The velocity of blood flow through a segment of the circulation has units of distance and time (e.g., centimeters/second). The flow of blood through the circulation has units of volume and time (e.g., liters/minute). At a constant flow, the velocity of blood through a vessel relates to the cross-sectional area of the vessel, expressed by the equation:

v = Q/A

where v is velocity, Q is flow, and A is the cross-sectional area.

Therefore, velocity is proportional to flow and inversely proportional to the cross-sectional area. Thus, peak velocity occurs in the aorta and reaches its nadir in the capillary beds, which have tremendous cross-sectional areas. Velocity increases again as blood moves from the capillaries toward the central veins.

The primary determinants of flow (Q) through a vascular segment are the inflow pressure (P_i), the outflow pressure (P_o), and the vascular resistance (R). For Newtonian fluids moving with laminar flow through cylindrical tubes, the relationship of flow to various physical factors can be expressed by Poiseuille’s Law, which is:

where r is radius, η is viscosity, and l is length.

Thus, flow through a vessel will increase as the pressure difference across the vessel increases. Furthermore, as the diameter of the vessel increases, so too will flow at any given pressure difference (P_i – P_o). Conversely, increases in viscosity and vessel length result in a decrease in flow.

Alterations in blood vessel diameter, resulting from changes in the contractile state of vascular smooth muscle, are central to regulating blood flow, particularly in the regional vascular beds. The relationship of pressure and flow to resistance can be understood by examining the hydraulic equivalent of Ohm’s Law:

which states that the resistance to flow through a vessel is equivalent to the change in pressure across the vessel divided by the flow through the vessel. For Newtonian fluids moving through cylindrical tubes, this relationship can be expressed by a rearrangement of Poiseuille’s Law to give the hydraulic resistance equation:

Therefore, when Poiseuille law is applied, the resistance to flow is determined solely by the dimensions of the vessel and the viscosity of the fluid. Moreover, since resistance changes with the fourth power of the radius, even small changes in vessel caliber resulting from vascular contraction or relaxation have a profound impact on flow through a vessel.

Studies indicate that pressure within the vasculature decreases progressively from the aorta to the vena cava, with the largest drop at the level of the arterioles (1). Thus, it follows from the relationships above that resistance is greatest at the level of the arterioles if blood flow is constant through the circulation. How, then, do we reconcile this fact with the effect of vessel diameter on resistance, in that the internal diameter of a capillary is far less than an arteriole? These findings can be reconciled by understanding that capillary beds are vessels in parallel, while the arterial system feeding a particular capillary bed is in series. When calculating the resistance of a system composed of a set of resistors in series (e.g., aorta, large arteries, small arteries, and arterioles), the total resistance is equal to the sum of the individual resistances. Conversely, when calculating the resistance of a system composed of a set of resistors in parallel, such as a capillary network, the total resistance is equal to the sum of the reciprocals of the individual resistances (1/R). Thus, for a capillary network, the total resistance is less than the resistance in any individual capillary.

In addition, organs may have a number of resistance vessels in parallel proximal to the capillary bed. These vessels may be patent or may be recruited with increased flow. Increased pulmonary blood flow that occurs with exercise, for example, is in part accommodated by the recruitment of vessels that were previously closed. Thus, an additional factor, k, which represents these recruited vessels, can be added to the resistance equation:

From this equation, it can be seen that an increase in k will reduce resistance. In addition, the loss of these vessels—that is, a reduction in k—that may occur with disease (such as the obliteration of distal pulmonary arteries in advanced pulmonary arterial hypertension or the occlusion of vessels by intravascular emboli) will result in increased resistance.

Finally, changes in pressure that occur in response to changes in flow and resistance can be expressed when Ohm law is rearranged as:

P_i = QR + P_o

Thus, vascular inflow pressure may increase when vascular resistance, blood flow, or outflow pressure increases. These factors are not independent. Pressure may remain constant with increased blood flow because the increase in flow has caused vascular resistance to decrease, for example, by dilating or recruiting previously closed vessels; that is, if the product QR does not increase, neither will pressure.

