Cardiac Output and Venous Return

At rest, each side of an adult human heart pumps about 5 litres of blood a minute, and over any few minutes it cannot pump out more than flows back in. So which sets cardiac output: the heart, or the veins that fill it?

Cardiac output is heart rate times stroke volume, and a ventricle that fills more ejects more (the Frank-Starling relation), as in circulation and the heart. Here you measure the output, give the veins an equation, and find output where the two curves cross.

Two ways to count the flow: Fick and dilution

The Fick principle is bookkeeping for oxygen. At steady state, the oxygen the lungs take up each minute leaves in the blood flowing through them:

Q = VO2 / (CaO2 - CvO2), where Q is pulmonary blood flow, VO2 is oxygen uptake, and CaO2 and CvO2 are arterial and mixed-venous oxygen contents

Oxygen content (mL O2 per L of blood) is bound plus dissolved oxygen (oxygen transport). A saturation will not do: it is a percentage and holds no volume of oxygen.

Mixed-venous blood is venous blood from the whole body after it has mixed, sampled in the pulmonary artery through the distal lumen of a pulmonary artery catheter. An arm vein reports only what the arm extracted. The direct Fick method measures uptake by respirometry; the estimated method assumes it, which makes it a different measurement. The direct method assumes steady state, no intracardiac shunt (so pulmonary and systemic flow are equal) and a true mixed-venous sample. It gives right-ventricular output; averaged over time the left ventricle pumps the same blood, so the outputs are never added.

Indicator dilution applies the same mass balance to something you inject. Put a known amount of dye into a central vein and record its concentration downstream. Faster flow dilutes the dye more and clears it sooner, so the area is smaller.

Q = amount injected / area under the first-pass concentration-time curve

It assumes complete mixing, no indicator lost from the blood, and recirculation excluded (the downslope is extrapolated before the second pass). Pulmonary artery thermodilution injects a cold crystalloid bolus into the central venous circulation and reads temperature in the pulmonary artery; transpulmonary thermodilution reads it in a systemic artery instead. The result depends on injectate volume, injection rate and temperature, and shunts and leaky valves such as tricuspid regurgitation make it less reliable.

Worked problem, part A: measure the output

Made-up round numbers for an adult human at rest, supine, at steady state, with no intracardiac shunt. Measured oxygen uptake is 260 mL O2 per min. Arterial oxygen content is 195 mL O2 per L; mixed-venous content, from the pulmonary artery, is 143 mL O2 per L.

1. Content difference. 195 - 143 = 52 mL O2 per L.
2. Flow. Q = 260 / 52 = 5.0 L per min.
3. Check. 5.0 L per min x 52 mL O2 per L = 260 mL O2 per min.
4. Stroke volume. At 80 beats per min, 5,000 / 80 = 62.5 mL per beat.
5. Dye cross-check. 5 mg of dye gives a first-pass area of 60 mg s per L. Q = 5 / 60 = 0.0833 L per s, which is 5.0 L per min. The methods agree.

Veins hold a pressure of their own

Stop the heart and blood moves from the stretched arteries into the veins until the whole circulation settles at one pressure, the mean circulatory filling pressure. The systemic veins hold most of the compliance, so this is normally almost the same as the mean systemic filling pressure (Pms), the pressure in the systemic store that drives blood back to the heart. This lesson’s lumped model treats the two as one zero-flow pressure.

Picture a rubber tank with an outlet partway up its side: fluid below the rim fills it without stretching it, and fluid above the rim stretches the wall, which pushes back. Unstressed volume fills the vessels without stretching their walls. Stressed volume stretches the walls and generates recoil pressure. Compliance is the change in volume per change in pressure, in L per mmHg (resistance, compliance and local flow). Treating the systemic circulation as one compliant reservoir:

Pms = stressed volume / compliance

The veins hold most of the blood and most of the compliance. Adding blood raises Pms. So does venoconstriction, sympathetic tightening of venous smooth muscle (hypothalamus and autonomic control): it lowers capacitance, the volume held at a given pressure, and turns unstressed into stressed volume without adding blood. The direction is easy to reverse (one review figure’s legend did, until a 2017 correction): decreased capacitance recruits stressed volume; increased capacitance stores blood and lowers Pms.

Guyton’s group measured about 6 to 7 mmHg in anaesthetized dogs after stopping the heart (6.3 mmHg in the 1954 report, strictly a mean circulatory filling pressure); textbooks use 7, but it is a dog stop-flow value, not a normal human one. In this lesson’s model, a compliance of 0.2 L per mmHg at 7 mmHg means 1.4 L of stressed volume.

Guyton’s dogs: set the atrial pressure, read the return

In an intact circulation, cardiac output and right atrial pressure (Pra) change together. Arthur Guyton, with A. W. Lindsey, B. Abernathy and T. Richardson, broke the loop in anaesthetized open-chest dogs (according to the paper’s abstract, 12 with intact circulatory reflexes and 14 made areflex). The right heart was bypassed: blood returning to the right atrium went to an external pump that delivered it into the pulmonary artery. The experimenters set Pra and measured the flow returning from the body.

