Dynamic Simulation of Jumping
Contents
1. 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 each lab you will need to turn in a written report created from pre formatted template that will be provided to you The written reports are where you will summarize your findings and address questions posed as part of the lab In addition for the first lab you will need to create plots using some of the output files from the jumper simulation V Getting Started Download the following files from the course web site e Simulation_Lab1_report docx This Word file contains the template for the lab report Revised as of January 10 2012 Page 6 of 11 e Simulation_Lab1 osim This model file contains the jumper model e Simulation_Lab1_Setup_Forward xml This setup file contains the parameters for running the jumper simulation e Simulation_Lab1_controls xml This controls file contains excitations for the muscles that will hold the jumping model in a static squat position e Simulation_Lab1_initial_states sto This storage file specifies the initial values for the generalized coordinates generalized velocities muscl2. you are able to get the model to jump anywhere near the jump height predicted by the optimal solution i e over 0 37 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 10 Choose a muscle to eliminate and as you did in exercise 8 make the model jump as high as possible without using this muscle Save the controls corresponding to your best performance to a file e g Simulation _Lab1_controls_second_best xml and again record your best performance numbers in your written report ligament penalty jump height overall performance 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 VII Analyses You will now take a brief look at some of the data which is available from your simulation Revised as of January 10 2012 Page 9 of 11 The following files should be generated e Jumper_ForceReporter_forces sto Time history of the muscle forces ground reaction forces individual contact point forces and ligament forces e Jumper_JointReaction_ReactionLoads sto Time history of the articular contact forces at the joints e Jumper_controls sto Time history of muscle excitations e Jumper_states sto Time history of muscle activations along with other states muscle fiber lengths and joint positions and velocit
3. Boca Raton Revised as of January 10 2012 Page 11 of 11
4. SIMULATION LAB 1 Dynamic Simulation of Jumping Modeling and Simulation of Human Movement BME 599 Laboratory Developers J eff Reinbolt B J Fregly Clay Anderson Allison Arnold Silvia Blemker Darryl Thelen Scott Delp 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 lower extremity with
5. e forces and muscle activations for the jumping simulation Computer work All labs for the class will be hands on and require that you use a PC with OpenSim 2 4 0 installed Muscle excitation editor In this lab you will use OpenSim to allow you to edit the excitation signals sent to the muscles The Excitation Editor allows you to visually inspect and edit muscle excitation patterns To bring up the Excitation Editor select Edit gt Excitations from the OpenSim main menu bar When you press the Load button you are prompted to browse for an XML file containing controls eg Simulation _Lab1_controls xml Upon selecting the file a filtering dialog box appears from which you can select the controls to be displayed in the Excitation Editor for inspection and editing Control points are selected in one of two ways either individually or using the box select functionality In particular to select a control point hold down the ctrl key and left click on the point To select multiple points hold down the ctrl shift keys while left clicking on the points You can also box select points by holding down the ctrl key and then press the left mouse button and drag the cursor to form the selection box If you hold down the shift key while box selecting you can select multiple sets of control points Once you have selected one or more control points you can drag them to a new location or you can set control points across multiple panels
6. 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 does not use wrapping surfaces however you should be familiar with the concept of muscle wrapping over underlying bone and musculature In Lab 2 you will use OpenSim to specify alter and visualize musculoskeletal geometry for a kinematic model you develop Figure 2 Path geo metry of psoas 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 capable of representing a range of muscles with different architectures are most commonly used in dynamic simulation of movement Zajac 1989 In th
