Analytical and Computational Approaches for Quantitative Tomography of Tissue

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This project will develop new non-invasive quantitative tomographic methods by imaging the electrical properties of biological matter, based on coupled physics inverse problems. The research holds promise to enable new technologies for decoding data used in current medical diagnostic practices and biomedical research by providing the theoretical basis for new imaging methods of higher accuracy and resolution than existing ones. The quantitative distribution of electrical conductivity and permittivity is known to distinguish a benign tumor from a malignant one, it can apply to monitor the pulmonary function of the lung, the thoracic blood volume, hyperthermia, the gastrointestinal function in newborns in intensive care, etc. This project will advance the understanding of information content in the data and produce quantitative images of biological tissues with anisotropic structures while using an optimal number of measurements. Another facet of this project is the development of robust methods which produce quantitative images of biological structure corresponding to frequencies where contrast is optimal. As a consequence, it will provide new tools in biological research by enabling imaging of biological processes at a smaller scale. During the course of the project, graduate students will be trained in an interdisciplinary area of research. The project's findings will be integrated in a student seminar and a special topics course for Mathematics, Physics, and Engineering students at the University of Central Florida.The project integrates novel advances in the mathematical analysis of nonlinear inverse problems with engineering advances in sensor design and data acquisition and aims to shift the paradigm in some of the current engineering practices. The analytical component of the project lies at the intersection of nonlinear Inverse Problems, Geometry, Optimization, and Geometric Measure theory. The principal investigator (PI) plans to improve the current knowledge of the anisotropic least gradient problems arising in physical models which are close to the actual engineering practices. In particular, the PI seeks to determine the anisotropic structure of biological tissue in reconstruction of two-tensors by employing minimal interior data. Another facet of this project seeks to produce quantitative images of the complex biological structure at radio frequencies by coupling the nonlinear inverse problem techniques for Maxwell electromagnetics with the quantum model of resonance of the magnetic spin. The project also aims to determine the electric conductivity distribution in materials with infinite limiting contrast on graphs or neural networks. Based on the analytical findings, the reconstruction methods will be translated in algorithms and tested on simulated data.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.