Phenomenological evolution equations for heat-induced shrinkage of a collagenous tissue

Optimization of clinical heat treatments for various pathologies requires accurate numerical modeling of the heat transfer, evolution of thermal damage, and associated changes in the material properties of the tissues. This paper presents two phenomenological equations that quantify time-dependent thermal damage in a uniaxial collagenous tissue. Specifically, an empirical rule-of-mixtures model is shown to describe well heat-induced axial shrinkage (a measure of underlying denaturation) in chordae tendineae which results from a spectrum of thermomechanical loading histories. Likewise an exponential decay model is shown to describe well the partial recovery (e.g., renaturation) of chordae when it is returned to body temperature following heating. Together these models provide the first quantitative descriptors of the evolution of heat-induced damage and subsequent recovery in collagen. Such descriptors are fundamental to numerical analyses of many heat treatments because of the prevalence of collagen in many tissues and organs.