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

摘要：DMS-0504858，A Kim，加州大学梅赛德斯分校题目：用于生理监测和组织成像的光在组织中传播的数学研究我们研究生物医学应用中的光在组织中的传播。特别是，我们研究了三个问题：i)生理监测的逆问题，ii)荧光成像，以及iii)组织中的正向和反向障碍散射。对于生理监测问题，人们试图检测组织结构和成分的变化，特别是在大多数癌前病变形成的器官的浅组织层。对于荧光成像问题，寻找肿瘤的荧光分子被引入到深层组织中，并由激光激发。通过检测发射的荧光光，人们希望确定载体以及荧光效率和寿命。对于直接障碍散射问题，人们寻找由于光源而被组织内的障碍(例如肿瘤)散射的光。对于反障碍物问题，人们试图从散射光测量中确定障碍物的区分特征(例如，支撑度、强度等)。在所有这些问题中，关键的挑战是理解复杂的光与组织之间的相互作用，因为组织对光的散射很强。这项拟议的研究旨在开发更准确的理论来预测和解释诊断数据。特别是，这项研究始于光在组织中传播的辐射传输理论。辐射输运方程边值问题的计算方法将被用来解决本文提出的正问题和反问题。我们特别注意计算这三个问题的定量分辨率估计。生物学和医学中的许多重大进展与生物医学成像系统的技术进步直接相关。特别是，基于激光的成像系统为安全、便携和经济的组织功能和健康监测和成像提供了巨大的潜力。本研究项目涉及基于激光的生物组织成像的理论和计算研究。特别是，我们寻求直接影响生理监测、荧光成像以及正向和反向障碍散射应用的数学结果。激光与生物组织的相互作用很难建模，因为组织对光的散射非常强烈。因此，本研究项目的首要目标是更好地了解光在组织中的多次散射。

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.