Abstract
We present a computational multiscale model for the efficient simulation of vascularized tissues, composed of an elastic three-dimensional matrix and a vascular network. The effect of blood vessel pressure on the elastic tissue is surrogated via hyper-singular forcing terms in the elasticity equations, which depend on the fluid pressure. In turn, the blood flow in vessels is treated as a one-dimensional network. Intravascular pressure and velocity are simulated using a high-order finite volume scheme, while the elasticity equations for the tissue are solved using a finite element method. This work addresses the feasibility and the potential of the proposed coupled multiscale model. In particular, we assess whether the multiscale model is able to reproduce the tissue response at the effective scale (of the order of millimeters) while modeling the vasculature at the microscale. We validate the multiscale method against a full scale (three-dimensional) model, where the fluid/tissue interface is fully discretized and treated as a Neumann boundary for the elasticity equation. Next, we present simulation results obtained with the proposed approach in a realistic scenario, demonstrating that the method can robustly and efficiently handle the one-way coupling between complex fluid microstructures and the elastic matrix.
Highlights
The mechanics of vascularized tissues involves processes happening on a wide range of spatial scales, as well as the intrinsic coupling of solid and fluid phases
We present a computational multiscale model for the efficient simulation of vascularized tissues, composed of an elastic three-dimensional matrix and a vascular network
In order to describe the hemodynamics in the vasculature, we introduce the one-dimensional blood pressure functions pcðsÞ : 1⁄20; L ! X & R
Summary
The mechanics of vascularized tissues involves processes happening on a wide range of spatial scales, as well as the intrinsic coupling of solid and fluid phases. This work is motivated by modern medical imaging protocols based on Magnetic Resonance Elastography (MRE), a quantitative imaging technique sensitive to the mechanical properties of living tissues. By combining mechanical excitations at moderate frequencies with phase-contrast MRI, MRE allows to acquire the internal displacement field within a tissue sample. This information, combined with a mechanical model, allows to retrieve, non invasively and in vivo, information about the elastic parameters of the tissue. Due to the limited resolution—typically order of millimeters—MRE allows to reconstruct properties at the effective tissue scale. The models currently used in MRE mostly describe tissues as linear (visco)elastic materials, for applications in the context of the diagnosis and monitoring of diseases such as cancer and fibrosis, that are characterized by different tissue stiffnesses.[11,24,27,31]
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