A change in intravascular pressure results in a proportional change in intravascular volume. The incremental change in volume (δV) per unit change in pressure (δP) defines the compliance (C) of a vessel, as indicated by the equation:

C = δV/δP

In addition, specific compliance can also be evaluated, since the implications of absolute volume changes are different between small and large structures. Specific compliance is calculated by dividing by the baseline volume, as in the equation:

When calculations are made in this way, comparisons can be made more easily between patients of different sizes. For example, right ventricular compliance is of concern in atrial septal defects, as it is only when right ventricular compliance increases that a left-to-right shunt can develop. In order to measure right ventricular compliance, allowances must be made for the base volume. The same principle applies to measuring compliance of the aorta, the vena cava, and other fluidfilled structures.

The walls of veins are thinner, less well organized, and contain less elastic tissue than those of arteries, and thus are ˜20 times more compliant. As a result, most of the circulating blood volume at any one time resides in the venous system, and therapeutic volume expansion has a disproportionate effect on venous, as opposed to arterial, volume.

The application of these mathematical relationships in the vasculature has important caveats. Blood is not a Newtonian fluid, although at normal hematocrits, this is probably of little consequence. The walls of small arteries are neither smooth nor straight; rather they branch, curve, and taper. Blood flow is pulsatile, so that additional energy (and therefore a higher pressure) is necessary to overcome inertia and to accelerate the blood at each ejection. Because of short distances between arterial branch points, laminar flow is unlikely in peripheral vascular beds, and viscous pressure losses would be greater than in a physical model. Arteries are also distensible, and continuously changing transvascular pressures alter their radii; therefore, pressure-flow relationships are not linear. Lastly, vascular beds are comprised of many blood vessels in parallel. These vessels are not all open all the time, and their radii vary. Despite these differences, the general principles of changes in physical factors, such as viscosity and radius, apply (2).

The vascular function curve describes how changes in cardiac output affect central venous pressure (CVP), or venous return (Fig. 69.1). To understand this relationship, a conceptual model can be used to partition the circulation into components, including a pump, an arterial compartment with a given compliance (C_a), a resistor (which represents the resistance through the arterioles, capillaries, and venules), and a venous compartment with a given compliance (C_v) (Fig. 69.2). The pump displaces blood from the venous compartment into the arterial compartment at some rate (Q), which, in this model, is equivalent to the cardiac output. The compliance of the arterial compartment accommodates a portion of this volume before blood is propelled across the microvascular resistor into the venous compartment, which can accommodate a much larger volume than the arterial compartment owing to its greater compliance. Increases in Q will decrease the volume
of blood that resides in the venous compartment and, hence, will decrease the pressure in the venous compartment, which is equivalent to the CVP. Conversely, decreases in Q will increase the volume of blood that resides in the venous compartment, which will increase CVP.

Important concepts can be seen at the extremes of the curve (Fig. 69.1). At some point, a maximal Q is achieved, whereby further reductions in the volume of blood in the venous compartment are not possible. Drawing blood from the venous compartment beyond this point would create a negative pres sure within the venous compartment, which would tend to collapse the vessel walls. This point is termed the critical closing pressure (P_cc) and represents the lowest possible CVP and highest possible Q for any given blood volume. On the opposite extreme, when Q becomes zero, the system reaches a steady state, where pressures within the arterial and venous compartments are determined solely by compliance. In this situation, CVP would be at its maximum for any given blood volume. It is also important to note that the curve is affected by the blood volume, with parallel increases from baseline with expansion of the circulating volume (such that occur with blood transfusions) and decreases with volume depletion (such that occur with hemorrhage) (Fig. 69.1).

The cardiac function curve is the reverse of the vascular function curve. It examines, how changes in CVP affect Q (Fig. 69.3). This relationship is based on Starling law that describes increases in Q that result from augmented contractility due to increased stretch of the myocardium (see Chapter 71). On the steep portion of the curve, increases in CVP—through increased venous return—distend the RV (i.e., increased preload), which, in turn, augments right ventricular contractility and flow through the pulmonary circuit. This ultimately increases pulmonary venous return, which increases left ventricular preload and output. Although the cardiac function curve is directly related to CVP, it may also be affected by the other determinants of cardiac output, including afterload, contractility, and heart rate. For example, increases in systemic vascular resistance that increase afterload can result in a downward shift in the curve, whereas systemic vasodilation that decreases afterload shifts the curve upward (Fig. 69.3).

