A brief extra post outside my usual schedule. I came across this paper while reviewing the recent haemodynamics literature and thought it was too relevant to leave until later. It connects directly with two themes I’ve been exploring here: dependent variables versus causes, and the arguments running through the Venous Return Wars series.
A recent sheep study by Robert Hahn asks what happens to mean systemic filling pressure during fluid loading, adrenergic stimulation and sepsis.
The results are intriguing. But the most interesting part of the paper may be what happens when a calculated haemodynamic variable starts to acquire the status of a measured physiological quantity.
Hahn analysed data from experiments in healthy and septic sheep receiving crystalloid fluid together with phenylephrine, norepinephrine, isoprenaline or dopamine. Mean systemic filling pressure was not measured by stopping flow and allowing systemic pressures to equilibrate. Instead, the study calculated the commonly used mean systemic filling pressure analogue, Pmsa, from cardiac output, mean arterial pressure and central venous pressure.
Read the full open-access paper
The distinction between Pms and Pmsa becomes central to interpreting the results.
What the study found
In the absence of vasoactive drugs, calculated Pmsa was almost identical at baseline in healthy and septic sheep: about 17 mmHg in both groups.
Fluid loading generally increased Pmsa. Phenylephrine combined with fluid produced the most sustained increase during sepsis. Across the entire experiment, however, septic animals had a 23% lower Pmsa than non-septic animals.
The septic circulation was markedly hyperdynamic:
cardiac output: 12.9 vs 7.7 L/min
MAP: 74 vs 109 mmHg
CVP: 5.3 vs 7.6 mmHg
The calculated resistance to venous return was 63% lower in septic animals: 1.41 versus 2.47 mmHg·min/L.
Adrenergic stimulation also produced some striking results. In healthy animals, beta-adrenergic stimulation with isoprenaline and dopamine was associated with substantial increases in calculated Pmsa and cardiac output, while alpha-1 stimulation with phenylephrine increased MAP and CVP but did not produce the same rise in Pmsa.
Taken at face value, the paper appears to show that fluids, sepsis and adrenergic drugs alter mean systemic filling pressure, the pressure gradient for venous return and resistance to venous return.
There is another way to read it.
Pms was never measured
True mean systemic filling pressure is an equilibrium property.
Stop the heart, wait for flow to cease and allow pressures in the systemic circulation to redistribute. The resulting equilibrium pressure reflects the interaction between vascular volume and the pressure–volume characteristics of the systemic circulation.
That experiment was not performed here.
Instead, Pmsa was calculated from:
Pmsa = 0.96 × CVP + 0.04 × MAP + c × CO
where c is an anthropometric coefficient adjusted for the size of the sheep. The equation also assumes a fixed 24:1 venous-to-arterial compliance ratio.
Pmsa is therefore a mathematical transformation of three variables measured during active circulation:
CVP, MAP and cardiac output.
This creates an interesting problem when those same variables change dramatically.
Cardiac output is inside the pressure
Consider the healthy animals given isoprenaline.
Cardiac output increased substantially. Calculated Pmsa also rose.
It is tempting to interpret that result physiologically:
beta stimulation increased stressed volume, which increased mean systemic filling pressure, which increased the gradient for venous return and therefore increased cardiac output.
But cardiac output is already an input to the Pmsa equation.
Increase CO and, all else being equal, Pmsa must increase.
The calculated pressure cannot therefore provide independent evidence that an increase in an underlying equilibrium pressure caused the increase in flow.
The same issue becomes even clearer when the paper calculates the ‘pressure gradient for venous return’:
dVR = Pmsa − CVP
Substituting the equation for Pmsa gives:
dVR = 0.04 × (MAP − CVP) + c × CO
The calculated ‘pressure gradient for venous return’ therefore contains cardiac output within it.
The study then calculates resistance to venous return:
RVR = dVR / CO
Substitution gives:
RVR = 0.04 × (MAP − CVP) / CO + c
So cardiac output appears once in the calculated upstream pressure and then again in the denominator used to calculate resistance.
These are mathematically valid derived quantities. They are not independent measurements of an upstream pressure, a driving gradient and a vascular resistance.
But if resistance changes, hasn’t resistance changed?
If resistance is calculated as a pressure difference divided by flow, then a change in that ratio means the effective resistance of the circulation has changed.
But that does not necessarily mean that the vessels themselves have become intrinsically more or less resistive.
In the circulation, resistance is not produced by a fixed resistor. It emerges from the state of the vascular bed: vessel calibre, smooth-muscle tone, distending pressure, recruitment and derecruitment of vessels, blood viscosity and the tendency of vessels to narrow or close at low pressure.
Change the haemodynamic state and the relationship between pressure and flow can change even if there has been no active vasoconstriction or vasodilatation.
