H–Q Curve in Centrifugal Pumps #2: Cardiac Cycle and Instantaneous LVAD Flow

1. Introduction

A continuous-flow centrifugal left ventricular assist device does not produce truly constant flow, even when rotor speed is fixed. Pump flow varies throughout each cardiac cycle because the pressure difference between the pump outlet and inlet changes continuously.

The LVAD inflow cannula receives blood from the left ventricle, whereas the outflow graft returns blood to the systemic arterial circulation, usually through the ascending aorta. Native left ventricular contraction therefore changes pump inlet pressure, while aortic pressure determines pump outlet pressure. Their instantaneous difference establishes the hydraulic load against which the pump operates.

During systole, rising left ventricular pressure generally reduces the pressure difference across the pump. The operating point moves toward higher flow on the H–Q curve. During diastole, falling left ventricular pressure increases the pressure difference, moving the operating point toward lower flow. The resulting LVAD flow waveform is pulsatile despite constant rotor speed.

The magnitude of this passive pulsatility depends not only on ventricular and arterial pressures but also on the slope and dynamic behavior of the pump’s H–Q relationship. Experimental work has demonstrated that centrifugal pumps with different H–Q curve slopes produce substantially different cardiac-synchronized flow patterns under otherwise comparable conditions [1].

2. Pump Head and the Transpump Pressure Difference

The vertical axis of the H–Q curve represents pump head, conventionally expressed as pressure. In an LVAD circuit, instantaneous pump head can be approximated as:

H(t) ≈ Poutflow(t) − Pinflow(t)

Because the pump outlet is connected to the aorta and the inlet is connected to the left ventricle:

H(t) ≈ PAo(t) − PLV(t)

This pressure difference is commonly written as ΔP:

ΔP(t) = PAo(t) − PLV(t)

where:

• PAo is instantaneous aortic pressure.
• PLV is instantaneous left ventricular pressure.
• ΔP is the pressure difference across the pump.
• t indicates that these variables change continuously during the cardiac cycle.

A large ΔP means that the pump must transfer blood against a greater pressure load. A small ΔP means that the opposing pressure is lower. At a fixed pump speed, centrifugal pump flow therefore generally changes inversely with ΔP:

Higher ΔP → lower pump flow

Lower ΔP → higher pump flow

In this context, ΔP should not be confused with systemic pulse pressure. It specifically describes the pressure difference between the LVAD outlet and inlet.

3. The Fixed-Speed H–Q Curve

The H–Q curve describes the relationship between pump head and pump flow at a specified rotor speed.

• The horizontal axis represents pump flow, usually in liters per minute.
• The vertical axis represents pump head, usually in millimeters of mercury.
• Each rotor speed has its own H–Q relationship.
• At a fixed speed, greater pump head generally corresponds to lower pump flow.

The instantaneous pump operating point is the combination of head and flow present at a specific moment. As ventricular and aortic pressures change, the operating point moves along the fixed-speed H–Q curve.

This relationship can be expressed conceptually as:

Qpump(t) = f[N, ΔP(t)]

where:

• Qpump is instantaneous pump flow.
• N is rotor speed.
• ΔP is the instantaneous pressure difference across the pump.

When N remains constant, changes in Qpump are produced primarily by changes in ΔP. The pump does not need to accelerate during systole or decelerate during diastole to create flow pulsatility.

The conventional steady-state H–Q curve is useful for understanding this principle, but actual pump behavior during pulsatile circulation is more complex. Under simulated physiological conditions, pressure head and flow may form a dynamic loop rather than retracing the same static curve during every phase of the cardiac cycle. This reflects phase differences between pressure and flow, pump inertia, fluid inertia, cannula resistance, and vascular compliance. Dynamic H–Q loops may therefore represent clinical operating conditions more accurately than a single steady-state curve [2].

4. Systole: Lower Pump Head and Higher LVAD Flow

4.1 Rise in Left Ventricular Pressure

During ventricular systole, myocardial contraction causes left ventricular pressure to rise. Aortic pressure also increases, but the rise in left ventricular pressure generally reduces the pressure difference between the aorta and the ventricle.

The systolic pressure difference can be approximated as:

ΔPS = PAo,S − PLV,S

As PLV approaches PAo, ΔPS becomes smaller. The pump therefore faces less opposing pressure.

On the H–Q curve, the operating point moves:

• Downward, toward lower pump head.
• Rightward, toward higher pump flow.

The sequence is:

LV pressure rises → ΔP decreases → operating point shifts rightward → LVAD flow increases

4.2 Native Contraction Augments Pump Flow

Native left ventricular contraction can increase LVAD flow even when the aortic valve remains closed. The ventricle does not need to eject through the native left ventricular outflow tract for contraction to affect pump performance.

