It is widely acknowledged that the resistance to flow within individual microvessels (R) results from the effective viscosity (h) of blood and geometric factors, where the latter is often referred to as vascular hindrance (z). Under idealized conditions of fluid flow with a constant viscosity (i.e., a Newtonian fluid) and Poiseuille flow (parabolic velocity profile), z is proportional to vessel length (L) and inversely proportional to D4, yielding the relationship that R ~ hz. It has been shown that over the broad range of diameters encountered as blood traverses the microvascular network, the principal determinant of resistance in the normal flow state is the relationship that R/L ~ 1/D4 and that substantial departures from this behavior in the low-flow state and pathological conditions arise from the rheological properties of blood [1].

Rheology (from Greek rheo, flow) is the study of the flow and deformation of materials. The general aim of rheological studies is to characterize the intrinsic mechanical properties of a fluid or solid in terms of the resistance it offers to deformation under a given load, or shear at a prescribed rate. The viscous properties of blood in large-bore tubes and vis-cometric instruments have provided a foundation for understanding the rheology of blood in microvessels. With the assumption that blood is a homogenous fluid with an intrinsic viscosity, these devices have revealed that blood viscosity falls as shear rates (g) rise (shear thinning) from on the order of 0.1 to 1,000seconds-1, in contrast to the behavior of a Newtonian fluid with constant viscosity. The intrinsic viscous properties of bulk suspensions are typified by a parametric set of curves of viscosity (h) versus shear rate (g), as illustrated in Figure 1 for cat blood using a cone-plate viscometer. The shaded area represents the general regime of g and hematocrit for the microcirculation in the normal flow state. At a given shear rate, blood viscosity rises exponentially with increasing red blood cell (RBC) concentration (hematocrit), to an extent dependent upon prevailing g. Viscosity of the suspending medium (plasma) has been shown to be invariant, with g (Newtonian) and is dependent mainly upon protein content and temperature.

Within the circulation, in large diameter vessels representative of the macrocirculation (i.e., > 100 mm), blood may be treated as a homogeneous continuum with intrinsic properties characterized by an "apparent viscosity." The term apparent viscosity is used since viscosity of a homogenous fluid (e.g., water, molasses) is a material property that may be dependent upon shear rate, is invariant with the size of the vessel through which it flows and is dependent mainly on temperature. In vitro viscometric studies h.ave revealed that apparent viscosity (h) rises as shear rate (g) is reduced. The decrease in h with increasing g depends strongly on levels of hematocrit. A comparison of this "shear thinning" of blood in the presence and absence of aggregating agents suggests that about 75 percent of the decrease is a result of the disruption of red cell aggregates, and 25 percent is due to red cell deformation in response to increased shear stresses. In vivo, the particulate nature of blood affects this relationship. The dominance of noncontinuum effects in the smallest microvessels result in an effective blood viscosity that is strongly dependent upon microvessel diameter.

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Essentials of Human Physiology

Essentials of Human Physiology

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