A 1D–0D–3D coupled model for simulating blood flow and transport processes in breast tissue. (21st May 2022)

• Record Type: Journal Article
• Authors: Fritz, Marvin; Köppl, Tobias; Oden, John Tinsley; Wagner, Andreas; Wohlmuth, Barbara; Wu, Chengyue
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 38:Number 7(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-05-21
• Subjects: discontinuous Galerkin method -- mathematical physiology -- mixed‐dimensional model -- multiscale blood flow models -- porous media -- transport processes; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.3612
• Languages: English
• ISSNs: 2040-7939

Abstract

Abstract: In this work, we present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These processes are considered, to start from the aortic inlet to the capillaries and tissue of the breast. Large variations in biophysical properties and flow conditions exist in this system necessitating the use of different flow models for different geometries and flow regimes. In total, we consider four different model types. First, a system of 1D nonlinear hyperbolic partial differential equations (PDEs) is considered to simulate blood flow in larger arteries with highly elastic vessel walls. Second, we assign 1D linearized hyperbolic PDEs to model the smaller arteries with stiffer vessel walls. The third model type consists of ODE systems (0D models). It is used to model the arterioles and peripheral circulation. Finally, homogenized 3D porous media models are considered to simulate flow and transport in capillaries and tissue within the breast volume. Sink terms are used to account for the influence of the venous and lymphatic systems. Combining the four model types, we obtain two different 1D–0D–3D coupled models for simulating blood flow and transport processes: The first model results in a fully coupled 1D–0D–3D model covering the complete path from the aorta to the breast combining a generic arterial network with a patient specific breast network and geometry. The second model is a reduced one based on the separation of the generic and patient specific parts. The information from a calibrated fully coupled model is used as inflow condition for the patient specific sub‐model allowing a significant computational cost reduction. Several numerical experiments are conducted to calibrate the generic model parameters and to demonstrate realistic flow simulations compared to existing data on blood flow in the human breast and vascular system. Moreover, we use two different breast vasculature and tissue data sets to illustrate the robustness of our reduced sub‐model approach. Abstract : We present mixed dimensional models for simulating blood flow and transport processes in breast tissue and the vascular tree supplying it. These models consist of hyperbolic 1D equations, 0D models and 3D porous media equations. A computationally expensive fully coupled model is introduced and compared to a reduced sub‐model, which only simulates flow and transport on the patient specific parts. Results for two different breast vasculature and tissue data sets illustrate the robustness of our reduced sub‐model approach.