Which type of stroke?

The blood supply to the brain is a web encased in a rigid box. I'd not expect the blood vessels to be able to expand much--between brain tissue and other fluid around them, there's not much to compress and no room to go thanks to the skull. But there should be a little elasticity to the blood vessels, and there are so many that the effect should add up.

With each heart beat we have a more or less predictable pressure wave going into the network, and so there should be a consistent pressure wave coming out. It can't be exactly the same shape, because in different parts of the network blood travels different distances facing different impedances, but it should be consistent.

Now suppose some major vessel has broken and there is bleeding in the brain. If the blood loss is significant I'd expect there to be a change in the wave shape. In particular, blood would leak out of the broken vessel and slowly reenter, giving the output pulse a longer tail.

So the obvious questions are:

1. Are the output pulse shapes (maybe convoluted with the input pulse if need be) consistent enough between people that we can use differences for diagnosis?
   
2. Is the tail from a leaky vessel discernible in the output pulse, and if so at what level?
   
3. Are there other things that would mimic this?
   

You have to measure the input also, since a long tail on the input is quite possible, and you'd need to correct for that.

If it is possible to distinguish a leaky vessel-brain from a normal one, it would be possible to distinguish a broken blood vessel stroke from a clot blockage stroke. (The instrumentation shouldn't be very expensive--transducers and some ADCs and a small processor to compare the results--a display if you want to get some human input.) Since you don't want to use blood thinners to treat someone with a broken blood vessel stroke, and since getting treatment fast is vital, this might be useful in an ER.

I don't think it would be possible to positively ID a blockage this way, since that would merely appear as larger impedance, and without some prior measurements you wouldn't know if this was normal or not--brains are different.