## Research Papers in Physics and Astronomy

#### Title

Simulation of a Microdosimetry Problem: Behavior of a Pseudorandom Series at a Low Probability

#### Date of this Version

August 1997

#### Abstract

The carcinogenic effects for low dose irradiations are not very well known. Estimations usually are made based on the effects observed at high doses that are then extrapolated to low doses. To estimate low dose effects, the ICRP (International Commission on Radiological Protection) uses a linear extrapolation matched with a dose-rate reduction factor equal to two. This proportionality of the effect and dose, even for the lowest doses and dose-rates, leads to two assumptions which must be questioned :

1. the efficiency of DNA repair in cells does not vary with the dose and the dose-rate,

2. when one single particle crosses one single cell, a carcinogenic transformation may occur.

Low doses are frequently generated by fast electrons at low fluence.

We must consider the irradiated medium as an assembly of targets and the cross section as a representation of the probable interaction between the incident particle and the target. Biologically, cells contain internal structures which are the sensitive elements. Physically, a hit is interpreted as a registered event caused by a particle passing through the sensitive site.

The Poisson law describes the statistic behavior of this event:

P(x) = (e^{–m}/x!) m^{x} (1)

where P(x) is the realization probability of the event x and m represents the average hits per target (ratio of the number of hits per number of targets). For example, consider that a flux of exactly 10^{6} particles/cm^{2} reaches a cell population whose sensitive elements have a geometric cross section of 100 μm^{2}. The average number of particles per cell will be one, but according to the Poisson statistics, about 37% of the cells will survive (0 hits), about 37% of the cells will be hit only once and 26% will be hit twice or more. This problem can be extended to the response of many radiation detectors—one-hit or multi-hits detectors.

## Comments

Published in

Microdosimetry: An Interdisciplinary Approach, edited by Dudley T. Goodhead, Peter O’Neill, and Hans G. Menzel. Cambridge: The Royal Society of Chemistry, 1997. Pages 282–285. Copyright © 1997 The Royal Society of Chemistry. Used by permission.