A Numerical Method for Estimating Tendon Slack Length

Abstract

Forces generated by muscle are transferred to bone via tendon. Since muscle force cannot be measured directly, computer modeling is a useful tool to enhance our understanding of normal and pathological movement. Hill-type muscle models have been used to estimate force based on information about a muscle’s architecture, activation and kinematics (Delp et al., 1995; Manal et al., 2002). Architectural parameters include optimal fiber length (lom), tendon slack length (lst), pennation angle (α), and maximum isometric force (Fmax). In addition, musculotendon length (lmt) and activation (a) are required inputs when estimating isometric muscle force (Equation I). Fm=f(lmt,lom,lst,Fmax,α,a)(1) Musculotendon length can be determined from MR images (Arnold et al., 2000), and activation recorded from EMGs (Manal, et al., 2002). Optimal fiber length and pennation angle can be measured experimentally (Murray, 2002), while Fmax can be estimated from the muscle’s physiologic cross-sectional area. Tendon slack length however cannot be measured readily, and therefore few estimates of lst can be found in the literature. In this paper we present a numerical method for estimating tendon slack from subject specific muscle parameters and musculotendon lengths. An advantage of this method is that it yields subject specific estimates of tendon slack length.