State variables for modelling physical aspects of articular cartilage

Abstract

Deformation in soft biological connective tissue is intimately coupled to interstitial fluid movement, tissue solute concentration, and electrical fields. The role of deformation and of the associated electrical and chemical gradients in connective tissue physiology is currently unknown, and is of major interest in the study of growth, healing, and remodelling in the tissue. A quantitative study aimed at assessing relevant physiologic effects in connective tissue awaits accurate physical analysis. This paper reviews the available poroelasticity formulations with specific emphasis on establishing physically relevant continuum variables and on methods for including coupling between electrical or chemical gradients and deformations, then proposes a new set of state variables useful for engineering analysis of the tissue. Since solid and fluid components intermingle on a molecular scale, phase boundaries do not exist and thus a porosity cannot be defined. Further, in a material which includes fixed charge groups, which must be balanced by mobile species to maintain electroneutrality, the physics inside the tissue are not amenable to standard analysis. Relevant continuum state variables can be defined relative to a reference medium, however. The chemical, electrical, and mass transfer potentials of a differential element are defined by the potentials of a medium into which an excised differential element can be immersed at constant strain without transferring energy. Given this new definition of state variables, an energy differential is written, and a new incremental equation of state is derived based on a definition of coenergy.