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Cherenkov Radiation: A Stochastic Differential Model Driven by Brownian Motions

Qingqing Li1,2, Zhiwen Duan1,2,*, Dandan Yang1,2
1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China
2 Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan, 430074, China
* Corresponding Author: Zhiwen Duan. Email: duanzhw@hust.edu.cn
(This article belongs to this Special Issue: Mathematical Aspects of Computational Biology and Bioinformatics)

Computer Modeling in Engineering & Sciences https://doi.org/10.32604/cmes.2022.019249

Received 11 September 2021; Accepted 17 May 2022; Published online 28 June 2022


With the development of molecular imaging, Cherenkov optical imaging technology has been widely concerned. Most studies regard the partial boundary flux as a stochastic variable and reconstruct images based on the steadystate diffusion equation. In this paper, time-variable will be considered and the Cherenkov radiation emission process will be regarded as a stochastic process. Based on the original steady-state diffusion equation, we first propose a stochastic partial differential equation model. The numerical solution to the stochastic partial differential model is carried out by using the finite element method. When the time resolution is high enough, the numerical solution of the stochastic diffusion equation is better than the numerical solution of the steady-state diffusion equation, which may provide a new way to alleviate the problem of Cherenkov luminescent imaging quality. In addition, the process of generating Cerenkov and penetrating in vitro imaging of 18 F radionuclide in muscle tissue are also first proposed by GEANT4 Monte Carlo method. The result of the GEANT4 simulation is compared with the numerical solution of the corresponding stochastic partial differential equations, which shows that the stochastic partial differential equation can simulate the corresponding process.


Cherenkov radiation; stochastic partial differential equations; numerical approximation and analysis; GEANT4 Monte Carlo simulation;
AMS Subject Classifications 2020: 94A08; 35Q68; 35Q92; 35R60
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