When the heart pumps blood into the aorta, the pressure gradient-the difference

Question

When the heart pumps blood into the aorta, the pressure gradient-the difference between the blood pressure inside the heart and the blood pressure in the artery-is an important diagnostic measurement. A direct measurement of the pressure gradient is difficult, but an indirect determination can be made by measuring the Doppler shift of reflected ultrasound. Blood is essentially at rest in the heart; when it leaves and enters the aorta, it speeds up significantly and-according to Bernoulli's equation-the pressure must decrease. A doctor using ultrasound of 2.5 measures a 5300frequency shift as the ultrasound reflects from blood ejected from the heart. Part A: What is the speed of the blood in the aorta? Assume that the speed of sound in human body is 1540 Part B: What is the difference in blood pressure between the inside of the heart and the aorta? Assume that the patient is lying down and that there is no difference in height as the blood moves from the heart into the aorta.

Explanation / Answer

The blood velocity is, as you say, initially zero, but rises quickly to a maximum as the wavefront of the ejected stroke volume crosses the aortic valve, then falls again, because the flow and pressure are initially out of phase, (max pressure, zero flow) then come into phase as pressure builds up the flow. But as flow builds up and driving pressure becomes in phase with flow, work is done as potential energy is transformed into kinetic energy, gained by the blood. As pressure decreases and finally is isolated from the ejected stroke volume when the aortic valve closes, velocity tends to fall asymptotically on the downstream side, to a value determined by the non-pulsatile gradient. Ventricular pressure on the other hand, proceeds through its previous filling and compression cycle, to the point where it and flow are again in anti-phase. So Bernoulli doesn't apply because that Law only pertains to laminar flow in uniform conduits. The velocity of blood along the aorta varies widely,- not only in space but also in time (at any location), at the root being quite different from what it is at a central aortic location, and different yet again from that downstream, dependent partially, as it is, (-at least at the root) upon which instant of the ejection cycle is chosen, - but 20 cms/sec. is generally cited as being 'representative'. That is to say, an order of magnitude slower than that of the pulse pressure wave. This does not in any way prevent the instantaneous velocity from being estimated by Doppler shift of course. It's how the Doppler-determined instantaneous value is used that matters. Not my field I'm afraid; sorry, I can't help there. Since the intra-ventricular pressure varies every fraction of a second, and central aortic pressure does too in a quite different phasing, it is not possible to say what the instantaneous difference in pressure is between the heart and the aorta, irrespective of whether the subject is standing up or lying down.

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