Use Case: AI-Based Surrogate Muscle Models for Cardiac Cycle Simulations of the Left Ventricle

In this chapter, we explore the development of surrogate models for left ventricle (LV) biomechanical simulations, focusing on the Huxley-type muscle model. The Huxley model, known for its ability to simulate nonuniform and unstable contractions, has been hindered by its substantial computational requirements. To overcome this limitation, we present two distinct yet complementary approaches: data-driven and physics-informed surrogate models. In the data-driven approach, we harnessed the power of deep neural networks to construct a surrogate model that emulates the behavior of the original Huxley model. Training data was gathered from numerical simulations, incorporating time series data to capture the history-dependent nature of muscle models. Recurrent and convolutional neural networks were employed to predict stress and instantaneous stiffness, while the primary challenges lay in achieving sufficient accuracy for multiscale numerical simulations. We detail the construction and training of the surrogate model and its seamless integration into a finite element solver. Comparative experiments between the original Huxley model and the surrogate counterpart demonstrate the surrogate model’s potential to replace the original, offering significant speedup benefits. Furthermore, we illustrate the surrogate model’s utility in a larger-scale context by simulating a full cardiac cycle. The method of characteristics is typically employed to solve Huxley’s muscle equation, characterizing the distribution of connected myosin heads to actin-binding sites. This allows for the determination of the generated forces and the stiffness of muscle fibers, which are used at the macro-level of simulations during finite element analysis. In an alternate physics-informed approach, we adopted a novel strategy to approximate the solution of Huxley’s muscle contraction equation. This approximation enabled us to predict the probabilities of cross-bridge formation. Leveraging these predicted probabilities, we calculated stresses and stress derivatives during finite element analysis, providing an innovative means of understanding muscle behavior.