Multiple interacting mechanisms control the formation and dissolution of clots to maintain blood in a state of delicate balance. In addition to a myriad of biochemical reactions, rheological factors also play a crucial role in modulating the response of blood to external stimuli. To date, a comprehensive model for clot formation and dissolution, that takes into account the biochemical, medical and rheological factors, has not been put into place, the existing models emphasizing either one or the other of the factors. In this paper, after discussing the various biochemical, physiologic and rheological factors at some length, we develop a model for clot formation and dissolution that incorporates many of the relevant crucial factors that have a bearing on the problem. The model, though just a first step towards understanding a complex phenomenon, goes further than previous models in integrating the biochemical, physiologic and rheological factors that come into play.

https://downloads.hindawi.com/journals/cmmm/2003/964040.pdf

A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood

Blood Flow Through an Artery with Mild Stenosis: A Two-layered Model, Different Shapes of Stenoses and Slip Velocity at the Wall

Blood flow in a stenosed tube has been modeled in the present studies. Blood flow is assumed to be represented by a couple stress fluid. Flow parameters such as velocity, resistance to flow, and shear stress distribution have been computed for different suspension concentrations (haematocrit), and for the blood diseases; polycythemia, plasma cell dyscrasias, and for Hb SS (sickle cell). The results have been compared with the case of normal blood and for other theoretical models. The importance of size effects in blood flow studies has been highlighted.

Modeling of arterial stenosis and its applications to blood diseases.

Pulsatile flow of blood through a porous medium has been studied under the influence of periodic body acceleration by considering blood as a couple stress, incompressible, electrically conducting fluid in the presence of magnetic field. An exact solution of the equation of motion is obtained by applying the Laplace and finite Hankel transforms. The expressions for axial velocity, flow rate, fluid acceleration and shear stress have been obtained analytically. The eects of magnetic field, body acceleration and permeability parameter have been discussed with the help of graphs. It is found that the velocity distribution increases with an increase of both body acceleration and permeability of the porous medium, while it decreases as the magnetic parameter increases.

/pdf/pulsatile-flow-of-couple-stress-fluid-through-a-porous-4jc1bf9qry.pdf

Pulsatile Flow of Couple Stress Fluid Through a Porous Medium with Periodic Body Acceleration and Magnetic Field

The problem of steady laminar fully developed flow and heat transfer in a horizontal channel consisting of a couple-stress fluid sandwiched between two clear viscous fluids is analyzed analytically. The fluids in all regions are assumed to be incompressible, immiscible, and the transport properties of the fluids in all regions are assumed to be constant. Under these assumptions, the resulting governing equations constitute a set of coupled linear ordinary differential equations that is solved analytically. The closed form solutions obtained for the velocity and temperature fields in the channel are evaluated numerically for various parametric conditions. These results are illustrated graphically to illustrate the effects of the physical parameters governing the flow such as the viscosity ratio, conductivity ratio, couple-stress parameter, Eckert number, and the Prandtl number on the velocity and temperature profiles. In addition, results for the rate of heat transfer are computed for different values of t...

V.S. Upadhya

Papers

A two-fluid model for blood flow through small diameter tubes.

Pulsatile flow of a couple stress fluid through circular tubes with applications to blood flow.

Gravity flow of a fluid with couple stress along an inclined plane with application to blood flow.

A note on Poiseuille flow of couple stress fluid.