Speaker
Description
A key aspect of vascularized tissues is the fact that their properties are heavily influenced by the presence of the vascular tree. On one hand vessels are expanding and contracting due to systemic circulation on the other hand the surrounding matrix reacts with a counter-active (elastic) response. This means that neither the circulation at the capillaries, nor the elastic properties of the matrix can be studied and modeled on their own. Here we present a computational model for the efficient simulation of such tissues. Our model is based on a geometrical multiscale 3D (elastic) -1D (fluid) coupled formulation, handling the effect of the vasculature on the elastic matrix with an immersed method. This allows us to treat fluid inclusions at a lower dimensionality and thus to capture the interaction between the two phases of the material without requiring the discretization of the fluid-solid interface within the computational mesh. In order to study the effect of complex vessel networks, we explore the relationship between the coupled system and parameters that can be estimated at larger scale (macroscale). This goes in the direction of solving inverse problems in the context of tissue imaging, as available medical data usually have a limited resolution, typically at the scale of an effective - macro scale - tissue, and cannot resolve the microscale. We will present a brief mathematical background, as well as key aspects of the coupling and its applications.
