The sloped portion of a venous return curve does look like the record of flow that would be obtained if flow were driven by the difference between Pmc (constant) and Pcv (variable). The size of the resistance across which this driving pressure acts would be computed as the negative reciprocal of the slope (details in Figure 3 legend).

Guyton and others adopted this interpretation in describing venous return as driven through a vascular resistance by the (Pmc - Pcv) gradient. The resistance was interpreted as corresponding physically to, or at least being dominated by, the resistance of the venous portion of the total peripheral resistance. (1, 9). In a paper that recognized that other parameters, including arterial resistance and capacitances of the system are combined in this apparent resistance, the term "venous impedance" was used (6). Perhaps this choice reinforced the idea that the slope revealed a venous system property. The term "impedance" readily generalizes to "resistance", since the data refer to steady-state conditions of flow in which the distinction between the two terms is irrelevant.

A system with venous return driven by the difference between Pmc and Pcv through a single hydraulic resistance, R, i.e., Qr equals (Pmc - Pcv) divided by R, would indeed show a negatively sloped relationship like the linear portion of venous return curves (Figure 3). But that does not mean that the linear sloped segment may be interpreted on the basis of the physical model in Figure 1, with Pmc as the pressure in the peripheral venous compartment that drives flow against the resistance of the venous system in proportion to the difference between Pmc and Pcv.

To see this, one needs to work out the mathematical details and describe the behavior of the physical model. Levy did this with a simple one resistance, two capacitance electrical equivalent (8), sufficient to show how the change in pressure profile caused by altered cardiac output would result in transfer of volume between two compliant compartments. But, recognizing that relatively little volume change occurs within the arterial compartment and that the differences between Qo and Qr are accommodated almost entirely through dynamic distribution of volume within the venous system, the model illustrated in Figure 4 is the simplest possible first approximation to physical properties of the peripheral vasculature. It is an electrical analog of the physical model illustrated in Figure 1, augmented by a hydraulic resistance and compliance representing the arterial system.

In this model, hydraulic resistances of the arterial and venous systems are modeled by electrical resistances and compliance of the arterial system and the two compartments of the venous system are modeled by capacitances. The analogous relationships are: electrical current as blood flow, electrical resistance as hydraulic resistance, voltage as pressure, and charge as volume. System "volume" is set by the initial condition of charge in the capacitors^* see footnote. The model is driven by a pure current source, i.e. one which produces a set level of current independent of voltages at its terminals. This is a reasonable analogy to the kind of pump used in setting Qo in the experiments described above.

With zero flow, voltages equilibrate, i.e. Pa = Ppv = Pcv, at a level that depends upon the total charge (system volume) set as an initial condition. Charge distributes among the capacitances in proportion to their capacitance. This uniform voltage and distribution of charge is the analog of the zero-flow situation in which mean circulatory pressure, Pmc, is seen. When flow is forced through, the development of pressure gradients causes increased charge in the arterial capacitance, and reduced charge in the venous capacitances. Progressive increase in flow results in progressive decrease in Pcv.

Figure 5 shows that the behavior of this model resembles that observed in the linear sloped segment of venous return curves. Naturally, the flat segment of high and fixed Qr over a range of Pcv is not predicted, because this is the consequence of non-linear behavior of the elastic and resistive components of the vasculature, e.g., collapse and fluttering of vessels in which subatmospheric pressures develop. But, is the slope determined by the resistance of the venous system and is flow driven by (Pmc - Pvc)?

Indeed, the equations that describe the flow:pressure relationship of the circuit can be combined in the following form:

In the above equation, Q represents flow, and Req represents the following:

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