The Cardiac Cycle and Pressure-Volume Loops

Plot the pressure inside your left ventricle against its volume, and each heartbeat draws a closed loop: four corners, four valve events, and an enclosed area equal to the work of the beat. Filling, arterial load and contraction strength each change its shape in a predictable way, and the predictions show why ejection fraction is a poor measure of contractility. The four phases and the stroke-volume arithmetic are in circulation and the heart; here they get numbers.

Valves open and close on pressure differences

A Wiggers diagram plots left ventricular (LV), left atrial (LA) and aortic pressure, LV volume, the heart sounds and the electrocardiogram (ECG) on one time axis, with the valve events marked. It rests on descriptions Wiggers published from 1915 and has been taught for more than 90 years.

A valve opens when the pressure behind it exceeds the pressure ahead and shuts when that reverses. For the adult human left heart at rest, in round textbook values:

Valve event	Pressure crossing	Sound	Phase that follows
Mitral closes	LV rises above LA (about 10 mmHg)	S1	Isovolumic contraction
Aortic opens	LV rises above aortic (about 80 mmHg)	none	Ejection
Aortic closes	LV falls below aortic (about 100 to 110 mmHg)	S2	Isovolumic relaxation
Mitral opens	LV falls below LA (low, the atrial pressure at that moment)	none	Filling

The 80 mmHg is the aorta’s diastolic pressure, not the ventricle’s. During ejection, ventricular and aortic pressure rise together to about 120 mmHg. The worked model below rounds end-systolic pressure up to 120 mmHg for simple numbers; echo-Doppler studies estimate it as about 0.9 times systolic pressure.

Taken from aortic closure to mitral closure, diastole has three main parts: isovolumic relaxation, early filling and atrial contraction (some texts add a slow-filling phase, diastasis, between the last two). In one illustrative subject, the ventricle held about 80 percent of its end-diastolic volume by the end of early filling and atrial contraction added the last 20 percent.

The ECG’s P wave comes just before atrial contraction, the QRS complex just before mitral closure, and the T wave around the end of ejection (cardiac electrophysiology and the ECG). S3 falls in rapid early filling; S4, when present, with atrial contraction.

Fold time away and the beat becomes a loop

Now drop the time axis: plot LV pressure against LV volume, and one beat runs counterclockwise. Bottom right is mitral closure at end-diastolic volume (EDV); the right side is isovolumic contraction; top right is aortic opening; the top is ejection. Top left is aortic closure at end-systolic volume (ESV) and pressure (Pes); the left side is isovolumic relaxation; the bottom, after mitral opening, is filling.

The width is the stroke volume; the area is stroke work, approximately stroke volume times mean ejection pressure.

SV = EDV - ESV EF = SV / EDV CO = SV x HR SW ≈ SV x mean ejection pressure

EDV 125 mL and ESV 45 mL is a common teaching example, not a reference value. Biplane echocardiography in healthy adults gave mean EDV of 106 mL in men and 76 mL in women, mean ESV of 41 and 28 mL, and mean EF of 62 percent (2-SD range 52 to 72) in men and 64 percent (54 to 74) in women.

Worked problem, part 1: read one loop

In this made-up example, a model adult left ventricle at rest has EDV 125 mL, ESV 45 mL, Pes 120 mmHg and heart rate 70 per min, at steady state with competent valves. The aortic valve opens at 80 mmHg; take mean ejection pressure as the average of opening and end-systolic pressure.

1. Stroke volume. 125 - 45 = 80 mL.
2. Ejection fraction. 80 / 125 = 64 percent.
3. Cardiac output. 80 mL x 70 per min = 5.6 L per min.
4. Stroke work. Mean ejection pressure (80 + 120) / 2 = 100 mmHg; 80 mL x 100 mmHg = 8,000 mmHg mL. Since 1 mmHg = 133.3 Pa and 1 mL = 10^-6 m^3, 1 mmHg mL = 1.333 x 10^-4 J, so this is 1.07 J per beat.
5. Power. 1.07 J x 70 / 60 beats per s = 1.24 W, the external work rate of this one ventricle.

