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The Virtual Skeleton:
Modeling Human Movement
with Supercomputers

by Jarrett Cohen

Supported by a Guest Computational Investigator grant from the NASA High Performance Computing and Communications (HPCC) Program's Earth and Space Sciences Project and additional NASA awards, researchers at the University of Texas at Austin are using the NAS IBM SP2 and other supercomputers to model the human musculoskeletal system during movement on Earth and in space.

As with subatomic particles and cosmology, supercomputers are supplying insight into workings of the human musculoskeletal system that are otherwise impenetrable.

"Numerical simulation provides us with a way of estimating the forces developed by the muscles in the body. We could not do this in vivo," said Marcus Pandy, associate professor of kinesiology and mechanical engineering at the University of Texas at Austin. "If you knew the forces developed by the muscles, you would really understand how muscles coordinate limb movements."

Pandy and mechanical engineering graduate students Clay Anderson and Brian Garner combine optimal control theory and mathematical modeling to determine musculoskeletal forces during different activities. Optimal control involves finding the best way to achieve a task. For example, going as high as possible is the goal in jumping, while expending minimal energy is typical for walking.

Mathematical equations "represent the way bones move in relation to each other and the relationships between the forces in the muscles and movements in the bones," Pandy said. These dynamical equations of motion, which are vast in number, can be derived using Symbolic Dynamics' (Sunnyvale, CA) software package SD/Fast. The software for the rest of the modeling had to be developed in-house. Using these methods, Pandy's research team has been constructing three-dimensional models for studying vertical jumping, walking, rising from a chair, kicking, knee rehabilitation exercises, and, in collaboration with NASA Ames' Malcolm Cohen, various arm movements.

The Modeling Process

Modeling a physical activity begins with deciding on the number of body segments. Pandy said they have used as few as four (foot, shank, thigh, and upper body) and as many as eight. The joints come next, and how complex their movements are depends on the activity. In rising from a chair, the ankles, knees, hips, and feet are hinge joints -- they only move in one plane, much like a door. Joints in the walking model, the most intricate, together have 23 degrees of freedom. For instance, the hips move in three planes.

With a skeleton in place, the researcher then chooses the muscles to activate it. Limitations in computer power make it "infeasible to represent all of the muscles and simulate movement," Pandy stressed, so the team only models the major muscles that pull on bones. The walking model includes the largest number at 56.

The last step before running a simulation is selecting muscle parameters, most of which are in related literature or obtainable through experiments. For the latter, "we take a pool [of] people and measure their strength and such things as mass and moment of inertia," Anderson said. "We scale the parameters to be an average of the subject pool." One key parameter -- the lengths of the tendons -- cannot be measured, so they estimate them using the model, Pandy said.

A graphical interface developed by Garner furnishes a highly interactive solution process. "You can change the muscle activation levels...often and quickly...if something is going badly," such as when movement is grossly uncoordinated or unnatural, he explained. The researcher also runs the simulation code and produces visualizations from this interface. "The input is muscle activation levels," Garner explained. "The output is kinematic motions and joint angles at each instant in time," which are visualized in software based on the Silicon Graphics Inc. GL library.

Computational Implementation

The overall task is to "find how all of the muscles should be activated so that the model can produce an optimum, coordinated movement," Pandy said. "You need a mathematical algorithm to search the solution space in order to find the best possible solution. This is why we need supercomputers; the computation time for conducting the search is prohibitive."

Anderson explained further: "In optimal control problems, the first step is calculating derivatives of performance with respect to the controls." The second step is running a parameter optimization routine to produce an improved set of controls."

Since the equations must be integrated thousands of times, the derivatives are too time-consuming for serial computers, Anderson said. The problem is better suited to parallel systems, on which the integrations can be distributed across multiple processors.

SP2 Gives Almost Ideal' Scaling

Beginning in 1990 as a co-investigator with Ames' Robert Whalen, Pandy was the first non-aeroscience researcher to have access to a NAS parallel supercomputer. A Guest Computational Investigator grant from the NASA High Performance Computing and Communications Program's Earth and Space Sciences Project, and other NASA awards, have funded parallel code development. Pandy's team has evaluated the Thinking Machines CM-5, the Intel iPSC/860, and the IBM SP2. They found the CM-5 impractical because it requires manually aligning many arrays of data (for example, the length and shortening velocity of a muscle) in the machine's memory. The iPSC/860 is not effective because its processors have too small a cache.

The IBM SP2 is a different matter altogether, Anderson said. The fast clock speed and large cache of its processors have enabled performance 15 to 20 times that of the CM-5 or iPSC/860, conservatively 2.5 gigaflops on 128 processors. "Our problem is ideally suited to MIMD [Multiple Instruction Multiple Data] parallel machines, to compute those derivatives," he added. "We get almost ideal scaling. Even with 150 processors on the SP2, we're seeing something like 80 to 90 percent ideal [scaling]."

Applying the Knowledge

The first three-dimensional model of its kind, a jumping run takes approximately 100 hours on eight SP2 processors. Simulating walking will require four times the computation. Anderson said that the primary reasons for this difference are that walking needs separate controls for the right and left sides of the body and that a step takes twice as long to perform in real time as a vertical jump.

Whatever the activity, the computational models are used in conjunction with other research methods to gain as complete an understanding as possible. Before simulation, Garner said that they often videotape human subjects and then input the joint angles into simpler graphical models. The researchers also conduct cadaver studies for comparison. "This is a way of validating the model," Pandy said. "It is much more accurate, as we can do things that we can't do to live people -- such as inserting pins directly into the bones to more accurately measure movement in 3D."

"If you have a validated model, you can study a variety of things without doing experiments," Pandy emphasized. For example, by tweaking the muscle strength and gravity parameters his team has simulated jumping in space, where strength is depleted. "This capability is potentially very attractive, even more so from a rehabilitation point of view," Pandy said. "One could envision simulating surgeries, where the tendons are cut and relocated to compensate for musculoskeletal abnormalities."

For more information on this virtual skeleton work, send email to pandy@mail.utexas.edu.

Jarrett Cohen, a senior science writer for the NASA HPCC Earth and Space Sciences Project, is based at NASA Goddard Space Flight Center.

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