What is PDE

In this chapter we described predictive model for plaque formation and progression in the coronary and carotid artery. A full three-dimensional model for plaque formation and progression, coupled with blood flow and LDL concentration is analysed. The Navier-Stokes equations together with the Darcy law for model blood filtration and Kedem-Katchalsky equations are implemented. Additionally, the system of three additional reaction-diffusion equations for simulation of the inflammatory process is coupled with full incremental iterative procedure. We developed hybrid genetic algorithm for fitting parameters of ODE model for oxidized LDL, macrophage, smooth muscle cell and foam cell concentration evolution in time. The animal carotid and coronary artery after 2 month of high fat diet are examined. We compared with CT our computer model of the plaque size for three groups of patients: De-novo, Old-lesions and Control patients. Detailed shear stress distributions for baseline and follow-up for these patients are given. There is a good matching for plaque size and location.