An Optimization-Based 3D-1D Coupling Approach for the Simulation of the Exchanges Between Tissues and Thin Embedded Tubular Structures
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This talk aims to propose the use of an optimization-based 3D-1D coupling strategy to model the exchanges between a tissue and thin tubular structures in two different biomedical applications. A discontinuous 3D-1D coupling is proposed to simulate the fluid and chemical exchanges between a growing capillary network and the surrounding tissue. On the other hand, a continuous 3D-1D coupling is used to simulate the heating of the tissues around a metallic cranial grid as the consequence of the exposure to a magnetic field. Despite the difference between the two applications, the optimization-based 3D-1D coupling approach appears to be a valid strategy for tackling both of them: the 3D-1D model reduction cuts the computational cost of simulations, whereas the optimization-based approach makes the method robust to geometrical complexities and provides the value of interface variables directly, without any need of post-processing.