Computation of the probability density function of radioactivity in the human body and the effective dose by using stochastic processes based on lumped hydrological method

This article aims to compute the probability density function of radioactivity in the human body and the effective dose based on lumped hydrological method. We treat the fluctuations of radioactivity in the human body as the stochastic process. There are three types equivalent formalisms regarding the stochastic processes, that is, Langevin equations, stochastic differential equations (SDEs), and Fokker-Planck equations. We adopt the Langevin equation as the starting point for discussion. We can get the Langevin equation of radioactivity in the human body by adding the random fluctuation term to the continuity equation of radioactivity in the human body. Deforming the Langevin equation to the equivalent Fokker-Planck equation, we compute the probability density function of radioactivity in the human body. We attempt to formulate the stochastic process of the effective dose. Although we cannot put the mathematical footing, we propose the likely stochastic process to consider the convergence in the average. (author)