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

The present review presents basic concepts of blood rheology related to vascular diseases. Blood flow in large arteries is dominated by inertial forces exhibited at high flow velocities, while viscous forces (i.e., blood rheology) play an almost negligible role. When high flow velocity is compromised by sudden deceleration as at a bifurcation, endothelial cell dysfunction can occur along the outer wall of the bifurcation, initiating inflammatory gene expression and, through mechanotransduction, the cascade of events associated with atherosclerosis. In sharp contrast, the flow of blood in microvessels is dominated by viscous shear forces since the inertial forces are negligible due to low flow velocities. Shear stress is a critical parameter in microvascular flow, and a force-balance approach is proposed for determining microvascular shear stress, accounting for the low Reynolds numbers and the dominance of viscous forces over inertial forces. Accordingly, when the attractive forces between erythrocytes (represented by the yield stress of blood) are greater than the shear force produced by microvascular flow, tissue perfusion itself cannot be sustained, leading to capillary loss. The yield stress parameter is presented as a diagnostic candidate for future clinical research, specifically, as a fluid dynamic biomarker for microvascular disorders. The relation between the yield stress and diastolic blood viscosity (DBV) is described using the Casson model for viscosity, from which one may be able determine thresholds of DBV where the risk of microvascular disorders is high.

/pdf/hemorheology-and-microvascular-disorders-4zhvibac43.pdf

Hemorheology and Microvascular Disorders

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.

We study theoretically and computationally the incompressible, non-conducting, micropolar, biomagnetic (blood) flow and heat transfer through a two-dimensional square porous medium in an (x,y) coordinate system, bound by impermeable walls. The magnetic field acting on the fluid is generated by an electrical current flowing normal to the x–y plane, at a distance l beneath the base side of the square. The flow regime is affected by the magnetization B0 and a linear relation is used to define the relationship between magnetization and magnetic field intensity. The steady governing equations for x-direction translational (linear) momentum, y-direction translational (linear) momentum, angular momentum (micro-rotation) and energy (heat) conservation are presented. The energy equation incorporates a special term designating the thermal power per unit volume due to the magnetocaloric effect. The governing equations are non-dimensionalized into a dimensionless (ξ,η) coordinate system using a set of similarity transformations. The resulting two point boundary value problem is shown to be represented by five dependent non-dimensional variables, fξ (velocity), fη (velocity), g (micro-rotation), E (magnetic field intensity) and θ (temperature) with appropriate boundary conditions at the walls. The thermophysical parameters controlling the flow are the micropolar parameter (R), biomagnetic parameter (NH), Darcy number (Da), Forchheimer (Fs), magnetic field strength parameter (Mn), Eckert number (Ec) and Prandtl number (Pr). Numerical solutions are obtained using the finite element method and also the finite difference method for Ec=2.476×10−6 and Prandtl number Pr=20, which represent realistic biomagnetic hemodynamic and heat transfer scenarios. Temperatures are shown to be considerably increased with Mn values but depressed by a rise in biomagnetic parameter (NH) and also a rise in micropolarity (R). Translational velocity components are found to decrease substantially with micropolarity (R), a trend consistent with Newtonian blood flows. Micro-rotation values are shown to increase considerably with a rise in R values but are reduced with a rise in biomagnetic parameter (NH). Both translational velocities are boosted with a rise in Darcy number as is micro-rotation. Forchheimer number is also shown to decrease translational velocities but increase micro-rotation. Excellent agreement is demonstrated between both numerical solutions. The mathematical model finds applications in blood flow control devices, hemodynamics in porous biomaterials and also biomagnetic flows in highly perfused skeletal tissue.

P. Chaturani

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.

Poiseuille flow of micropolar fluid with non-zero couple stress at boundary with applications to blood flow

Theory for flow of casson and Herschel-Bulkley fluids in cone-plate viscometers