Mathematical and mechanical modeling of stress-strain relationship of pericardium

Abstract

Several mathematical expressions (models) were compared for use in describing the stress-strain (sigma - epsilon) relationship of pericardium. The expression sigma = alpha[ebeta epsilon - 1] was preferred because of its simpler form, theoretical consistency, and "good fit" of experimental data. A method was developed for estimating the precisions of the estimates of the parameters alpha and beta. This approach can have general usefulness in assessing the significance of a change in stress-strain relationship of various soft tissues following different interventions. A mechanical model was formulated for the pericardium which consisted of springs representing the collagen and elastin fibers connected in parallel. It could be simulated by the above equation and could describe the behavior of the pericardium.