open access

https://doi.org/10.14943/doctoral.k14153

https://hdl.handle.net/2115/78942

蛍光拡散トモグラフィの数理的研究 : 直方体近似を用いた蛍光体分布同定

英語

2020-06-30

Hokkaido University

xvii, 94p.

In this thesis 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. Since the distance between the source and detectors are short, the initial boundary value problem for the DE can be considered in the half space. 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. 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 cuboidal shape neglecting its precise shape. 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.

2020-06-30

甲第14153号

博士(理学)

(主査) 教授 久保 英夫, 教授 栄 伸一郎, 助教 西村 吾朗（電子科学研究所）

理学院（数学専攻）

博士論文

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