Application of the Theory of Interacting Continua to Blood Flow

Micro-scale investigations of the flow and deformation of blood and its formed elements have been studied for many years. Early in vitro investigations in the rotational viscometers or small glass tubes revealed important rheological properties such as the reduced blood apparent viscosity, Fahraeus effect and Fahraeus-Lindqvist effect [1], exhibiting the nonhomogeneous property of blood in microcirculation. We have applied Mixture Theory, also known as Theory of Interacting Continua, to study and model this property of blood [2, 3]. This approach holds great promise for predicting the trafficking of RBCs in micro-scale flows (such as the depletion layer near the wall), andother unique hemorheological phenomena relevant to blood trauma. The blood is assumed to be composed of an RBC component modeled as a nonlinear fluid, suspended in plasma, modeled as a linearly viscous fluid.

Direct Numerical Simulation of Cellular Blood Flow Through a Model Arteriole Bifurcation

Blood is composed of a suspension of red blood cells (RBCs) suspended in plasma, and the presence of the RBCs substantially changes the flow characteristics and rheology of these suspensions. The viscosity of blood varies with the hematocrit (volume fraction of RBCs), which is a result not seen in Newtonian fluids. Additionally, RBCs are deformable, which can alter suspension dynamics. Understanding the physics in these flows requires accurately simulating the suspended phase to recover the microscale, and a subsequent analysis of the rheology to ascertain the continuum-level effects caused by the changes at the particle level. The direct numerical simulation of blood flow including RBC migration effects has the capability to resolve the Fåhraeus effect of observing low hematocrit values near walls, the subsequent cell-depleted layer, and the presence of velocity profile blunting due to the distribution of RBCs.

A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow

The earlier constitutive model of Fang & Owens (Biorheology, vol. 43, 2006, p. 637) and Owens (J. Non-Newtonian Fluid Mech. vol. 140, 2006, p. 57) is extended in scope to include non-homogeneous flows of healthy human blood. Application is made to steady axisymmetric flow in rigid-walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the Fåhraeus–Lindqvist effect whereby the apparent viscosity of healthy blood decreases as a function of tube diameter in sufficiently small vessels. That this is due to the development of a slippage layer of cell-depleted fluid near the vessel walls and a decrease in the tube haematocrit is demonstrated from the numerical results. Although clearly influential, the reduction in tube haematocrit observed in small-vessel blood flow (the so-called Fåhraeus effect) does not therefore entirely explain the Fåhraeus–Lindqvist effect.

Complex Biological Fluid Flow Through Microfabricated Polysilicon Microneedles

Microneedles can be used for sample extraction or injection for biomedical applications. It is important to understand how complex biological fluids behave within the needles because non-newtonian effects are associated with fluid flow of concentrated biological solutions. Different concentrations of sheep blood diluted with phosphate buffered saline (PBS) were investigated in different planar needle geometries. Only slight shear thinning behavior was observed, and only slight changes in apparent viscosity were recorded even at higher hematocrit levels. This is hypothesized to be a result of the Fahraeus effect in which cells are excluded from the wall regions in small channels. Microneedles with complex features clogged easily whereas needles with larger hydraulic radii allowed higher concentrations of blood to flow through them. However, at higher hematocrit levels (>25%) even the lower resistance needle clogged. Further investigations are needed to correlate how geometry affects flow of complex cellular suspensions.

A model for red blood cell motion in glycocalyx-lined capillaries

The interior surfaces of capillaries are lined with a layer (glycocalyx) of macromolecules bound or adsorbed to the endothelium. Here, a theoretical model is used to analyze the effects of the glycocalyx on hematocrit and resistance to blood flow in capillaries. The glycocalyx is represented as a porous layer that resists penetration by red blood cells. Axisymmetric red blood cell shapes are assumed, and effects of cell membrane shear elasticity are included. Lubrication theory is used to compute the flow of plasma around the cell and within the glycocalyx. The effects of the glycocalyx on tube hematocrit (Fahraeus effect) and on flow resistance are predicted as functions of the width and hydraulic resistivity of the layer. A layer of width 1 μm and resistivity 108dyn ⋅ s/cm4leads to a relative apparent viscosity of ∼10 in a 6-μm capillary at discharge hematocrit 45% and flow velocity of ∼1 mm/s. This is consistent with experimental observations of increased flow resistance in microvessels in vivo, relative to glass tubes with the same diameters.