Blood vessels are made up of endothelial cells, which create the basic tissue barrier between the blood itself and other tissues such as collagen. When the vessel is punctured or damaged blood rushes from the wound carrying with it platelets. To combat the rapid blood loss and stop your body from losing excessive blood the platelets which are small portions of cells come together sticking together upon the damaged portion of vessel. The reason the platelets stick together is due to collagen and tissue factor, which creates a coagulation cascade wherein the platelets begin activating changing their shape. Basically the clumping activated platelets call on other platelets which then activate doing the same changing shape continuously repeating the process and causing a flood of platelets to arrive at the site of the wound. Eventually the whole thing begins to release thrombin which converts fibrinogen to fibrin which acts as a reinforcement like concrete and rebar would for a building causing the clot to become more structurally sound.
As the tissue heals over time the same thrombin that creates fibrin converts plasminogen to plasmin which dissolves the firbrin eventually causing the clot to dissolve and break apart after the damaged tissue has healed. Obviously several named proteins or chemicals have been left out of my explanation but I didn't want to get closer to essay length so I cut a lot back and went as streamlined as I felt necessary.
When it comes to the narutoverse, where we have things like the blood producing pills and chakra the above becomes a process that can be controlled, instigated, and quickened. The ninja is able to forcibly help the clotting process making it happen at a quicker and safer pace allowing the medical ninja to save others from usually fatal damage.
Blood coagulation relates to the Narutoverse greatly because it is a natural occurrence that happens with all living beings that possess blood inside of them. Coagulation of the blood is a natural process that is initiated by the body itself when trauma occurs inside of the body like raptured vessels/tissues and blood begins escaping the body. Blood coagulation is said to always be "active" and it controls the fluidity of the blood in terms of how thick or thin it has to be to effectively travel throughout the circulatory system to fuel the body/metabolism. Blood is equivalent to fuel in a sense to the body, and thus when trauma occurs, the blood coagulation process begins to thicken the blood in that specific traumatized area, creating a clog of gel-like blood that reduces or sometimes stops, the bleeding from continuing. The gel-like substance is produced when proteins are released and scattered throughout the wound. Said proteins are released when an area is traumatized, like a wound. When the blood and protein make contact, the process begins to take place. The Blood Coagulation process is such a complex thing to understand, that a Medical Shinobi is unable to forcefully activate it or replicate it himself. The only thing he can do, is utilize his own medical chakra to fuel that injured area to help aid the natural process of coagulation, speeding things up before they take a turn for the worse. If the patient is unable to activate or release those special proteins among other things, he will be left unable to coagulate his blood, and thus continuously continue bleeding.
Coagulation is the bodies natural response to wounds that cause bleeding and serves the purpose of stopping bleeding so that the body may proceed back towards homeostasis. The cavity of a blood vessel is called the lumen, when punctured into (or crushed into) bleeding occurs. The Endothelium is the tissue that lines the inner walls of a blood vessel, when blood is exposed to its rear areas and the area behind it the process of coagulation will immediately begin. This can be divided into two processes, the first is that collagen (A structual protein), which is normally hidden beneath the endothelium is exposed to blood, and reacts-and-binds-to the plateles (tiny fragments of cells that have no nucles) in the blood, and the now activated platelets will immediately plug the site of injury - Coagulating - together. The second is that multiple factors are released which stimulate the creation of fibrin strands, a type of protein, that helps to reinforce the created plug.
The physical Anatomy of the inhabitants of the Narutoverse is largely the same as our own, as such Coagulation is likely to work the same for them as it does to us. What they have that we do not however, is Chakra - through the use of Chakra multiple events, processes and phenomena can be enhanced, stimulated, or even outright replicated, it stands to reason then that a Ninja could hasten the process of coagulation through the usage of chakra. Which is exactly what a Medical Shinobi does, through fine chakra control they are capable of aiding their bodies natural responses and recovery process, just as a Fire Release user could make a flame larger, so too can a Medical Shinboi pour chakra into their wounds to stimulate a faster activation of platelets, release of factors and dramatically hasten the plug creation process.
A medical Ninja's role, then, is to use their knowledge of the anatomy and their advanced chakra control to enhance, stimulate, replicate, distort or even outright create events, processes and phenomena related to biology, just as a fire release user would do so for Fire.
