Past Event: Babuška Forum

3D Soft Tissue Simulations Using a Neural Network PDE Approach

Michael Sacks, Professor, Oden Institute, UT Austin

Abstract

The ability to fully characterize and simulate the three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their function in health and disease. The complex 3D hierarchical structure of soft tissues results in their highly anisotropic mechanical behaviors, and it particular the spatial variations in fiber structure gives rise to structural and mechanical heterogeneity. To addresses issues in a full 3D context, we have developed a novel numerical-experimental approach to determine the optimal model form and parameter estimation for continuum constitutive models of soft tissues, as applied to the myocardium. This approach utilizes optimal experimental design of the full 3D kinematic (triaxial) experiments coupled to an inverse model that incorporated local fibrous structure to perform robust parameter estimation. However, in-silico implementation of such complex 3D continuum soft tissue constitutive models to obtain the responses of varying boundary conditions and fibrous structures requires the solution of the associated hyper-elasticity problem, which remains impractical in translational clinical time frames. To alleviate the associated substantial computational costs at the time of simulation, we have developed a neural network-based method that can simulate the 3D mechanical behavior of soft tissues. A physics-informed approach was employed to train the neural network to give physically correct solution by minimizing the potential energy without any labelled training datasets. The extensibility of the neural network for problems with fiber structures and loading path conditions is also discussed. Bio Michael Sacks is professor of biomedical engineering and holder of the W. A. "Tex" Moncrief, Jr. Endowment in Simulation-Based Engineering and Sciences Chair No. 1. He is also director of the Oden Institute's Willerson Center for Cardiovascular Modeling and Simulation. Sacks formerly held the John A. Swanson Chair in the Department of Bioengineering at the University of Pittsburgh. He earned his B.S. and M.S. in engineering mechanics from Michigan State University, and his Ph.D. in biomedical engineering (biomechanics) from The University of Texas Southwestern Medical Center at Dallas. He is a world authority on cardiovascular biomechanics, with a focus on the quantification and simulation of the structure-mechanical properties of native and engineered cardiovascular soft tissues. He is a leading authority on the mechanical behavior and function of heart valves, including the development of the first constitutive models for these tissues using a structural approach. He is also active in the biomechanics of engineered tissues, and in understanding the in-vitro and in-vivo remodeling processes from a functional biomechanical perspective. His research includes multiscale studies of cell/tissue/organ mechanical interactions in heart valves and he is particularly interested in determining the local stress environment for heart valve interstitial cells. His recent research has included developing novel constitutive models of right ventricular myocardium that allow for the individual contributions of the myocyte and connective tissue networks. (The Babuška Forum series was started by Professor Ivo Babuška several years ago to expose students to interesting and curious topics relevant to computational engineering and science with technical content at the graduate student level (i.e. the focus of the lectures is on main ideas with some technical content). Seminar credit is given to those students who attend.)