This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
The investigator and his collaborators study a new non-invasive method for imaging the electrical conductivity of the inside of the body. Inner knowledge of the conductivity has found applications in various fields ranging from Medicine, Geophysics, Environmental Sciences, to Nondestructive Testing and Mine Detection, to mention only some. The model is based on the Maxwell system and combines methods from Electrical Impedance Tomography and Current Density Imaging. The novelty lies in the augmentation of the Maxwell model with the knowledge of the magnitude of the current density field generated while maintaining a voltage at the boundary. The latter data is currently obtained by using Magnetic Resonance measurements of the magnetic field. Mathematically, the problem is to study minimal surfaces in a singular Riemannian space with a metric determined by the magnitude of the current density field. Alternatively, the problem can be reduced to a Non-smooth Optimization problem. Taking advantage of the tools from the areas of Inverse Problems, Partial Differential Equations, Riemannian Geometry, Geometric Measure Theory and Non-smooth Optimization the investigator and his collaborators aim to change the existing and accepted theories and provide mathematical support and methods to image inner conductivity accurately and with high resolution.
This investigation belongs to the current government research priority on Information Technology. The results of this study are to produce new methodologies for non-invasive imaging of the interior of conductive bodies, such as the human body. The benefits to society are important since one componenent of the results of this study concerns the affordability of the new methods applied to Medical Imaging. More precisely, the new technology is to complement the classical Magnetic Resonance Imaging scan, method which is fairly expensive at the moment. This investigation integrates research and education in two ways. On the one hand, an integrate part is the training and mentoring of graduate and undergraduate students, including from the under-represented categories of students. On the other hand, the investigator is concurrently designing a special topics course, whose scope is based on this study.
