Gradient Based Optimization for Muscle-Epithelial Bilayer Morphing System

Optogenetically modified muscles, contracting in response to external lasers, provide us a way to mimic the morphogenesis of lizard lung. When 3D printing the muscle layer on top of an inactive epithelial layer, the in-plane contraction will cause the bilayer to have 3D out-of-plane deformation. Given the 2D print pattern of the muscle, we simulate this process using Finite Element Analysis (FEM). Beyond the forward simulation, we are interested in solving the inverse problem: Given a desired 3D shape, what is the optimal 2D pattern for the printed muscle? Due to the strong nonlinearity involved in geometry and energy function, we follow the gradient based topological optimization roadmap to solve the inverse problem. However, finding the gradient for a nonlinear system with hundreds of thousands of degrees of freedom and mechanical instability is not trivial. We explore both variational calculus based and auto-differentiation based approaches. This research will set the foundation for the optimal design problem that involves large scale nonlinear deformation and mechanical instability. In addition, understanding the inverse problem for the muscle-epithelial bilayer morphing system is useful for designing artificial organoids that mimic biological morphogenesis.