Real-Time Nonlinear Solid Mechanics Computations for Fast Inverse Material Parameter Optimization in Cardiac Mechanics
Publication: Journal of Engineering Mechanics
Volume 145, Issue 4
Abstract
The aim of this work is to significantly accelerate the process of parameter optimization of cardiac mechanics problems. This is achieved by coupling a reduced-order method, called the proper orthogonal decomposition with interpolation (PODI), with the frequently used Levenberg-Marquardt method (LVM). The PODI method involves a database to generate solution fields of the problem at hand. This database consists of precomputed solution fields such as displacement, strain, and stress fields that are associated with a parametric domain. When coupling PODI with LVM, the parametric domain of the database coincides with the parametric bounds of LVM. For each optimization step, the solutions corresponding to the updated set of parameters and their perturbations can then be obtained by using these data sets for the purpose of interpolation in the low-dimensional space. Two cardiac problems are investigated to compare the PODI-LVM method with a conventional approach where LVM makes use of full-scale simulations to compute the update of the parameters. Here, this is the element-free Galerkin method. In the first example, the diastolic filling of a left-ventricle heart model is considered and in the second one, a biventricle model is studied. In both cases, optimized values of the parameters of the cardiac constitutive equation are found that match the given diastolic pressure-volume curve. The PODI-LVM optimization procedure results in a computation speed-up factor of 900 on a standard desktop computer at high levels of accuracy.
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Acknowledgments
This research has been supported by the National Research Foundation (NRF) of South Africa (Grant Nos. 104839 and 105858). Opinions expressed and conclusions arrived at are those of the author and are not necessarily to be attributed to the NRF.
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Journal of Engineering Mechanics
Volume 145 • Issue 4 • April 2019
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©2019 American Society of Civil Engineers.
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Received: Apr 26, 2018
Accepted: Aug 20, 2018
Published online: Feb 14, 2019
Published in print: Apr 1, 2019
Discussion open until: Jul 14, 2019
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