Generalized stochastic microdosimetric model: The main formulation

Particle Beam Radiobiology Status and Challenges: A PTCOG Radiobiology Subcommittee Report

Particle therapy (PT) represents a significant advancement in cancer treatment, precisely targeting tumor cells while sparing surrounding healthy tissues thanks to the unique depth-dose profiles of the charged particles. Furthermore, their linear energy transfer and relative biological effectiveness enhance their capability to treat radioresistant tumors, including hypoxic ones. Over the years, extensive research has paved the way for PT's clinical application, and current efforts aim to refine its efficacy and precision, minimizing the toxicities. In this regard, radiobiology research is evolving toward integrating biotechnology to advance drug discovery and radiation therapy optimization. This shift from basic radiobiology to understanding the molecular mechanisms of PT aims to expand the therapeutic window through innovative dose delivery regimens and combined therapy approaches. This review, written by over 30 contributors from various countries, provides a comprehensive look at key research areas and new developments in PT radiobiology, emphasizing the innovations and techniques transforming the field, ranging from the radiobiology of new irradiation modalities to multimodal radiation therapy and modeling efforts. We highlight both advancements and knowledge gaps, with the aim of improving the understanding and application of PT in oncology.

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

Objective.In this paper, we present MONAS (MicrOdosimetry-based modelliNg for relative biological effectiveness (RBE) ASsessment) toolkit. MONAS is a TOPAS Monte Carlo extension, that combines simulations of microdosimetric distributions with radiobiological microdosimetry-based models for predicting cell survival curves and dose-dependent RBE.Approach.MONAS expands TOPAS microdosimetric extension, by including novel specific energy scorers to calculate the single- and multi-event specific energy microdosimetric distributions at different micrometer scales. These spectra are used as physical input to three different formulations of themicrodosimetric kinetic model, and to thegeneralized stochastic microdosimetric model(GSM2), to predict dose-dependent cell survival fraction and RBE. MONAS predictions are then validated against experimental microdosimetric spectra andin vitrosurvival fraction data. To show the MONAS features, we present two different applications of the code: (i) the depth-RBE curve calculation from a passively scattered proton SOBP and monoenergetic12C-ion beam by using experimentally validated spectra as physical input, and (ii) the calculation of the 3D RBE distribution on a real head and neck patient geometry treated with protons.Main results.MONAS can estimate dose-dependent RBE and cell survival curves from experimentally validated microdosimetric spectra with four clinically relevant radiobiological models. From the radiobiological characterization of a proton SOBP and12C fields, we observe the well-known trend of increasing RBE values at the distal edge of the radiation field. The 3D RBE map calculated confirmed the trend observed in the analysis of the SOBP, with the highest RBE values found in the distal edge of the target.Significance.MONAS extension offers a comprehensive microdosimetry-based framework for assessing the biological effects of particle radiation in both research and clinical environments, pushing closer the experimental physics-based description to the biological damage assessment, contributing to bridging the gap between a microdosimetric description of the radiation field and its application in proton therapy treatment with variable RBE.

Cell Survival Computation via the Generalized Stochastic Microdosimetric Model (GSM2); Part II: Numerical Results

In the present paper we numerically investigate, using Monte Carlo simulation, the theoretical results predicted by the Generalized Stochastic Microdosimetric Model (GSM2), as shown in the published companion paper. Taking advantage of the particle irradiation data ensemble (PIDE) dataset, we calculated GSM2 biological parameters of human salivary gland (HSG) and V79 cell lines. Further, exploiting the TOPAS-microdosimetric extension, we simulated the microdosimetric spectra of different radiation fields of therapeutic interest generated by four different ions (protons, helium-4, carbon-12 and oxygen-16) each at three different residual ranges. We investigated the properties of the initial damage distributions as well as the cell survival curve predicted by GSM2, focusing especially on the non-Poissonian effects naturally included in the model. GSM2 successfully computed cell survival curves, accurately describing experimental behavior even under challenging LET and dose conditions.

A spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation condition

In the present work, we develop a general spatial stochastic model to describe the formation and repair of radiation-induced DNA damage. The model is described mathematically as a measure-valued particle-based stochastic system and extends in several directions the model developed in Cordoni et al. (Phys Rev E 103:012412, 2021; Int J Radiat Biol 1-16, 2022a; Radiat Res 197:218-232, 2022b). In this new spatial formulation, radiation-induced DNA damage in the cell nucleus can undergo different pathways to either repair or lead to cell inactivation. The main novelty of the work is to rigorously define a spatial model that considers the pairwise interaction of lesions and continuous protracted irradiation. The former is relevant from a biological point of view as clustered lesions are less likely to be repaired, leading to cell inactivation. The latter instead describes the effects of a continuous radiation field on biological tissue. We prove the existence and uniqueness of a solution to the above stochastic systems, characterizing its probabilistic properties. We further couple the model describing the biological system to a set of reaction-diffusion equations with random discontinuity that model the chemical environment. At last, we study the large system limit of the process. The developed model can be applied to different contexts, with radiotherapy and space radioprotection being the most relevant. Further, the biochemical system derived can play a crucial role in understanding an extremely promising novel radiotherapy treatment modality, named in the community FLASH radiotherapy, whose mechanism is today largely unknown.

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

In this paper, we study the system size expansion of a stochastic model for radiation-induced DNA damage kinetics and repair. In particular, we characterize both the macroscopic deterministic limit and the fluctuation around it. We further show that such fluctuations are Gaussian-distributed. In deriving such results, we provide further insights into the relationship between stochastic and deterministic mathematical models for radiation-induced DNA damage repair. Specifically, we demonstrate how the governing deterministic equations commonly employed in the field arise naturally within the stochastic framework as a macroscopic limit. Additionally, by examining the fluctuations around this macroscopic limit, we uncover deviations from a Poissonian behavior driven by interactions and clustering among DNA damages. Although such behaviors have been empirically observed, our derived results represent the first rigorous derivation that incorporates these deviations from a Poissonian distribution within a mathematical model, eliminating the need for specific ad hoc corrections.

The complexity of DNA damage by radiation follows a Gamma distribution: insights from the Microdosimetric Gamma Model

Introduction

DNA damage is the main predictor of response to radiation therapy for cancer. Its Q8 quantification and characterization are paramount for treatment optimization, particularly in advanced modalities such as proton and alpha-targeted therapy.

Methods

We present a novel approach called the Microdosimetric Gamma Model (MGM) to address this important issue. The MGM uses the theory of microdosimetry, specifically the mean energy imparted to small sites, as a predictor of DNA damage properties. MGM provides the number of DNA damage sites and their complexity, which were determined using Monte Carlo simulations with the TOPAS-nBio toolkit for monoenergetic protons and alpha particles. Complexity was used together with a illustrative and simplistic repair model to depict the differences between high and low LET radiations.

Results

DNA damage complexity distributions were were found to follow a Gamma distribution for all monoenergetic particles studied. The MGM functions allowed to predict number of DNA damage sites and their complexity for particles not simulated with microdosimetric measurements (yF) in the range of those studied.

Discussion

Compared to current methods, MGM allows for the characterization of DNA damage induced by beams composed of multi-energy components distributed over any time configuration and spatial distribution. The output can be plugged into ad hoc repair models that can predict cell killing, protein recruitment at repair sites, chromosome aberrations, and other biological effects, as opposed to current models solely focusing on cell survival. These features are particularly important in targeted alpha-therapy, for which biological effects remain largely uncertain. The MGM provides a flexible framework to study the energy, time, and spatial aspects of ionizing radiation and offers an excellent tool for studying and optimizing the biological effects of these radiotherapy modalities.

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

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 GSM², in its original full form, the Dirac GSM² the Poisson GSM² and the Repair-Misrepair Model (RMR). While GSM² and the RMR models are known in literature, the Dirac and the Poisson GSM²  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 GSM², the Poisson GSM² and the RMR can be obtained from the GSM² 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.

