Physical Laws Describing Blood Flow

The flow of blood through the vascular system, like the flow of any fluid through a tube, depends in part on the difference in pressure at the two ends of the tube. If the pressure at both ends of the tube is the same, there will be no flow. If the pressure at one end is greater than at the other, blood will flow from the region of higher to the region of lower pressure. The rate of blood flow is proportional to the pressure difference (p - P2) between the two ends of the tube. The term pressure difference is abbreviated AP, in which the Greek letter A (delta) means "change in."

If the systemic circulation is pictured as a single tube leading from and back to the heart (fig. 14.13), blood flow through this system would occur as a result of the pressure difference between the beginning of the tube (the aorta) and the end of the tube (the junction of the venae cavae with the right atrium). The average pressure, or mean arterial pressure (MAP), is about 100 mmHg; the pressure at the right atrium is 0 mmHg. The "pressure head," or driving force (AP), is therefore about 100 - 0 = 100 mmHg.

Blood flow is directly proportional to the pressure difference between the two ends of the tube (AP) but is inversely proportional to the frictional resistance to blood flow through the vessels. Inverse proportionality is expressed by showing one of the factors in the denominator of a fraction, since a fraction decreases when the denominator increases:

resistance

The resistance to blood flow through a vessel is directly proportional to the length of the vessel and to the viscosity of the blood (the "thickness," or ability of molecules to "slip over" each other; for example, honey is quite viscous). Of particular physiological importance, the vascular resistance is inversely proportional to the fourth power of the radius of the vessel:

■ Figure 14.13 Blood flow is produced by a pressure difference. The flow of blood in the systemic circulation is ultimately dependent on the pressure difference (AP) between the mean pressure of about 100 mmHg at the origin of flow in the aorta and the pressure at the end of the circuit—0 mmHg in the vena cava, where it joins the right atrium (RA). (LA = left atrium; RV = right ventricle; LV = left ventricle.)

where

L = length of vessel n = viscosity of blood r = radius of vessel

For example, if one vessel has half the radius of another and if all other factors are the same, the smaller vessel will have sixteen times (24) the resistance of the larger vessel. Blood flow through the larger vessel, as a result, will be sixteen times greater than in the smaller vessel (fig. 14.14).

When physical constants are added to this relationship, the rate of blood flow can be calculated according to Poiseuille's (pwa-zuh'yez) law:

Vessel length (L) and blood viscosity (the Greek letter eta, written n) do not vary significantly in normal physiology, although blood viscosity is increased in severe dehydration and in the polycythemia (high red blood cell count) that occurs as an adaptation to life at high altitudes. The major physiological regulators of blood flow through an organ are the mean arterial pressure (P, driving the flow) and the vascular resistance to flow. At a given mean arterial pressure, blood can be diverted from one organ to another by variations in the degree of vasoconstriction and vasodilation of small arteries and arterioles (that is, by variations in vessel radius, r). Vasoconstriction in one organ and vasodilation in another result in a diversion, or shunting, of blood to the second organ. Since arterioles are the smallest arteries and can become narrower by vasoconstriction, they provide the greatest resistance to blood flow (fig. 14.15). Blood flow to an organ is thus largely determined by the degree of vasoconstriction or vasodilation of its arterioles. The rate of blood flow to an organ can be increased by dilation of its arterioles and can be decreased by constriction of its arterioles.

Radius = 1/2 mm Resistance = 16 R Blood flow = 1/16 F

Radius = 1/2 mm Resistance = 16 R Blood flow = 1/16 F

Arterial blood

Arterial blood

■ Figure 14.14 The relationships between blood flow, vessel radius, and resistance. (a) The resistance and blood flow are equally divided between two branches of a vessel. (b) A doubling of the radius of one branch and halving of the radius of the other produces a sixteenfold increase in blood flow in the former and a sixteenfold decrease of blood flow in the latter

Large veins

re cl

Large veins

re cl

Gender Exchange
Resistance Exchange Capacitance vessels vessels vessels

■ Figure 14.15 Blood pressure in different vessels of the systemic circulation. Notice that the pressure generated by the beating of the ventricles is largely dissipated by the time the blood gets into the venous system, and that this pressure drop occurs primarily as blood goes through the aterioles and capillaries.

Total Peripheral Resistance

The sum of all the vascular resistances within the systemic circulation is called the total peripheral resistance. The arteries that supply blood to the organs are generally in parallel rather than in series with each other. That is, arterial blood passes through only one set of resistance vessels (arterioles) before returning to the heart (fig. 14.16). Since one organ is not "downstream" from another in terms of its arterial supply, changes in resistance within one organ directly affect blood flow in that organ only.

Vasodilation in a large organ might, however, significantly decrease the total peripheral resistance and, by this means, might decrease the mean arterial pressure. In the absence of compensatory mechanisms, the driving force for blood flow through all organs might be reduced. This situation is normally prevented by an increase in the cardiac output and by vasoconstriction in other areas. During exercise of the large muscles, for example, the arterioles in the exercising muscles are dilated. This would cause a great fall in mean arterial pressure if there were no compensations. The blood pressure actually rises during exercise, however, because the cardiac output is increased and because there is constriction of arterioles in the viscera and skin.

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