At any given time, the cardiovascular system operates at one theoretical point of intersection between the vascular and cardiac function curves (Fig. 69.4). Deviations from this point are transient. For example, according to the simplified model presented here, if the pump suddenly ejected an increased volume of blood, volume and pressure would increase in the arterial compartment and decrease in the venous compartment, which would transiently shift the vascular function curve to the left. According to the cardiac function curve, subsequent ejection would decrease, as CVP was reduced. Over a short period of time, this decrease in Q would result in an increase in CVP in accordance with the vascular function curve, returning the system to the initial point of intersection.

The superimposition of these curves in various physiologic states is useful, as it illustrates relationships between contractility, preload (including blood volume), and afterload. For example, Figure 69.5 shows that alterations in vascular resistance might shift both the vascular and cardiac function curves, whereas a single cardiac function curve can intersect with several vascular function curves with changes in blood
volume (Fig. 69.6). Furthermore, whereas alterations in blood volume result in parallel changes in the vascular function curve (Figs. 69.1 and 69.6), alterations in resistance alter the slope of the curve but not the CVP at zero Q, because this point depends only on blood volume and compliance (Fig. 69.5). As the cardiovascular system operates at the point of intersection between the two curves, alterations in blood volume will shift the operative state of the system, even though it does alter intrinsic cardiac function (Fig. 69.6). However, adding an inotrope could shift the cardiac function curve, which explains the common practice of fluid administration and inotropic support in the setting of shock. Indeed, critical illnesses with their attendant physiologic derangements will variably affect the cardiovascular system and may differentially affect the vascular and cardiac function curves. Likewise, therapies may also have differential effects. Thus, although the theoretical model described by the vascular and cardiac function curves is overly simplified, it is useful as a foundation with which to rationalize a therapeutic approach to various cardiovascular derangements.

The hemodynamic and mechanical events of the cardiac cycle in the LV can be graphically represented by the instantaneous relationship of pressure and volume (Fig. 69.7). In this diagram, end-diastole is represented by point A; this is also the point in the cardiac cycle when the mitral valve closes. From points A to B, the ventricle undergoes isovolumic contraction. At point B, the aortic valve opens, and there is ejection with relatively little decrease in pressure until aortic valve closure (point C). Point C also represents end-systole. Then, diastole begins with isovolumic relaxation until point D, which represents mitral valve opening. From points D to A, there is filling of the ventricle.

By imposing a change in preload or afterload without altering cardiac contractility (e.g., transient vena caval occlusion or phenylephrine administration), an informative series of pressure-volume loops can be generated (Fig. 69.8). The end-systolic points of this family of loops will have a linear relationship, which defines the end-systolic pressure-volume relationship (ESPVR). The slope of this line is Ees, a loadindependent index of the inotropic state of the myocardium. Interventions that affect inotropy (e.g., increase with epinephrine infusion or decrease with acute β-blockade) will alter the slope of the ESPVR. Thus, the ventricle has a different Ees for any given contractile state (Fig. 69.9); note that changes in inotropy (Ees) dramatically affect stroke volume at the same end-systolic pressure. In clinical practice, physiologic or pharmacologic states that alter Ees may also increase afterload, thus having competing effects on stroke volume. The total area enclosed by the pressure-volume loops represents preloadrecruitable stroke work (PRSW) and can be used to extrapolate energy expenditure by the ventricle.

The end-diastolic pressure-volume relationship (EDPVR) is defined by connecting the end-diastolic points of the family of loops (Fig. 69.7). EDPVR reflects the pressure-volume relationship of the ventricle in its most relaxed state; it is inherently nonlinear as different muscle fibers are stretched at different points in the pressure-volume relationship. Constants can be derived from EDPVR to compare ventricular stiffness and diastolic function among individuals and between disease states. EDPVR is altered in patients with diastolic dysfunction, but, unlike ESPVR, EDPVR is less adaptable to changing physiologic states and altered hormonal control. Understanding the
differing effects of the EDPVR and ESPVR on stroke volume and the stroke work done by the heart provides unique insight into cardiovascular physiology in both disease and health.