Direct and inverse problems for reflectance optical tomography and spectroscopy in layered tissues

University Of California - Merced, Merced CA

Investigators

Abstract

We study light propagation in layered tissues for applications in reflectance optical tomography and spectroscopy. Light propagation in tissues is governed by the radiative transport equation. This integral-partial differential equation takes into account absorption and scattering by inhomogeneities. Layered media are important tissue models because they take into account the different optical properties of superficial epithelial tissues (where most precancers form) and those of deep stromal tissues. A key point throughout this research lies in understanding how diagnostic information is contained in measurements of multiply scattered light. In particular, we will study three general problems: (i) Direct problems of partially polarized light in tissues, (ii) Inverse problems for reflectance optical tomography, and (iii) Parameter identification and estimation for reflectance optical spectroscopy. These three problems involve a broad variety of mathematics research in numerical analysis and scientific computing, asymptotic analysis, and inverse problems. A key theme throughout this research project is extracting the most diagnostic information from very limited data inherent in reflectance measurements. Through this applied mathematics research, we hope to develop novel methods that find use in engineering devices used for the early detection and diagnosis of cancer. We study light propagation in layered tissues using analytical and computational methods. We apply our results to biomedical optical imaging problems in reflectance optical tomography and spectroscopy. Layered tissue models are necessary to understand the interaction of light with a thin epithelium (where most precancers form) situated on top of a thick stroma. The overarching goal of this research is to develop more sophisticated theories to predict and interpret diagnostic data. In particular, we are working to develop methods for detecting and diagnosing early stages of cancer in epithelial tissues. The key to developing theory that translates directly to the laboratory is developing methods that extract the most information out of the inherently limited data in reflectance measurements. By doing so, we hope to develop methods for the early detection and diagnosis of cancer.