Appendix B to responses to referees
Another attempt to make the point: Venous return curves from a “gedanken experiment”
The referees and I agree, I am sure, on the fundamental concept that we may think of the cardiovascular system as having two mechanical components, cardiac and peripheral vasculature, respectively, which we can characterize separately. In the cardiac component, assuming constant contractility and afterload, we can think of stroke volume as a dependent variable we can manipulate through the independent variable, right atrial pressure. In the peripheral vasculature, we can think of right atrial pressure as a dependent variable that we can manipulate through the independent variable, cardiac output. With these separate relationships in mind, we conceive how the combined cardiac and peripheral vascular components come into a typical negative feedback equilibrium. The equilibrium is associated with a particular right atrial pressure that is simultaneously (1) the consequence in the peripheral vasculature of the particular cardiac output and (2) the exact level that sets the current cardiac output via its influence on stroke volume. It's negative feedback because the effect of right atrial pressure on the cardiac pump and the effect of the cardiac output on right atrial pressure countervail.
I think that Guyton’s work and writings manifested this conceptual view which is expressed much more concisely in the graphical overlay of cardiac output and venous return curves. What I hope to get across is that prevailing interpretations of venous return curves look at them backwards. In my view, one example is the statement that right atrial pressure acts as a back pressure. Another is the notion that venous return can be described as driven by a fixed gradient between right atrial pressure and mean systemic pressure. These misapply interpretations of venous return curves in attempts to describe those transient circumstances in which cardiac output and venous return differ. But, since venous return curves are data from strictly steady state conditions of equality of venous return and cardiac output, they do not provide the basis for analysis of temporal details of what happens while changes are occurring.
The misinterpretations I am pointing to make me wonder if people think that one could study the isolated peripheral vasculature by manipulating right atrial pressure. Imagine starting with an isolated vasculature -- no flow, root of aorta tied off, right atrial outflow connected to a source of controlled pressure, blood volume adjusted to bring the system to a particular mean systemic pressure. Is there any way to manipulate right atrial pressure and see what happens to "venous return"? Of course not. If one were to think of adjusting right atrial pressure by raising or lowering a container of blood connected to a tee at the right atrium, the associated volume transfer would violate the requirement to hold system volume constant and, of course, no flow would result in the steady state anyway.
So how do we take apart the intact cardiovascular system and study the vasculature separately? We open the circuit at the outflow end and contrive a way to control flow through the circuit. That's the brilliant thing in the Guyton experiments, particularly their way of making sure that no change in system volume occurred.
But, we don't have to do it with a Starling resistor. Experiments like Levy's and Shoukas’s cited in the present revision reveal the cardiac output - Pra relationship via adjustment of pump output and no Starling resistor. These, however, can only reveal the flow-pressure relationship over the limited range of right atrial pressure (Pra) between mean systemic pressure (Pms) and the slightly subatmospheric pressure below which venous collapse prevents further flow increase. I’ll refer to this range as the SS, for sloped segment, the range of interest in my paper. My focus on that range is due to the interpretation that its intercept at Pms and its slope reveal that venous return is driven by the gradient betwean Pms and Pra.
In principle, there's another way that would reveal not only the SS but the relatively flat segment of a wide range of subatmospheric Pra at nearly constant flow. I present this as a “gedanken” experiment, not one that I expect would be practical to perform, but one whose outcome we can confidently predict from what we know.
An hypothetical way to obtain venous return curves.
We will use a reservoir of blood to supply a pump connected to the aorta. We will let the venous return flow out of the right atrium into a sink (as a practical matter, we could collect this blood and return it to the reservoir). The outflow detail is critical. Let's say we capture the venous return by means of a cannula in the right atrium (preventing outflow via the tricuspid valve by tying it off). We use tubing to route the outflow to the sink. Terminate the tubing in an L fitting, one leg horizontal, the other vertical, pointing up. Put the top of the vertical leg a few cm above the level of the zero reference at the RA. We need to fill the vasculature with blood sufficient to bring the meniscus up to the top of the L fitting. We can do that with the pump. We’ll just turn it on until venous outflow starts to spill over into the sink. Turn off the pump. Outflow will continue for a few moments and the meniscus will settle at the top of the L. At this point we have zero flow in the vasculature, and right atrial pressure and mean systemic pressure equal at the level set by the hydrostatic column between the top of the L and the RA reference level, let’s say 5 mm Hg. What happens if we start the pump?