Consider a vascular bed in which increasing pressure distends previously narrow vessels. More flow can now pass for each additional increase in pressure. The calculated pressure-to-flow ratio falls. We can legitimately say that the effective vascular resistance is lower, but it would be wrong to assume that vascular tone must therefore have fallen. The vessels may simply be operating at a different pressure and calibre.
The opposite can occur as pressure falls. Vessels become narrower, some may begin to close, and progressively less of the vascular bed remains available to carry flow. The pressure-to-flow ratio rises even without any active increase in smooth-muscle tone.
Critical closing pressure is an extreme example of the same behaviour. Flow can cease while there is still a positive pressure within the vessel because the vessel is no longer patent. The pressure remaining at zero flow is therefore not being dissipated across a conventional resistance. It is maintaining, or failing to maintain, vessel patency.
So a calculated resistance tells us something real about the current relationship between pressure and flow. It does not, on its own, tell us which physical property of the vascular system produced that relationship.
The same caution applies to Hahn’s calculated resistance to venous return, with an additional problem: the upstream pressure used to calculate the gradient is itself partly calculated from cardiac output.
A fall in calculated RVR therefore means exactly what it says: the model-derived ratio of pressure gradient to flow has fallen.
It does not independently demonstrate that the physical venous circulation has undergone an equivalent fall in some fixed, intrinsic ‘resistance to venous return’.
What Pmsa can still tell us
A model can provide a useful descriptor without being a direct measurement. Pmsa has been compared with other estimates of mean systemic filling pressure and can track haemodynamic changes under some circumstances.
The problem begins when the calculated variable is treated as independent experimental evidence for the causal model from which it was derived.
If we want to know whether isoprenaline genuinely increases the equilibrium pressure of the systemic vascular system, the strongest experiment would be to measure that equilibrium pressure independently while manipulating beta-adrenergic tone.
If measured Pms rose alongside calculated Pmsa, we could then ask why: altered venous tone, redistribution of blood volume, changes in compliance, or some combination of these.
This study cannot make that separation.
Its assumptions may also be least secure under the very conditions being studied. Pmsa assumes a fixed 24:1 venous-to-arterial compliance ratio, while the paper itself acknowledges that sepsis alters arterial compliance and venous vascular behaviour.
The more interesting interpretation
The paper reports that sepsis reduced calculated Pmsa by 23%, the calculated gradient for venous return by 23%, and calculated resistance to venous return by 63%, while cardiac output increased by about 70%.
Those numbers describe how the Pmsa model represents the haemodynamic state.
They do not independently establish that:
an equilibrium Pms fell by 23%;
a physical pressure gradient driving venous return fell by 23%;
or the intrinsic resistance of the venous circulation fell by 63%.
The distinction is especially important when a derived variable is then placed into a causal sequence.
CO rises → calculated Pmsa rises is partly built into the equation.
That result cannot then be turned around without further evidence into:
Pmsa rose → therefore CO rose.
The calculation and the causal explanation are different things.
A useful paper for exactly that reason
Hahn’s study is valuable. The experiments generate large, physiologically interesting changes in flow, arterial pressure and venous pressure under fluid loading, adrenergic stimulation and sepsis.
It also provides an unusually clear example of a broader problem in cardiovascular physiology.
We often begin with an equation that describes relationships between variables. We calculate a new quantity from those variables. We give that quantity the name of a physiological entity. Then, almost imperceptibly, the calculated quantity begins to appear in the causal explanation of the very measurements from which it was constructed.
Pmsa may be a useful estimate of systemic vascular state.
It is not the same thing as stopping the circulation and measuring mean systemic filling pressure.
And a calculated gradient is not evidence, by itself, that the gradient was the independent cause of the flow from which it was calculated.
The equation can describe the haemodynamic state without telling us which way causality runs.
References
Parkin G, Wright C, Bellomo R, Boyce N. Use of a mean systemic filling pressure analogue during the closed-loop control of fluid replacement in continuous hemodiafiltration. J Crit Care. 1994;9(2):124–133.
https://doi.org/10.1016/0883-9441(94)90023-XMaas JJ, Pinsky MR, Geerts BF, de Wilde RB, Jansen JR. Estimation of mean systemic filling pressure in postoperative cardiac surgery patients with three methods. Intensive Care Med. 2012;38(9):1452–1460.
https://doi.org/10.1007/s00134-012-2586-0Werner-Moller P, Heinisch PP, Hana A, Bachmann KF, Sondergaard S, Jakob SM, Takala J, Berger D. Experimental validation of a mean systemic pressure analog against zero-flow measurements in porcine VA-ECMO. J Appl Physiol.2022;132(3):726–736.
https://doi.org/10.1152/japplphysiol.00804.2021Hahn RG. Influence of adrenergic drugs and volume loading on mean systemic filling pressure in non-septic and septic sheep. Front Med (Lausanne). 2026;13:1871295.
https://doi.org/10.3389/fmed.2026.1871295