Model Based Optimal Inverse Design: Muscle-Epithelial Bilayer Morphing System

Bilayer systems, composed of two materials with different contraction ratios under stimuli, provide a mechanism for morphing from a planar sheet to an out-of-plane configuration. For example, lizard lungs develop from a smooth epithelial surface into a corrugated 3D structure through contractions of surrounding muscle cells. This mechanism can be exploited in design of artificial organoids by printing optogenetically modified muscle cells onto a passive epithelial layer. When stimulated by light, the muscles contract and deform the bilayer sheet into a 3D shape. While previous research has focused on mathematical and computational models of the bilayer morphing, our work addresses the inverse design problem: given a target 3D shape, what is the optimal 2D muscle pattern? By combining autodifferentiable simulation with the adjoint method, we developed an efficient gradient-based algorithm that treats the morphing bilayer model as a constraint and minimizes the difference between the simulated and target shapes. This framework addresses the challenge of computationally expensive simulation-based constrained optimization, thus offering a new approach of designing of artificial organoids that emulate biological morphogenesis.