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

我们研究光在层状组织中的传播，以应用于反射光学层析成像和光谱学。光在组织中的传播受辐射传输方程的支配。该积分-偏微分方程计及非均匀材料的吸收和散射。层状介质是重要的组织模型，因为它们考虑了浅表上皮组织(大多数癌前病变形成的地方)和深层间质组织的不同光学性质。这项研究的一个关键点在于理解诊断信息是如何包含在多次散射光的测量中的。特别是，我们将研究三个一般性问题：(I)部分偏振光在组织中的正问题，(Ii)反射光学层析成像的逆问题，以及(Iii)反射光学光谱的参数识别和估计。这三个问题涉及在数值分析和科学计算、渐近分析和反问题方面的广泛的数学研究。整个研究项目的一个关键主题是从反射率测量中固有的非常有限的数据中提取最具诊断性的信息。通过这项应用数学研究，我们希望开发出用于癌症早期检测和诊断的工程设备中的新方法。我们使用解析和计算方法研究光在层状组织中的传播。我们将我们的结果应用于反射光学层析成像和光谱学中的生物医学光学成像问题。分层组织模型对于理解光线与位于厚基质上的薄上皮(大多数癌前病变形成的地方)的相互作用是必要的。这项研究的首要目标是开发更复杂的理论来预测和解释诊断数据。特别是，我们正在努力开发检测和诊断上皮组织中早期癌症的方法。开发直接转化为实验室的理论的关键是开发方法，从反射率测量中固有的有限数据中提取最多的信息。通过这样做，我们希望开发出癌症的早期检测和诊断方法。

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.