On a Limb

Dana Bauer
January 01, 2002
drawing of two legs on weight

Wonder how much your leg weighs?

You could measure its length and circumference, then estimate its mass based on data gathered from cadavers—mostly old, white guys. But what if you're African-American? A runner? Pregnant?

"There are practically no data in the literature for special populations," says Todd Pataky, a graduate student in kinesiology.

"No doubt there are differences between men and women, between ethnic groups: different mass distributions, different tissue densities," he says. But, regression equations—a statistical tool used to calculate live limb masses from cadavers—do not take such differences into account.

Currently, the best way to accurately measure the limb mass of a live person is to X-ray the limb, but this method is expensive and unnecessarily exposes subjects to radiation. Pataky is helping to develop a method that is quick, easy, and inexpensive. He recruited a very special population—the Penn State women's volleyball and swim teams—to help him test it.

But, first: why would anyone need to know the mass of a leg, or an arm? Pataky smiles. It's not about admiring the sinewy limbs of athletes, although sports therapists could use the information. It can help elderly people as well. For example, if you're trying to determine muscle strength in an elderly person, you need to know the mass of her limbs. If she is taking short steps when she walks, it may be her natural gait, or it may be because she doesn't have the limb strength to take longer steps. "We could develop a strength program to increase the muscle mass in the limb," Pataky suggests. Also, he notes, knowing the mass could help distinguish between muscular weaknesses and pathological conditions.

Pataky's method for estimating limb mass, " is not a new idea," he says. "We're just using new technology." The idea is based on classical methodology first developed by French scientist George Demeny, and published by the Academie des Sciences in 1887.

The method is based on Newton's law of motion: force equals mass times acceleration. "If we want to know mass, we need to know force," says Pataky. A force vector—an imaginary arrow pulled downward by the force of gravity—acts through a person's center of mass. As the person moves a limb, the center of mass shifts, and the imaginary force vector shifts too.

drawing of arms with list of weights

"Normally, my center of mass is somewhere around here," says Pataky, pointing to his belly button. "But when I move my arms," he says, raising them above his head, "my center of mass rises. Like this." He traces an imaginary line from his belly button to his breastbone.

Subjects lie on a wooden platform that Pataky and colleague Mike Duffey crafted. "The bed of the platform had to be long enough to accommodate the volleyball players," he says. The platform rests on top of a force plate—sort of like a giant bathroom scale—in the floor of the biomechanics laboratory. "The plate has four sensors connected to a computer," Pataky explains. "A force on the plate changes the amount of current that flows through the system." The computer registers the changes.

A volleyball player lying on Pataky's platform raises her arm, and her center of mass (and the force vector) shifts a few centimeters to compensate for the new position of the arm.

"It's a simple statics equation," says Pataky. "Think back to algebra. The mass of her limb equals the mass of her body multiplied by the change in the location of her body's center of mass divided by the change in location of her limb's center of mass."

Pataky also measured female swimmers and regular male college students. What can he say about their limbs? The females had heavier thighs. The volleyball players had longer, thinner forearms. Female swimmers had more mass in their upper body than the male students and the female volleyball players. "Most likely this means they have more muscle mass in their shoulders and upper backs, but another test is needed to determine the composition of the mass," says Pataky.

The strength of this technique is that it's quick and sensitive enough to detect differences between populations. Also, it's inexpensive. Most biomechanics laboratories already have force plates, and a platform can be constructed easily. So far, Pataky has used his method to measure masses of the forearm and hand, the lower leg and foot, the upper arm, and the thigh.

"If people start using this method, we can start collecting normative data for special populations: children, pregnant women, obese people," says Pataky. And star athletes.

Todd Pataky received a master's degree in kinesiology in May 2001; tcp120@psu.edu. He won first place in the Health and Life Sciences category of the 2001 Graduate Exhibition for his research, "A method for estimating the limb masses of live subjects belonging to special populations." His advisers are Vladimir Zatsiorsky, Ph.D, 267F Recreation Bldg, University Park, PA 16802; 814-863-3772; vxz1@psu.edu; and John Challis, Ph.D., assistant professor of kinesiology, 266 Recreation Bldg.; 863-3675; jhc10@psu.edu.

Last Updated January 01, 2002