A new gradient had entered the circulation…
In 1955, Arthur Guyton changed the way physiologists thought about cardiovascular function. The circulation was no longer viewed simply as a heart pumping into a passive network of vessels, but as an integrated system in which the properties of the heart and circulation interacted to determine the final cardiovascular state.
At the centre of this framework was a deceptively simple relationship, which can be expressed in compact notation as:
VR = (MCFP − RAP) / ZVR
Venous return was related to the difference between mean circulatory filling pressure and right atrial pressure, divided by what Guyton called the impedance to venous return. This terminology reflected an important insight: the denominator depended not on a single vascular resistance, but on the distribution of resistance and capacitance throughout an elastic vascular network.
The interpretation seemed obvious. Blood flowed from the higher pressure of the systemic circulation toward the lower pressure of the right atrium. Mean systemic pressure promoted venous return, right atrial pressure opposed it, and the difference between them represented the pressure gradient for venous flow.
For more than two decades, this framework shaped how physiologists understood the circulation.
Then, in 1979, Levy returned to Guyton’s equation and asked whether the problem was not the mathematics, but the interpretation placed upon it.
The same equation could tell a very different story…
One circulation, not two
Guyton’s experimental approach was extraordinarily powerful because it allowed the heart and vasculature to be examined separately.
The heart and circulation form a closed loop. Any change in cardiac function alters the circulation, while any change in the circulation alters the conditions presented back to the heart. Understanding the behaviour of each component separately is therefore extremely difficult.
Guyton’s solution was to open the loop experimentally. In different preparations, he replaced either the whole heart or the right heart with a mechanical pump, allowing him to examine the properties of the vascular system separately before recombining the two systems mathematically.
It was an elegant solution, but Levy argued that the success of the experiment had created a conceptual problem. A separation that was useful experimentally had gradually become a separation in the way people thought about the circulation itself.
Cardiac output and venous return began to appear as two competing processes: one generated by the heart, the other generated by the circulation.
But in an intact cardiovascular system there is only one flow. The blood leaving the heart is the same blood returning to it. Cardiac output and venous return are not opposing forces negotiating a compromise; they are the same circulation viewed from different locations.
Explaining a steady-state change in cardiac output by invoking an equal change in venous return was, Levy wrote, a “patent example of circular reasoning”. It was equivalent to explaining a change in total flow by the same change in total flow.
The question was not whether cardiac output controlled venous return or venous return controlled cardiac output.
The question was whether either could be considered the independent controller of the system.
The numerator strikes back
Levy’s most powerful argument came from looking again at the equation itself. Focusing specifically on the systemic circulation, he used mean systemic pressure (Pms)—the pressure to which the systemic vasculature would equilibrate if flow ceased—rather than Guyton’s mean circulatory filling pressure. By this stage, Guyton’s impedance term was also generally expressed as the resistance to venous return (RVR):
VR = (Pms − RAP) / RVR
The interpretation appeared straightforward. The numerator, Pms − RAP, seemed to be the independent factor. Increase mean systemic pressure and venous return increased. Increase right atrial pressure and venous return decreased.
The pressure gradient appeared to determine flow.
But Levy pointed out something deceptively simple: rearranging an equation does not change the physiology.
The same relationship can also be written:
Pms − RAP = VR × RVR
Now the interpretation looks very different. If resistance remains constant, the pressure gradient is not the variable controlling flow. It is the variable created by flow.
The circulation does not flow because a gradient has appeared between mean systemic pressure and the right atrium. The gradient exists because blood is flowing through a resistance.
This was not a mathematical trick. It was a reminder that equations describe relationships, and the way they are written can subtly influence which variable we imagine to be the cause.
In Guyton’s experiments, this was more than a question of presentation. The venous return curves were not created by observing a passive pressure gradient spontaneously producing flow. They were generated by altering flow through the experimental preparation and measuring the resulting pressure response.
In some preparations, pump output was directly varied and right atrial pressure was measured as the response. In later experiments, Guyton retained the mechanical pump but added a collapsible tube acting as a Starling resistor in an attempt to control right atrial pressure more directly.
This was an ingenious experimental solution, but Levy argued that it did not remove the fundamental problem. Establishing a new steady state still required a change in flow through the circulation. The experiment could therefore be interpreted in the opposite direction: rather than right atrial pressure determining venous return, changing flow altered the distribution of pressure within the vascular system.
The details of this experimental debate would continue for decades, but Levy’s central point was more forceful than mere ambiguity. The curves certainly demonstrated a relationship between pressure and flow, but he argued that their usual interpretation had reversed cause and effect: flow was the experimentally imposed variable, and right atrial pressure was the response.
The numerator had struck back.
Where do pressures come from?
Levy’s argument went beyond rearranging an equation. If right atrial pressure was not simply a back pressure opposing venous return, then a more fundamental question followed: where did the observed pressures come from?
