Myocardial material parameter estimation: the influences of constitutive relation and experiental protocol

Abstract

The study of ventricular mechanics - analysing the distribution of strain and stress in myocardium throughout the cardiac cycle - is critically dependent on the accuracy of the constitutive law chosen to represent the highly nonlinear and orthotropic properties of passive cardiac muscle. A recent study has examined four of these laws and has compared them [1]. This study, however, had been restricted to the assumption of a homogeneous simple shear deformation. Here we relax the assumption of a homogeneous deformation and study a full 3D finite element model. Furthermore, we enriched the scope of experimental protocols by including uniaxial extension along all three microstructural axes. A tri-linear finite element model was built. Displacement boundary conditions of the corresponding deformation modes were specified. Firstly, we investigated the effects of incorporating the non-homogeneous deformation and compared the parameter fits to those obtained from the homogeneous model. Secondly, we investigated the effects of the various experimental protocols as the basis for the inverse material parameter investigation. Here we compared the results of using a) simple shear, b) combinations of simple shear and uniaxial data. We were able to show that for the case of including only simple shear data the incorporation of the non-homogeneous deformation stayed very closely to the results of the homogeneous model (difference of-15%). When comparing the various experimental protocols within the FE environment we showed that when incorporating as much data as possible, we obtained the least variances and most importantly the inclusion of uniaxial extension data aletered the parameters associated with axial deformation considerably. When comparing the various laws for for a fixed experimental protocol, we showed that the exponential Fung-type performed best with respect to the Akaike information criteria which suggests that this law is favourable for FE studies.