2011 **Abstract:** ᮀ A stochastic model based on the Markov Chain Monte Carlo process is used to describe responses to ionizing radiation in a group of cells. The results show that where multiple relationships linearly depending on the dose are introduced, the overall reaction shows a threshold, and, generally, a non-linear response. Such phenomena have been observed and reported in a number of papers. The present model permits the inclusion of adaptive responses and bystander effects that can lead to hormetic effects. In additi…

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“…The shape of all of the curves is virtually identical, differing only by a multiplication factor. These curves are, however, quite different from the ones obtained by Fornalski et al 17 who used Monte Carlo simulations of the cancer cells’ growth. As mentioned earlier, these curves can be perfectly described by the Gompertz curve; Figure 6 shows the fit of the Gompertz curve N cancer ( t ) = 8.27844·exp[−6.51319·exp(−0.010028· t )] to the calculated points for the exemplary case of k = 4 from Figure 5.…”

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“…The shape of all of the curves is virtually identical, differing only by a multiplication factor. These curves are, however, quite different from the ones obtained by Fornalski et al 17 who used Monte Carlo simulations of the cancer cells’ growth. As mentioned earlier, these curves can be perfectly described by the Gompertz curve; Figure 6 shows the fit of the Gompertz curve N cancer ( t ) = 8.27844·exp[−6.51319·exp(−0.010028· t )] to the calculated points for the exemplary case of k = 4 from Figure 5.…”

“…Obviously, it is the product of the thickness of the target (in cm) and the numerical density of the interacting objects, (eg, number of cells per cm 3 ). The concept of P hit in Equation (1) was originally used by us in the Monte Carlo chain cellular model, 17 but the validity of this formula has not been verified. Now, such a validation is presented in Appendix B.…”

“…Cell killing effects can explain the high-dose saturation; there will be fewer “initiating cells” in the high-dose region. This explanation has been qualitatively confirmed by Monte-Carlo simulations ( Fornalski et al . 2011 ); their analysis also shows sigmoidal behavior as the most likely one when a number of linear phenomena are imposed on each other.…”

“…Nevertheless, the comparative analysis of the VC generated data with prior studies (discussed above), support the use of the VC simulator as a useful tool in the field of radiobiology, with particular interest in the context of radiotherapy. Several other mathematical models have been proposed to quantify the impact of low absorbed doses on the dose-response curves for ionizing radiation (Brenner et al 2001;Fornalski et al 2011;Leonard 2008;Little et al 2005;Nikjoo and Khvostumov 2003).…”