Adjoint Multi-Start Based Estimation of Cardiac Hyperelastic Material Parameters using Shear Data

TL;DR

This paper introduces an adjoint-based gradient computation method combined with a multi-start optimization approach to efficiently estimate hyperelastic material parameters of cardiac tissue from shear data, improving accuracy and robustness.

Contribution

It presents a novel adjoint equation framework for efficient gradient calculation and integrates a multi-start procedure to enhance parameter estimation robustness.

Findings

Efficient gradient computation reduces optimization time.

Multi-start approach mitigates initial guess dependency.

Successful estimation of cardiac tissue parameters using experimental shear data.

Abstract

Cardiac muscle tissue during relaxation is commonly modelled 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.