Modelling the HPRT-gene mutation induction of particle beams: systematic in vitro data collection, analysis and microdosimetric kinetic model implementation

Objective. Since the early years, particle therapy treatments have been associated with concerns for late toxicities, especially secondary cancer risk (SCR). Nowadays, this concern is related to patients for whom long-term survival is expected (e.g. breast cancer, lymphoma, paediatrics). In the aim to contribute to this research, we present a dedicated statistical and modelling analysis aiming at improving our understanding of the RBE for mutation induction ( RBE M ˜ ) for different particle species. Approach. We built a new database based on a systematic collection of RBE data for mutation assays of the gene encoding for the purine salvage enzyme hypoxanthine-guanine phosphoribosyltransferase from literature (105 entries, distributed among 3 cell lines and 16 particle species). The data were employed to perform statistical and modelling analysis. For the latter, we adapted the microdosimetric kinetic model (MKM) to describe the mutagenesis in analogy to lethal lesion induction. Main results. Correlation analysis between RBE for survival (RBES) and RBE M ˜ reveals significant correlation between these two quantities (ρ = 0.86, p < 0.05). The correlation gets stronger when looking at subsets of data based on cell line and particle species. We also show that the MKM can be successfully employed to describe RBE M ˜ , obtaining comparably good agreement with the experimental data. Remarkably, to improve the agreement with experimental data the MKM requires, consistently in all the analysed cases, a reduced domain size for the description of mutation induction compared to that adopted for survival. Significance. We were able to show that RBES and RBE M ˜ are strongly related quantities. We also showed for the first time that the MKM could be successfully applied to the description of mutation induction, representing an endpoint different from the more traditional cell killing. In analogy to the RBES, RBE M ˜ can be implemented into treatment planning system evaluations.

An exploratory study of machine learning techniques applied to therapeutic energies particle tracking in microdosimetry using the novel hybrid detector for microdosimetry (HDM)

In this work we present an advanced random forest-based machine learning (ML) model, trained and tested on Geant4 simulations. The developed ML model is designed to improve the performance of the hybrid detector for microdosimetry (HDM), a novel hybrid detector recently introduced to augment the microdosimetric information with the track length of particles traversing the microdosimeter. The present work leads to the following improvements of HDM: (i) the detection efficiency is increased up to 100%, filling not detected particles due to scattering within the tracker or non-active regions, (ii) the track reconstruction algorithm precision. Thanks to the ML models, we were able to reconstruct the microdosimetric spectra of both protons and carbon ions at therapeutic energies, predicting the real track length for every particle detected by the microdosimeter. The ML model results have been extensively studied, focusing on non-accurate predictions of the real track lengths. Such analysis has been used to identify HDM limitations and to understand possible future improvements of both the detector and the ML models.

Cell Survival Computation via the Generalized Stochastic Microdosimetric Model (GSM2); Part I: The Theoretical Framework

The current article presents the first application of the Generalized Stochastic Microdosimetric Model (GSM2) for computing explicitly a cell survival curve. GSM2 is a general probabilistic model that predicts the kinetic evolution of DNA damages taking full advantage of a microdosimetric description of a radiation energy deposition. We show that, despite the high generality and flexibility of GSM2, an explicit form for the survival fraction curve predicted by the GSM2 is achievable. We illustrate how several correction terms typically added a posteriori in existing radiobiological models to improve the prediction accuracy, are naturally included into GSM2. Among the most relevant features of the survival curve derived from GSM2 and presented in this article, is the linear-quadratic behavior at low doses and a purely linear trend for high doses. The study also identifies and discusses the connections between GSM2 and existing cell survival models, such as the Microdosimetric Kinetic Model (MKM) and the Multi-hit model. Several approximations to predict cell survival in different irradiation regimes are also introduced to include intercellular non-Poissonian behaviors.