A fiber matrix model for interstitial fluid flow and permeability in ligaments and tendons\thanks Partial results were presented in the 1993 Summer Bioengineering Conference,Breckenridge,CO,June 17,1993,and in the 40th Annual Meeting of the Orthopaedic Research Society,New Orleans,LA,February 23,1994.

Abstract

Collagen fibrils in ligaments and tendons are highly organized into parallel arrays which influence interstitial fluid transport. Finite element (FE) models were developed analogous to the fibrillar arrays in ligaments and tendons to investigate interstitial fluid flow and tissue permeability as a function of interfibrillar spacing and fluid properties. Collagen fibrils were assumed to be a periodic square array of impermeable cylinders. A two‐dimensional FE model was used to study transverse fluid flow and a three‐dimensional model was used to study flow parallel to the collagen fibrils. Parametric FE analysis provided data to formulate empirical expressions for permeability ( $\kappa$ ) as a function of porosity ( $\phi$ ). Results show that longitudinal permeability ( $\kappa=1.1\cdot 10^{-15} \phi^{2.5}[1-\phi]^{-0.333}$ ) can be up to 50 times higher than transverse permeability ( $\kappa=1.2\cdot 10^{-15} \phi^{0.5}[\phi-\phi_{\min}]^{2.5}$ ) in a compact array. Maximum fluid shear stresses occur at the narrowest zones of adjacent fibrils (1.21 Pa or 12.1 dyn/cm $^{2}$ at 10 $\mu$ m/s of average transverse influx). If interstitial fluid is highly non‐Newtonian, the permeability should be considered as flow (shear)‐dependent. The computational results suggest that tissue permeability in ligaments and tendons is highly anisotropic, porosity‐dependent, and can be estimated by analytic expressions.