A filtration model and parallel computing of the blood flow characteristics in the circulatory system in case of an occluding circular clot

The authors have mathematically described the blood flow in the circulatory system based on the general filtration equations at the presence of an occluding circular porous clot located on the vessel wall, taking into account clot destruction under the action of hydrodynamic forces. The change in the internal forces occurring in the clot material leads to forming an inhomogeneous permeability distribution, which is a function of spatial coordinates and time. Under the assumption of a symmetric toroidal shape of the thrombus, the paper considers a flat two-dimensional problem in the cross section of the vessel and a clot. The authors have developed finite-difference schemes and iterative algorithms using parallel com-puting technologies to solve corresponding two-dimensional problem in a blood vessel and a blood clot with heterogeneous permeability. They have also carried out parallelization at the visualization of the hydrodynamic characteristics of the flows. The software package with the implemented numerical and algorithmical models enables computational experiments with simultaneous visualization of their results. There is the analysis of the influence of the shape and the structure of a clot formed at the blood vessel wall on the main hydrodynamic characteristics determining the probability of a clot breakage from the wall. It is shown that the most dangerous are the blood clots which boundary forms an acute angle with the vessel wall. This is caused by to two factors: the occurrence of the rotary moment of the forces tending to the break of the blood clot front edge down the vessel wall, as well as by the action of a local pressure gradient at the clot base, which significantly exceeds the pressure gradient in the vessel outside the blood clot. At the same time, the clot permeability affects the total pressure drop and the maximal pressure gradient magnitude, but it practically does not change the direction of the fluid flow in the blood vessel.