Quick Dips

X-ray Visions of Blood Vessel Networks

A few years ago now, a physicist who worked in a hospital showed me a pair of X-rays -- pictures of the blood vessels in a patient's brain. One picture was from the front and the other from the side. The physicist asked me if I could write a computer program that used these pictures to make, automatically, a three-dimensional model of the patient's blood vessels. This is an example of what is called "reconstruction" from images. A three-dimensional model was wanted so the radiologists had a model to help them plan treatment of abnormalities associated with vessels, and communicate their plans to colleagues untrained in anatomy.

In turns out the physicist's request poses a very considerable challenge for me and my colleagues Peter Andreae and Milton Ngan. The underlying difficulty is the problem is "under-determined", to use the jargon. The outcome for us is quite straightforward -- it means the problem is impossible to solve! Impossible, that is from images alone.

We can see the germ of a solution if we consider the same problem in another way. The under-determined nature of the problem means that an infinite number of different vessel networks will look identical to each other when viewed from the front and side -- in principle at least. In practice, most of these are theoretical possibilities and will not correspond to any real vessel network. If we can somehow tell the difference between real networks and mere possibilities, then we are on our way to a solution -- a three-dimensional model.

One way to tell the difference is to supply a catalogue of known vessel networks. All we need do then is to take X-rays of these networks, from the from and side, and choose the network whose X-rays look most like those of the patient. The idea of using a catalogue of models, and choosing amongst them, is the basis of the computer program we wrote. We made some important changes to this idea, though.

First of all we could not find a catalogue of blood vessel networks that was suitable for us. So, our catalogue learns its contents -- each time a new vessel network is made up it can be added into the catalogue. In this way, the catalogue will grow to accommodate all the individual variations present in blood vessel networks. Also, the catalogue is stored on the computer in a very compact way -- all the different networks are squashed into one.

Second, our method for choosing the right model from the catalogue allows not just for models already in it, but the method can "chop" networks from different people and paste the chopped pieces together to make new networks. This means our program can make reconstructions from images even when there is no catalogue entry for the X-rays.

Finally, our method produces not just one model but several, each of which could have produced the X-rays for the patient. The models are given an order of preference to assist a radiologist in choosing between them. If the chosen model is still not good enough, then it can be repaired using interactive computer graphics -- that is, repaired manually by the expert. Finally, the new model is added to the catalogue; next time round this model will be reconstructed without assistance.

We've got all the parts of this program working. Happily, our tests give room for us to think we're on the right track. One next step is to bind them together into a single package, then conduct extensive clinical trials to test the system. Another next step is to consider reconstructing models of vessel that move; we've dealt with vessel in the brain -- not those around a beating heart. Clearly, there is much work to do.

Peter Hall was formerly in Victoria University's Computer Science Department.