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 the difference between estimating a physiological state and establishing what caused it to change.
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. CVP itself was measured through a catheter.
Read the full open-access paper.
The distinction between Pms and Pmsa becomes central to interpreting the results. An estimated pressure can still contain real physiological information. The question is how confidently we can interpret that information in these experiments.
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, the paper reports a 23% lower calculated Pmsa in the septic cohort than in the non-septic cohort.
The pooled summary describes the septic cohort as markedly hyperdynamic:
cardiac output: 12.9 vs 7.7 L/min;
MAP: 74 vs 109 mmHg;
CVP: 5.3 vs 7.6 mmHg.
Table 2 lists calculated resistance to venous return as 1.41 versus 2.47 mmHg·min/L. Those means imply approximately 43% lower RVR in the septic cohort, whereas the paper’s text reports 63%. This discrepancy remains unresolved; 43% is the reduction calculated from the tabulated means.
Adrenergic stimulation also produced some striking results. In healthy animals, isoprenaline and dopamine were associated with substantial increases in calculated Pmsa and cardiac output, while phenylephrine increased MAP and CVP but did not produce the same rise in Pmsa.
These findings may reflect genuine changes in the upstream vascular state. To understand what they establish, we first need to ask what the calculation is trying to estimate.
Pms was never measured
True mean systemic filling pressure is an equilibrium property.
At zero systemic blood flow, after pressures have equilibrated, it reflects the interaction between vascular volume and the pressure–volume characteristics of the systemic circulation.
That equilibrium pressure was not independently measured here.
Instead, Pmsa was calculated from:
Pmsa = 0.96 × CVP + 0.04 × MAP + c × CO
Here, c is a coefficient with the dimensions of resistance, adapted for the size of the sheep. The equation also assumes a fixed 24:1 venous-to-arterial compliance ratio.
Pmsa is therefore a model-derived estimate constructed from three variables measured during active circulation: CVP, MAP and cardiac output.
This is an attempt to reconstruct an upstream equilibrium state from measurements obtained while blood is flowing. That purpose explains why cardiac output belongs in the equation.
Why cardiac output is inside the pressure
During circulation, right atrial pressure (RAP), represented clinically by CVP, generally lies below the upstream equilibrium pressure. To estimate the latter, the model has to account for the pressure differences associated with ongoing flow. The presence of CO is therefore physiologically reasonable. It does not, by itself, make the equation circular or invalid.
The inputs also need to be interpreted together. Suppose cardiac acceptance, the heart’s ability to accommodate incoming flow, improves while true Pms and venous-pathway resistance remain unchanged. Cardiac output rises and right atrial pressure falls. In the Parkin equation, those changes contribute in opposite directions. A successful estimator should account for the increased flow without incorrectly identifying it as increased upstream filling pressure. Whether the contributions offset sufficiently depends on how well the model represents the circulation.
Compare that with a reduction in venous capacitance that genuinely raises Pms. If the heart has sufficient reserve, it may accommodate more flow with little increase in RAP. A rise in estimated Pmsa could then correctly reflect a change in the upstream pressure–volume state.
These are patterns that a valid estimator could represent differently. But estimating the upstream state is not, by itself, a diagnostic test that separates changes in delivery from changes in acceptance.
Now consider the healthy animals given isoprenaline. Cardiac output increased substantially and calculated Pmsa also rose. One possible explanation is that the intervention changed the venous pressure–volume relationship, raising the upstream equilibrium pressure and supporting greater flow.
The calculation may be consistent with that explanation. But it cannot independently establish the entire causal sequence. The question is whether the model accurately tracks the upstream state under this intervention, and what additional evidence distinguishes the possible mechanisms.
The same distinction applies to the calculated ‘pressure gradient for venous return’:
dVR = Pmsa − CVP
Substituting the equation for Pmsa gives:
dVR = 0.04 × (MAP − CVP) + c × CO
The study then calculates resistance to venous return:
RVR = dVR / CO
Substitution gives:
RVR = 0.04 × (MAP − CVP) / CO + c
These are mathematically valid derived quantities. If Pmsa is accurate, they may provide useful estimates of the pressure gradient and effective resistance. But they remain connected outputs of the same model, rather than independent measurements confirming one another.
There is a further detail in Hahn’s comparison: c was set to 1.71 in the non-septic cohort and 1.06 in the septic cohort. Because c appears as an additive term in calculated RVR, the between-cohort comparison depends partly on that calibration. A size adjustment may be appropriate, but its contribution must be distinguished from a physiological effect attributed to sepsis.
But if resistance changes, hasn’t resistance changed?
