Mechanically driven accumulation of microscale material at coupled solid–fluid interfaces in biological channels

The accumulation of microscale materials at solid–fluid interfaces in biological channels is often the initial stage of certain growth processes, which are present in some forms of atherosclerosis. The objective of this work is to develop a relatively simple model for such accumulation, which researchers can use to qualitatively guide their analyses. Specifically, the approach is to construct rate equations for the accumulation at the solid–fluid interface as a function of the intensity of the shear stress. The accumulation of material subsequently reduces the cross-sectional area of the channel until the fluid-induced shear stress at the solid–fluid interface reaches a critical value, which terminates the accumulation rate. Characteristics of the model are explored analytically and numerically.