How does the cut arteries and veins maintain the circulatory system of the oxygenated and deoxygenated blood
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First, some info you probably already know but is good for us to remember.
* **Arteries** carry oxygen rich blood away from the heart
* **Veins** carry oxygen poor blood back toward the heart
* **Arteries** and **Veins** are connected by **capillaries**, which is the kind of tissue that your veins and arteries turn into as they branch into smaller and smaller pathways.
So to Visualize this a bit, just imagine one giant artery coming out of your heart, which then splits into 3 smaller arteries, which in turn split off into 10 smaller arteries each, which in turn split off into thousands of different beds of capillaries, which in turn merge back into larger veins, which in turn merge into bigger veins, until they finally merge back into one giant vein that feeds into your heart, forming your circulatory system.
The thing is, when you think of your arm, you might be tempted to think about an artery that goes all the way down to your fingers, where it branches out into capillaries, which merges back into veins, which travel back up your arm. This mental image is sort of thinking about the circulatory system as if it were a racetrack, and blood flows through the entire racetrack like a car. With a mental model of the circulatory system like this, your question is very understandable: If your remove a segment of the track, how do the cars keep going around it?
This isn’t the case, however, and that mental image of your circulatory system is flawed. An important thing to know about capillaries is that capillaries are the **only** place where the rest of your body can receive nourishment from blood. Capillary tissue is porous (covered in tiny holes) and is what allows blood fluid rich in gasses (like oxygen) and nutrients (like sugar/glucose) to flow out into your body’s tissue, which then uses those gasses and nutrients, and passes the “exhausted” blood fluid back into the capillaries where it can be carried away by the veins. This “capillary exchange” happens **only** in capillaries; your veins and arteries are **not** porous, and are **not** able to provide gasses and nutrients to the surrounding body tissue on their own.
This means that capillaries are ***everywhere*** in your body. Wherever you have tissue in your body, there are capillaries there feeding that tissue. This means that the capillaries in your hand are **not** the only place where blood is being transferred between your arteries and veins, [it is happening **everywhere**, throughout your **entire** body.](https://i.imgur.com/M3msR3S.jpg)
As an artery passes your shoulder and down into your arm, smaller branches of it are **constantly** branching off, branching into smaller branches that eventually branch into capillaries that are found throughout your biceps, your bones, your skin, your elbow, everywhere, where they then also merge back into veins that rejoin the bigger vein, taking a bit of a “shortcut” back to the heart.
So not 100% of your blood volume travels the **entire** length of your circulatory system every trip, a good amount of it is taking shorter routes through organs and tissue that are located closer to your heart. The blood that oxygenates your bicep takes a shorter path through your circulatory system than the blood that oxygenates your hand. The blood that oxygenates your heart, for example, takes a **ridiculously** short path, as the Coronary arteries (the arteries that provide blood to your heart) branch off from the Aorta (the big artery that leaves your heart) almost immediately, and after going through capillary exchange throughout your heart tissue, returns directly to the heart chambers for reoxygenation via the Cardiac Veins.
So **part** of the answer to your question is to note that just because your hand was amputated doesn’t mean that it is now harder for your bicep to get blood. Blood getting into your bicep never relied on your hand, as your bicep has it *own* capillary bed that nourishes it, and there was always a pathway to accomplish that without using your hand at all.
***However***, there is still a problem. With your hand now gone, there are way, way fewer capillaries available to exchange blood between the arteries in your arm and the veins in your arm. Since the same amount of blood is still being pumped by your heart, the remaining capillaries are having to shoulder a bigger burden, and the pressure in those capillaries goes up, which can cause a ton of problems.
Your body is able to rectify this problem on its own, generally speaking. It is able to create new blood vessels, new arterial tissue, new veinous tissue, and new capillaries to connect them, in order to keep the pressure in your capillaries where it needs to be in order to facilitate proper “Capillary exchange,” I.e the exchange of gasses and nutrients with the rest of your body. This process of creating new blood vessils, called Angiogenesis, is the 2nd part of the answer to your question, which is that your body is able to create new blood vessels to replace the ones that were lost in order to keep your circulatory system healthy.
[Watch this video about Capillary Exchange](https://www.youtube.com/watch?v=dFRa2ECm5pY) to learn more about the specifics of how capillaries work, as it is quite fascinating.
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