Stochastic modelling for biodosimetry: Predicting the chromosomal response to radiation at different time points after exposure*
1 Mark Kac Complex Systems Research Center and Marian
Smoluchowski Institute of Physics, Jagiellonian University in Kraków, Poland
2 GSI Helmholtzzentrum für Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany
Received: 6 January 2014
Received in final form: 15 April 2014
Published online: 29 July 2014
Cytogenetic data accumulated from the experiments with peripheral blood lymphocytes exposed to densely ionizing radiation clearly demonstrate that for particles with linear energy transfer (LET) >100 keV/μm the derived relative biological effectiveness (RBE) will strongly depend on the time point chosen for the analysis. A reasonable prediction of radiation-induced chromosome damage and its distribution among cells can be achieved by exploiting Monte Carlo methodology along with the information about the radius of the penetrating ion-track and the LET of the ion beam. In order to examine the relationship between the track structure and the distribution of aberrations induced in human lymphocytes and to clarify the correlation between delays in the cell cycle progression and the aberration burden visible at the first post-irradiation mitosis, we have analyzed chromosome aberrations in lymphocytes exposed to Fe-ions with LET values of 335 keV/μm and formulated a Monte Carlo model which reflects time-delay in mitosis of aberrant cells. Within the model the frequency distributions of aberrations among cells follow the pattern of local energy distribution and are well approximated by a time-dependent compound Poisson statistics. The cell-division cycle of undamaged and aberrant cells and chromosome aberrations are modelled as a renewal process represented by a random sum of (independent and identically distributed) random elements SN = ∑Ni=0 Xi. Here N stands for the number of particle traversals of cell nucleus, each leading to a statistically independent formation of Xi aberrations. The parameter N is itself a random variable and reflects the cell cycle delay of heavily damaged cells. The probability distribution of SN follows a general law for which the moment generating function satisfies the relation ΦSN = ΦN(ΦXi). Formulation of the Monte Carlo model which allows to predict expected fluxes of aberrant and non-aberrant cells has been based on several input information: (i) experimentally measured mitotic index in the population of irradiated cells; (ii) scored fraction of cells in first cell cycle; (iii) estimated average number of particle traversals per cell nucleus. By reconstructing the local dose distribution in the biological target, the relevant amount of lesions induced by ions is estimated from the biological effect induced by photons at the same dose level. Moreover, the total amount of aberrations induced within the entire population has been determined. For each subgroup of intact (non-hit) and aberrant cells the cell-division cycle has been analyzed reproducing correctly an expected correlation between mitotic delay and the number of aberrations carried by a cell. This observation is of particular importance for the proper estimation of the biological efficiency of ions and for the estimation of health risks associated with radiation exposure.
© The Author(s) 2014. This article is published with open access at Springerlink.com
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.