On fluorescence imaging:The diffusion equation model and recovery of the absorption coefficient of fluorophores  

作　　者：Jijun Liu Manabu Machida Gen Nakamura Goro Nishimura Chunlong Sun 

机构地区：[1]School of Mathematics,Southeast University,Nanjing 210096,China [2]Institute for Medical Photonics Research,Hamamatsu University School of Medicine,Hamamatsu 431-3192,Japan [3]Department of Mathematics,Hokkaido University,Sapporo 060-0810,Japan [4]Research Institute for Electronic Science,Hokkaido University,Sapporo 060-0810,Japan

出　　处：《Science China Mathematics》2022年第6期1179-1198,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11531005,11971104 and 11421110002);supported by Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science(JSPS)(Grant Nos.17K05572 and 17H02081);from the JSPS A3 foresight program:Modeling and Computation of Applied Inverse Problems;supported by Grant-in-Aid for Scientific Research of the JSPS(Grant Nos.19K03554 and 15H05740);supported by Grant-in-Aid for Scientific Research of the JSPS(Grant No.19K04421)。

摘　　要：To quantify fluorescence imaging of biological tissues,we need to solve an inverse problem for the coupled radiative transfer equations which describe the excitation and emission fields in biological tissues.We begin by giving a concise mathematical argument to derive coupled diffusion equations with the Robin boundary condition as an approximation of the radiative transfer system.Then by using this coupled system of equations as a model for the fluorescence imaging,we have a nonlinear inverse problem to identify the absorption coefficient in this system.The associated linearized inverse problem is to ignore the absorbing effect on the excitation field.We firstly establish the estimates of errors on the excitation field and the solution to the inverse problem,which ensures the reasonability of the model approximation quantitatively.Some numerical verification is presented to show the validity of such a linearizing process quantitatively.Then,based on the analytic expressions of excitation and emission fields,the identifiability of the absorption coefficient from the linearized inverse problem is rigorously analyzed for the absorption coefficient in the special form,revealing the physical difficulty of the3-dimensional imaging model by the back scattering diffusive system.

关 键 词：fluorescence imaging diffusion equation inverse problem LINEARIZATION error estimates IDENTIFIABILITY 

分 类 号：O175[理学—数学] O657.3[理学—基础数学]