具有荧光的时间分辨漫射光学层析成像的直接Robin边值抛物系统

IF 0.8 4区数学

数学研究 Pub Date : 2019-02-01 DOI:10.4208/jms.v52n3.19.07

Zakaria Belhachmi sci

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引用次数: 2

摘要

我们考虑一个具有测量数据的抛物型偏微分方程系统，它是一个具有荧光项和Robin边界条件的时间分辨漫射光学层析成像问题。我们将重点放在直接问题上，其中感兴趣的量是扩散方程中的光子密度，这是解决荧光标记物扩散、吸收和浓度的可识别性和重建反问题的重要一步。本文用有限元方法研究了变分形式下的问题及其离散化，并给出了一些数值模拟结果作为验证，并用层析成像的真实数据进行了模拟。AMS学科分类:65N21、65J22、78A46

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The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence

We consider a system of parabolic PDEs with measure data modelling a problem of the time resolved diffuse optical tomography with a fluorescence term and Robin boundary conditions. We focus on the direct problem where the quantity of interest is the density of photons in the diffusion equations and which constitutes a major step to solve the inverse problem of identifiability and reconstruction of diffusion, absorption and concentration of the fluorescent markers. We study the problem under a variational form and its discretization with finite element method and we give some numerical simulation results for verification purpose as well as simulations with real data from a tomograph. AMS subject classifications: 65N21, 65J22, 78A46

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来源期刊

数学研究 MATHEMATICS-

自引率

0.00%

发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.