It is a period of haemodynamic uncertainty. The gradient has been challenged, the numerator has struck back, and the old equation can no longer explain itself. From the compliant depths of the venous circulation, a forgotten state is about to return…
From pressure and flow to volume
Levy had taken the venous return equation apart and put it back together in reverse. The same relationship that Guyton had read as a pressure difference determining flow could equally be read as flow determining the pressure difference. Neither arrangement established causality. Guyton himself had acknowledged the deeper implication: in the intact circulation, pressure and flow were both dependent variables.
But that left an obvious question unanswered. Dependent on what?
The equation related venous return to mean systemic filling pressure, right atrial pressure and resistance, but said little about the vascular properties from which those pressures arose. Blood did not occupy a rigid system of pipes. It was distributed through vessels that expanded, recoiled and changed shape. The same total blood volume could therefore produce very different pressures, depending on the vessels containing it.
This was the territory explored most systematically by Carl Rothe. Rather than beginning with the pressure difference said to drive venous return, he examined how the circulation contained blood: where that blood resided, how easily the vessels expanded, and how smooth-muscle activity altered the available vascular space.
The veins were central to this account. Their large resting volume and high compliance mean that they contain most of the systemic blood volume and provide most of the circulation’s ability to accommodate changes in volume. Their importance was therefore not simply that blood passed through them on the way to the heart. Venous elastic and contractile properties helped determine how the blood volume was distributed and what pressures appeared throughout the circulation.
Two ways to redistribute blood
Rothe began with a distinction that sounds obvious but is easily lost. Venous return is a rate of flow, not a parcel of blood being emptied from a reservoir. In a steady circulation, blood does not progressively leave the veins and accumulate in the heart or arteries. Cardiac output and venous return are the same continuous flow viewed at different locations.
Vascular volumes can, however, change while the circulation moves from one steady state to another. Rothe demonstrated this in preparations where cardiac output was imposed by a mechanical pump. Increasing flow altered the distribution of blood within the vasculature: arterial pressure and volume rose, while volume fell in the small and great veins. He then applied the same principle to the intact circulation. If increased cardiac activity succeeded in producing a higher flow, the heart would temporarily transfer a finite volume from the venous side into the arterial system. Once that redistribution was complete, cardiac output and venous return would again be equal—but at a new operating state, with more blood residing on the arterial side and less in the veins.
No active venoconstriction is required. The venous walls already possess passive elastic properties. As the circulation establishes the new state, the veins move to a lower-pressure, lower-volume point on their existing pressure–volume relationship. The recoil occurs during the transition; it is not another pump that continues to propel blood afterwards. The higher flow, where one develops, remains sustained by the heart’s continuing energy input.
Flow can redistribute blood regionally as well. If resistance to inflow into an organ rises, regional flow and downstream vascular pressure may fall. Its distensible venous vessels then contain less blood, leaving more of the fixed total volume elsewhere in the circulation. Vasodilation can have the opposite effect, allowing a vascular bed to contain more. Rothe argued that passive volume changes of this kind could be substantial and could easily be mistaken experimentally for active contraction of the veins.
Active venous redistribution is fundamentally different. Venous smooth-muscle contraction changes the volume-containing properties of the vessel itself. Blood then redistributes through the circulation as volume, pressure and flow settle into a state compatible with the altered vascular compartment.
Both processes therefore move real blood between compartments. The distinction concerns what changes first. In a passive response, the vessels move to a new operating point while their underlying mechanical properties remain the same. In an active response, vascular smooth muscle changes those properties, and a new distribution follows.
The shape of the container
Rothe needed a more exact vocabulary to describe this behaviour. Capacity meant the volume currently contained within a vascular compartment. Compliance described the relationship between a change in contained volume and the associated change in distending pressure:
C = ΔV / ΔP
Compliance was therefore the slope of the volume–pressure relationship over the range being examined. A highly compliant vessel could accommodate a large change in volume with only a small change in pressure. A less compliant vessel produced a larger pressure change for the same change in volume.
Compliance alone was not enough. Two vascular compartments could have the same compliance—the same slope—yet be very different sizes and therefore contain very different volumes at the same pressure. Rothe used vascular capacitance for the whole volume–pressure relationship, including both the resting size of the compartment and how readily it expanded.
The terminology is potentially confusing. Electrical capacitance maps more naturally onto vascular compliance than onto Rothe’s broader definition. I will use vascular accommodation for the broader property: the relationship governing how much blood a vascular compartment can contain at different pressures.
Rothe described the approximately linear portion of this relationship as:
V = Vᵤ + CP
where V is the total contained volume, Vᵤ is unstressed volume, C is compliance and P is transmural pressure.
In this simplified model, unstressed volume represented the resting size of the vascular container: the volume-axis intercept obtained by extending the measured relationship back to zero transmural pressure. Stressed volume was the remaining part of the contained volume associated with elastic distension:
Vₛ = CP
These were calculated components of the same contained blood volume, not two anatomically separate reservoirs. In later teaching, unstressed volume came to be imagined as a hidden reserve waiting to be recruited, while stressed volume was pictured as a separate pool already placed under tension. Rothe’s definitions were more careful. They provided a mathematical way of separating the resting size of the container from the additional volume associated with its distension. All the blood within a pressurised vessel is physically exposed to pressure; stressed volume is a model-derived partition, not the only blood that is literally under stress.
