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I work with left ventricular assist devices in patients with heart failure. These devices operate by maintaining a fixed speed of a centrifugal or axial rotor. The native heart continues to contract creating pressure differences between the pump inflow (heart) and outflow (aorta).

The device and the heart are in parallel by my reckoning. Volume A enters the heart. Volume B exits the aortic valve. Volume C exits the pump. Flow in the body is A= B+C. If the pump is off, flow in the body is A=B. If the aortic valve is sewn shut, the flow in the body is A=C. It is considered dogma that when flow through the device increases, device power consumption increases. The heart and the pump share the pulsatility of the heart and are subject to the same afterload in most situations.

I want to understand why power increases when pressure across the pump decreases. I understand that there will be more mass-flow through the pump with a lower delta-P across the pump. What I don't understand is why this mass-flow slows the pump, ostensibly requiring more power to overcome apparent resistance. It seems more logical that increased flow decreases energy of rotor rotation as the reduction in pressure difference would seem to have the action of imparting energy to the rotor.

Why is more power required to turn the rotor with a lower delta P across the pump and what principles/equations explain this effect?

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  • $\begingroup$ The last setence in para 1 explains it : the more fluid that is pumped requires an increase in power - it’s mass-flow rate... $\endgroup$ – Solar Mike Jan 3 '18 at 20:13
  • $\begingroup$ In my view, the heart is pumping more, not the device. $\endgroup$ – Todd D Jan 3 '18 at 20:53
  • $\begingroup$ Your edit helped. A schematic of the installed device would help even more. Are you asking about the power variance during each heartbeat, or are you asking about long term trends as the heart continues to fail? $\endgroup$ – Phil Sweet Jan 7 '18 at 0:38
  • $\begingroup$ The effect of each heart beat. $\endgroup$ – Todd D Jan 7 '18 at 0:44
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This is entirely a design choice. If you imagine a positive displacement pump such as a piston pump running at constant speed, then the work done is basically a function of pressure difference, since the flow rate is constant. The greater the pressure, the more work required. The opposite extreme would be a pump like the squirrel cage fan in your house's heating system. If you apply enough back pressure, the flow goes to zero. Inside the scroll, the air is just spinning around with the fan blades. There is no torque and no work required to just keep the system running, doing nothing. As you begin to reduce back pressure, the fan begins to move air. Now there is a torque on the blades because the incoming air mass has to be accelerated to scroll perimeter speed. The loaded motor will slow down a bit.

Axial pumps can be designed to be very stiff, having a big power rise in the face of backpressure rise, or soft, having a small power rise in the face of increasing back pressure. But if the flow really gets choked down, the power drops in all cases. These devices would be set up to top out below normal diastolic pressure, so they would be choked and just free spinning during the ventricular contraction. What the power response looks like as flow increases from stall is at the designers discretion.

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I believe the aspect that you are missing with your intuition, is efficiency. For a given impeller diameter, there will be a specific flow rate through the pump at which it is able to operate at maximum efficiency. Have a look at the standard graph below. You can see how despite the Head (delta P for you) dropping off at higher flow rates, and the Power keeps rising to compensate for the falling efficiency.

Generic Pump Efficiency Curve

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If one wishes for the flow rate of blood through the pump to increase, the power output of the pump must increase and the consequence of this is that the output pressure of the pump increases. the pressure differential is not decreased if the heart is assisting the mechanical pump by increasing the inlet pressure applied to the pump; note that the heart and the pump are in series which means that the pressures developed by the heart and the pump are additive.

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  • $\begingroup$ With a pump in place, the heart can eject out the aortic valve and blood moves through the pump. The reservoir for both is the left ventricular cavity. I don't think the system is purely in series in this setting. $\endgroup$ – Todd D Jan 4 '18 at 0:11
  • $\begingroup$ well, the definition of a series connection is that all the flow that traverses the first component also flows through the second. there may be compliance between them or resistance, but they are in series. $\endgroup$ – niels nielsen Jan 4 '18 at 1:28
  • $\begingroup$ Volume A enters the heart. Volume B exits the aortic valve. Volume C exits the pump. Flow in the body is A= B+C. If the pump is off, flow in the body is A=B. If the aortic valve is sewn shut, the flow in the body is A=C. Is this series or parallel? $\endgroup$ – Todd D Jan 4 '18 at 14:34
  • $\begingroup$ I am sorry, from the original description I thought all the volume discharged thru the aortic valve went through the pump! $\endgroup$ – niels nielsen Jan 4 '18 at 18:09

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