Porth's Essentials of Pathophysiology, 4e

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Control of Cardiovascular Function

C h a p t e r 1 7

Wall Tension, Radius, and Pressure In a blood vessel, wall tension is the force in the ves- sel wall that opposes the distending pressure inside the vessel. French astronomer and mathematician Pierre de Laplace described the relationship between wall tension, pressure, and the radius of a vessel or sphere more than 200 years ago. This relationship, which has come to be known as the law of Laplace, can be expressed by the Equation P = T/r, in which T is the wall tension, P is the intraluminal pressure or pressure within the vessel, and r is the vessel radius (Fig. 17-3A). Accordingly, the internal pressure expands the vessel until it is exactly balanced by the tension in the vessel wall. The smaller the radius, the greater is the pressure needed to balance the wall tension. The law of Laplace can also be used to express the effect of the vessel radius on wall tension (T = P × r). This correlation can be compared with a partially inflated balloon (Fig. 17-3B). Because the pres- sure is equal throughout, the tension in the part of the balloon with the smaller radius is less than the tension in the section with the larger radius. The same holds true for an arterial aneurysm in which the tension and risk of rupture increase as the aneurysm grows in size (see Chapter 18). The law of Laplace was later expanded to include wall thickness (T = P × r/wall thickness). Wall tension is inversely related to wall thickness, such that the thicker the vessel wall, the lower the tension, and vice versa. In hypertension, for example, arterial vessel walls hyper- trophy and become thicker, thereby reducing the ten-

sion and minimizing wall stress. The law of Laplace can also be applied to the pressure required to maintain the patency of small blood vessels. Provided that the thick- ness of a vessel wall remains constant, it takes more pres- sure to overcome wall tension and keep a vessel open as its radius decreases in size. The critical closing pres- sure refers to the point at which vessels collapse so that blood can no longer flow through them. In circulatory shock, for example, there is a decrease in blood volume and vessel radii, along with a drop in blood pressure. As a result, many of the small vessels collapse as the blood pressure drops to the point where it can no longer over- come the wall tension. The collapse of peripheral veins often makes it difficult to insert venous lines that are needed for fluid and blood replacement. Vascular Distensibility Distensibility refers to the ability of a blood vessel to be stretched and accommodate an increased volume of blood. It is normally expressed as the fractional increase in volume for each millimeter of mercury (mm Hg) increase in pressure. Vascular compliance or capacitance refers to the total quantity of blood that can be stored in a given portion of the circulation for each millimeter of mercury rise in pressure. Both compliance and capaci- tance can be used to as a measure of the distensibility or flexibility of a blood vessel. The most distensible of all vessels are the veins, which can increase their vol- ume with only slight changes in pressure, allowing them to function as a reservoir for storing large quantities of blood that can be returned to the circulation when it is needed. Although arteries have a thicker muscular wall than veins, their distensibility allows them to store some of the blood that is ejected from the heart during systole, providing for continuous flow through the capillaries as the heart relaxes during diastole. ■■ Blood flow is determined largely by the pressure difference between the two ends of a vessel or group of vessels and the resistance that the blood must overcome as it moves through the vessel or vessels.The resistance or opposition to blood flow, which is directly related to the viscosity of the blood as determined by the percentage of red blood cells and inversely related to the fourth power of the vessel radius, increases as the viscosity of the blood increases and decreases as the radius of a vessel increases and vice versa. ■■ The relationship between the wall tension of a vessel, its intraluminal pressure, and its radius can be described using the law of Laplace (wall tension = pressure × radius).Thus, at any given SUMMARY CONCEPTS

P

T

P

T

A

Radius

Tension = Pressure × radius

B FIGURE 17-3. The law of Laplace relates pressure (P), tension (T), and radius (r) to a cylindrical blood vessel. (A) The pressure expanding the vessel is equal to the wall tension divided by the vessel radius. (B) Effect of the radius on tension in a cylindrical balloon. In a balloon, the tension in the wall is proportional to the radius because the pressure is the same everywhere inside the balloon.The tension is lower in the portion of the balloon with the smaller radius. (From Rhoades RA,Tanner GA. Medical Physiology. Boston, MA: Little, Brown; 1996:627.)

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