RESUMEN
Considering the nonlinear hyperelastic or viscoelastic nature of soft tissues has an important effect on modeling results. In medical applications, accounting nonlinearity begets an ill posed problem, due to absence of external force. Myocardium can be considered as a hyperelastic material, and variational approaches are proposed to estimate stiffness matrix, which take into account the linear and nonlinear properties of myocardium. By displacement estimation of some points in the four-dimensional cardiac magnetic resonance imaging series, using a similarity criterion, the elementary deformations are estimated, then using the Moore-Penrose inverse matrix approach, all point deformations are obtained. Using this process, the cardiac wall motion is quantized to mechanically determine local parameters to investigate the cardiac wall functionality. This process was implemented and tested over 10 healthy and 20 patients with myocardial infarction. In all patients, the process was able to precisely determine the affected region. The proposed approach was also compared with linear one and the results demonstrated its superiority respect to the linear model.