By raising pressure at the inflow cannula, ventricular contraction reduces the pressure difference that the pump must overcome. Blood is then transferred more readily from the left ventricle through the inflow cannula, pump, outflow graft, and aorta.

The magnitude of systolic flow augmentation depends on:

• Left ventricular contractility
• Ventricular preload
• Degree of LV unloading
• Systemic arterial pressure
• Pump speed
• H–Q curve slope
• Inflow and outflow pathway resistance
• Cardiac rhythm and atrioventricular synchrony

A patient with substantial residual ventricular contractility may therefore have a prominent systolic LVAD flow peak despite constant rotor speed.

4.3 Relationship to Aortic Valve Opening

If left ventricular pressure exceeds aortic pressure, the aortic valve may open and native ventricular ejection may occur. Systemic output is then supplied through two parallel pathways:

1. Native ejection through the aortic valve
2. Pump-mediated flow through the LVAD circuit

Aortic valve opening does not necessarily cause LVAD flow to decrease. The elevated LV pressure that opens the valve may simultaneously reduce pump head and increase flow through the LVAD.

At higher levels of mechanical support, the ventricle may remain sufficiently unloaded that left ventricular pressure does not exceed aortic pressure. The aortic valve can remain closed while the LVAD waveform still demonstrates a systolic flow increase.

5. Diastole: Higher Pump Head and Lower LVAD Flow

5.1 Fall in Left Ventricular Pressure

During ventricular relaxation, left ventricular pressure falls rapidly. Aortic pressure also declines during diastole, but it generally remains substantially higher than left ventricular pressure.

The diastolic pressure difference can be approximated as:

ΔPD = PAo,D − PLV,D

As PLV falls, ΔPD becomes larger. The pump must therefore operate against a greater pressure head.

On the H–Q curve, the operating point moves:

• Upward, toward higher pump head.
• Leftward, toward lower pump flow.

The sequence is:

LV pressure falls → ΔP increases → operating point shifts leftward → LVAD flow decreases

5.2 Continued Forward Flow During Diastole

Although LVAD flow decreases during diastole, it usually remains forward because the rotating impeller continues to add energy to the blood. This permits systemic flow throughout both systole and diastole.

This differs fundamentally from native transaortic flow, which occurs predominantly during systole. A centrifugal LVAD can maintain forward flow even when the aortic valve is closed and native ejection is absent.

Forward diastolic flow is not guaranteed under all conditions. Markedly elevated aortic pressure, very low pump speed, severe outflow resistance, or an extreme transpump pressure difference can reduce flow toward zero. Depending on device design and operating conditions, transient retrograde flow may occur when the pressure gradient exceeds the pump’s forward-flow capability.

6. H–Q Curve Slope and Flow Pulsatility

The slope of the H–Q curve determines how strongly a change in pressure head is translated into a change in pump flow.

For a given cyclic change in ΔP:

• A flatter or shallower H–Q curve produces a larger change in flow.
• A steeper H–Q curve produces a smaller change in flow.

Conceptually:

ΔQ ≈ ΔH / |H–Q slope|

Because the H–Q curve slopes downward, its mathematical slope is negative. Clinically, the relevant variable is the magnitude of that slope.

Experimental comparison of centrifugal pump designs demonstrated that a shallower H–Q curve generated greater flow pulsatility synchronized with native cardiac contraction [1]. The effect reflects greater flow sensitivity to the cyclic pressure difference between the ventricle and aorta.

Contemporary numerical modeling has similarly shown that pumps with flatter H–Q curves generate greater pump-flow pulsatility and higher arterial pulse pressure than pumps with steeper curves [3]. This behavior was observed across simulated left heart failure, right heart failure, myocardial recovery, and acute preload-change scenarios.

However, greater pulsatility does not automatically mean superior global support. At matched operating speeds, flatter H–Q characteristics may produce slightly less ventricular unloading and peripheral organ perfusion. Increasing pump speed may compensate for these differences while preserving greater pulsatility [3].

The H–Q curve slope therefore represents a design tradeoff among:

• Flow pulsatility
• Preload responsiveness
• Ventricular unloading
• Systemic perfusion
• Suction susceptibility
• Required operating speed

7. Formation of the LVAD Flow Waveform

The LVAD flow waveform is generated by repeated movement of the pump operating point during the cardiac cycle:

1. The left ventricle begins to contract.
2. Left ventricular pressure rises.
3. The aorta-to-LV pressure difference decreases.
4. Pump flow accelerates.
5. Peak pump flow occurs during systole.
6. The ventricle relaxes.
7. Left ventricular pressure falls.
8. The pressure difference across the pump increases.
9. Pump flow decelerates during diastole.
10. The sequence repeats with the next contraction.

