A mathematical model for the study of interstitial fluid movement vis-a-vis the non-newtonian behaviour of blood in a constricted artery

A mathematical model is developed with an aim to study the transport of interstitial fluid in the wall of a constricted artery by taking into account the microrotation of the erythrocytes of blood. The movement of the interstitial fluid has been described by the Debye-Brinkman equation. Exact solutions are obtained for the displacement of the solid matrix of the porous interstitial space, the velocity of the interstitial fluid movement, and the pressure distribution in the constricted arterial segment, for large and small consolidation times. Expression for the wall shear stress is also obtained for the constricted segment of the artery. Theoretical estimates of the distributions of the axial velocity of blood in the stenosed zone, rotational velocity of the erythrocytes, wall shear stress, and wall displacement, as well as the pressure and velocity profiles for the interstitial fluid movement, have been presented in the form of graphs.