Objective: The overall goal of this research is to develop computational algorithms for Multiple Instruction Multiple Data (MIMD) parallel architectures that will allow previously intractable, large-scale optimal control problems to be solved. We propose to solve optimal control problems for human movement using a detailed musculoskeletal model of the human body. The solution to these problems will yield the time histories of muscle forces and bone-loading patterns during activity.
Approach: The combination of optimal control theory and mathematical modeling has emerged as a powerful tool for determining musculoskeletal forces during human movement. However, accurate simulation of human movement incurs great computational expense. In fact, detailed simulation of human movement in 3D is not feasible with conventional serial machines. With the emergence of high-speed parallel supercomputers together with the availability of fast, efficient computational algorithms, high-dimension dynamical models can be used to accurately simulate human movement and to determine musculoskeletal loading patterns during daily physical activity. Our approach is divided into four major tasks:
Accomplishments: We have developed a very detailed 3D, 23-degree-of-freedom, 54-muscle model of the human body. Each muscle in the model is represented by a three-element entity in series with tendon. Parameters describing the mechanical properties of each muscle were obtained from the literature and scaled to the strength of individual subjects.
Our serial optimal control algorithm decomposes very efficiently into a parallel algorithm. The serial algorithm consists of three parts: (1) forward simulation, (2) computation of derivatives, and (3) parameter optimization. Of these three parts, computation of the derivatives dominates total CPU time (i.e., over 90 percent). When implemented on a MIMD supercomputer, computation of the derivatives scales almost linearly with the number of processors used. Specifically, on any MIMD computer, we can compute derivatives 100 times faster with 128 processors than with just 1 processor (see figure).
We have evaluated the performance of two MIMD computers. The Intel iPSC/860 and CM-5 were each able to compute optimal control solutions 100 times faster than a Silicon Graphics 4D25, a 33 MHz serial RISC workstation. This improvement in performance is due mainly to the fact that computation of the derivatives scales linearly on MIMD computers and is not the result of individual processor speed.
A solution for maximum-height jumping has been obtained using the CM-5. There was favorable agreement between the predictions of the model and experimental data obtained from humans performing a maximum-height jump.
Significance: The ability to simulate human movement and accurately compute musculoskeletal loading histories is particularly important to the space program, where exposure to different loading environments or gravitational fields can alter the morphology, biochemistry, and functional properties of muscle and bone tissue. Such information is also vital for clinical treatment of musculoskeletal disorders. In particular, acknowledgment of musculoskeletal forces will help identify the role of individual muscles during pathological movement, enhance surgical procedures for correcting muscle and joint pathology, and improve the design of total joint replacements.
Status/Plans: Currently, we are evaluating the performance of the parallel algorithm on the IBM SP-2. We expect to achieve the same linear scaling as was obtained on the iPSC/860 and CM-5. However, we also expect to see significant improvements in single-processor speed. Our final step will be to solve an optimal control problem for walking on the IBM SP-2. The solution to this problem will present novel information relating to muscle coordination during gait.
Points of Contact:
Frank C. Anderson
Marcus G. Pandy
The University of Texas at Austin
clay@soleus.ath.utexas.edu, 512-471-2176
pandy@mail.utexas.edu, 512-471-1273