TY - EJOU
AU - Li, Qingqing
AU - Duan, Zhiwen
AU - Yang, Dandan
TI - Cherenkov Radiation: A Stochastic Differential Model Driven by Brownian Motions
T2 - Computer Modeling in Engineering \& Sciences
PY - 2023
VL - 135
IS - 1
SN - 1526-1506
AB - 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.
KW - Cherenkov radiation; stochastic partial differential equations; numerical approximation and analysis; GEANT4 Monte Carlo simulation;

**AMS Subject Classifications 2020:** 94A08; 35Q68; 35Q92; 35R60
DO - 10.32604/cmes.2022.019249