Figure 5.1 illustrates the processes that underlie anomalous viscosity in the bloodstream. When the blood is flowing relatively fast (A–B), the cellular components travel as a core in the centre of the vessel, surrounded by a cell-free layer of plasma. The cells are oriented so that they travel edge-on, producing minimal friction between the cell layers and between cells and plasma. The viscosity of the blood in this situation is around 50% greater than that of plasma alone. If the flow velocity falls sufficiently then the orientation of the suspension becomes less organized, with some cells starting to rotate and collide with adjacent cells. This process absorbs some of the energy creating the pressure gradient and so viscosity rises (C–D). If flow rate falls even further, the cellular constituents fall out of suspension and form an aggregate on the gravitationally lowest surface of the vessel. Because of the mass of the aggregate, a substantial amount of energy is required to lift the cells back into suspension again, reflected in a very high viscosity (E).

Figure 5.1 Changes in viscosity and the associated changes in red blood cell behaviour as the velocity of blood flow falls. A & B represent velocities typical of flow in the normal, intact circulation.

The dependence of blood viscosity on the cellular components has several implications. First, alteration of the haematocrit will change the size of the cell-rich core relative to surrounding plasma. Therefore, increased haematocrit will proportionately elevate viscosity. This can impose a substantial extra cardiac workload particularly during exercise. Thus, ‘blood doping’ with erythropoietin, although it is likely to improve maximal exercise performance by enhancing oxygen delivery to muscles, also carries a significant risk of damage to the heart. A second consequence of anomalous viscosity is that very low rates of blood flow can result in cells falling out of suspension. If the cell aggregates remain unsuspended for more than a few minutes, they begin to stick together and, in small vessels, may completely obstruct the lumen. This situation is most likely to occur in the postcapillary venules and will be discussed in Chapter 10 in relation to hypotensive states associated with prolonged exercise.

HANDY HINTS

The width of the cell-free plasma layer is relatively independent of vessel size, because it is dictated by the profiles of the endothelium and the blood cells. By contrast, the number of layers of blood cells that can travel in the cell-rich core must decrease progressively through the microcirculation; in the small arterioles only two or three cells will be able to travel in parallel. With a fall in vessel size, the local blood viscosity must also fall, both because there is reduced friction between the cell core and the surrounding plasma and because there is less friction between adjacent layers of cells. As a result, absolute viscosity in the smallest arterioles may be only about two-thirds that in the aorta.

This has practical implications for measurement of haematocrit during human experiments. Since the usual technique of blood sampling involves finger prick, the origin of the sample is primarily from the superficial microcirculation. It can be predicted that the haematocrit measured in this way is likely to underestimate the true value by at least several per cent and, further, that haematocrit will rise under conditions where the vessels of the finger microcirculation are dilated, such as during heat stress or exercise. Routinely warming the hand in hot water before taking finger prick samples ensures more reproducible and accurate measurements of haematocrit in resting subjects.

Blood flow through systemic capillaries is rather different to that through either precapillary or postcapillary vessels. All these other vessels have diameters greater than that of blood cells, whereas the typical capillary diameter of around 6 μm is marginally less than that of an erythrocytes (8 μm). In consequence, blood cells have to be partially folded in order to pass along the capillary. This process is important in that it ensures the closest contact possible between erythrocyte and endothelial membranes and so minimizes the distance for gas diffusion between blood and tissue. However, in theory it should also produce very high frictional forces between blood cells and the capillary wall, greatly increasing local viscosity and impeding the efficiency of capillary perfusion. To avoid such a disadvantageous situation, the endothelium of capillaries secretes a lubricant mucopolysaccharide that virtually eliminates frictional interaction with the blood cells and results in local viscosity that is almost as low as that of cell-free plasma.

Poiseuille’s law

The equation relating flow, pressure and resistance (see p. 45) can be rewritten by substitution of vessel radius (r) and length (L) and blood viscosity (V) for resistance, and adding a factor for numerical accuracy (k), thus:

This equation was derived by the scientist Poiseuille and is known as Poiseuille’s law. In its full form, with the factor k expressed numerically, it reads:

The practical importance of Poiseuille’s law is that it describes the main factors affecting the relationship between flow and pressure. It does not of course take account of homeostatic feedback so does not necessarily predict the end result of manipulating these factors in the whole body. For example, if blood pressure were elevated by a sudden increase in blood volume, there would normally be baroreflex compensation that would lower peripheral resistance and return the pressure to its initial level (see Chapter 7, p. 81). A second difference from the events in the intact circulation is that Poiseuille’s law assumes that the vasculature is a system of rigid tubes. As soon as we deal with tubes that might distend in response to internal pressure, then obviously the association between pressure and flow becomes different.

RESISTANCE TO FLOW OF DISTENSIBLE VESSELS

Roles of connective tissue and muscle in determining distensibility

In rigid tubes, there is a linear relationship between the pressure gradient and the resulting volume flow, presuming that resistance remains constant (Fig 5.2A). In distensible tubes, by contrast, increased internal pressure will cause some increase in tube volume, so that the rate of volume flow rise with pressure will be lower. In blood vessels, distensibility is conferred by the presence of elastin in the vessel wall, while the presence of collagen confers rigidity (Fig. 5.2B–D). The property of distensibility is usually referred to as compliance.