A1D–0D–3Dcoupled model for simulating blood flow and transport processes in breast tissue

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.

Accelerated simulation methodologies for computational vascular flow modelling

“…A prominent use of SDR models is providing boundary conditions to 3D models that incorporate information from significantly larger portions of the vasculature than it would be feasible to model in 3D [62][63][64][65][66][67][68][69][70]. In this way, SDR models can facilitate multi-scale spatial models that provide well-resolved 3D flow information in local regions of interest while still including the effect of distal or proximal regions.…”

Review of cardiac–coronary interaction and insights from mathematical modeling

“…Hybrid models coupling 3D models with 1D or 0D models can offer a more comprehensive and efficient approach that leverages the strengths of each type of model while mitigating their individual limitations in modeling blood flow (Esmaily Moghadam et al, 2013; Fritz et al, 2022; Pourmodheji et al, 2022; Zambrano et al, 2022, 2022; Figure 2). Hybrid models can span multiple scales in the cardiovascular system and allow investigation of interactions between local and global flow dynamics.…”

Numerical simulation and fast method for the 0D‐1D multi‐scale coupled model and its application in ischemic brain tissue blood flow problems

“…Notably, the geometric multi‐scale coupled model has carved a niche in cardiovascular and cerebrovascular problems. Recently, many scholars have ardently explored the applications of geometric multi‐scale models in biomedical and treatment fields 12–15 . A computational model of the cerebral circulation coupled with the global cardiovascular system was crafted by Liang et al 16 to investigate hemodynamic events tied to carotid artery surgery (CAS).…”

“…Recently, many scholars have ardently explored the applications of geometric multi-scale models in biomedical and treatment fields. [12][13][14][15] A computational model of the cerebral circulation coupled with the global cardiovascular system was crafted by Liang et al 16 to investigate hemodynamic events tied to carotid artery surgery (CAS). Merging the 1D wave propagation models for the blood vessels with the 0D lumped models for the microcirculation, Kroon et al 17 established a computational method for vascular hemodynamics.…”