Modelling growth and formation of thrombi: a multiphasic approach based on the theory of porous media

Abstract

AbstractAortic dissection (AD) has a high mortality rate. About 40% of the people with type B AD do not live for more than a month. The prognosis of AD is quite challenging. Hence, we present a triphasic model for the formation and growth of thrombi using the theory of porous media (TPM). The whole aggregate is divided into solid, liquid and nutrient constituents. The constituents are assumed to be materially incompressible and isothermal, and the whole aggregate is assumed to be fully saturated. Darcy’s law describes the flow of fluid in the porous media. The regions with thrombi formation are determined using the solid volume fraction. The velocity- and nutrient concentration-induced mass exchange is defined between the nutrient and solid phases. We introduce the set of equations and a numerical example for thrombosis in type B AD. Here we study the effects of different material parameters and boundary conditions. We choose the values that give meaningful results and present the model’s features in agreement with the Virchow triad. The simulations show that the thrombus grows in the low-velocity regions of the blood. We use a realistic 2-d geometry of the false lumen and present the model’s usefulness in actual cases. The proposed model provides a reasonable approach for the numerical simulation of thrombosis.