  Human blood flow is a multi-scale problem: in first approximation, blood is a
dense suspension of plasma and deformable red cells. Physiological vessel
diameters range from about one to thousands of cell radii. Current
computational models either involve a homogeneous fluid and cannot track
particulate effects or describe a relatively small number of cells with high
resolution, but are incapable to reach relevant time and length scales. Our
approach is to simplify much further than existing particulate models. We
combine well established methods from other areas of physics in order to find
the essential ingredients for a minimalist description that still recovers
hemorheology. These ingredients are a lattice Boltzmann method describing rigid
particle suspensions to account for hydrodynamic long range interactions
and---in order to describe the more complex short-range behavior of
cells---anisotropic model potentials known from molecular dynamics simulations.
Paying detailedness, we achieve an efficient and scalable implementation which
is crucial for our ultimate goal: establishing a link between the collective
behavior of millions of cells and the macroscopic properties of blood in
realistic flow situations. In this paper we present our model and demonstrate
its applicability to conditions typical for the microvasculature.