7. ies 1 Plot the vertical ground reaction force sum of 5 contact point forces per foot normalized by body weight predicted by your solution and by the optimal solution The mass of the model is 75 1658 kg and the acceleration due to gravity is assumed to be 9 80665 m s2 Include this plot in your report The vertical ground reaction force Fy for the optimal solution is in the file Simulation_Lab1_optimal_ground_reactions xlsx 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 normalized by body weight Include this plot in your written report Why are the hip contact forces so large 3 On a plot superimpose the excitation levels activation history and normalized force history predicted by your solution for VAS To normalize the force predicted by VAS divide by the force by the maximum isometric strength of VAS 6865 N see Anderson and Pandy 1999 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 VIII References 1 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 2 Arnold AS Salinas S Asakawa DJ Delp SL 2000 Accuracy of muscle moment arms estimated from MRI based musculoskeletal model
8. is 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 F optimal muscle fiber length 1 tendon slack length 7 maximum shortening velocity vv 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 fer O fMT IMT yMT a 2 where f 7 IMT and v are the force length and velocity of the muscle tendon actuator respectively a is the muscle activation level and is a non linear Revised as of January 10 2012 Page 4 of 11 function Zajac 1989 In Lab 4 you will concentrate specifically on modeling muscle AAA AJ hie EEKE OWON Zo WL uw uw a i o o o0 oo N 5 ge RES v aH 58 ES Ee Q z on On O F es 033 E 1 T 47 normalized A M normalized M tendon ls muscle fiber 14M lo fi strain T length o muscle iber PTY ls velocity V a lo 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 a passive elastic element top Muscle force is dependent on
9. 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 a 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 and tendon length 1 are normalized by optimal fiber length 1 Tendon slack length 12 is the length at which tendons begin to transmit force when stretched Velocities are normalized by the maximum contraction velocity of muscle Vax For a given muscle tendon length IMT velocity and activation level the model computes muscle force F and tendon force F Activation dynamics A muscle is not capable of generating force or relaxing instantaneously The development of force is a complex sequence of events that 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 Revised as of January 10 2012 Page 5 of 11 myosin filaments see Guyton 1986 for review In isolated muscle twitch experiments the delay between a motor unit action pote
10. ntial 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 _ x xa oa 3 a Trise Tfall where a is the activation level of a muscle x is the excitation level of a muscle and Trise ANd Tfay 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 complex dynamic simulations
11. nts e Investigate the actions of muscles when 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 Ill 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 a t the muscle forces f t the generalized speeds q t and the generalized coordinates q t 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 t 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 will conduct in this lab a variable step integrat
12. oad the static equilibrium controls i e Simulation _Lab1_controls xml Repeat exercise 1 above for glut_max2_r and glut_max2_I GMAXM and glut_max1_r and glut_max1_ GMAXL together Revised as of January 10 2012 Page 8 of 11 6 Use the Excitation Editor to reload the static equilibrium controls i e Simulation Lab1_controls xml Repeat exercise 1 above for bifemlh_r bifemlb_I bifemsh_r and bifemsh_ HAMS 7 Use the Excitation Editor to reload the static equilibrium controls i e Simulation_Lab1_controls xml Repeat exercise 1 above for add_mag2_r and add_mag2_ ADM 8 By manually editing the muscle excitation histories find a set of muscle excitation patterns that 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 0 9633 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 can be computed on your own or you can use the included MATLAB script i e jumpPerformance m Record your best performance numbers in your written report and save the corresponding set of controls to a file e g Simulation_Lab1_controls_best xml ligament penalty jump height overall performance 9 If
13. ol Strategies for Maximizing J ump 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 Simulation Lab1_controls xml use the Excitation Editor to select all the nodes for vas_int_r and vas_int_ collectively VAS Then by dragging or setting a new value for all nodes increase the excitation of all nodes to maximum and save these controls to a new file e g vas_modified_controls xml Next use the Forward Dynamics Tool to start a forward integration using the newly modified controls Let the integration complete Briefly describe how exciting VAS affects the joint angles states_degrees mot and the ground reaction force forces sto 2 Why do a forces in VAS which are uniarticular knee extensors accelerate joints they do not span Explain this dynamic coupling both physically and in terms of the inertia matrix of Eq 1 3 Use the Excitation Editor to reload the static equilibrium controls i e Simulation_Lab1_controls xml Repeat exercise 1 above for soleus_r and soleus_ SOL 4 Use the Excitation Editor to reload the static equilibrium controls i e Simulation_Lab1_controls xml Repeat exercise 1 above for med_gas_r and med_gas _ GAS 5 Use the Excitation Editor to rel
