Summary: valid and invalid interpretations of venous return curves

Faced with experimental data in which venous return is zero at a certain positive pressure, say 7 mm Hg, and increases with declining Pcv up to a point beyond which flow increases no more, we are inclined to interpret the data as consistent with what we know about the physical properties of the vasculature expressed in simple models like that in Figure 1.

We say that, at zero cardiac output, Pcv is an operationally meaningful way of observing mean circulatory pressure, Pmc.

We say that the flat portion of the curve where ever-decreasing Pcv was associated with no increase in Q shows deviation from the model easily understood in terms of the non-linear nature of the true venous resistance -- the veins collapse and impose greater resistance that prevents increase in Q. Indeed, the non-linear flow:pressure behavior of the true venous system must limit the applicability of a model based on a fixed venous resistance.

These are reasonable statements. However, if we say that this experimentally-obtained relationship between Pcv and Q reveals how venous return is driven through the venous system by mean circulatory pressure, against the resistance of the venous system, we are forgetting how we got to this point. What we found was that the data fit an expression like (1) and (2) above. In terms of the model from which the expressions were derived, we must recognize that Pmc has no physical meaning as a driving pressure in the model nor can the slope of the linear portion of the data be interpreted as a physically meaningful resistance. The apparent resistance is like the Thevenin equivalent resistance of a simple electrical network that is a composite of the actual physical components of the network.

Fallacious interpretation of the sloped segment of venous return curves

On the other
hand, you could approach the data *de novo* and simply
interpret a venous return curve as what we would find if a fixed
pressure source, Pmc, were driving flow through a fixed
resistance, R, so that flow, at least over the linear range
equaled (Pmc - Pcv) divided by R. Nobody can
say that these data, by themselves, cannot support your
interpretation. You are free to speculate that R represents the
hydraulic resistance of the venous system; that the driving
pressure, Pmc, at the upstream end of the resistance is constant;
and, therefore, that Pcv determines Qr.

However, if you happen to know that the vascular system from which you obtained these data was driven by a pump set at particular levels of flow you have to reject this interpretation. Your view that Pmc is at the upstream end of a fixed resistance, Rven, with a physical meaning connected to resistance properties of the venous vasculature, is untenable.

First, with each output setting of the pump, the physical points at which at which a pressure equal to Pmc could be found would move -- upstream with increased levels of flow. Consequently the physical segment of the vasculature over which the Pmc - Pcv gradient extends cannot be fixed nor can the resistance of this segment be regarded as associated with a fixed, anatomically identifiable, segment of the vasculature.

Second, your interpretation requires that you view Pmc as constant by virtue of an energy source that supplies whatever flow is necessary to hold it constant as Pcv varies. That is inconsistent with the fact that the energy source was the pump that drove prescribed levels of flow through the vasculature. Pmc is constant because it is a parameter of the vasculature set by total volume and vascular compliance.

Fallacious concept that venous return can be stopped by elevating central venous pressure

The most flagrant misinterpretation of venous return curves is to suggest that elevation of Pcv to Pmc would stop venous return. Even authors who stress that the relationship between Pcv and Q should be thought of as a "vascular function curve" in which Q is the independent variable make this statement. Does it have an meaning?

Just how would you accomplish this elevation of Pcv? By quickly injecting some volume in the vena cavae? No, that would not do because altering system volume alters Pmc which is supposed to remain fixed.

One author [cite Rothe ?] suggested that Pcv could be altered by rapid transfer of volume, injecting a fixed quantity into the arterial side as quickly as it was removed from the venous side. However, this would immediately be followed by a rapid readjustment that brought the volume distribution back to the original state. The only way to bring Pcv up to Pmc is to stop cardiac output.

The utility of vascular function curves in describing cardiovascular equilibrium through the negative feedback relationship between cardiac output and central venous pressure

In quantitative simulations based on the elementary models of the physical properties of the vasculature, Pcv changes inversely with changes in Qo. Consequently, if the model is altered to include representation that Qo is driven by Pcv (Starling’s law), it resembles a negative feedback control system. Any tendency for the heart to change Qo causes Pcv to change in the opposite direction, thus acting on the heart to counter the Qo tendency.

The easy way to see the outcome of this negative feedback interaction is simply to plot the dependence of Pcv on Qo on a graph that also shows the dependence of Qo on Pcv. The latter is, of course, a cardiac output curve. Call the former a venous return curve, if you wish, but Levy's "vascular function curve" is less confusing. Plotting it this way, with Pcv on the " x" axis, does not have anything to do with Pcv as an independent variable affecting Qr, it is simply a convenient way to look at one side of the negative feedback interaction between the effects of Pcv on Qo and the effects of Qo on Pcv.

Limitations

Of course, the simple series connection of components with single capacitors representing major subdivisions of the vascular compliance overlooks the distributed nature of the physical parameters of the vasculature as well as the disparity relative to actual pressure:volume properties of vessels.

Interpreting even the linear sloped portion of actual vascular function curves in terms of two resistances and three capacitances overlooks the subdivision of the system properties among the organ vasculatures and, where reflexes are intact, the importance of the consequences for pressure profiles in the individual organ vasculatures.

The lack of consideration of other energy sources in determination of overall vascular function properties has limited applicability of venous function curves to understanding of cardiac output control. Guyton, et al., did discuss the role of respiration-related volume displacements. Only recently have investigators taken on the daunting objective of recording Pcv in relation to cardiac output during exercise, when skeletal muscle contraction couples mechanical energy into the vasculature (10, 11). These reveal radical displacement relative to the vascular function curves obtained in a resting animal but still with a reciprocal relationship between cardiac output and central venous pressure.

Conclusion

To interpret the experimentally obtained "venous return curves" as revealing that venous return is driven by the gradient between a fixed mean circulatory pressure and central venous pressure across a fixed venous resistance is to confuse a mathematical abstraction with reality. Especially absurd is the statement that venous return can be reduced to zero by elevating central venous pressure to mean circulatory pressure. It is cardiac output that determines central venous pressure in steady states. Mean circulatory pressure is a conceptual abstraction we can use for thinking about the instantaneous elastic state of the vasculature in relation to total blood volume and is not in any sense the driving force for venous return.

In the brief transient periods in which the rate of flow returning to the right atrium differs from the cardiac output, the difference between them is accumulating in or being withdrawn from the elastic compartments of the vasculature. We can describe such transients in intuitive terms, reasoning out how the pressure profile in the vasculature changes and how volume is thereby redistributed among the compliant compartments. We can imagine the consequences of more physiological situations in which arterial blood pressure does not change passively by thinking out the consequences for pressure profiles in the organ vasculatures.

If we wish to go beyond this level of intuitive treatment, we can use simple models of the vasculature to show quantitative representations of the inverse relationship between cardiac output and central venous pressure, or we can use experimentally obtained "venous return curves", better called "vascular function curves". Plotting these relationships with central venous pressure on the "x" axis does not signify that central venous pressure determines venous return. It is merely a convenient way of combining them with cardiac output curves to find the single central venous pressure that is simultaneously consistent with the effects of cardiac output on the vasculature and with the effects of central venous pressure on cardiac output.