The TCL has recently developed a computational model of the biphasic poroviscoelasticity, a viscoelastic model of articular cartilage which accounts for both the fluid flow-dependant viscoelastic and fluid flow-independent viscoelastic mechanisms of the tissue. The fluid flow-dependent viscoelastic mechanism of articular cartilage is known for its famous pseudonym, 'Biphasic Theory', which is based on an interfacial energy loss caused by a frictional interaction at the interface between the two distinctive constituent phases, i.e., the mobile interstitial fluid phase and the porous extracellular matrix of the tissue. On the other hand, the fluid flow-independent viscoelastic mechanism of articular cartilage is based on an internal energy loss within each phase, independent of the apparent fluid flow through the porous matrix. This is similar to the viscoelastic mechanism of polymeric materials. We have found that this new computational model can accurately predict mechanical behaviors of articular cartilage in many cases, including creep and stress relaxation phenomena of articular cartilage under confined compression, unconfined compression, and indentation.

This new computational model of articular cartilage is expected to become a useful tool in predicting the mechanical behaviors of normal and pathological cartilage tissues during daily activities, such as walking, running, climbing stairs, etc. The model will also provide us with an engineering framework to study the relationship between the mechanical force and the metabolic response of articular cartilage in the joints.

Abstract From Selected Publications

Finite Element Formulation Of Biphasic Poroviscoelastic Model For Articular Cartilage
J. Biomech. Eng., 120:195-201, 1998

The purpose of the present study was to develop a computationally efficient finite element model that could be useful for parametric analysis of the biphasic poroviscoelastic (BPVE) behavior of articular cartilage under various loading conditions. The articular cartilage was modeled as the BPVE mixture of a porous, linear viscoelastic, and incompressible solid and an inviscid and incompressible fluid. A finite element (FE) formulation of the BPVE model was developed using two different algorithms, and continuous and discrete spectrum relaxation functions for the viscoelasticity of the solid matrix. These algorithms were applied to the creep and stress relaxation responses to the confined compression of articular cartilage, and a comparison of their performances was made. It was found that the discrete spectrum algorithm significantly saved CPU time and memory, as compared to the continuous spectrum algorithm. The consistency analysis for the present FE formulation was performed in comparison with the IMSL, a commercially available numerical software package. It was found that the present FE formulation yielded consistent results in predicting model behavior, whereas the IMSL subroutine produced inconsistent results in the velocity field, and thereby in the strain calculation.

Biphasic Poroviscoelastic Behavior Of Hydrated Biological Soft Tissue
J. Appl. Mech. 66:528-535, 1999

Hydrated biological soft tissue consists of a porous extracellular matrix (ECM) and an interstitial fluid. The poroelastic theory, which was originally developed for soil mechanics, has been widely used for mathematical modeling of such hydrated biological tissue. This theory assumes that the ECM is incompressible and purely elastic, and that the interstitial fluid is incompressible and inviscid. The overall viscoelasticity of the tissue is expressed as a result of the frictional interaction between the elastic porous matrix and the interstitial fluid. The poroelastic theory, also known as the biphasic theory in the biomechanics field, has served well over the past twenty years as an excellent modeling tool for the interstitial fluid flow-dependent viscoelastic response of hydrated soft tissue. It has been demonstrated that hydrated soft tissue also possesses a significant intrinsic viscoelasticity, independent of the interstitial fluid flow. The biphasic poroviscoelastic (BPVE) theory, which was first introduced by Mak (1986a and 1986b), incorporates a viscoelastic relaxation function into the effective solid stress of the poroelastic theory thus accounting for both intrinsic fluid flow-independent and fluid flow-dependent viscoelasticity. The objective of the present study is to investigate the biphasic poroviscoelastic characteristics of hydrated soft tissue, with an emphasis on the relative contribution of fluid flow-dependent and fluid flow-independent viscoelasticity to the overall viscoelastic behavior of soft tissues.

See our Publications for the further details about our projects on biomechanics of articular cartilage.

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