14. or is used Revised as of January 10 2012 Page 2 of 11 Forward Dynamics ACTIVATION 2 DYNAMICS Muscle Tendon GEOMETRY MUSCLE TENDON 49 DYNAMICS Muscle Excitations x t a t dt Muscle Activations Activations alt 9 f t dt Muscle Tendo Muscle Tendon Forces O D E 5 Z ii LIGAMENT Veau MECHANICS ia SKELETAL q t q g t dt DYNAMICS Joint Angles i amp Velocities Velochigs FOOT FLOOR a ait CONTACT sag Reaction 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 as follows q 14 1 C G4 G R fu E fe 1 Eq 1 is simply an elaboration of Newton s second law for a multi link system rearranged so that one can compute acceleration i e a m t f The vector of generalized coordinates q is used to specify position and orientation of the body segments The time derivatives of g g amp and g therefore represent the velocities and accelerations of the segments Depending on how one chooses to model the body elements of q may be translational displacements 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 gene
15. ralized coordinates are one s assumptions about the how the 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 extension q4 ab adduction q2 and internal external rotation q3 The system mass matrix 1 q characterizes the inertial properties of the body i e masses and moments of inertia The remaining terms in Eq 1 express the generalized forces or torques that act on the body C 4 q7 represents centripetal forces that arise from the angular velocities of the segments G q represents gravitational forces R q fy represents the moments applied at the joints by the muscles and E q f represents external forces applied to the body such as the ground reaction force The matrix R q is a matrix of moment arms that transform the muscle forces fy into joint torques The matrix E q performs a similar function for the external forces fr Revised as of January 10 2012 Page 3 of 11 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 OpenSim Del et al 2007 In subsequent labs you will use OpenSim to
16. s of the lower extremity Computer Aided Surgery 5 108 119 3 Atkinson LV Harley PJ Hudson JD 1989 Numerical methods with FORTRAN 77 Addison Wesley Publishing Company Menlo Park 4 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 5 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 Revised as of January 10 2012 Page 10 of 11 6 Guyton AC 1986 Textbook of medical physiology Seventh Edition W B Saunders Company Philadelphia 7 Hatze H 1976 The complete optimization of human motion Mathematical Biosciences 28 99 8 135 McMahon TA 1984 Muscles Reflexes and Locomotion Princeton University Press 9 Princeton New Jersey 10 Symbolic Dynamics Inc 1996 SD FAST User s Manual Version B 2 Mountain View CA 11 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 12 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
17. 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 as high as possible 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 that will focus in greater depth on the various components that comprise a dynamic musculoskeletal model Revised as of January 10 2012 Page 1 of 11 Il 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 joi
18. to a fixed value by typing in the new value in the text box labeled Set to Modified excitations may be saved to the file that they came from select Save or a new controls file select Save As See the Excitation Editor chapter in the OpenSim User Guide for additional details Forward Dynamic Simulation Given the controls e g muscle excitations the Forward Dynamics Tool can drive a forward dynamic simulation To bring up the Forward Dynamics Tool select Tools gt Forward Dynamics from the OpenSim main menu bar Like all tools the Revised as of January 10 2012 Page 7 of 11 operations performed by the Forward Dynamics Tool apply to the current model At the bottom of the window are four buttons The Settings gt button is used to load or save settings for the tool The Run button starts execution The Close button closes the window The Cancel button closes the window and cancels all operations that have not yet been completed When the Settings gt button is clicked you are presented with the choice of loading or saving settings for the tool If you click Load Settings you will be presented with a file browser that displays all files ending with the xml suffix You may browse for an appropriate settings file e g Simulation_Lab1_Setup_Forward xml and click Open to populate the tool with the settings in that setup file See the Forward Dynamics chapter in the OpenSim User Guide for additional details VI Muscular Contr
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