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 F; (3) calculate σ with the equation σ=2πF/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.

Identification of Young’s modulus and equivalent spring constraint boundary conditions of the soft tissue with locally observed displacements for endoscopic liver surgery

“…Phillips et al presented a finite element model of pelvis which was supported by ligamentous boundary conditions using spring elements distributed over realistic attachment sites (Phillips et al 2007). Barrett et al discovered a procedure of determing parameters of a simplified ligament model (Barrett and Callaghan 2018). In our previous work (Xu and Lei 2020), a novel method was proposed to identify unknown Young's modulus and equivalent spring constraint boundary conditions.…”

“…In the methods based on biomechanical model, some methods (Gambarotta et al 2005;Wang et al 2011;Lago et al 2015;Sim on-Allu e et al 2017) mainly focused on solving unknown elastic parameters while ignoring unknown boundary conditions, the others (Peterlik et al 2014;Plantef eve et al 2014;Ozkan and Goksel 2018) required global displacements of soft tissue obtained from CT/MR or ultrasound images to identify unknown boundary conditions and elastic parameters. Moreover, the mechanical properties of the boundary, such as ligaments which would affect the accuracy of the biomechanical model (Phillips et al 2007;Kawauchi et al 2008;Bosman et al 2014;Barrett and Callaghan 2018), were not modeled in these studies (Morita et al 2017(Morita et al , 2018Hajhashemkhani et al 2018) for unknown boundary conditions.…”