Modeling Viscoelastic Wall Properties of Ovine Arteries

INTRODUCTION Generation of a complete map of arterial wall mechanical properties can improve treatment of cardiovascular diseases via contributions to design of patient specific vascular substitutes used to alleviate athero-sclerosis and stenoses, which are predominant in arterial pathways (i.e., abdominal aorta, carotids, or femoral arteries). Clinically useful estimation of arterial properties from patient data requires both efficient algorithms and models that are both complex enough to capture clinically important properties and simple enough to allow rapid computation. In this study, we used mechanical models accounting for both elastic and viscoelastic wall deformation to analyze how vessel properties and associated model parameters vary with artery type. It is known that for the aorta wall, deformation is dominated by nonlinear elastic dynamics, while for the smaller vessels (e.g. the carotid artery) deformation is dominated by viscoelastic responses. The latter is correlated with composition of the vessels; the aorta contains significantly less smooth muscle cells (~40%) than the carotid artery (~60%), and has significantly more elastin (see Fig 1). To predict vessel properties we used a two-parameter elastic model , a four-parameter Kelvin viscoelastic model, and a seven-parameter extended viscoelastic model that relate blood pressure and vessel area. We validated these models using experimental data from in-vitro measurements of vessel diameter and arterial blood pressure. To understand how the elastic and viscoelastic properties (represented by the model parameters) vary across vessel sites we compared two approaches: an ordinary least squares (OLS) approach that used pressure as an input to predict mechanical properties minimizing the OLS error between computed and measured values of vessel area, and a total least squares (TLS) method that used an optimal control formulation minimizing the TLS error including both area and pressure. Finally, to analyze results we employed standard statistical techniques.