Dear all I'm trying to build a 1-D MODEL OF BLOOD FLOW IN THE barachia [arm artery]. I'll be gratefull if someone will send me where in the net I can find that model assuming the blood is incompresible fluid. what is the easiest way to integrated the pde. I'll also need a matlab source code that solve the equations calculating the velocity of the blood. If there is a simple model that deals with the the blood flow in a collapse artery and the velocity when the external pressure is reduced. best regards.

Depending on whether your model needs something more sophisticated than a Newtonian viscosity model, you may well be able to get by with an analytic solution to your problem.

Indeed, the early work of Poiseuille in the 19th century which forms the basis of introductory fluid mechanics was motivated by his desire to understand blood flow.

Even if you need a more sophisticated model that accounts for the fluid/structural interaction between the blood and an elastic artery, there is some literature on this already that you should be able to locate with Google or SciSearch.