner BA Pandy MG 2000 The obstacle set method for representing muscle paths in musculoskeletal models Computer Methods in Biomechanics and Biomedical Engineering 3 1 30 Guyton AC 1986 Textbook of medical physiology Seventh Edition W B Saunders Company Philadelphia Hatze H 1976 The complete optimization of human motion Mathematical Biosciences 28 99 135 McMahon TA 1984 Muscles Reflexes and Locomotion Princeton University Press Princeton New Jersey Symbolic Dynamics Inc 1996 SD FAST User s Manual Version B 2 Mountain View CA Van der Helm FCT Veeger HEJ Pronk GM Van der Woude LHV Rozendal RH 1992 Geometry parameters for musculoskeletal modeling of the shoulder system Journal of Biomechanics 2 129 144 Zajac FE 1989 Muscle and tendon properties models scaling and application to biomechanics and motor control CRC Critical Reviews in Biomedical Engineering Edited by Bourne JR 17 359 411 CRC Press Boca Raton 10
11. he joints of the body function For example one often models the hip joint as a three degree of freedom ball and socket joint which requires three generalized coordinates flexion Sesion q ab adduction q2 and internal external rotation 43 The system mass matrix q characterizes the inertial properties of the body i e masses and moments of inertia phe remaining terms in Eq 1 express the generalized forces or torques that act on the body a represents centripetal forces that arise from the angular velocities of the segments G 7 represents gravitational forces ROD fu represents the moments applied at the joints by the muscles and q f Er represents external forces applied to the body such as the ground reaction force The matrix RO is a matrix of moment arms that transform the muscle forces f m into joint torques The matrix E 4 performs a similar function for the external forces fr For simple models it is possible to derive the equations of motion by hand However for more complex models this is generally not feasible and the equations of motion are generated on a computer The jumping model used in this lab has 23 degrees of freedom Anderson and Pandy 1999 and the equations of motion for the jumping model were generated using SD Fast a commercially available software package from Symbolic Dynamics Inc Symbolic Dynamics Inc 1996 In subsequent labs you will use SD Fast and SIMM Softw
12. hen they are fired in isolation and in conjunction with other muscles e Compare the ground reaction forces predicted by your simulation with the forces predicted by the optimal solution found by Anderson and Pandy 1999 e Quantify the magnitude of the articular contact forces in the hip e Examine the force generated by the vasti muscle group during jumping in relation to its excitation level and in relation to its maximum isometric force e Take a look at the computer code which constitutes the dynamic musculoskeletal model lll Background Dynamic models of the musculoskeletal system are typically comprised of four important components 1 the equations of motion for the body or skeletal dynamics 2 a representation of musculoskeletal geometry 3 a model of muscle tendon mechanics and 4 a model of activation dynamics Figure 1 illustrates how these components are combined to execute a forward dynamic simulation Based on a set of initial states which include the muscle activations t the muscle forces f t the generalized speeds t and the generalized coordinates 7 differential equations See Eqs 1 3 below are used to compute the time rate of change of the states Then a numerical integration is performed to compute the states at time dt The new states are fed back and the forward dynamics process repeats advancing the states in time until the final time of the simulation is reached In the simulations you
13. icking the save button in the lower left corner of the ExcitationEditor This will write your controls to a file called jcontrols new If you wish to start up the dynamic simulator from a saved control files it is necessary to quit the simulator left click the QUIT button copy the saved controls file to jcontrols and restart the simulator The 3DView allows you to view the musculoskeletal model as an integration executes The long red cylindrical shapes represent the paths of muscles The activation level of a muscle is proportional to the intensity of red with which its path is drawn The joint axes of the model are shown as short blue arrows The magnitude and direction of the ground reaction forces applied to the feet are displayed as green vectors applied at five locations under each foot Each of the five locations corresponds to a location at which a spring and damper force is applied see Anderson and Pandy 1999 for details It is possible to rotate and translate the 3DView to obtain different perspectives on the model Table 2 With respect to the computer screen the x y and z axes of the window are up to the right and out of the screen respectively To interrupt the integration and return to the ExcitationEditor you can type the ESC key while the mouse pointer is within the 3DView window BUG Note that if you attempt to control the 3D View while the 3D View window is not integrating the dynamic simulator will lock up and you w
