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For any reason, a human heart is replaced with a pump that instead of pulses provides a continuous stream of blood. It varies the pressure, as a heart does, as needed.
Ignore such technical issues as energy, immune system rejecting strange body, etc...
Is that viable/compatible with life?
What problems derived from this continuous blood-flow will arise?
The pump console usually comprises several rotating motor-driven pumps that peristaltically "massage" tubing. This action gently propels the blood through the tubing.
The pumps used in VADs can be divided into two main categories – pulsatile pumps, that mimic the natural pulsing action of the heart, and continuous flow pumps.
Start reading there to learn more about them.
It is possible, indeed it is already done today, it is called a Extracorporeal membrane oxygenation.
But, I can't find any problem related to the continuous blood flow nor its benefits.
From what I have read in medical magazines, the exact answer is still subject to research. There are "artifical hearts" that do exactly that (inside or externally, both exist) but some have the suspicion that this kind is suboptimal for prolonged use.
There are other studies that show that stem cells (and probably also other cells) react and differentiate differently whether they are under a constant or a (rather) quickly varying pressure.
The details are not very well understood, but at least it is understood that if there are any risks with a continuous flow pump involved, their statistic relevance is likely lower than any other issues the patients have, so research is done in that field as many people believe those are more reliable.
It should be noted that everything that is involved here is about patients with (possibly terminal) illnesses and that the artificial hearts are often used to fill the gap until a transplant becomes available. In the context of worldbuilding one might want to consider that doing this on a big scale for healthy people might have a much worse outcome, given current understanding of the human body.
I'm not aware of any negative physiological effects of maintaining a steady blood pressure, PROVIDED the pressure is around the regular average a human has today. So, for example, if a normal human has an arterial pressure between 120 mmHg and 80mmHg, their average pressure is 100mmHg. So you couldn't run your synthetic heart at 120mmHg all the time, as that would start to induce the negative changes we associate with hypertension. The higher the continuous pressure, the more negative the effects (typically increased risk of stroke, decreasing kidney function, etc). Of course these devices have lots of other complications, but we'll ignore those (the need for anti-coagulation, etc).
But you have to be able to vary the pressure to some extent because otherwise in a fight or flight response (gotta run!!!) you won't be able to increase blood flow to deliver more oxygen and remove lactic acid. Plus it helps to be able to vary blood pressure when going from laying down to standing up (problems doing this is called orthostatic hypotension). So a continuous pressure heart, inherently, isn't a problem, but one that is LOCKED TO A SPECIFIC PRESSURE is.
Humans vary their blood pressure through adjusting heart rate AND changing the muscular tension on arterial side blood vessels. Venous blood vessels have little to no muscular walls so they can only dilate to compensate for increased pressure or respond to the muscular action of the tissues they are embedded in. If you remove the natural heart, the replacement will have to either be manually controlled, somehow interpret the brains call for increased heart rate by increasing the flow rate and elevating blood pressure (or sense dropping oxygen levels, rising lactic acid, or whatever), or the person would be forced to regulate their activity very carefully lest they deplete oxygen and cramp up due to lactic acid build up. Here is a good technical article discussing various total heart and left ventricular assist devices and exercise tolerance. To my knowledge, all artificial heart type devices meant for prolonged use (i.e. getting out of bed and walking around) replicate or assist a beating heart. ECMO and the like are for sedated/bed-ridden patients, so exercise tolerance is not an issue.
These already exist. In 2010, Dick Cheney received exactly this sort of thing; it wasn't a fully artificial heart, but it took over for his failing left ventricle, and for over a year he lived with no pulse at all. The comedians went nuts over this, but the truth is somewhat more boring: his life during this time was fairly typical for someone with severe heart trouble. After about 15 months he got a heart transplant, so now he has a pulse again.
It is entirely possible and the subjects are still able to live a very healthy, normal life. Some, like Andrew Jones in the link, even reach extraordinary levels such as bodybuilding while still being without a pulse.
It is important to note that this is usually temporary while the subjects wait on the donor list for a new heart.
Long-term continuous blood flow does cause physiological problems, but the full scope of the problems it causes is still the subject of ongoing research.
Pulsatile blood flow causes a phenomenon called endothelial shear stress (ESS). I still remember a set of electron micrograph slides from medical school a few years ago comparing arterial endothelium - that's the innermost layer of arteries - which have been subjected to both continuous and pulsatile blood flow. I no longer remember the experimental details, but there is a clear difference between the two. The surface of the endothelium subjected to pulsatile flow looks smooth and healthy, the other one looks positively jagged.
This jagginess causes all sorts of problems, especially the deposition of artheroscletoric plaques. Here is a 2007 paper from the Journal of the American College of Cardiology that describes the phenomenon in detail.
In the context of worldbuilding, while it certainly will not kill the subject immediately, there may be other long-term effects that we don't know about. If the continuous blood flow is the side-effect of a life-saving operation, like a heart transplant, I'd say that's not too bad :)
Taking an intuitive/common-sense perspective, with a little everyday science thrown in...
The goal of the device is to match the mean flow rate (litres per minute) of a natural heart. Continuous flow will result in a certain uniform fluid velocity through the arteries, veins, vessels, and capillaries; pulsed flow will produce time-varying velocities, peaking much higher than the mean to make up for reduced velocities occurring between the pulses. Blood is a suspension; when not in sufficient motion, things in a suspension will begin to settle out. The higher peak velocities could be beneficial in preventing things normally suspended in the blood from settling out on the vessel walls, or "scouring" things which have begun to settle. The uniform velocity produced by a continuous flow device might not be high enough to accomplish this.
