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Lab Simulation #4: Dynamic Modeling and Simulation of Muscle-Tendon Actuators Professor B.J. Fregly Mechanics of the Human Locomotor System EML 5595 - Fall 2005 Laboratory Developers: Darryl Thelen, Silvia Blemker, Clay Anderson, Scott Delp Neuromuscular Biomechanics Lab, Stanford University VI. Using SIMM/Pipeline to Simulate Muscle-Tendon Dynamics VI-B. Muscle Tug of War Model Chapter 2 of the Pipeline manual describes how the muscle excitation-time relationship can be specified as either a step function or spline fit. Sketch out the excitations of muscles A and B that were used to generate the previous simulation. 1 VII. Exploration Phase VII-A. Exploration of SIMM Pipeline Code 1. As mentioned previously, muscle length is a state variable that is solved for by numerical integration of the contraction dynamics equation. However, tendon force is what must be applied to the mechanical system during an actual simulation. Investigate the pipeline code and document how the transformation from muscle length to muscle tendon force is made. Write down all the routines that are called and explain how the curves shown in Figure 1 are actually implemented in the code to make the transformations from muscle length to tendon force. 2. By further exploring the code, explain how muscle tendon forces are actually applied to the skeleton within a dynamic simulation. 3. Often we are interested in knowing the net muscle moment about a joint, since that quantity can be compared with joint moments computed using inverse dynamics. How would you go about computing net muscle moments about a joint using SD/FAST and/or Pipeline code? 2 VII-C. Affect of Model Parameters on Dynamic Response 1. Isometric Responses: Perform isometric simulations with a range of tendon to fiber T l S / l 0M length ratios: = 0.5, 1.0, 2.0, 4.0, 8.0. For each tendon to fiber length ratio, maintain the sum of the slack tendon length and optimal fiber length constant ( T l S + l0M = 0.3 m ). Overlay curves of the muscle force time for histories each tendon to fiber length ratio. Describe any differences that you see between the curves in terms of the rate of force development and steady state force achieved. Using what you know about muscle activation dynamics and muscle tendon mechanics, explain why the muscle force responses differ the way they do with changes in tendon to fiber length ration. 2. Isokinetic Responses: You should modify your formain.c driver program such the block translates at a constant 0.1 m/s to the right after starting an initial position 0.05 m to the left of the mid position. Perform isometric simulations with the following tendon to fiber T M length ratios: l S / l 0 = 0.5, 1.0, 2.0. For each tendon to fiber length ratio, maintain the T M sum of the slack tendon length and optimal fiber length constant ( l S + l0 = 0.3 m ). Overlay plots of the muscle force as a function of time from the three simulations. Describe any differences that you see between the curves in terms of the magnitude and timing of peak force, and the shape of the curve. Explain why the simulations vary the way they do. Your explanation should describe how the muscle force length velocity and tendon force strain properties combine to give the response you see. 3 VIII. Design Phase The design process and results should be clearly documented in a brief report. The report, excluding figures and tables, should not be more than 2 pages. It should include the following sections: Introduction Objectives of your design Methods Outline of steps used in your design process Results Should include a combination of mathematical analysis, parameter sensitivity studies and results of prototype muscle simulations. Description of the final muscle design Discussion Justification of your final design Evaluation of the strengths and potential weaknesses of your design, e.g. under what conditions do you expect your muscle to perform well? References List of references used 4

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