Abstract
This paper outlines a phenomenological approach towards cell survival curve at low dose using tools of extensive Statistical Mechanics and nonextensive Statistical Mechanics. An Ising chain model is developed for the cell survival curve and the canonical ensemble formalism based on Boltzmann Gibbs statistic and Tsallis statistic is presented. The resulting cell survival curve shows excellent agreement with the experimental data and the physical parameters from our Tsallis model (N’, q) can be shown to provide clear classification between healthy and cancerous cells. In this paper, we also provides possible biophysical interpretation to the (N’, q) parameters where N’ is representative of the amount of repairable DNA content in the nucleus and q represents the degree of correlation in DNA damage. Overall, this is the first time a Statistical Mechanics approach is used in Radiobiology, and could present a new perspective.
Highlights
The modelling of the cell survival has always attracted attention as it is widely used in radiotherapy and fractionation schemes [1,2]
There are various variants of the target theory such as Single Hit Multi-Target (SHMT), Multi-Hit Single Target (MHST) etc but they fail to agree with the experiment data at large dose
This paper is motivated by the work of Sotolongo-Grau [6]. They make use of Tsallis entropy to deduce a phenomenological cell survival curve which gives a better fit to experimental data compared to Linear Quadratic (LQ) model
Summary
The modelling of the cell survival has always attracted attention as it is widely used in radiotherapy and fractionation schemes [1,2]. It is a graph of the proportion of cell survival against the dose of the radiation. Despite the wide use of the LQ model in radiotherapy and fractionation, it still does not fully agrees with the experimental data in the large dose regime [2]. The cell survival curve will be deduced from a statistical mechanics point of view using the Boltzmann’s canonical ensemble formalism.
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