Modelling Cellular Response to Ionizing Radiation: Mechanistic, Semi-Mechanistic, and Phenomenological Approaches - A Historical Perspective.

Radiation research is a multidisciplinary field, and among its many branches, mathematical and computational modelers have played a significant role in advancing boundaries of knowledge. A fundamental contribution is modelling cellular response to ionizing radiation as that is the key to not only understanding how radiation can kill cancer cells, but also cause cancer and other health issues. The invention of microdosimetry in the 1950s by Harold Rossi paved the way for brilliant scientists to study the mechanism of radiation at cellular and sub-cellular scales. This paper reviews some snippets of ingenious mathematical and computational models published in microdosimetry symposium proceedings and publications of the radiation research community. Among these are simulations of radiation tracks at atomic and molecular levels using Monte Carlo methods, models of cell survival, quantification of the amount of energy required to create a single strand break, and models of DNA-damage-repair. These models can broadly be categorized into mechanistic, semi-mechanistic, and phenomenological approaches, and this review seeks to provide historical context of their development. We salute pioneers of the field and great teachers who supported and educated the younger members of the community and showed them how to build upon their work.

Modelling DNA damage-repair and beyond.

The paper presents a review of mechanistic modelling studies of DNA damage and DNA repair, and consequences to follow in mammalian cell nucleus. We hypothesize DNA deletions are consequences of repair of double strand breaks leading to the modifications of genome that play crucial role in long term development of genetic inheritance and diseases. The aim of the paper is to review formation mechanisms underlying naturally occurring DNA deletions in the human genome and their potential relevance for bridging the gap between induced DNA double strand breaks and deletions in damaged human genome from endogenous and exogenous events. The model of the cell nucleus presented enables simulation of DNA damage at molecular level identifying the spectrum of damage induced in all chromosomal territories and loops. Our mechanistic modelling of DNA repair for double stand breaks (DSB), single strand breaks (SSB) and base damage (BD), shows the complexity of DNA damage is responsible for the longer repair times and the reason for the biphasic feature of mammalian cells repair curves. In the absence of experimentally determined data, the mechanistic model of repair predicts the in vivo rate constants for the proteins involved in the repair of DSB, SSB, and of BD.

Feasibility of collagen matrix tiles with cesium-131 brachytherapy for use in the treatment of head and neck cancer.

BACKGROUND: Locoregional failure is a unique and challenging problem in head and neck cancer with controversy surrounding the use of re-irradiation in the treatment. We aimed to evaluate the dosimetry and technical parameters in utilizing a collagen matrix with embedded Cesium-131 (Cs-131) radioactive isotope seeds as it relates to dose distribution and dose to carotid artery. METHODS AND MATERIALS: Cadaveric feasibility study randomizing Cs-131 strands alone or Cs-131 with collagen matrix to be placed into neck dissection defects. For the dose computation, physicists employed the TG-43 dosimetry calculation algorithm with a point source assumption to compute the dose. Carotid arteries were contoured in MIM-Symphony software and the carotid artery maximum and mean doses were calculated in accordance with TG-43 specifications. Ease of use of collagen matrix tiles on a 7-point Likert scale and mean radiation dose to the carotid artery. RESULTS: Ease of use score was higher in collagen matrix compared to stranded seeds with a mean score of 6.3 +/- 1.2 compared to 4.5 +/- 0.87. Time of implantation was statistically significantly, p = 0.031, lower in the collagen matrix group (M = 5.17 min, SD = 4.62) compared to stranded seeds (M = 15.83 min, SD = 3.24). Mean radiation dose to the carotid artery was 62.8 Gy +/- 9.46 in the collagen matrix group compared to 108.2 Gy +/- 55.6 in the traditional Cs-131 seeds group. CONCLUSIONS: We present a feasibility and concept cadaveric study using a collagen matrix with Cesium-131 demonstrating preliminary evidence to support its ease of use, decreased time to implantation, and decreased dose delivered to the carotid artery.

Mitigating disruptions, and scalability of radiation oncology physics work during the COVID-19 pandemic.

PURPOSE: The COVID-19 pandemic has led to disorder in work and livelihood of a majority of the modern world. In this work, we review its major impacts on procedures and workflow of clinical physics tasks, and suggest alternate pathways to avoid major disruption or discontinuity of physics tasks in the context of small, medium, and large radiation oncology clinics. We also evaluate scalability of medical physics under the stress of "social distancing". METHODS: Three models of facilities characterized by the number of clinical physicists, daily patient throughput, and equipment were identified for this purpose. For identical objectives of continuity of clinical operations, with constraints such as social distancing and unavailability of staff due to system strain, however with the possibility of remote operations, the performance of these models was investigated. General clinical tasks requiring on-site personnel presence or otherwise were evaluated to determine the scalability of the three models at this point in the course of disease spread within their surroundings. RESULTS: The clinical physics tasks within three models could be divided into two categories. The former, which requires individual presence, include safety-sensitive radiation delivery, high dose per fraction treatments, brachytherapy procedures, fulfilling state and nuclear regulatory commission's requirements, etc. The latter, which can be handled through remote means, include dose planning, physics plan review and supervision of quality assurance, general troubleshooting, etc. CONCLUSION: At the current level of disease in the United States, all three models have sustained major system stress in continuing reduced operation. However, the small clinic model may not perform if either the current level of infections is maintained for long or staff becomes unavailable due to health issues. With abundance, and diversity of innovative resources, medium and large clinic models can sustain further for physics-related radiotherapy services.