Pump-flow pulsatility can be described as:

Qpulsatility = Qmax − Qmin

where Qmax is generally the systolic maximum and Qmin is generally the diastolic minimum.

The waveform is therefore not simply a pump-generated signal. It is the integrated result of:

• Native ventricular pressure generation
• Ventricular filling
• Aortic pressure
• Vascular compliance
• Pump speed
• Pump hydraulic characteristics
• Cannula and graft resistance
• Cardiac rhythm

Because pressure and flow do not always change simultaneously, the dynamic operating trajectory may form a loop in the H–Q plane. The width and orientation of this loop contain information about the interaction between native contraction and pump support [2].

8. Effects of Preload, Afterload, and Contractility

8.1 Preload

Preload determines the volume available to the left ventricle and LVAD inflow cannula. Increased venous return raises LV filling and generally increases pump flow. Reduced preload decreases LV filling, lowers inflow pressure, increases the effective pressure difference across the pump, and reduces flow.

Common causes of reduced LVAD preload include:

• Hypovolemia
• Right ventricular failure
• Pulmonary hypertension
• Cardiac tamponade
• Excessive positive-pressure ventilation
• Pulmonary vascular obstruction
• Impaired systemic venous return

Severe preload reduction may cause the ventricular wall or interventricular septum to approach the inflow cannula, producing a suction event.

Changes in preload and afterload produce characteristic changes in LVAD flow, power, and pulsatility parameters, although interpretation must remain device-specific [4].

8.2 Afterload

A rise in systemic arterial pressure increases pressure at the pump outlet. Unless left ventricular pressure rises proportionally, ΔP increases and pump flow falls.

Higher aortic pressure → higher pump head → lower LVAD flow

Systemic hypertension can therefore reduce LVAD flow despite unchanged rotor speed and circulating blood volume.

Conversely, lower aortic pressure decreases pump head and tends to increase flow. Severe hypotension, however, may result from low preload, right ventricular failure, vasodilation, bleeding, or impaired systemic perfusion. The flow response must therefore be interpreted in its full hemodynamic context.

8.3 Contractility

Improved native ventricular contractility produces a more rapid and greater systolic rise in left ventricular pressure. This reduces systolic pump head and increases flow acceleration and peak pump flow.

Reduced contractility blunts the systolic pressure rise and may decrease flow pulsatility. Low pulsatility is not specific for poor myocardial function, however, because it may also occur with low preload, excessive pump speed, arrhythmia, or mechanical obstruction.

Flow-waveform analysis has been used to derive physiological indices of LV preload and contractility. Diastolic flow-rate change, expressed as dQ/dtdiastolic, has been evaluated as a preload-related parameter. A contractility index, RIQ, has been defined as the ratio of maximum flow acceleration to peak-to-peak flow pulsatility [5].

In a longitudinal study of 17 LVAD patients, higher waveform-derived preload was associated with poorer waveform-derived contractility. These observations suggest that flow waveform analysis may help assess unloading and myocardial recovery, although such indices require further validation before replacing invasive hemodynamics or echocardiography [5].

9. Effect of Pump Speed

Increasing rotor speed changes the pump’s hydraulic operating curve and allows greater flow against a given pressure difference.

At higher speed:

• Mean pump flow generally increases.
• Left ventricular volume and pressure decrease.
• Aortic valve opening may become less frequent.
• Native arterial pulsatility may decrease.
• Suction risk may increase when preload is inadequate.

The effect on pump-flow pulsatility is not determined by speed alone. Higher speed raises baseline flow but may also unload the ventricle sufficiently to reduce its systolic pressure rise. The difference between systolic and diastolic flow may therefore narrow.

Decreasing pump speed reduces mechanical unloading and may permit greater ventricular filling, higher LV pressure, and more frequent aortic valve opening. Excessively low speed may result in inadequate systemic support and, in susceptible pump circuits, retrograde flow.

Pump speed must therefore be interpreted together with ventricular geometry, aortic valve behavior, arterial pressure, filling pressures, and the device-specific H–Q curve.

10. Clinical Interpretation of the Flow Waveform

The LVAD flow waveform can provide useful physiological information, but no single waveform pattern establishes a definitive diagnosis.

