On the adaption of biological transport networks affected by complex domains

This paper aims to simulate and analyze scenarios involving obstacles and parasitic organisms during the growth of biological structures. We introduce an innovative model of biological transport networks in complex domains. By manipulating sources and sinks, we simulate two distinct types of domains. One obstructs nutrient transport without absorbing energy. The other one obstructs transport and absorbs energy. Our model adheres to the continuous functional energy dissipation law. Employing a Crank-Nicolson type method ensures second-order time accuracy. The phase field-based discrete system is decoupled, linear, and unconditionally stable, facilitating straightforward implementation of the algorithm. Our scheme maintains stability in addressing the stiffness of the hybrid system. Our research demonstrates that effective mathematical modeling and numerical methods can accurately simulate and analyze the growth of biological transport networks in complex domains.