There are a number of different factors that must be accounted for when attempting to model internal or external blood flow. For internal bleeding the most important variables are the rate of flow, and the internal pressure. Flow rate determines how the patient's circulatory system will respond to the injury, whereas high fluid pressure causes expansion of the liquid filled cavity and may affect the function of adjacent organs. To simulate these effects it is important to accurately characterize the motion of a fluid in terms of its local velocity and pressure. For external bleeding however, fluid pressure is irrelevant for diagnosis as the blood has left the patient. Flow rate on the other hand, not only indicates the extent of tissue damage but may also be a good indicator of whether intervention will be useful. An additional requirement for external flow, is that the blood has a realistic free surface that moves over time under gravity and the influence of its own volume. Although this is not medically important, the appearance and physical behavior of an injury is part of the required level of realism for the simulation as a whole.
Another practical consideration is computation speed. Internal and external bleeding are just two of a number of trauma manifestations within a framework designed for real time interaction with a human medic. Thus, although it is desirable to achieve accurate behavior this should not be at the expense of computational, and hence overall simulation speed. This desire, together with the need for medical realism, suggests that two different algorithms are necessary; one for scientifically accurate internal flow and a second, more ad-hoc approach for real-time simulation of external bleeding.
For the MediSim project, two different techniques have been developed for animating the behavior of a viscous liquid such as blood. The two methods are based on the Navier-Stokes and wave equations respectively. A detailed description of each system is given in [16,15,21] and only a brief overview is repeated here.