Increased Flow Pulsatility

Potential causes include:

• Increased preload
• Improved native contractility
• Myocardial recovery
• Reduced LV unloading
• Lower pump speed
• Increased native ventricular contribution

Reduced Flow Pulsatility

Potential causes include:

• Reduced preload
• Right ventricular failure
• Severe LV systolic dysfunction
• Excessive pump speed
• Sustained arrhythmia
• Cardiac tamponade
• Inflow or outflow obstruction
• Abnormal cannula position

Reduced Mean Flow

Potential mechanisms include:

• Hypovolemia
• Right ventricular failure
• Increased systemic afterload
• Inflow cannula obstruction
• Outflow graft obstruction
• Pump thrombosis
• Suction
• Markedly impaired native ventricular filling

Mechanical obstruction cannot be reliably distinguished from preload limitation using the flow waveform alone. Evaluation should incorporate device power, rotor speed, arterial pressure, central venous and pulmonary pressures when available, echocardiography, cannula position, ventricular dimensions, and outflow graft imaging.

For many contemporary devices, displayed pump flow is estimated from rotor speed, motor power, and a device-specific hydraulic algorithm rather than measured directly by an implanted flow probe. Small changes in the displayed waveform must therefore be interpreted within the limitations of the device’s estimation method [4].

11. Flow Pulsatility as a Physiological Control Signal

Because pump-flow pulsatility reflects the interaction between ventricular filling, native contraction, and pump loading, it has been investigated as a feedback variable for physiological pump control.

A Starling-like controller can use changes in flow pulsatility to adjust pump output according to preload. In vitro validation demonstrated a preload sensitivity of approximately 0.39 L/min/mmHg with adaptive Starling-like control, compared with 0.04 L/min/mmHg during conventional constant-speed operation [6].

During simulated pulmonary hypertension, constant-speed support produced ventricular suction, whereas adaptive control reduced pump flow and maintained safer ventricular loading. The controller also increased flow during simulated transition from sleep to wake in response to increased residual LV pulsatility [6].

These findings illustrate the physiological information contained in the flow waveform. Nevertheless, active control systems must balance responsiveness against the risks of suction, excessive unloading, inadequate support, and instability during rapid hemodynamic changes.

12. Practical Physiological Summary

At constant centrifugal LVAD speed, cyclic changes in ventricular and arterial pressure repeatedly move the pump operating point along its H–Q relationship.

Systole

• The left ventricle contracts.
• LV pressure rises.
• The aorta-to-LV pressure difference decreases.
• Pump head decreases.
• The operating point shifts rightward.
• LVAD flow increases.

Diastole

• The left ventricle relaxes.
• LV pressure falls.
• The aorta-to-LV pressure difference increases.
• Pump head increases.
• The operating point shifts leftward.
• LVAD flow decreases.

The central relationship is:

Systole: lower ΔP and higher pump flow

Diastole: higher ΔP and lower pump flow

The magnitude of this cardiac-synchronized flow variation depends strongly on the H–Q curve slope. Flatter curves translate cyclic pressure changes into larger flow changes, producing greater pump-flow pulsatility and arterial pulse pressure. Steeper curves produce smaller flow changes for the same pressure variation.

The waveform therefore reflects the combined effects of preload, afterload, contractility, native ventricular contribution, pump speed, and device-specific hydraulic behavior. It is a valuable physiological signal but must be interpreted together with clinical examination, hemodynamic data, echocardiography, and device parameters.

References

[1] Tagusari O, Yamazaki K, Litwak P, Antaki J, Watach M, Gordon L, Kono K, Mori T, Koyanagi H, Griffith B, Kormos R. Effect of pressure-flow relationship of centrifugal pump on in vivo hemodynamics: a consideration for design. Artif Organs. 1998. doi:10.1046/j.1525-1594.1998.06157.x.

[2] Noor M, Ho C, Parker K, Simon A, Banner N, Bowles C. Investigation of the characteristics of HeartWare HVAD and Thoratec HeartMate II under steady and pulsatile flow conditions. Artif Organs. 2016. doi:10.1111/aor.12593.

[3] Yang Y, Wang Z, Xie Z, Yu S, Zou L. Hemodynamic consequences of pressure-flow curve gradient variations in continuous-flow ventricular assist devices. Front Physiol. 2026. doi:10.3389/fphys.2025.1730883.

[4] Belkin M, Kagan V, Labuhn C, Pinney S, Grinstein J. Physiology and clinical utility of HeartMate pump parameters. J Card Fail. 2021. doi:10.1016/j.cardfail.2021.11.016.

[5] Ramanayake A, Robson D, Gunawan A, Krishnaswamy R, Muthiah K, Adji A, Hayward C. Determination of left ventricular preload and contractility using waveform analysis in continuous-flow left ventricular assist device patients. J Heart Lung Transplant. 2022. doi:10.1016/j.healun.2022.01.1711.

[6] Gaddum N, Stevens M, Lim E, Fraser J, Lovell N, Mason D, Timms D, Salamonsen R. Starling-like flow control of a left ventricular assist device: in vitro validation. Artif Organs. 2014. doi:10.1111/aor.12221.