A Poroelastic Model That Predicts Some Phenomenological Responses of Ligaments and Tendons

Abstract

Experimental evidence suggests that the tensile behavior of tendons and ligaments is in part a function of tissue hydration. The models currently available do not offer a means by which the hydration effects might be explicitly explored. To study these effects, a finite element model of a collagen sub-fascicle, a substructure of tendon and ligament, was formulated. The model was microstructurally based, and simulated oriented collagen fibrils with elastic-orthotropic continuum elements. Poroelastic elements were used to model the interfibrillar matrix. The collagen fiber morphology reflected in the model interacted with the interfibrillar matrix to produce behaviors similar to those seen in tendon and ligament during tensile, cyclic, and relaxation experiments conducted by others. Various states of hydration and permeability were parametrically investigated, demonstrating their influence on the tensile response of the model.

Permeability of human medial collateral ligament in compression transverse to the collagen fiber direction

“…These include viscoelasticity of the collagen fibers (Rubin and Bodner, 2002), the extracellular matrix (Weiss et al, 2002), collagen fibril crosslinking (Bailey et al, 1974;Puxkandl et al, 2002;Redaelli et al, 2003) and fluid content (Chimich et al, 1992) and fluid movement within and in/out of the tissue during loading (Atkinson et al, 1997;Butler et al, 1997). However, most proposals have been based on conjecture and there is little experimental data available to support or refute the proposed mechanisms.…”

“…The flow of water through a tissue in response to mechanical or chemical loading is governed by the apparent permeability, sometimes referred to as the hydraulic permeability (Holmes, 1985;Holmes and Mow, 1990;Mansour and Mow, 1976). In the case of ligaments, it has been suggested that the tissue may exhibit anisotropic permeability due to the highly aligned collagen fiber structure (Atkinson et al, 1997;Butler et al, 1997).…”

“…Experimental and modeling studies have suggested that the movement of water within and in/out of ligament may partially or entirely explain the viscoelastic response of ligaments (Atkinson et al, 1997;Butler et al, 1997;Chen et al, 1998;Chimich et al, 1992;Hannafin and Arnoczky, 1994). Exudation of water from ligament occurs under cyclic loading (Hannafin and Arnoczky, 1994).…”

“…Previous computational simulations of ligaments have used ranges of permeability that were motivated primarily by the range of reported values for articular cartilage (Atkinson et al, 1997;Butler et al, 1997). The direct permeation experiment provides a means to determine tissue permeability directly (Holmes, 1985;Holmes and Mow, 1990;Mansour and Mow, 1976).…”

“…Here, J ¼ detðFÞ is the volume ratio and F is the deformation gradient (Spencer, 1980) (J ¼ 1 À for the permeation experiment), f 0 is the initial volume fraction of the solid phase, taken to be 0.3 for ligament (Atkinson et al, 1997;Butler et al, 1997;Chimich et al, 1992;Hey et al, 1990), f f ¼ 1 À f 0 =J is the current volume fraction of the fluid phase and f s ¼ f 0 =J is the current volume fraction of the solid phase. k 0 represents the intrinsic permeability in the absence of strain.…”