﻿ Origins of Pressure in the Circulation - Organization of the Cardiovascular System - The Cardiovascular System - Medical Physiology, 3rd Edition

## Medical Physiology, 3rd Edition

### Origins of Pressure in the Circulation

Four factors help generate pressure in the circulation: gravity, compliance of the vessels, viscous resistance, and inertia.

Gravity causes a hydrostatic pressure difference when there is a difference in height

Because gravity produces a hydrostatic pressure difference between two points whenever there is a difference in height (Δh; see Equation 17-4), one must always express pressures relative to some reference h level. In cardiovascular physiology, this reference—zero height—is the level of the heart.

Whether the body is recumbent (i.e., horizontal) or upright (i.e., erect) has a tremendous effect on the intravascular pressure. In the horizontal position (Fig. 17-8A), where we assume that the entire body is at the level of the heart, we do not need to add a hydrostatic pressure component to the various intravascular pressures. Thus, the mean pressure in the aorta is 95 mm Hg, and—because it takes a driving pressure of ~5 mm Hg to pump blood into the end of the large arteries—the mean pressure at the end of the large arteries in the foot and head is 90 mm Hg. Similarly, the mean pressure in the large veins draining the foot and head is 5 mm Hg, and—because it takes a driving pressure of ~3 mm Hg to pump blood to the right atrium—the mean pressure in the right atrium is 2 mm Hg.

FIGURE 17-8 Arterial and venous pressures in the horizontal and upright positions. The pressures are different in A and B, but the driving pressures (ΔP) between arteries and veins (separation between red and blue lines, violet shading) are the same.

When a 180-cm tall person is standing (see Fig. 17-8B), we must add a 130-cm column of blood (the Δh between the heart and large vessels in the foot) to the pressure prevailing in the large arteries and veins of the foot. Because a water column of 130 cm is equivalent to 95 mm Hg, the mean pressure for a large artery in the foot will be 90 + 95 = 185 mm Hg, and the mean pressure for a large vein in the foot will be 5 + 95 = 100 mm Hg. On the other hand, we must subtract a 50-cm column of blood from the pressure prevailing in the head. Because a water column of 50 cm is equivalent to 37 mm Hg, the mean pressure for a large artery in the head will be 90 − 37 = 53 mm Hg, and the mean pressure for a large vein in the head will be 5 − 37 = −32 mm Hg. Of course, this “negative” value really means that the pressure in a large vein in the head is 32 mm Hg lower than the reference pressure at the level of the heart.

In this example, we have simplified things somewhat by ignoring the valves that interrupt the blood column. In reality, the veins of the limbs have a series of one-way valves that allow blood to flow only toward the heart. These valves act like a series of relay stations, so that the contraction of skeletal muscle around the veins pushes blood from one valve to another (see p. 516). Thus, veins in the foot do not “see” the full hydrostatic column of 95 mm Hg when the leg muscles pump blood away from the foot veins.

Although the absolute arterial and venous pressures are much higher in the foot than in the head, the ΔP that drives blood flow is the same in the vascular beds of the foot and head. Thus, in the horizontal position, the ΔP across the vascular beds in the foot or head is 90 − 5 = 85 mm Hg. In the upright position, the ΔP for the foot is 185 − 100 = 85 mm Hg, and for the head, 53 − (−32) = 85 mm Hg. Thus, gravity does not affect the driving pressure that governs flow. On the other hand, in “dependent” areas of the body (i.e., vessels “below” the heart in a gravitational sense), the hydrostatic pressure does tend to increase the transmural pressure (intravascular versus extravascular “tissue” pressure) and thus the diameter of distensible vessels. Because various anatomical barriers separate different tissue compartments, it is assumed that gravity does not appreciably affect this tissue pressure.

Low compliance of a vessel causes the transmural pressure to increase when the vessel blood volume is increased

Until now, we have considered blood vessels to be rigid tubes, which, by definition, have fixed volumes. If we were to try to inject a volume of fluid into a truly rigid tube with closed ends, we could in principle increase the pressure to infinity without increasing the volume of the tube (Fig. 17-9A). At the other extreme, if the wall of the tube were to offer no resistance to deformation (i.e., infinite compliance), we could inject an infinite volume of fluid without increasing the pressure at all (see Fig. 17-9B). Blood vessels lie between these two extremes; they are distensible but have a finite compliance (see p. 454). Thus, if we were to inject a volume of blood into the vessel, the volume of the vessel would increase by the same amount (ΔV), and the intravascular pressure would also increase (see Fig. 17-9C). The ΔP accompanying a given ΔV is greater if the compliance of the vessel is lower. The relationship between ΔP and ΔV is a static property of the vessel wall and holds whether or not there is flow in the vessel. Thus, if we were to infuse blood into a patient's blood vessels, the intravascular pressure would rise throughout the circulation, even if the heart were stopped.

