Multiple levels of stochasticity accounted for in different radiation biophysical models: from physics to biology

Abstract

Purpose: in the present paper we investigate how some stochastic effects are included in a class of radiobiological models with particular emphasis on how such randomnesses reflect into the predicted cell survival curve.Materials and Methods: we consider four different models, namely the Generalized Stochastic Microdosimetric Model GSM 2 , in its original full form, the Dirac GSM 2 , the Poisson GSM 2 and the Repair-Misrepair Model (RMR). While GSM 2 and the RMR models are known in literature, the Dirac and the Poisson GSM 2 have been newly introduced in this work. We further numerically investigate via Monte Carlo simulation of four different particle beams, how the proposed stochastic approximations reflect into the predicted survival curves. To achieve these results, we consider different ion species at energies of interest for therapeutic applications, also including a mixed field scenario.Results: we show how the Dirac GSM 2 , the Poisson GSM 2 and the RMR can be obtained from the GSM 2 under suitable approximations on the stochasticity considered. We analytically derive the cell survival curve predicted by the four models, characterizing rigorously the high and low dose limits. We further study how the theoretical findings emerge also using Monte Carlo numerical simulations.Conclusions: we show how different models include different levels of stochasticity in the description of cellular response to radiation. This translates into different cell survival predictions depending on the radiation quality.

Integrating microdosimetric in vitro RBE models for particle therapy into TOPAS MC using the MicrOdosimetry-based modeliNg for RBE ASsessment (MONAS) tool

“…Recently, starting from the building assumptions of the MKM, a novel microdosimetry-based radiobiological model, GSM 2 , was presented, (Cordoni et al 2021(Cordoni et al , 2022a(Cordoni et al , 2022b. GSM 2 aims at providing a fully probabilistic model that takes into account the effects of stochasticity in different aspects of radiation-induced damage, e.g.…”

“…Recently, the generalized stochastic microdosimetric model (GSM 2 ) has been developed, (Cordoni et al 2021), which is a theoretically grounded mechanistic radiobiological model able to include several spatiotemporal stochastic effects inherent to the formation and repair of radiation-induced DNA damage, (Cordoni et al 2022a, 2022b, Missiaggia et al 2023b. GSM 2 is a fully probabilistic model that overcomes one of the main assumptions shared by most existing radiobiological models including the MKM, that is the fact that the distribution of the number of damages induced by radiation on DNA is Poissonian.…”

On the Emergence of the Deviation from a Poisson Law in Stochastic Mathematical Models for Radiation-Induced DNA Damage: A System Size Expansion

“…Therefore, we have shown that the macroscopic limit of GSM 2 MME coincides with the main deterministic governing equation of the MKM (4). Explicit solutions to system (11) can be derived with the further property that they are globally stable and converging to a stationary solution [19]. Consider first:…”

“…Recently, a series of papers addressed these issues, and the Generalized Stochastic Microdosimetric Model (GSM ) [ 10 , 18 , 19 , 20 , 21 ] has been introduced. GSM is a probabilistic model able to describe the time evolution of the DNA damage in a cell nucleus based on a differential equation governing the time evolution of the probability distribution of the number of DNA damages.…”

An artificial intelligence-based model for cell killing prediction: development, validation and explainability analysis of the ANAKIN model

“…reference radiation isoeffect RBE allows quantifying how much more lethal certain radiation is compared to the reference radiation, usually x-rays, and is used in Treatment Planning Systems (TPS) to calculate the biological dose, namely the physical dose multiplied by the RBE. For this reason, over the last decades a plethora of mathematical mechanistic models, (Kellerer and Rossi 1974, 1978, Tobias 1980, 1985, Hawkins 1994, Kase et al 2006, Elsässer et al 2010, Vassiliev 2012, Friedrich et al 2013a, 2013b, Manganaro et al 2017, Vassiliev et al 2017, Inaniwa and Kanematsu 2018, Bellinzona et al 2021, McMahon and Prise 2021, Cordoni et al 2022a, as well as data-driven phenomenological models, (Wilkens and Oelfke 2004, Tilly et al 2005, Carabe et al 2012, Chen and Ahmad 2012, McNamara et al 2015, Mairani et al 2017 have been developed to estimate RBE based on biological as well as physical quantities. At the base of most models is the linear-quadratic (LQ) behavior of the cell survival logarithm with respect to the imparted dose:…”