This is why venoconstriction is often described as “recruiting” unstressed volume. When venous smooth muscle contracts, the effective resting size of the vascular compartment becomes smaller. Within Rothe’s model, the same total volume is then represented by a larger stressed-volume term. Blood also genuinely redistributes into other compartments as the circulation establishes a new state. What has not occurred is a literal transfer from an unstressed reservoir into a separate stressed reservoir; the mathematical partition changes because the vascular compartment has changed.
Passive redistribution is different. If increased cardiac activity transfers a finite volume from veins to arteries without changing vascular tone, the venous stressed-volume term falls while the arterial term rises. Vascular accommodation has not changed; blood has simply changed location within the same set of compartmental relationships.
The distinction can therefore be stated simply:
Passive redistribution changes where blood resides without changing vascular accommodation. Active venoconstriction changes vascular accommodation itself—usually by reducing unstressed volume, but sometimes by changing compliance as well.
The pressure of the whole circulation
These relationships existed in every vascular compartment. Mean systemic filling pressure, Pms, described their aggregate state across the systemic circulation. Rothe generally wrote of mean circulatory filling pressure, Pmcf, for the circulation as a whole. Here I use Pms for the corresponding systemic equilibrium pressure relevant to systemic venous return.
The concept predated Rothe. His contribution was to explain its physical meaning and measurement in much greater detail. During normal flow, pressures differ widely: arterial pressure is high, right atrial pressure is low, and pressures within individual organs lie between them. If the heart stops, blood redistributes until these differences disappear and the systemic vasculature approaches a common equilibrium pressure. That pressure is Pms.
In Rothe’s linearised description:
Pₘₛ = ΣVₛ / ΣC
The numerator is total systemic stressed volume and the denominator is total systemic vascular compliance. Pms is therefore not the pressure of one vessel, nor a simple arithmetic average of the pressures measured during flow. It is the equilibrium pressure produced by the interaction between total stressed volume and the combined compliance of the systemic circulation.
This helps explain why the veins matter so much. Most systemic blood volume and most vascular compliance reside on the venous side. The arteries contain less blood and are much stiffer, so even large changes in arterial pressure involve relatively small changes in contained volume. The systemic elastic state is therefore determined primarily—although not exclusively—by the volume–pressure properties of the veins and venules.
Rothe sometimes described Pms as an index of the circulation’s “fullness”. The word is useful only if it is understood as an elastic filling state, rather than as blood volume alone. The same blood volume can produce a lower Pms when it is accommodated within a larger vascular space, or a higher Pms when vascular accommodation is reduced.
Increasing blood volume can therefore raise Pms by increasing total stressed volume. Venoconstriction can also raise Pms without changing total blood volume. By reducing unstressed volume, changing compliance, or both, it alters the relationship between the existing blood volume and the vascular compartment containing it. The same blood volume can therefore equilibrate at a higher pressure. Reducing blood volume or increasing venous accommodation has the opposite effect.
Passive redistribution between arteries and veins need not alter Pms. If total blood volume and vascular accommodation remain unchanged, it changes how stressed volume is distributed during flow rather than its aggregate amount. If the heart is stopped, that arterial–venous distribution is undone as the same total stressed volume spreads across the same total compliance and returns to approximately the same equilibrium pressure.
Rothe had therefore restored something essential to the argument. Pms was not merely a number that appeared after the pump stopped. It was a compact pressure expression of the systemic circulation’s elastic state: the relationship between the contained blood volume and the vascular system accommodating it.
But then he went one step further.
The pivot and the phantom
During flow, pressure falls progressively from the arterial system towards the right atrium. Arterial pressure lies above Pms and right atrial pressure lies below it, so somewhere along the flowing circulation the local pressure must cross the numerical value of Pms.
When the heart stops, arterial pressure falls towards Pms while central venous pressure rises towards it. Compartments whose pressure was initially above Pms lose volume; those initially below it gain volume. Near the point where local pressure already approximated Pms, relatively little changes. Rothe called this the pivot pressure.
The pivot had legitimate descriptive value. It marked the approximate crossover between regions that gained volume and those that lost it as cardiac activity changed. Because much vascular volume and compliance reside in small veins and venules, the crossover often appeared in that part of the circulation. Its precise location was not fixed and could differ between organs or move as flow and vascular tone changed.
Rothe nevertheless gave the numerical resemblance greater significance. Because pressure in the small veins could approximate Pms during flow, he treated Pms as an estimate of their distending pressure and therefore as the upstream pressure for venous return.
That step is difficult to justify.
Was the local venous pressure during flow truly the same physical quantity as Pms—or had Rothe given an equilibrium property an anatomical home it did not possess?
Continued in Episode IV: The Phantom Pressure.
Original papers
Rothe CF. Reflex control of veins and vascular capacitance. Physiological Reviews. 1983;63(4):1281–1342.
Rothe CF. Mean circulatory filling pressure: its meaning and measurement. Journal of Applied Physiology. 1993;74(2):499–509. https://doi.org/10.1152/jappl.1993.74.2.499
I think Fig. 5 from Brengelmann's article is a good illustration of this – different distribution at different flow but the same Pms. (Although he assumed that flow could be arbitrary, as if the heart were a piston pump.) But Brengelmann's introduction might be a spoiler alert for your series...
https://journals.physiology.org/doi/full/10.1152/ajpheart.00381.2019?rfr_dat=cr_pub++0pubmed&url_ver=Z39.88-2003&rfr_id=ori%3Arid%3Acrossref.org