FIGURE 17-9 Compliance: changes in pressure with vessels of different compliances.

The viscous resistance of blood causes an axial pressure difference when there is flow

As we saw in Ohm's law of hydrodynamics (see Equation 17-1), during steady flow down the axis of a tube (see Fig. 17-2), the driving pressure (ΔP) is proportional to both flow and resistance. Viewed differently, if we want to achieve a constant flow, then the greater the resistance, the greater the ΔP that we must apply along the axis of flow. Of the four sources of pressure in the circulatory system, this ΔP due to viscous resistance is the only one that appears in Poiseuille's law (see Equation 17-9).

The inertia of the blood and vessels causes pressure to decrease when the velocity of blood flow increases

For the most part, we have been assuming that the flow of blood as well as its mean linear velocity is steady. However, as we have already noted, blood flow in the circulation is not steady; the heart imparts its energy in a pulsatile manner, with each heartbeat. Therefore,  in the aorta increases and reaches a maximum during systole and falls off during diastole. As we shall shortly see, these changes in velocity lead to compensatory changes in intravascular pressure.

The tradeoff between velocity and pressure reflects the conversion between two forms of energy. Although we generally state that fluids flow from a higher to a lower pressure, it is more accurate to say that fluids flow from a higher to a lower total energy. This energy is made up of both the pressure or potential energy and the kinetic energy (KE = ). The impact of the interconversion between these two forms of energy is manifested by the familiar Bernoulli effect. As fluid flows along a horizontal tube with a narrow central region, which has half the diameter of the two ends, the pressure in the central region is actually lower than the pressure at the distal end of the tube (Fig. 17-10). How can the fluid paradoxically flow against the pressure gradient from the lower-pressure central to the higher-pressure distal region of the tube? We saw above that flow is the product of cross-sectional area and velocity (see Equation 17-8). Because the flow is the same in both portions of the tube, but the cross-sectional area in the center is lower by a factor of 4, the velocity in the central region must be 4-fold higher (see table at bottom of Fig. 17-10). Although the blood in the central region has a lower potential energy (pressure = 60) than the blood at the distal end of the tube (pressure = 80), it has a 16-fold higher kinetic energy. Thus, the total energy of the fluid in the center exceeds that in the distal region, so that the fluid does indeed flow down the energy gradient.

FIGURE 17-10 Bernoulli effect. For the top tube, which has a uniform radius, velocity (v) is uniform and transmural pressure (P) falls linearly with the length, which we artificially compress to fit in the available space. The bottom tube has the same upstream and downstream pressures but a constriction in the middle that is short enough so as not to increase overall resistance or overall fall in P. The constriction has cross-sectional area that is only one fourth that of the two ends. Thus, velocity in the narrow portion must be 4-fold higher than it is at the ends. Although the total energy of fluid falls linearly along the tube, pressure is lower in the middle than at the distal end.

This example illustrates an interconversion between potential energy (pressure) and kinetic energy (velocity) in space because velocity changes along the length of a tube even though flow is constant. We will see on pages 511–513 that during ejection of blood from the left ventricle into the aorta, the flow and velocity of blood change with time at any point within the aorta. These changes in velocity contribute to the changes in pressure inside the aorta.

The Bernoulli effect has important practical implications for measurement of blood pressure with an open-tipped catheter. The pressure recorded with the open tip facing the flow is higher than the actual pressure by an amount corresponding to the kinetic energy of the oncoming fluid (Fig. 17-11). Conversely, the pressure recorded with the open tip facing away from the flow is lower than the actual pressure by an equal amount. The measured pressure is correct only when the opening is on the side of the catheter, perpendicular to the flow of blood.

FIGURE 17-11 Effects of kinetic energy on the measurement of blood pressure with catheters.

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