Mathematical applications in modern medicine

by Alexander Ploier, Johannes Kepler University Linz

My name is Alex and I’m studying industrial mathematics in Linz. I chose this degree after my exchange year in Norway where we had lots of projects, which showed me that in nearly every real world application or problem there is mathematics included. And if one wants to solve this kind of problems this is the degree to go. Together with medical doctors in Graz, Austria, we work on helping patients getting a better recovery from upper arm injuries such as a broken bone.

The first thing that needs to be done is to scan a lot of CT scans, to get the images which show the curvature of the bone best. After this, the scan has to be prepared to be able to work with. We do this by applying some algorithms to see what parts of the picture are bones and which are not.

prep

image 1: the captured radiograph

After this is done, the program advances and clears some errors that might occur due to the scan being only a couple of mm thick. We apply an edge detection algorithm to get the outlines of the upper arm. The next step is for the doctor to choose the area of interest, with this we filter everything else out and just get a curve that resembles the bone structure.

roentgen

image 2: edited radiograph to fix the medical doctor’s field of interest

This curve is then compared to the one of other scans to see if there are any similarities between people, depending on their height or gender – and maybe some other factors.

curve

image 3: the curve the medical doctors consider in their work