Identification of nonlinear hyperelastic material parameters for healthy myocardial tissue via an inverse method based on modelling the passive filling stage of the cardiac cycle

摘要

In order to fully comprehend the function of biological tissue in the context of the caninernleft ventricle, it is required that proper material parameters are identified that govern the materials behaviourrnaccording to a particular set of constitutive laws. For the purposes of this research, the passive filling stage of therncardiac cycle is modelled with a non linear hyperelastic orthotropic material law (Usyk, Mazhari, & McCullochrn2000). Inherent to this constitutive law are eight material parameters namely A, A_(compr) and b_(ij) , where I, j ∈ (1,rn2, 3). In order to calibrate the material parameters of this model to experimental data, or any patient specificrnapplication for that matter, a nonlinear optimization algorithm in the form of the Bounded Levenberg-Marquardtrnalgorithm, with the additional option of a line search is implemented in the in-house modelling software SESKA.rnIn order to test the algorithm implementation, pseudo experimental data are generated with a set of assumed tornbe true parameters for a canine ellipsoidal left ventricle geometry. Consequently, the implemented algorithmsrnability to converge towards this true set of parameters from a number of different initial starting points is tested.rnFor the case of the conventional Bounded Levenberg-Marquardt algorithm implementation, material parametersrnconverge quickly towards the true values provided that the initial guess for parameters is close enough to therntrue set. However, for initial parameter guesses that are far from the true values, parameters may converge to arnridge in the cost function, which does not represent a minimum in the cost function surface. Furthermore, whenrnthe conventional Levenberg-Marquardt algorithm is combined with a line search, parameters are more likelyrnto converge towards a local minimum within a well defined range, regardless of whether the initial parameterrnguess is good or not. However, it should be noted that the line search does not assure convergence of materialrnparameters to a global minimum in the cost function, it just prevented convergence of parameters towards ridgesrnin the cost function.