报告题目：Mathematical Study on Fluorescence Diffuse Optical Tomography—Recovering the Distribution of Fluorophores Using an Approximate Substitute

主 讲 人：孙春龙

单 位：南京航空航天大学

时 间：8月16日15:00

腾 讯 ID：815 574 002

摘 要：

In this talk the time-domain fluorescence diffuse optical tomography (FDOT) is theoretically and numerically investigated based on analytical expressions for a three-space dimensional diffusion equation model (DE model). Physically the radiative transfer equation model (RTE model) is a better model to describe the physical process behind the measurement of the FDOT. We carefully analyzed the derivation of the DE model from RTE model to consider about the modelling error. Here there are two diffusion equations coupled in one of its source term. Each of them describes the emission of angularly averaged excited photon density (i.e. excited light) and that of emitted photon density (i.e. emitted light). Usually for the excited light the distribution of fluorophores in biological tissue is ignored and have the so-called linearized DE model. The emission light is analytically calculated by solving an initial boundary value problem for coupled diffusion equations in the half space. Based on the analytic expression of the solution to this initial boundary value problem, we establish an error estimate for linearizing the DE model. Our FDOT is to recover the distribution of fluorophores in biological tissue based on the linearized DE model by using the time-resolved measurement data on the boundary surface. We theoretically analyzed the identifiability of this inverse absorption problem. Further, aiming a fast and robust algorithm for our FDOT inverse problem, we identify the location of a fluorescence target by assuming that it has a regular shape such as sphere and cuboid. We call this identification the FDOT using approximate substitute. We proposed and verified our inversion strategy which is a combination of theoretical arguments and numerical arguments for an inversion, which enables to obtain a stable inversion and accelerate the speed of convergence. Its effectivity and performance were tested numerically using simulated data and experimental data obtained from ex vivo beef phantoms. (Joint work with Prof. Jijun Liu, Prof. Gen Nakamura, Prof. Goro Nishimura and Prof. Manabu Machida).

简 介：

孙春龙，南京航空航天大学讲师。2020年6月和8月分别获得北海道大学和东南大学博士学位，2021年入职南京航空航天大学。主要研究方向为数学物理反问题的理论分析和数值计算方法，已在Inverse Probl.，Sci. China. Math.，J. Opt. Soc. Am. A等期刊发表学术论文10余篇，主持江苏省自然科学青年基金1项。