AN INVERSE APPROACH TO DETERMINING MYOCARDIAL MATERIAL PROPERTIES

Passive myocardial material properties have been measured previously b y subjecting test samples of myocardium to in vitro load-deformation a nalysis or, in the intact heart, by pressure-volume relationships. A n ew method for determining passive material properties, described in th is paper, couples a p-version finite element model of the heart, a non linear optimization algorithm and a dense set of transmural measured s trains that could be obtained in the intact heart by magnetic resonanc e imaging (MRI) radiofrequency tissue tagging. Unknown material parame ters for a nonlinear, nonhomogeneous material law are determined by so lving an inverse boundary value problem. An objective function relatin g the least-squares difference of model-predicted and measured strains is minimized with respect to the unknown material parameters using a novel optimization algorithm that utilizes forward finite element solu tions to calculate derivatives of model-predicted strains with respect to the material parameters. Test cases incorporating several salient features of the inverse material identification problem for the heart are formulated to test the performance of the inverse algorithm in typ ical experimental conditions. Known true material parameters can be de termined to within a small tolerance and random noise is shown not to affect the stability of the inverse solution appreciably. On the basis of these validation experiments, we conclude that the inverse materia l identification problem for the heart can be extended to solve for un known material parameters that describe in vivo myocardial material be havior.