Although most of you covered the basis, I cannot correct each of your works individually pointing out what was missing or not so I'll simply make a small concise explanation of what I want you guys to know.
The Coagulation process is one of the most basic but yet complicated processes of the human metabolism (and all animals with blood). In simple terms, its the process through which blood becomes thicker and ultimately solid (cloth) if necessary; its the process through which blood thickness is altered. Taking this basic idea, Blood Coagulation is often dispicted as a stagnant occurrence, triggered only when a trauma occurs and hemostasis is needed.. However, its beyond that idea and is actually an active process constantly changing and balancing the blood's fluidity.
Its a simple idea, although the process itself is complicated. The blood, as a fluid, tends to escape the pathways through which it circulates. These pathways are the blood vessels (arteries and veins). Blood vessels have, inherently a given permeability to enable exchanges between the blood and the cells on the outside of the vessel. The coagulation process serves as a basis for these exchanges to work and is constantly adjusting the blood fluidity in order to keep it flowing in a correct way, containing it in the vessels but maintaining circulation. If the blood is too thin and fluid it will escape the vessels and a passive hemorrhage occurs, disabling the normal exchanging process. If the blood is too thick, it will form cloths, clogging the blood vessel and preventing circulation (trombosis).
This is the process that keeps working 24/7 on adjusting the blood in order for the human body to work and is an automated passive process of our metabolism. Many factors revolve around them and I don't expect you guys to know them all obviously. Vitamin K, Platelets, Fibrogen, Colagen, Water, Ionic Concentrations, Genetic Intrinsic Factors (also named often the coagulation factors), etc all play a part in keeping the passive balance in order. However, this process serves another purpose, which is the main one for our application here in Med School. If blood vessels are ruptured, the blood spills outside of them and a traumatic hemorrhage occurs. Because blood is one of the core participants in the metabolism, the organism can't afford to lose too much of it, so it has to stop the bleeding. This is done through the hemostasis process, a process through which blood is used to produce a cloth of platelets and fribin in the rupture, stopping the bleeding and enabling the repairs to start.
Coagulation works through 2 main factors: The Cell Factor (platelets) and the Protein Factor (Coagulation factor). Basically and resuming it way down since I only want you guys to hav an idea of it, not all the medical details, when a tissue is ruptured and cells are damaged, a special batch of proteins are scattered throughout the wound and surrounding area (they are released as a byproduct of the traumatic destruction of the cells and celular tissue). When the blood comes in contact with these proteins, the platelets and a special protein in the plasm (the "water" base of the blood where all the nutrients and minerals and etc are transported) called fribrogen changes and immediately the primary hemostasis occurs, as a "tampon" of aggregated platelets forms at the rupture, stopping the bleeding. At the same time,the secondary hemostasis ocurrs, through which a complicated chemical and physical reaction ocurrs in the proteins in the plasma, triggering a cascade of reactions that has the byproduct of producing fibrin strands that strengthened the platelet "tampon" and form the definitive cloth. These proteins in the plasma and the cascade reaction of them is the process through which blood becomes thinner or thicker, by the presence of more or less fibrin and its thicker or thinner structure. Fibrin is a thick and gel like protein that combines with water to give plasma its main body (and through more or less "gel", more or less thicker it becomes).
Okay, so, with my explanation and while writing your homework, you all learned (hopefully) what's the basis needed for blood to coagulate. This technique and the procedure around it doesn't makes it do so, and there is nothing you can do to make successful blood coagulation occur, because it is simply too complicated and has too many factors involved. What you can do, however, is help the body while it's trying to do it on its own. This implies that the patients blood has to be able to coagulate on its own already, meaning that all coagulation factors must be present and functioning in his body, he has to have blood, etc. This means that you simply make your patients blood coagulate faster than normal by aiding it with your chakra.
You do so by laying your hand on the wound and infusing it with your chakra, molding, willing your chakra to be of a certain nature that will help the body in the coagulation process; and you do so by simply imagining the chakra how it goes to the blood vessel and starts sticking fibrin and blood platelets together over the damaged area. Pretty simple and doesn't count as a move or requires a technique.
Are there any questions?