The inverse problem of electrocardiography : increasing the stability by using a simplified geometry for the ischemic region

We aim to obtain stability when using ECG recordings, the bidomain model and lab measurements to locate an ischemic region in the heart. Historically, this has proven to be a difficult task when using a general geometry, so our approach is to assume a priori that we can approximate the ischemic region as a ball. The approximation has been viewed from both a theoretical stand as well as more practically with numerical simulations. First, the theoretical continuity properties of the system with the simplified geometry were explored, followed by several numerical simulations to illuminate the practical behavior with this geometry. We did find a theoretical stability, as well as promising numerical results. From a small compact domain of the heart, we have proved a continuous inverse. In addition, we found a necessary demand for uniqueness of the inverse solution throughout the entire heart – which then also guarantee continuity. Numerically, we were able to retrieve the ischemic region without noise as well as with a proper amount of noise on our synthetic forward data. These findings are interesting to pursuit further. Since we worked on synthetic data in this thesis, it will be of great importance to further work with true patient data to see how well we can approximate the ischemic region in a real case. Also, the key point of this thesis was to gain more stability. In theory we found this to be stable, but we do not know how stable it is when it comes to numerical simulations. It might therefore be interesting to try to determine how sensitive the numerics can be to noise