title: Adjoint multi-start-based estimation of cardiac hyperelastic material parameters using shear data.
abstract: Cardiac muscle tissue during relaxation is commonly modeled as a hyperelastic material with strongly nonlinear and anisotropic stress response. Adapting the behavior of such a model to experimental or patient data gives rise to a parameter estimation problem which involves a significant number of parameters. Gradient-based optimization algorithms provide a way to solve such nonlinear parameter estimation problems with relatively few iterations, but require the gradient of the objective functional with respect to the model parameters. This gradient has traditionally been obtained using finite differences, the calculation of which scales linearly with the number of model parameters, and introduces a differencing error. By using an automatically derived adjoint equation, we are able to calculate this gradient more efficiently, and with minimal implementation effort. We test this adjoint framework on a least squares fitting problem involving data from simple shear tests on cardiac tissue samples. A second challenge which arises in gradient-based optimization is the dependency of the algorithm on a suitable initial guess. We show how a multi-start procedure can alleviate this dependency. Finally, we provide estimates for the material parameters of the Holzapfel and Ogden strain energy law using finite element models together with experimental shear data.
authors.affiliation: Simula Research Laboratory, P.O. Box 134, 1325, Lysaker, Norway. gabrib@simula.no.|Department of Informatics, University of Oslo, Blindern, P.O. Box 1080, 0316, Oslo, Norway. gabrib@simula.no.
authors.forename: Gabriel
authors.identifier: 0000-0002-6794-9611
authors.initials: G
authors.lastname: Balaban
authors.affiliation: Simula Research Laboratory, P.O. Box 134, 1325, Lysaker, Norway.
authors.forename: Martin S
authors.initials: MS
authors.lastname: Alnæs
authors.affiliation: Simula Research Laboratory, P.O. Box 134, 1325, Lysaker, Norway.|Department of Informatics, University of Oslo, Blindern, P.O. Box 1080, 0316, Oslo, Norway.
authors.forename: Joakim
authors.initials: J
authors.lastname: Sundnes
authors.affiliation: Simula Research Laboratory, P.O. Box 134, 1325, Lysaker, Norway.|Department of Mathematics, University of Oslo, Blindern, P.O. Box 1053, 0316, Oslo, Norway.
authors.forename: Marie E
authors.initials: ME
authors.lastname: Rognes
mesh_terms: D000465:Algorithms; D004548:Elasticity; D020342:Finite Element Analysis; D006321:Heart / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D013314:Stress, Mechanical
keywords: Adjoint equation; Cardiac mechanics; Hyperelasticity; Multi-start optimization; Parameter estimation