When pressures and flow are adequately established, a change in their ratio means that effective resistance at the operating point has changed.
But that does not necessarily mean that vascular smooth-muscle tone has changed.
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 a given pressure difference. 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 an active increase in smooth-muscle tone.
Critical closing pressure is an extreme example of this behaviour. Flow can cease while upstream pressure is still positive because the vessel is no longer patent. A simple pressure-to-flow ratio does not capture that closing behaviour.
So effective resistance tells us about the resolved relationship between pressure and flow. It does not, on its own, tell us which physical property of the vascular system produced that relationship.
Hahn’s calculated RVR carries an additional qualification: the upstream pressure used in the gradient is estimated by the same model. A fall in RVR establishes that this model-derived ratio has fallen. Its correspondence to a change in the physical circulation depends on the accuracy of the pressure estimate as well as the interpretation of resistance.
What Pmsa can still tell us
Pmsa is intended to estimate a physiological state, and there is experimental evidence that it can do so.
In a porcine ECMO model, Werner-Moller and colleagues compared it with zero-flow equilibrium pressure during norepinephrine-induced vasoconstriction and volume expansion. Average agreement was good: the overall bias was approximately 0.5 mmHg. However, limits of agreement extended from approximately −2.7 to +3.8 mmHg, indicating appreciable uncertainty in individual estimates. Read the validation study.
Changing vascular tone therefore does not automatically invalidate the estimator.
Human comparisons also show why tracking changes and estimating absolute pressure are different claims. In postoperative cardiac surgery patients, Maas and colleagues found directionally concordant changes during head-up tilt and fluid loading, while Pmsa averaged approximately 6 mmHg below the inspiratory-hold estimate. Read the human comparison.
Validation in one setting does not establish accuracy under every combination of sepsis, adrenergic stimulation and altered vascular compliance. Hahn acknowledges that the assumed compliance ratio may not remain constant. The appropriate conclusion is that accuracy under these particular conditions remains uncertain; changing vascular properties alone does not demonstrate model failure.
If we want to know whether isoprenaline genuinely increases systemic equilibrium pressure, an independent estimate or measurement during the intervention would strengthen the inference. If it rose alongside calculated Pmsa, we could then investigate why: altered venous tone, redistribution of blood volume, changes in compliance, or some combination.
Even a confirmed rise in Pms would not, by itself, measure the change in stressed volume or identify its mechanism.
The more interesting interpretation
The reported pooled means imply approximately 23% lower calculated Pmsa and venous-return gradient, approximately 43% lower calculated RVR, and about 70% higher cardiac output in the septic cohort.
Those numbers describe the reported model outputs. They may reflect real physiology, but the precise magnitudes of the underlying equilibrium pressure and effective venous resistance were not independently established.
The pooled summaries also require clarification: non-septic mean Pmsa of 20.0 mmHg and mean CVP of 7.6 mmHg imply a mean gradient of 12.4 mmHg, whereas Table 2 gives 13.8 mmHg. Averaging alone cannot explain this difference if all three means use the same observations. Different data subsets could contribute, but the published summary does not resolve it. These figures should therefore be treated as reported results that have not been fully reconciled.
The comparison also brings together different experimental conditions. The non-septic sheep were awake; the septic sheep were anaesthetised and ventilated. Cardiac output was assessed with different methods, and the drug regimens were not identical. These differences limit how confidently the contrast can be attributed to sepsis alone.
The distinction becomes especially important when estimated variables are placed into a causal sequence. A rise in Pmsa may support an interpretation of increased upstream delivery if the estimator performs adequately. It does not, by itself, establish that increased delivery was the cause of the rise in CO, or exclude simultaneous changes in acceptance.
The calculation, its validation and the causal explanation are three related questions. They need to be assessed separately.
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.
The Parkin analogue offers a coherent way to interpret those observations as an estimate of upstream vascular state. Its use of cardiac output has a physiological purpose, and its validation deserves to be taken seriously.
The remaining uncertainty concerns how accurately the model performs in these conditions and what mechanisms produced the changes. Neither the appearance of CO in the equation nor the absence of a direct Pms measurement settles those questions.
A model can estimate a physiological state without independently establishing the causal sequence that produced it.
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. doi:10.1016/0883-9441(94)90023-X.
Maas 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. doi:10.1007/s00134-012-2586-0.
Werner-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. doi:10.1152/japplphysiol.00804.2021.
Hahn RG. Influence of adrenergic drugs and volume loading on mean systemic filling pressure in non-septic and septic sheep. Front Med. 2026;13:1871295. doi:10.3389/fmed.2026.1871295.