How does that flow depend on Pra? A naive guess: lowering Pra sucks blood back without limit.

As Pra was lowered, return rose along a roughly straight line, and in these open-chest dogs it stopped rising once Pra reached about -2 to -4 mmHg. Veins collapse when the pressure inside falls below the pressure around them, and a collapsed vein limits flow however low the downstream pressure goes. Raising Pra reduced return, which reached zero where Pra equalled Pms. Their 1957 paper in the American Journal of Physiology gave the venous return curve:

Qvr = (Pms - Pra) / Rvr

The resistance to venous return (Rvr) lies between the elastic store and the right atrium (mmHg min per L). Plotted against Pra, the line meets zero flow at Pms with slope -1/Rvr. Pms is the upstream driving pressure; Pra is the back-pressure.

A 1958 follow-up, with Lindsey, Kaufmann and Abernathy, compared 10 reflex-intact with 10 areflex dogs. Transfusion raised and blood withdrawal lowered return at the atrial pressures tested, and after transfusion, return drifted back toward control over 10 to 20 minutes.

Ruled in: the periphery has its own pressure-flow relation, capped by collapse. Ruled out: unlimited suction, and accounts of output that look at the heart alone. Not shown: a human collapse threshold, a lasting volume effect, or that Pra causes the flow change. Matthew Levy argued in 1979 that in a closed loop the pump sets flow and Pra follows; Beard and Feigl revisited the argument in 2011.

Contracting leg muscles squeeze deep veins against their valves (skeletal muscle mechanics), and spontaneous inspiration lowers intrathoracic pressure (lung mechanics and surfactant); both aid return.

Where the pump meets the veins

The cardiac function curve plots output against Pra: as Pra rises, preload (end-diastolic stretch) usually rises, and by the Frank-Starling relation output rises. Pra is only a stand-in for preload: stretch depends on the pressure across the heart wall (Pra minus the pressure around the heart) and on how stiff the ventricle is, so raising chest pressure can raise Pra while filling falls. The curve also describes the whole heart, not one ventricle. Contractility, the strength of contraction at a given preload, and afterload, the load the ventricle ejects against, set how high the curve sits (pressure-volume loops). Averaged over time at steady state, output equals venous return, so the circulation settles where the lines cross: the operating point, which fixes both flow and Pra.

Worked problem, part B: find the operating point

An illustrative model, not fitted to data: Qc = b + k x Pra, with b = 3 L per min and k = 1 L per min per mmHg (valid only at the positive Pra used), and venous return with Pms = 7 mmHg and Rvr = 1 mmHg min per L.

1. Set them equal. 3 + Pra = (7 - Pra) / 1.
2. Solve. 2 x Pra = 4, so Pra = 2 mmHg.
3. Flow. Q = 3 + 2 = 5 L per min.
4. Check. (7 - 2) / 1 = 5 L per min.
5. In general, Pra = (Pms - Rvr x b) / (1 + Rvr x k), and Q = b + k x Pra.

Pms, mean systemic filling pressure 7.0 mmHg (stressed volume 1.40 L) Rvr, resistance to venous return 1.0 mmHg min per L Heart's line height b (contractility, afterload) 3.0 L per min (k fixed at 1 L per min per mmHg) Venous collapse: cap return at its value at Pra = 0 mmHg (an illustrative cap, not a measured threshold)

Set the controls to a row of the lesson’s table:

Right atrial pressure at the crossing

Flow, cardiac output = venous return (L per min)

Veins' side

Heart's side

Illustrative model, not fitted to data. In this sketch (made up for the sketch unless the lesson gives it): steady state, so output equals venous return; the heart's line is Qc = b + k × Pra with the lesson’s k = 1 L per min per mmHg, which the lesson gives only at the positive Pra it uses, so the line is drawn dashed below 0 mmHg; the veins' line is Qvr = (Pms − Pra) / Rvr; the baseline (grey, dashed) is the lesson’s b = 3 L per min, Pms = 7 mmHg and Rvr = 1 mmHg min per L, where 7 mmHg is a dog stop-flow value, not a normal human one; the slider ranges are made up; stressed volume is Pms × the lesson’s 0.2 L per mmHg; the venous collapse cap is a made-up rule (in Guyton’s open-chest dogs return stopped rising near −2 to −4 mmHg, and the lesson shows no human threshold). The lesson’s model ignores reflexes, the waning of a transfusion and the flattening of the heart’s curve at high Pra. Readout arithmetic uses unrounded values.

Rule to keep: the circulation runs where the heart’s line and the veins’ line cross, which fixes both flow and Pra; volume and venous tone move the veins’ line sideways, Rvr rotates it, and the heart moves its own line.

Moving the operating point

Change one thing at a time. Volume and venous tone shift the venous curve sideways (Pms); Rvr rotates it about its intercept; the heart moves the cardiac curve. Blood added or lost is all stressed volume, at 0.2 L per mmHg.