His answer began with the vascular system itself. Blood vessels are not rigid pipes but elastic compartments whose pressures depend on how much blood they contain and on their pressure–volume properties. The heart supplies the energy for circulation and transfers blood from the venous side into the arterial side. As flow increases, arterial pressure rises and the arterial compartment contains more blood. Because the total systemic blood volume in Levy’s model is fixed, that additional arterial volume must come from the venous compartment, causing venous and right atrial pressures to fall.
For Levy, this redistribution explained the familiar inverse relationship between flow and right atrial pressure. Right atrial pressure did not independently limit venous return; it changed because the heart had altered the distribution of blood within an elastic vascular system.
Mean systemic pressure still mattered, but Levy treated it as a zero-flow boundary condition determined by total blood volume and systemic vascular capacitance, not as the source of energy for flow. Flow and resistance determined the arteriovenous pressure difference, while blood volume and the arterial and venous capacitances determined how that difference was distributed into the actual levels of arterial and venous pressure.
This was why Levy treated flow as the independent variable in Guyton’s experiments. The pump imposed the flow, and the vascular system generated the corresponding pressure distribution.
The disappearing gradient
Levy also highlighted a striking consequence of interpreting the venous return equation too literally.
In a typical circulation, mean systemic pressure is only a few millimetres of mercury above right atrial pressure. If Pms is approximately 7 mmHg and right atrial pressure is approximately 2 mmHg, then the pressure gradient for venous return is only around 5 mmHg.
A small increase in right atrial pressure would therefore have a dramatic effect on this gradient.
If Pms were held constant, increasing right atrial pressure by just 5 mmHg would make the gradient disappear completely.
Taken literally, venous return should stop.
But Levy argued that this was a strange way to view the circulation. The heart had generated a much larger pressure difference across the systemic circulation. An arterial pressure of approximately 100 mmHg and a right atrial pressure of 2 mmHg represented a pressure difference almost twenty times larger.
Increasing right atrial pressure by a few millimetres of mercury barely changed this total systemic pressure difference.
To Levy, this revealed the problem with focusing on the numerator of the venous return equation. The small difference between Pms and right atrial pressure was not the energy source responsible for circulating blood around the body. It was a pressure difference created within the systemic circulation as blood flowed through it.
The gradient was real, but Levy argued that its meaning had been misunderstood.
Guyton replies
Levy’s paper contained an unusual postscript. Arthur Guyton had reviewed it, and the editors published his response in full.
What followed was not the rebuttal one might expect.
Guyton wrote that he found himself in “complete agreement” with Levy on almost every conceptual point. He agreed wholeheartedly that venous pressure was a dependent variable. His objection was that Levy had not gone far enough: venous return—and therefore cardiac output—was no more independent than venous pressure.
Levy’s analysis treated flow as the input to the vascular system. This was entirely appropriate in an experiment where the investigator controlled the output of a mechanical pump and measured the resulting pressures. Under those conditions, flow was the manipulated variable and right atrial pressure was the response.
But Guyton argued that this experimental arrangement should not be mistaken for the intact circulation. The heart does not freely select a cardiac output and impose it upon the vasculature. Flow and pressure emerge from the interaction between the functional state of the heart and the mechanical properties of the circulation. In his reply, Guyton identified factors such as cardiac contractility, heart rate, vascular resistance and vascular capacitance as the more fundamental variables; cardiac output, venous return, arterial pressure and venous pressure were all dependent variables determined simultaneously.
This was remarkably close to the systems interpretation contained in his original 1955 paper. The venous return curve could be constructed by temporarily treating right atrial pressure as the independent variable, just as Levy’s vascular function curve could be constructed by temporarily treating flow as independent. Both were legitimate “what if” analyses. Neither assignment described the actual hierarchy of the intact circulation.
The disagreement between Levy and Guyton was therefore narrower than it first appeared. Levy had shown why the venous return curve should not be read as proof that right atrial pressure controlled flow. Guyton accepted that criticism, but insisted that reversing the axes did not make flow the ultimate controller either.
Pressure did not determine flow alone.
Flow did not determine pressure alone.
They were resolved together by the system.
That leaves the obvious question for the next episode: what were the physical properties of the vascular system that helped determine them?
Continued in Episode 3: Return of the Elastic State
Previous Episode: The Phantom Pressure
Original papers
1. Levy MN. The cardiac and vascular factors that determine systemic blood flow. Circulation Research. 1979;44:739–747.
2. Guyton AC. Determination of cardiac output by equating venous return curves with cardiac response curves. Physiological Reviews. 1955;35:123–129.
3. Guyton AC, Lindsey AW, Kaufmann BN. Effect of mean circulatory filling pressure and other peripheral circulatory factors on cardiac output. American Journal of Physiology. 1955;180:463–468.