Two boundaries: a stiff line at end-systole, a soft curve at end-diastole

The loop’s top left corner lies on the end-systolic pressure-volume relation (ESPVR):

Pes = Ees x (ESV - V0)

Ees, the end-systolic elastance, is the slope (mmHg per mL) and V0 the volume intercept; over the physiological range the line is approximately linear. Ees is a relatively load-independent index of contractility, the strength of contraction at a given fibre length. It rises with positive inotropes and sympathetic activation and falls with ischaemia and infarction, but geometry and passive stiffness affect it too. Once relaxation is complete, the bottom of the loop lies on the end-diastolic pressure-volume relation (EDPVR), the passive filling curve. It is non-linear; its slope indexes chamber stiffness, and the inverse is compliance, volume change per unit pressure. Relaxation speed is summarized by tau, the time constant of the isovolumic pressure fall: about 20 to 40 ms in invasive human recordings and about 60 to 100 ms when relaxation is impaired, depending on how tau is fitted.

Suga, Sagawa and Shoukas reported in 1973 that the instantaneous pressure-volume ratio of the canine left ventricle did not depend on load, and by 1977 Sagawa and colleagues described the end-systolic ratio in isolated canine ventricles as relatively insensitive to loading, so that end-systolic points of differently loaded beats fall on one near-linear line. In a living heart, a brief inferior vena caval occlusion lowers filling over a few beats, and the corners of the shrinking loops trace both lines. That needs volume beat by beat, which the conductance catheter supplies: an eight-electrode catheter that Baan and colleagues had used for stroke volume in dogs and, in 1984, calibrated for absolute volume in dogs and patients. Tissue around the cavity adds a parallel conductance, found by briefly changing blood conductivity with a bolus (hypertonic saline in modern practice; Baan used cold glucose solution in patients).

The classic experiment. What sets the oxygen cost of a beat? Khalafbeigui, Suga and Sagawa (American Journal of Physiology, 1979) used 13 excised dog hearts, each cross-circulated by a support dog that supplied the coronary blood. A volume servo pump set the load, beats were isovolumic or ejecting, and oxygen consumption per beat was measured.

They tested the pressure-volume area (PVA), stroke work plus the end-systolic potential energy, the roughly triangular region between the ESPVR, the EDPVR and the loop’s left side. Oxygen use per beat correlated linearly with PVA (mean r = 0.92):

MVO2 (mL O2 per beat) ≈ 1.5 x 10^-5 x PVA (mmHg mL per beat) + 0.019

The intercept is oxygen use that does not depend on PVA. It includes basal metabolism and the cost of exciting and activating the muscle: in later canine experiments, epinephrine or calcium raised it by more than 50 percent while basal metabolism stayed unchanged. Ruled in: an isovolumic beat, which does no external work, still costs oxygen in proportion to its PVA. Ruled out: stroke work alone as the cost. Not shown: that the line holds when contractility changes (the authors noted a new inotropic state shifts it), or anything in intact humans.

Worked problem, part 2. For the part 1 loop with V0 = 5 mL, treating potential energy as a triangle, 0.5 x (45 - 5) mL x 120 mmHg = 2,400 mmHg mL, so PVA = 10,400 mmHg mL. The dog fit, used only to show its form, gives 1.5 x 10^-5 x 10,400 + 0.019 = 0.175 mL O2 per beat; that is not a human prediction.

Preload, afterload and contractility each change the loop in a different way

Preload is end-diastolic stretch, read as EDV: the bottom right corner. Afterload is the load the ventricle ejects against, summarized here as effective arterial elastance, Ea = Pes / SV, a lumped ratio set mainly by peripheral resistance and heart rate (resistance, compliance and local flow). Ea is the steepness of a line from EDV on the volume axis to the end-systolic corner, and contractility is summarized by Ees, a chamber-level index that also reflects wall geometry and passive stiffness. The corner sits where the two lines meet:

Ees x (EDV - SV - V0) = Ea x SV, so SV = (EDV - V0) / (1 + Ea / Ees)

The ratio Ea/Ees is the ventricular-arterial coupling. In humans at rest it is reported near 0.6; a review places mechanical efficiency at its best near 0.5 and stroke work at its maximum near 1, but in isolated blood-perfused dog hearts the measured peaks were nearer 0.7 and 0.8, and both stayed within 10 percent of their best from about 0.3 to 1.3.