14. ill have to type lt cNTRL gt c to exit the simulator Table 2 3DView Commands left mouse drag left and right Rotate about window y axis vertical axis left mouse drag up and down Rotate about window x axis horizontal axis Rotate about window z axis out of the screen Translate along window x axis horizontal axis Z_Keytleft mouse drag up and down middle mouse drag left and right middle mouse drag up and down Translate along window y axis vertical axis Zz Keytmiddle mouse drag up and down Translate along window z axis out of the screen ESC_Key Interrupt integration and return to ExcitationEditor NOTE For this lab it is assumed that the muscles on the left and right sides of the body are excited symmetrically You must therefore make all your changes to the muscle excitation histories on the left side of the ExcitationEditor You will notice that as you make changes to the left side excitations they are mirrored on the right side of the ExcitationEditor Vil Muscular Control Strategies for Maximizing Jump Height Following are a series of tasks for you to perform and questions for you to answer The answers to the questions constitute your written report for Lab 1 For a list of muscle abbreviations used in this lab see Table III in Anderson and Pandy 1999 1 Starting from the static controls i e cp jcontrols stat jcontrols use the left mouse button to select all the nodes for VAS Then by dragging one
15. lower extremity with the goal of making a musculoskeletal model jump as high as you can Jumping was chosen as the activity for this lab because it has a well defined objective i e jump high and although still complex its muscular coordination is relatively simple compared to walking The musculoskeletal model you will use was used previously by Anderson and Pandy 1999 to find the optimal set of excitation histories for maximum height jumping For details concerning the model and the optimal solution consult the attached paper by Anderson and Pandy 1999 By working through this lab you will get a feel for the computational cost of dynamic simulation and gain some insight into the roles played by individual muscles during jumping By examining the simulation results you will get some exposure to what data are available from dynamic musculoskeletal models Finally by stepping through this lab you will get a preview of upcoming labs which will focus in greater depth on the various components that comprise a dynamic musculoskeletal model ll Objectives The purpose of this lab is to give you hands on experience with a complex dynamic model of the human musculoskeletal system In the course of this lab you will e Find a set of muscle excitations that produce a well coordinated jump The specific aim is to make the musculoskeletal model jump as high as possible without hyper extending its joints e Investigate the actions of muscles w
16. n Editor Command Summary left mouse click select deselect a node left mouse drag in open space select a group of nodes left mouse drag of selected node s decrease increase excitation middle mouse click clear all selected nodes right mouse click in left column integrate left mouse click On SAVE save controls to file jcontrols new left mouse click On QUIT quit shift left mouse click On QUIT forced quit without saving To begin an integration click the right mouse in the blue area of any of the excitation fields on the left side of the ExcitationEditor The first time you request an integration the 3DView will appear and display the model in its initial position As the integration progresses a vertical white line will trace across the ExcitationEditor from left to right indicating the current time of the integration As the integration passes each node the states are stored so that 6 subsequent integrations can start from any node which has associated with it a valid set of states A vertical black line indicates the most advanced node from which an integration can be started To start an integration from a particular node right mouse click just to the right of the node For example if you want to integrate starting the beginning right mouse click to the right of the first node if you want to integrate from the third node right click to the right of the third node At any time you can save your edited controls by left cl
17. ode Place a sTOP in the main program by left clicking the mouse in the left margin Start execution by clicking the Run button in the upper right hand corner of the cvd debugger window or by typing rerun in the command window at the bottom of the main window Once the process is executing you can step through the code using the cvd buttons or by entering commands in the lower command window Consult the dbx man pages for the basic commands 9 You should step down into the code deep enough that you go through the integrator and execute lines of code in ydot23 You do not need to include anything in your report from this exercise A note regarding how the cvd debugger was started for this exercise The programs you have been running were actually started with script files so executing the command cvd jumpData would NOT have worked with cvd because jumpData is only a script file To invoke the debugger on jumpData the script file jumpDat aDebug was created which internally starts the cvd debugger X References Anderson FC and Pandy MG 1999 A dynamic optimization solution for jumping in three dimensions Computer Methods in Biomechanics and Biomedical Engineering 2 201 231 Arnold AS Salinas S Asakawa DJ Delp SL 2000 Accuracy of muscle moment arms estimated from MRI based musculoskeletal models of the lower extremity Computer Aided Surgery 5 108 119 Atkinson LV Harley PJ Hudson JD 1989 Numerical methods wit
