Multiscale Coupling of One-dimensional Vascular Models and Elastic Tissues

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.

Assimilation of magnetic resonance elastography data in an in silico brain model

“…The validation for the available in vivo data is planned for a follow-up work. However, further improvements of the proposed data assimilation algorithm that will be addressed in future research efforts include the use of a nonlinear tissue biomechanics (e.g., viscoelasticity), anisotropic constitutive models, or by enhancing the modeling through multiscale formulations (e.g., [52,53]). Also, other challenging extensions of the presented research concerns the possibility of tackle the reconstruction of the ICP gradient, instead of the whole pressure field.…”

Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains

“…With this work, we aim at shedding light on the common mathematical framework that embraces many recent works involving the applications mentioned above. LM formulations for Dirichlet-Neumann type interface conditions for these problems were recently proposed [1,18,19]. In these works, a three dimensional bulk problem for mechanical deformations is coupled to a one dimensional model for the mechanical behavior of fibers and vessels, respectively.…”

Special Issue of the VPH2020 Conference: “Virtual Physiological Human: When Models, Methods and Experiments Meet the Clinic”

“…Modeling vascularized tissues presents specific challenges as vessel networks essentially represent connected segments within a 3D block of tissue. Multiscale model strategies are derived to account for the effect of blood flow pressure on the surrounding elastic tissue 7 or to investigate oxygen transport. 12 In order for in silico medicine to become a reality, the methods developed to solve the model equations need to be efficient.…”