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

Journal of Exposure Science & Environmental Epidemiology volume 32, pages 188–194 (2022)Cite this article

Abstract

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.

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Fig. 1: Schematic representation of the random walk motion.
Fig. 2: Analytical solution for dose distribution function.
Fig. 3: Average absorbed dose (Sv) to a random walker as a function of exposure time, population density, and outer radius of the circle (bounded area).
Fig. 4: Comparison of average dose from moments method and random walk simulations.
Fig. 5: Temporal evolution of average dose and its standard deviation.

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Author information

Authors and Affiliations

  1. Health Physics Division, Bhabha Atomic Research Centre, Mumbai, India

    Praveen Kumar, S. Anand, Kapil Deo Singh & M. S. Kulkarni

  2. Homi Bhabha National Institute, Mumbai, India

    S. Anand & M. S. Kulkarni

  3. Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai, India

    Y. S. Mayya

Authors
  1. Praveen Kumar
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  2. S. Anand
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  3. Kapil Deo Singh
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  4. M. S. Kulkarni
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  5. Y. S. Mayya
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Corresponding author

Correspondence to S. Anand.

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Kumar, P., Anand, S., Singh, K.D. et al. Dose distribution to a random walker moving in a two-dimensional surface around a radioactive source. J Expo Sci Environ Epidemiol 32, 188–194 (2022). https://doi.org/10.1038/s41370-021-00367-9

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  • DOI: https://doi.org/10.1038/s41370-021-00367-9

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