18. omplex dynamic simulations In the jumping model the muscle excitation signal is assumed to represent the net effect of both motor neuron recruitment and firing frequency and like muscle activation is also allowed to vary continuously between zero no excitation and one full excitation The rise and fall time constants for muscle activation are assumed to be 22 and 220 milliseconds respectively Zajac 1989 IV Deliverables At the completion of most labs you will need to turn in computer files from you remodeling and simulation work They should be copied to home me382 username L where username is your workstation login name and is a number corresponding to the lab your working on i e 1 2 for Labs 1 2 You are the only person who will have read and write permission to these directories during the week or two that a lab is in progress In addition you will often be asked to turn in a written report summarizing your findings and addressing questions which are posed as part of the lab Deliverables for Lab 1 1 A 2 3 page written report A Microsoft Word template for the report called lab1_report doc is available on the BME workstations in software nmb1 tutorials me382 L1 Deposit the following computer files to home me382 username L1 Ds jcontrols best Excitation histories for your best performance jump 3 jcontrols best muscle Excitation histories for your best performance jump without using a particular
19. rs in your written report and make sure to save the corresponding set of controls to file left mouse click on SAVE then in the UNIX shell cp jcontrols new jcontrols best ligament penalty jump height overall performance 9 If you are able to get the model to jump anywhere near the jump height predicted by the optimal solution i e over 1 41 meters you should be congratulated It is not easy to do In the more likely event that your solution was not as high as the optimal solution explain why 11 Before you started on the lab you should have been assigned a muscle e g SOL HAMS VAS Now as you did in exercise 8 make the model jump as high as possible without using this muscle Make sure to save the controls corresponding to your best performance to file see the Deliverables section above What is the performance difference between this jump and your best jump when you could use all the muscles What would you infer is the function of this muscle during jumping Vill Analyses You will now take a brief look at some of the data which is available from your simulation First you will need to generate the data Execute the following commands cp jcontrols best jcontrols jumpData The following files should be generated model gfre Time history of the ground reaction force sum of spring forces model jfre Time history of the articular contact forces at the joints model mexc Time history of muscle exci
20. tations model matv Time history of muscle activations 8 model mfrce Time history of muscle forces 1 Plot the vertical ground reaction force predicted by your solution and by the optimal solution Include this plot in your report The ground reaction forces for the optimal solution are in the file jmodel gfrc opt which you can find in software nmb1 tutorials me382 L1 Does your ground reaction force have a higher or lower peak Is the time to lift off longer or shorter 2 Plot the resultant articular contact force at the hip as a percentage of body weight Include this plot in your written report Why are the hip contact forces are so large 3 On a plot superimpose the excitation levels activation history and force history predicted by your solution for VAS Include this plot in your written report Given what you know about muscle mechanics explain why the force generated by VAS was less than its isometric strength IX Stepping through the Code Now that you have an idea of how a dynamic musculoskeletal model can be used take a look at the computer code that was used to generate the simulation programs you have been using To do this you will use the SGI debugger to step through the code Also available to you are some hardcopy printouts of some routines which should have been distributed with this lab This exercise is an opportunity to begin getting familiar with dynamic simulation code and also an opportunity to start learning th
21. will conduct in this lab a variable step 5 6 Runge Kutta Felberg integrator is used Atkinson et al 1989 Forward Dynamics Miracle we ACTIVATION AU E a DYNAMICS Muscle ini _ Activations lee al ath pimanmi _ i i MUSC LE TENDGH M0 E Lia OYMANGC 5 Muace Tendon agg ee 3 Forces a LIGAMENT an z MECHANICS SKELETAL ae lo qr a DYNAMICS Joint Velocities ne Angusa FOOT FLOOR i Ln CONTACT Om Mee Figure 1 Schematic of a forward dynamic simulation Skeletal dynamics The equations of motion for the body allow one to compute the accelerations of the body segments when forces and torques are applied to the body The equations of motion can be expressed agio follows Ba CB ED RD Ju ED fed D Eq 1 is simply an elaboration of Newton S third law for a multi link system rearranged SQ that one can compute acceleration i e a m tf The vector of generalized coordinates 4 ns as to re position and orientation of the segments of the body The time derivatives of 7 and 7 therefore represent the velocities and acceleyations of the segments Depending on how one chooses to model the body elements of 7 may be translational displacements 2 orientations of segments with respect to the lab frame segment angles or orientations of segments with respect to other segments joint angles Implicit in one s choice of generalized coordinates are one s assumptions about the how t
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