A simple model for shear stress mediated lumen reduction in blood vessels.

The goal of this paper is to qualitatively describe the dominant flow characteristics associated with shear stress mediated lumen reduction due to atherosclerotic plaque growth. The approach is to develop rate equations for the reduction of the lumen as a function of the shear stress near the intima wall. Elementary, qualitative, models for fully developed laminar and turbulent flows are employed, leading to nonlinear ordinary differential equations. The model provides a qualitative description of one aspect of the long-term reduction, perhaps taking years, of the lumen due to wall growth. This is useful because of the extreme complexity of long-term experiments.