Let’s start the pump, set for a low level of flow, say 600 ml/ per minute (halfway up the SS of a typical venous return curve for a dog). Sure enough, we observe that venous outflow soon begins to spill out of our L at the rate of one liter per minute. Shall we record Pra = 5 mm Hg as a data point for our study of the relationship between venous return and Pra? No, we’ve violated the provision that we must study the system with a fixed blood volume. We still have Pra = 5 mm Hg, but volume has been added to the system. At the original system volume, Pra has to be below 5 mm Hg when flow at 600 ml/min is present – the more the flow, the lower the Pra. This present Pra = 5 mm Hg was made possible only by addition of volume – the integrated difference between the pump output and the rate at which blood spilled into the sink in the first few seconds during which venous return was less than pump output.
How do we get around this? We'll need high-precision flowmeters on the inflow and outflow lines and a zero-drift integrator that integrates the difference between the inflow and outflow signals so we always know how much volume has been added or lost. Keeping pump rate at 600 ml/min, we'll lower the L fitting carefully. We’ll see that outflow now exceeds inflow. We keep an eye on the integrated volume and try to get it back to the original level. We'll have to be careful not to lower the L too far. It's easy to end up oscillating around the right level.
It’s reasonable to assume that we will succeed in finding the level of the L in equilibrium with flow at 600 ml/min and the original system volume because we know that one and only one level of steady-state Pra is consistent with this particular flow rate and initial volume, thanks to Guyton and co-workers an the subsequent studies that corroborated this.
Having found this first data point, we can gather others, each time turning up the flow and lowering the L as necessary. We're keeping systemic volume constant and discovering the right atrial pressure that is in equilibrium with each of our various flow levels. In this way we map out the relationship between Pra and flow in the range of Pra below Pms. We even note that lowering the L below a certain level no longer increases outflow relative to inflow because of collapse in sections of the venous vasculature at subatmospheric pressures, i.e. we can construct not only the sloped segment (the limitation of the setup of Levy) but the entire "venous return curve". We can do it all over again with a different initial mean systemic pressure to show the influence of system volume.
Whether this could be practically accomplished, even in a dead animal, I do not know. The difficulty of obtaining data on the relationship between Pra and flow in steady states of cardiac output-venous return balance with fixed system volume illustrates the brilliance of the design in the experiments of Guyton, et al. The Starling resistor technique eliminated the necessity of this complicated management of volume and Pra. However, one would never misinterpret data from the “gedanken” experiment as showing that venous return is driven by (Pms – Pra). One wouldn't fall into the misconception that it was Pra that was determining the steady state flow in the system. Nor would one think that elevating Pra to Pms would stop flow.
For example, consider the notion of back pressure. Rothe (handbook chapter), and Guyton himself (textbook among other places) wrote of the consequences of elevating Pra as increasing the "back pressure" and thus reducing venous return since the (Pms – Pra) gradient is reduced. Guyton’s textbook chapter includes a similar argument. They are overlooking something that can be seen in the context of the "gedanken" experiment. Let's set the pump for a modest level of flow. We locate the right level for the L and get systemic volume corrected and (in principle) could indefinitely maintain this fixed level of flow and Pra. Now let’s elevate Pra by elevating the L a few cm. Here's your increase in "back pressure" but I assure you the pump doesn't care. What does happen is that this elevated Pra is not in equilibrium with the current level of flow. Temporarily, outflow from the L will be less than pump output and volume will accumulate in the system -- building up pressure not only in the RA, but back through the whole system. Of course, the pump doesn't care about another few mm Hg and keeps on pumping at the same rate. The increase in "back pressure" hasn't done anything to flow. What it has done is result in altered systemic volume. We're no longer working with a system with the same Pms. We now have a system described by a different venous return curve, one in which the present level of output is in equilibrium with a higher level of Pra (see footnote).
I hope the referees agree that this “gedanken” experiment would, in principle, yield the same venous return curves obtained by Guyton et al. and their successors. I hope that they find the brief treatment included in the present paper an effective way of making the point.