Dose distribution to a random walker moving in a two-dimensional surface around a radioactive source.

Background: Modeling of dose distribution of randomly moving population around a radioactive source is a complex problem.

Objective: The objective is to develop a model and solution techniques to estimate radiation absorbed dose to the population randomly moving around a radioactive source.

Methods: The problem is formulated using a second-order partial differential equation; different moments of the dose distribution function are defined related to physically realizable quantities, and solutions are obtained using standard moments methods. Alternatively, numerical simulations are performed to estimate the radiation doses using Monte Carlo approach for individual positions and random motions of the people around the source.

Results: A good agreement is found between average doses obtained from moments method and numerical simulations. A typical application of this model to different exposure conditions shows that the average dose is highly dependent on the population density. The study results show that average dose decreases with increase in the population density and movement area of random walker.

Significance: This mathematical model can be used as a rapid assessment tool by the emergency planners in resource optimization by providing quick estimates of likely exposures for triage and emergency response.