Roughly speaking, our main efforts address the following challenge: Is it possible to use mathematics, medical knowledge, computers and ECG recordings to determine the size and location of an ischemic region in the human heart? (ischemia is a reversible precursor of infarction). In mathematical terms, this problem may be formulated as an inverse problem for a system of partial differential equations. It typically leads to a so-called ill-posed problem, and is thus extremely difficult to solve. We are therefore mainly occupied with analyzing the mathematical properties of the involved equations, inlcuding various regularization and level set techniques, along with suitable solution algorithms and software.
To make this project to something more than “yet another collection of theoretical research papers without any practical impact”, we believe that our methods should be tested on real world problems. That is, to make our efforts matter in a broader sense, our models and algorithms will be validated. This goal can obviously only be reached in close collaboration with the medical community. Currently we are thus undertaking a validation study in collaboration with Rikshospitalet University Hospital.
