A Free Boundary Mathematical Model of Atherosclerosis

Atherosclerosis is an inflammatory disease of the arterial wall that involves abnormal cholesterol deposits in the inner layers of arteries. The chronic accumulation of fat contributes to the formation of fibrofatty lesions, called atheromatous plaques, which grow through the opposite direction of the vessel and narrow the blood flow to vital organs.
In this work, we model the arterial inflammation in atherosclerosis in a one-dimensional free boundary problem. The plaque growth causing the motion of the domain boundary is not only considered as resulting from the influx of cells through the boundary, but also from their interaction in the subendothelial space. The main objective of this work is findinding the solution of the model and drawing conclusions on the plaque growth. For this purpose, we simplify the model, formulate the model, by a change of variables, with a fixed boundary, space and time dependent coefficients and non linear terms. The study of the latter model allows us to prove the existence of solution by applying the fixed point theorem. We also investigate the wave solution and analyze the numerical results. Finally, the results obtained are generalized to the original model.