The analysis of interactions between the cardiac and vascular components of the circulatory system involves the use of two types of graphed curves in this chapter. The first curve, known as the cardiac function curve, demonstrates the relationship between cardiac output and preload, specifically central venous or right atrial pressure. This curve focuses on the heart itself and is typically studied in isolated hearts. The second curve, called the vascular function curve, examines the relationship between central venous pressure and cardiac output. It depends solely on various characteristics of the vascular system, such as peripheral vascular resistance, arterial and venous compliance, and blood volume. Unlike the cardiac function curve, the vascular function curve is independent of heart characteristics and can be experimentally derived using a mechanical pump in place of the heart.

In terms of variables, the vascular function curve considers central venous pressure (Pv) as the dependent variable and cardiac output as the independent variable. This is opposite to the cardiac function curve, where central venous pressure (or preload) is the independent variable and cardiac output is the dependent variable.

To explain how cardiac output affects Pv, a simplified model of the circulation is presented in Figure 19.2. This model condenses the essential components of the cardiovascular system into four elements. The heart's right and left sides, along with the pulmonary vascular bed, form a pump-oxygenator similar to an artificial heart-lung machine used during open heart surgery. The peripheral resistance refers to the high-resistance microcirculation. The compliance of the system is divided into arterial compliance (Ca) and venous compliance (Cv). Compliance (C) of a blood vessel is defined as the change in volume (ΔV) accommodated per unit change in transmural pressure (ΔP). Venous compliance is approximately 20 times greater than arterial compliance, and for simplicity, the ratio of Cv to Ca is set at 19:1.

In this hypothetical model, a change in cardiac output leads to an inverse change in Pv. The model replicates characteristics of an average adult, where cardiac output (Qh) is 5 L/minute, mean arterial pressure (Pa) is 102 mm Hg, and Pv is 2 mm Hg. Peripheral resistance (R) is determined by the ratio of the arteriovenous pressure difference (Pa − Pv) to flow (Qr) through the resistance vessels, which is equal to 20 mm Hg/L/minute.

Under equilibrium conditions, the flow rate through the peripheral resistance (Qr) matches the flow rate pumped by the heart (Qh). This results in a constant volume of blood in the arteries (Va) and veins (Vv), as the volume transferred from veins to arteries by the heart equals the volume flowing from arteries through resistance vessels to the veins.

Hence, if it were necessary to increase arterial pressure by 1 mm Hg by adding x mL of blood to the arterial system, 19x mL of blood would need to be added to the venous system to achieve the same increase in venous pressure.
In this chapter, two kinds of graphed curves are used to analyze interactions between the cardiac and vascular components of the circulatory system. The first curve, the cardiac function curve, is an expression of the well-known Frank-Starling relationship, and it illustrates the dependence of cardiac output on preload (i.e., central venous or right atrial pressure). The cardiac function curve is a characteristic of the heart itself and is usually studied in hearts completely isolated from the rest of the circulation. This curve has already been discussed in detail in . Later in this chapter, this curve is discussed in association with the other characteristic curve, the vascular function curve, to analyze interactions between the heart and the vasculature. The vascular function curve defines the dependence of central venous pressure on cardiac output. This relationship depends only on several vascular system characteristics, including peripheral vascular resistance, arterial and venous compliance, and blood volume. The vascular function curve is entirely independent of the characteristics of the heart. Because of this independence, it can be derived experimentally even if a mechanical pump replaces the heart.
The vascular function curve defines the changes in central venous pressure (Pv) that are caused by changes in cardiac output. In this curve, Pv is the dependent variable (or response), and cardiac output is the independent variable (or stimulus). These variables are opposite those of the cardiac function curve, in which Pv (or preload) is the independent variable and cardiac output is the dependent variable.
The simplified model of the circulation shown in
Fig.
19.2 helps explain how cardiac output determines the level of Pv. In this model, all essential components of the cardiovascular system have been lumped into four basic elements. The right and left sides of the heart, as well as the pulmonary vascular bed, constitute a pump-oxygenator, much like an artificial heart-lung machine used to perfuse •Fig. 19.1 Thefourfactors(inblue squares)thatdeterminecardiacoutput.
the body during open heart surgery. The high-resistance microcirculation is designated the peripheral resistance. Finally, the compliance of the system is subdivided into arterial compliance (Ca) and venous compliance (Cv). As defined in , the compliance (C) of a blood vessel is the change in volume (ΔV) that is accommodated in that vessel per unit change in transmural pressure (ΔP); that is,
Equation 19.1
Venous compliance is approximately 20 times greater than arterial compliance. In the example in
Fig. 19.2, the ratio of Cv to Ca is set at 19:1 to simplify calculations.
To show how a change in cardiac output causes an inverse change in Pv, the hypothetical model has certain characteristics that mimic those of an average adult (see
Fig. 19.2A ). The flow generated by the heart (i.e., cardiac output; Qh) is 5 L/minute; mean arterial pressure (Pa) is 102 mm Hg; and Pv is 2 mm Hg. Peripheral resistance (R) is the ratio of the arteriovenous pressure difference (Pa − Pv) to flow (Qr) through the resistance vessels; this ratio is equal to 20 mm Hg/L/minute.
An arteriovenous pressure difference of 100 mm Hg is sufficient to force a flow rate (Qr) of 5 L/minute through a peripheral resistance of 20 mm Hg/L/minute (see
Fig.
19.2A ). Under equilibrium conditions, this flow rate (Qr) is precisely equal to the flow rate (Qh) pumped by the heart. From heartbeat to heartbeat, the volume of blood in the arteries (Va) and the volume of blood in the veins (Vv) remain constant because the volume of blood transferred from the veins to the arteries by the heart is equal to the volume of blood that flows from the arteries through the resistance vessels and into the veins.
*Thus if it were necessary to add x mL of blood to the arterial system to produce a 1–mm Hg increase in arterial pressure, 19x mL of blood would need to be added to the venous system to raise venous pressure by the same amount.