Worked problem, part 3: move the corners

Same model, with Ees 3.0 mmHg per mL, V0 5 mL and Ea 1.5 mmHg per mL. Assume a linear ESPVR, Ea constant within each part, and heart rate fixed at 70 per min.

• Baseline. SV = 120 / (1 + 0.5) = 80 mL; Pes = 1.5 x 80 = 120 mmHg; ESV = 45 mL (check: 5 + 120 / 3.0 = 45). Ea/Ees = 0.50, near the efficiency optimum that models predict.
• Afterload up. Arteriolar constriction raises Ea to 2.0: SV = 120 / 1.667 = 72 mL; Pes = 144 mmHg; ESV = 53 mL; EF = 57.6 percent; Ea/Ees = 0.67.
• Preload up. EDV rises to 140 mL: SV = 135 / 1.5 = 90 mL; Pes = 135 mmHg; ESV = 50 mL; EF = 64.3 percent.
• Contractility up. Ees rises to 4.5: SV = 120 / 1.333 = 90 mL; Pes = 135 mmHg; ESV = 35 mL; EF = 72 percent.

Higher afterload raised ESV and lowered stroke volume, and EF fell with contractility unchanged. Higher preload slid the end-systolic corner up the same ESPVR: stroke volume rose by 10 mL, less than the 15 mL rise in EDV, because Pes rose too; only at fixed Pes would it rise by the full 15 mL. Sympathetic nerves raise Ees (blood pressure regulation) through cyclic AMP inside the cell (cAMP and PKA).

• loop (counterclockwise; shaded area is the area stroke work approximates)
• ESPVR, slope Ees
• EDPVR (invented curve for this sketch)
• Ea line, slope Ea
• reference loop (the lesson’s baseline)

1 mitral closes · 2 aortic opens · 3 aortic closes · 4 mitral opens, then filling along the bottom

EDV, preload 125 mL Ea, afterload 1.5 mmHg per mL (effective arterial elastance) Ees, an index of contractility 3.0 mmHg per mL (slope of the ESPVR) Show reference loop (the lesson’s baseline, in grey)

Set the sliders to a line of the lesson’s worked problem, part 3:

Stroke volume, SV = (EDV − V0) / (1 + Ea/Ees)

End-systolic volume, ESV = EDV − SV

Ejection fraction, EF = SV / EDV

End-systolic pressure, Pes = Ea × SV

Cardiac output, CO = SV × HR (HR fixed at 70 per min)

Stroke work ≈ SV × mean ejection pressure (aortic opening taken as 2/3 of Pes in this sketch)

Ea/Ees (humans at rest: reported near 0.6)

Fixed in this sketch

V0 = 5 mL, HR = 70 per min

Illustrative model, not fitted to data. In this sketch (made up for the sketch unless the lesson gives it): a model adult left ventricle at rest, steady state, competent valves, linear ESPVR with the lesson’s V0 = 5 mL, heart rate fixed at the lesson’s 70 per min, and Ea held constant as in the lesson’s part 3; the grey reference loop is the lesson’s baseline (EDV 125 mL, Ea 1.5, Ees 3.0 mmHg per mL); the slider ranges are made up; the EDPVR is an invented convex curve, not a measurement, drawn to pass near the lesson’s about 10 mmHg at 125 mL (the lesson says only that the EDPVR is non-linear); aortic opening at 2/3 of Pes and mean ejection pressure at 5/6 of Pes are scaled from the lesson’s 80 and 120 mmHg and are a made-up rule; the top left corner is drawn at Pes, which the lesson rounds to 120 mmHg for simple numbers; the ejection arc is a smooth curve of made-up shape. Readouts use unrounded values. At the extremes of the sliders, pressures and ejection fractions fall far outside the lesson’s examples.

Rule to keep: the end-systolic corner sits where the Ea line, which starts at EDV on the volume axis, meets the ESPVR; preload moves the start of that line, afterload tilts it and contractility tilts the ESPVR, so EF can change without any change in Ees.

