Mathematical investigation of light propagation in tissues for physiological monitoring and tissue imaging

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Abstract: DMS-0504858, A Kim, University of California - MercedTitle: Mathematical investigation of light propagation in tissues for physiological monitoring and tissue imaging We study light propagation in tissues for biomedical applications. In particular, we study three problems: i) inverse problems for physiological monitoring, ii) fluorescence imaging, and iii) direct and inverse obstacle scattering in tissues. For the physiological monitoring problem, one seeks to detect changes in tissue structure and composition, especially in superficial tissue layers of organs where most pre-cancers form. For the fluorescence imaging problem, tumor-seeking fluorescent molecules are introduced into deep tissues and are excited by a laser. By detecting the emitted fluorescent light, one wishes to determine the support, and fluorescent efficiency and lifetime. For the direct obstacle scattering problem, one seeks the light scattered by an obstacle (e.g. a tumor) inside tissue due to a light source. For the inverse obstacle problem, one seeks to determine distinguishing characteristics (e.g. support, strength, etc) about the obstacle from scattered light measurements. The key challenge in all of these problems is to understand the complicated light-tissue interactions because tissues multiply scatter light strongly. This proposed research aims to develop more accurate theory to predict and interpret diagnostic data. In particular, this research begins with the theory of radiative transport for light propagation in tissues. Computational methods for boundary value problems of the radiative transport equation will be developed to solve the direct and inverse problems proposed here. We pay special attention to computing quantitative resolution estimates for these three problems.Many of the significant advances in biology and medicine correlate directly with technological advances in biomedical imaging systems. In particular, laser-based imaging systems offer great potential for safe, portable and economical monitoring and imaging of tissue function and health. This research project involves the theoretical and computational study of laser-based imaging of biological tissues. In particular, we seek mathematical results that impact directly applications in physiological monitoring, fluorescence imaging and direct and inverse obstacle scattering. The interaction of laser light with biological tissues is complicated to model because tissues scatter light very strongly. Hence, the overarching goal of this research project is to gain a better understanding of multiple scattering of light in tissues.