Change from baseline	Curve moved	Pms (mmHg)	Pra (mmHg)	Q (L per min)
Baseline	none	7	2	5
Transfuse 0.4 L (1.8 L / 0.2)	venous, right	9	3	6
Lose 0.4 L (1.0 L / 0.2)	venous, left	5	1	4
Positive inotrope, b = 5	cardiac, up	7	1	6
Acute pump failure, b = 1	cardiac, down	7	3	4
Compensated failure, b = 1	both	9	4	5
Halve Rvr to 0.5	venous, rotated	7	3.67	6.67
Halve Rvr, heart lifted to b = 4	both	7	3.33	7.33

For the inotrope, Pra = (7 - 5) / 2 = 1 mmHg and Q = 5 + 1 = 6 L per min. A stronger pump raises output and lowers Pra: at any atrial pressure it moves more blood on, so the atrium is drawn down along the unchanged venous curve.

Take systolic heart failure as a mechanism, treating the heart as one pump (when the left ventricle fails alone, blood also shifts into the lungs, which needs a two-ventricle account). An acute fall in contractility drops the cardiac curve: Q falls from 5 to 4 L per min and Pra rises from 2 to 3 mmHg. Reflex venoconstriction can recruit stressed volume within seconds, and over hours to days renal retention of sodium and water (water, sodium and potassium) adds blood volume. Together they raise Pms, shifting the venous curve right. At a Pms of 9 mmHg, Q is back to 5 L per min at a Pra of 4 mmHg, with higher upstream venous and capillary pressures that favour edema (capillary exchange and lymph). The inotrope, by contrast, raises output while lowering Pra. Reflex responses are in blood pressure regulation.

Rvr is not total peripheral resistance (TPR): TPR = (MAP - Pra) / Q, with mean arterial pressure (MAP) upstream. With an illustrative MAP of 92 mmHg, baseline TPR = (92 - 2) / 5 = 18 mmHg min per L, while Rvr is 1. So “TPR fell” has no single answer for Pra. In the lumped model, arteriolar dilation lowers the effective Rvr (a little, since resistance near the atrium counts for more) and afterload, which can lift the cardiac curve. The last two rows halve Rvr to make the direction clear; arteriolar dilation alone would lower Rvr much less, and a large fall needs lower venous resistance. Venodilation lowers Pms. Say which vessels dilated. The model ignores reflexes, the waning of a transfusion, the collapse plateau and the flattening of the cardiac curve at high Pra.

Can you trace the curve with the chest closed? Van Loon, van der Hoeven, Veltink and Lemson (2020) tried in nine healthy pigs, anaesthetized and mechanically ventilated, with an ultrasound transit-time flow probe on the main pulmonary artery. A 30-second inspiratory hold at raised airway pressure raises intrathoracic pressure and so Pra, and flow falls. The line through pressure-flow pairs from several holds, extrapolated to zero flow, estimates Pms in a beating heart. Each animal was studied in euvolaemia and in hypovolaemia after withdrawing 10 mL of blood per kg, in randomised order with the shed blood retransfused, and flow was then stopped by ventricular fibrillation for comparison.

The regressions were close to linear (R-squared 0.92, range 0.67 to 0.99). Withdrawal lowered cardiac output, and the hold-derived Pms fell from 19.9 ± 5.1 to 16.3 ± 3.6 mmHg (mean ± SD). Retransfusion restored output and mean arterial pressure to baseline. The hold estimate correlated strongly with the post-fibrillation pressure, but the two were not interchangeable.

Correlation says two measures rise and fall together; agreement says one can replace the other (a thermometer reading 3 degrees high correlates perfectly with a true one). The authors concluded that the hold value is a dynamic characteristic of the circulation, not an absolute measure of volume state. It does not test the method in humans or conscious animals, and a pig value near 20 mmHg does not contradict the dog value near 6 to 7: species, anaesthesia, ventilation and method differ.

Design problem

Two descriptions fit the same steady-state curve. In Guyton’s reading, Pra is the back-pressure that sets venous return; in Levy’s, the pump sets flow and Pra is the consequence. You have an anaesthetized pig whose right heart is replaced by an external pump, with flow probes on the venae cavae and a right atrial pressure transducer. Design a protocol that separates the two readings.

One way to do it

1. Two independent manipulations. Change pump speed at constant airway pressure. Separately, change Pra without touching the pump, by raising airway pressure or the outflow reservoir. Møller and colleagues (2017) did both in ten closed-chest pigs on venoarterial bypass.
2. Continuous records. Record flow and Pra beat by beat, so the first seconds, while flow and Pra are still out of balance, stand apart from the new steady state.
3. Fixed volume. Hold total blood volume constant and measure reservoir volume, since blood entering or leaving it changes stressed volume and Pms.
4. Reflexes and time. Repeat with reflexes blocked, as Guyton compared intact and areflex dogs, and sample for 10 to 20 minutes after any volume change.
5. Prediction. If raising Pra at fixed pump speed immediately lowers caval flow, Pra acts as a back-pressure here. In Møller’s pigs, airway-pressure changes moved Pra and caval flow immediately in opposite directions.
6. The limit. At steady state in a closed loop, flow and Pra are solved together, so this shows which description predicts transients here, not “the” cause in an intact person.