A procedure for determining parameters of a simplified ligament model

Abstract

A previous mathematical model of ligament force-generation treated their behavior as a population of collagen fibres arranged in parallel. When damage was ignored in this model, an expression for ligament force in terms of the deflection, x, effective stiffness, k, mean collagen slack length, μ, and the standard deviation of slack lengths, σ, was obtained. We present a simple three-step method for determining the three model parameters (k, μ, and σ) from force-deflection data: (1) determine the equation of the line in the linear region of this curve, its slope is k and its x -intercept is -μ; (2) interpolate the force-deflection data when x is -μ to obtain F0; (3) calculate σ with the equation σ=2πF0/k. Results from this method were in good agreement to those obtained from a least-squares procedure on experimental data – all falling within 6%. Therefore, parameters obtained using the proposed method provide a systematic way of reporting ligament parameters, or for obtaining an initial guess for nonlinear least-squares.