  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. 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 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 1D-0D-3D model covers the whole path from the aorta to the
breast, while the second model is a sub-model obtained by restriction to breast
vasculature and tissue making possible a significant reduction in computational
cost. Several numerical experiments are conducted that demonstrate realistic
flow simulations compared to existing data on blood flow in human breast and
vascular system.