When the loop changes shape: failure and valve disease

In heart failure with reduced EF, remodelling shifts the ESPVR, the EDPVR and the loops to the right, and the ESPVR is usually flatter (lower Ees): a large chamber ejecting a small fraction of its volume.

In heart failure with preserved EF, catheter studies found the diastolic relation shifted up and to the left, with higher passive stiffness and a longer tau (59 versus 35 ms in Zile, Baicu and Gaasch’s 2004 comparison). Ees was raised too in a small 2003 catheter study of 10 patients (4.7 mmHg per mL versus 2.1 in normotensive and 3.3 in matched hypertensive controls), and Ea and Ees tend to rise together. In an echo-Doppler community sample, Borlaug and colleagues (2009) found chamber and myocardial contractility depressed in this group although Ees was raised: a stiff chamber can raise Ees without stronger muscle.

The modern experiment. Is the problem with a normal EF a stiff chamber? Westermann and colleagues (Circulation, 2008) recorded conductance-catheter loops in 70 people with heart failure and normal EF and 20 without heart-failure symptoms, at baseline, during isometric handgrip (raising afterload) and during atrial pacing at 120 beats per min. Diastolic stiffness was raised at baseline; with pacing, stroke volume fell and the loops shifted left; with handgrip, end-diastolic pressures rose more. Ruled in: a stiff chamber, with filling pressure rising more during handgrip and stroke volume falling during pacing. Not shown: cause, that lowering stiffness would help (the authors’ hypothesis), or that systolic and vascular changes found in other groups are absent.

Valves. In aortic stenosis the valve adds to afterload: LV systolic pressure rises and the loop’s top domes upward. When Ea is taken from LV pressure it includes the valve, and Ea/Ees rises. EDV stays near normal. ESV is often larger, but in compensated stenosis a thickened wall can keep ESV and EF near normal until the ventricle starts to fail. In mitral stenosis preload falls and pulmonary venous pressure rises, while the ESPVR is usually preserved (relaxation can be slowed too).

Pathophysiology: chronic mitral regurgitation. A leaking mitral valve gives the systolic ventricle two outlets, the aorta and the low-pressure left atrium. Ejection into the atrium starts before the aortic valve opens, so isovolumic contraction shortens and the loop’s right side leans left. The low-pressure outlet helps the ventricle empty, so ESV stays normal or small early on (it grows later as the chamber dilates and wall stress rises), and left atrial pressure rises, with a large v wave (the atrial pressure rise during ventricular systole) when the atrium is stiff or the leak is sudden, while a large, compliant atrium can keep it small. Over time the chamber dilates and the EDPVR and loops shift right; by the Frank-Starling mechanism the large EDV keeps total stroke volume high, so EF can stay normal or supernormal while the myocardium is damaged and forward output is normal or reduced. The end-systolic corners still lie on the ESPVR, so Ees remains a valid contractility index where EF is not.

Design problem

An anaesthetized dog (or pig) has a left-ventricular conductance catheter and a balloon catheter in the inferior vena cava. A drug is said to be a positive inotrope; it also dilates arterioles. A student reports that EF rose from 55 to 65 percent and concludes that the drug raises contractility. Design the experiment that tests the claim.

One way to do it

Afterload reduction alone raises EF (part 3 run backwards), so EF cannot separate the two effects.

1. Fix the rate by atrial pacing, since Ea and Ees both depend on heart rate.
2. Calibrate volume: parallel conductance by a hypertonic saline bolus, scale by an independent volume or flow measurement.
3. Record baseline steady loops, then brief caval occlusions, and fit Ees and V0 to the end-systolic corners. Use only the first few beats, before reflexes act, or block the reflexes.
4. Give vehicle, then drug, repeating loops and occlusions after each.
5. Separate the effects: Ea = Pes / SV for afterload, Ees and V0 for contractility. A shift of V0 alone can mimic a change in slope if V0 is fixed or a single beat is used, so fit both.

If the end-systolic points before and after the drug lie on one ESPVR while Ea falls, the EF rise reflects loading, not contractility (afterload, plus any change in EDV). A steeper ESPVR after drug than after vehicle would support the claim.

Limits: anaesthesia, open or closed chest, one species, and an Ees that also responds to geometry and passive stiffness.