Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources

Abstract

We present a new method for modeling tissue perfusion on the capillary scale. The microvasculature is represented by a network of one-dimensional vessel segments embedded in the extra-vascular space. Vascular and extra-vascular space exchange fluid over the vessel walls. This exchange is modeled by distributed sources using smooth kernel functions for the extra-vascular domain. It is shown that the proposed method may significantly improve the approximation of the exchange flux, in comparison with existing methods for mixed-dimension embedded problems. Furthermore, the method exhibits better convergence rates of the relevant quantities due to the increased regularity of the extra-vascular pressure solution. Numerical experiments with a vascular network from the rat cortex show that the error in the approximation of the exchange flux for coarse grid resolution may be decreased by a factor of $3$. This may open the way for computing on larger network domains, where a fine grid resolution cannot be achieved in practical simulations due to constraints in computational resources, for example in the context of uncertainty quantification.

References in corpus (2)

• DuMu${}^{\text{x}}$ 3 -- an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling
• Hybrid models for simulating blood flow in microvascular networks

Cited by in corpus (8)

• Modeling and simulation of vascular tumors embedded in evolving capillary networks
• A 1D-0D-3D coupled model for simulating blood flow and transport processes in breast tissue
• 3D-1D coupling on non conforming meshes via three-field optimization based domain decomposition
• Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake
• Projection-based resolved interface mixed-dimension method for embedded tubular network systems
• A new and consistent well model for one-phase flow in anisotropic porous media using a distributed source model
• Modeling, well-posedness and discretization for a class of models for mixed-dimensional problems with high dimensional gap
• 3D-1D modelling of cranial mesh heating induced by low or medium frequency magnetic fields