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The creature has several hearts, each supplying blood to one limb. For all other intents and purposes the creature is human. Of the six smaller hearts, one supplies each arm and leg, one supplies the head, and one supplies the torso.

How large does each heart have to be in order to supply enough blood to said extremities (arms, legs, head) for each of them to be supplied with enough blood to function properly?

Note that hearts for different types of extremities will likely be different sizes; also, it might be best to, as a measure of size, express answers in terms of the hearts of real-life animals; for instance, the hearts supplying the legs might be the size of a labrador retriever's heart, the one supplying the brain might be the size of a housecat's heart, and so on and so forth.

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    $\begingroup$ Does the creature have a single circulatory system, or does each heart have its own closed-loop? A single circulatory system would allow the other hearts to cut each other some slack if they fail/weaken for some reason but might cause a 'lazy heart?'. At the same time, multiple closed loops won't have synchronisation issues, as pumping out of phase wouldn't disturb the system, but will make a failure in an organ that isn't directly fatal(arm/leg) to make that limb a literal dead weight. $\endgroup$
    – vinzzz001
    May 17 at 10:38
  • $\begingroup$ It's a single circulatory system; it's just that each heart is designed to provide most of the blood for its respective part of the body in order to minimize blood pressure. $\endgroup$
    – KEY_ABRADE
    May 17 at 10:51
  • $\begingroup$ We already do this with body parts that are not hearts but work to make the blood flow up from our legs for example. This might be useful for creatures of immense size to function, if that is what you are going for I would also recommend multiple "brains" and a nervous system that is not centralized. $\endgroup$
    – TurtleTail
    May 19 at 16:27
  • $\begingroup$ the one supplying the brain may be large than you think since it needs to pump against the highest gravitation gradient. your creature may be less prone to hemorrhoids at least, since the torso can have lower pressure. $\endgroup$
    – John
    May 19 at 21:57

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This is already the case in the human body, to a limited extent. The pumping action of the blood through the arteries is not just restricted to the heart. The muscles all along the arteries contract in a wave action, continuing to push the blood along.

All that would be required is for the major arteries feeding the limbs and head to have check valves in them, so the blood could not reverse direction and flow back to the heart. Then, enlarge the artery and place a stronger muscle around it. No need for a separate organ.

It is, in fact, unlikely that the auxiliary hearts would be dual chambered, one chamber for the veins and one for the arteries, as the two chambers would no longer be able to beat in synchrony. The pulse travels in a wave through the body, from the heart in arteries and to the heart in the veins, and these waves coming from the heart and going to the heart would not occur in the same place at the same time coming and going, except in the main heart. If you tried to create a pulse simultaneously in the arteries and the veins somewhere other than the heart, the pumping action would act against the main heart in either the vein or the artery. The arterial and venous auxiliary pulses would work against each other. You would need a separate auxiliary heart for the vein and the artery.

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The size of the heart of a creature the size of the limb.

A heart has to counter the resistance of the circulatory system. This is in large part the capillaries, the smallest blood vessels that perfuse the tissue and do the actual work of supplying the cells with what they need to function. While the exact amount of resistance will depend on many factors, you are going to get close by assuming it is constant for any mass of tissue, so a 10 Kg leg will need about the same size heart as a 10 Kg animal.

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The case of the Extra Hearts:

Some creatures, like the octopus, already have multiple hearts. In the case of the octopus, this is to compensate for hemocyanin, which is less efficient than hemoglobin at carrying oxygen.

A cockroach was once thought to have 13 hearts, but scientists now understand that is a 13-chambered heart that operates fairly differently than ours. It runs sequentially and the individual parts can compensate for each other, making their hearts more resilient.

Perhaps an even better model is the hagfish, with 5 hearts (one central and four peripheral). A hagfish heart will keep pumping up to 36 hours in an anoxic environment (the kind of place hagfish tend to live).

Heart design is going to be pretty conserved evolutionarily, so you should have an idea WHY all these separate hearts evolved. It sounds like your vision is that the creature needs them because of great size. But blue whales only have and need one heart, so scale alone isn't necessarily an issue. Do these hearts attach to separate lungs/gills? Is each limb it's own independent circulatory system?

The size of your creature shouldn't be a factor with multiple hearts unless you want it to be. Mice have hearts similar in design to an elephant. Biology is often a case of a pre-existing structure evolving to a new function whether it is better for it or not. The mammalian eye, for example, had to re-evolve a different way of perceiving color than, say, birds, because our deep ancestors lost the ability to see color. But while it is hard to prove, the barosaurus may have had 8 hearts, so if you want size to be the reason, you can certainly justify it. The blue whale has a 400 lb. heart, thought to be at the outer limits of heart function. Getting much bigger than that would likely require changes in the circulatory system (like extra hearts...?).

As for the exact size of the heart, that depends on many additional factors. Mass of the creature and demand are going to be the biggest factors. Find a creature with a similar evolutionary niche and divide the mass of the heart by the mass of the tissue supported. (this part is similar to the answer given by user65535, who answered it before I did). The hearts may be smaller than this in a combined circulatory system, since the central heart will be doing more of the work, so exact details depend greatly on biology and function.

But you will want a reason for multiple hearts if you desire to be true to biology. This reason can, however, be something that existed in an ancestor of your current species.

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The torso heart would still be almost the same size as a human heart's. This is because the blood volume that needs to be circulated in the unit time remains the same, so the work to do remains essentially identical.

Perhaps the reduced differential pressure in the aortic trait might lead to the left half being slightly smaller, but I wouldn't expect much. And you'd get significant complications in keeping the hearts synchronised to avoid straining either the hearts or the intervening vessels: a synced systolic stroke between torso and lower limbs would raise the pressure in the aortic trait significantly.

If you had two separate hearts, one each managing pulmonary circulation and global distribution, then those could be a bit more than half a normal heart's volume (they would be essentially the left and right halves of a normal heart, connected by a large valved artery instead of being back-to-back). But I suspect this would lead to a loss of hydraulic load in the middle, leading to a need for both hearts to be larger.

You can maybe decrease heart size by having contractile vessels (i.e. supplementing with peristaltic pumping). This already happens to a point, but it will require some synchronisation to work at speed.

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