3D-1D coupled approach for vascularized tissues
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In the context of tissue imaging available medical data (such as those obtained via Magnetic Resonance Elastography) have a limited resolution, typically at the scale of an effective - macro scale - tissue; however, the parameter estimation heavily depends on the included vasculature and on the interaction between vessels and tissue at the micro scale. A mechanical model for vascularized tissue allows the recovery of effective tissue properties through the resolution of inverse problems. In order to tackle the micro scale problem we proceed in a two-fold manner: on one hand the vascular tree inside the elastic tissue is treated in the framework of reduced Lagrangian multipliers, exploiting a non-matching immersed boundary formulation, thus reducing computational complexity significantly. On the other hand the fluid vessel interaction is modeled through pressure and displacement exchange in a two-way coupling between a 3D model solid model and a 1D model for the flow inside the vessels.
