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Describing Passive Moments with a Nonlinear Viscoelastic Model

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Kofi Amankwah, Robert F. Kirsch, Ronald J. Triolo

Case Western Reserve University
Cleveland, OH, USA

The resistance imposed by passive joint properties can impede the functionality of Functional Electrical Stimulation (FES) systems during limb movements. However, at fixed postural positions, the resistance provided by passive properties could aid postural stability by providing disturbance rejection. Consequently, to better understand the role of passive joint properties, a musculoskeletal model of the lower extremity joints is being developed which will include the passive joint properties of the ankle, knee and hip. The objective of this study was to develop a mathematical model that could be used to describe the elastic and viscous elements of passive joint properties. A model based upon the Kelvin model for viscoelasticity was implemented to accomplish this goal because it had the ability to describe the nonlinear elastic element as well as the viscous element of the passive moment with one equation. To confirm that the model could be fitted to a set of data, the passive moments at the knee joint of an able-bodied male subject were measured using isokinetic testing at three different velocities. To account for the effects of biarticulate muscles, measurements were also performed with the hip joint and ankle joint in different fixed positions. The results from these measurements showed shapes and trends similar to data found in the literature. Also, it was shown that the parameters for this nonlinear viscoelastic model could be estimated from the data. Therefore, these results indicate that one equation can be used to describe the elastic as well as viscous elements of the passive moments developed at a joint. Further testing of spinal cord injured and able-bodied individuals will be performed to estimate model parameters for the remaining lower extremity joints.

Last Updated Date: 11/30/2012
Last Reviewed Date: 11/30/2012
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