Electrical Impedance Tomography (EIT) is a medical imaging technique employing voltage applied to different points on the body to reconstruct an image of what’s inside.

Figure 4: Left: Schematic of an electrode array applied to the thorax. On the right a current-voltage pattern superimposed on a CT scan. The input data B consists of the current going through the positive electrode on the top left, its position and the position of the negative electrode on the right (the current through it is the same by Kirchoff’s law). The scattering data S is the voltage on the boundary – here represented by the ends of the purple lines. In order to obtain a current-to-voltage map this measurement has to be repeated for all pairs of electrodes. Source: wikipedia/Electric Impedance Tomography

From a mathematical standpoint, EIT is related to the solution of a D-bar problem. From a medical standpoint, EIT has the potential to provide valuable, rapid medical imaging for the diagnosis of conditions such as aneurysms and pulmonary embolisms, but its uses are currently limited due to the low resolution of the images on offer.

I am now managing a project to improve the quality of EIT images through techniques in mathematical physics and mathematical computing.

This poster by IMB postdoctoral fellow Nikola Stoilov provides more information on the project.

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