Calculation of the initial DNA damage induced by alpha particles in comparison with protons and electrons using Geant4-DNA.

Purpose: Interaction of ionizing radiations with cells leads to single- and double-strand breaks (SSBs and DSBs) as well as base lesions of DNA. Employing the Geant4-DNA toolkit, we simulated the transportation of primary alphas and secondary particles in liquid water to study the damage in the form of SSBs and DSBs.Materials and Methods: Simulations were performed in a spherical water medium, where we used a B-DNA model and classified the DNA damage and its complexity. We assumed that in a certain vicinity of the DNA volume, energy depositions of more than 17.5 eV or hydroxyl radicals with a chemical-reaction probability of 0.13 would lead to strand breaks.Results: The results of 2 to 20 MeV alpha particles showed that more than 65% of the energy-deposition cases within the DNA volume would result in a form of break. The frequency pattern of higher-complexity damage types appeared to peak at higher deposited energies. Conclusion: We observed a reasonable agreement in terms of trend and value between our DSB yield results and experimental data. The yield results, as function of LET, suggested independence from particle type and converge to some extent at large LET. This manifests the dominant contribution of secondary electrons.

MODELLING DSB REPAIR KINETICS FOR DNA DAMAGE INDUCED BY PROTON AND CARBON IONS.

Proton and carbon therapy are the main choices of particle therapy for cancer treatment. Particle dose distribution is superior to conventional photon therapy dose distribution due to Bragg peak. However, the basic biology of cellular damage and cell death is not well understood. The aim of this work is to present a mechanistic model of double strand break (DSB) repair that predicts the repair kinetics of damage induced by particles employed in cancer therapy. Monte Carlo Track Damage Simulation (MCDS) was employed to model DNA damage. The frequency of DSB and SSB was computed for proton and carbon ions. DSBs were subjected to repair model to calculate the repair kinetics. Two distinct DSB repair models dependent on the cell cycle were proposed. The DSB repair model contains non-homologous end joining (NHEJ), homologous recombination (HR) and back up non-homologous end joining (B-NHEJ) repair processes. The DSB complexity results in the switch in the repair pathway from NHEJ to a slower process that starts with DSB end resection. DSB end resection in early S and G1 phases of the cell cycle enhances the B-NHEJ repair pathway, while in late S and G2 phases of the cell cycle promotes HR repair pathway. The repair model was transformed to a set of nonlinear differential equations. The model calculates the overall repair kinetics and protein temporal repair activity at the site of damage. The damage and repair model provides a detailed mechanistic understanding of all processes that are involved in the damage induction and repair. The number of DSB and their complexity increase as the particle energy decreases due to the proximity of particle interactions in water. The repair kinetics show a biphasic behaviour that is due to the NHEJ fast repair of simple type DSB and HR slow repair of complex type DSB.

A simulation approach for determining the spectrum of DNA damage induced by protons.

To study the molecular damage induced in the form of single-strand and double-strand breaks by ionizing radiation at the DNA level, the Geant4-DNA Monte Carlo simulation code for complete transportation of primary protons and other secondary particles in liquid water has been employed in this work. To this aim, a B-DNA model and a thorough classification of the complexity of the DNA damage were used. Strand breaks were assumed to have primarily originated by direct physical interactions via energy depositions, assuming a threshold energy of 17.5 eV, or indirect chemical reactions of hydroxyl radicals, assuming a probability of 0.13. The simulation results on the complexity and frequency of various damages are computed for proton energies of 0.5-20 MeV. The yield results for a cell (Gy cell)-1 are presented, assuming 22 chromosomes per cell and a mean number of 245 Mbp per chromosome. The results show that for proton energies below 2 MeV, more than 50% of the energy depositions within the DNA volume resulted in strand breaks. For double-strand breaks (DSBs), there is considerable sensitivity of DSB frequency to the proton energy. A comparison of DSB frequencies predicted by different simulations and experiments is presented as a function of proton linear energy transfer (LET). We show that our yield results (Gy Gbp)-1 are generally comparable with various experimental data and there seems to be a better agreement between our results and a number of experimental studies when compared to other simulations.

Proton therapy dosimetry using the scintillation of the silica fibers.

We investigate the feasibility of proton therapy dose measurement by using scintillation of a bare silica glass fiber. The emission spectra of the optical fiber at various depths in tissue-mimicking phantoms, irradiated with proton beams of energies 100-225 MeV show two distinct peaks at 460 and 650 nm whose nature is connected with the silica point defects. Our experimental results and Monte Carlo simulation showed that the Cerenkov radiation cannot be responsible for such a phenomenon. We showed that the intensity of the peak at 650 nm correlates with the proton dose with a minimal effect of ionization quenching, while the intensity peak at 460 nm under-reports the radiation dose.

The visible signal responsible for proton therapy dosimetry using bare optical fibers is not Cerenkov radiation.

PURPOSE: Proton beam dosimetry using bare plastic optical fibers has emerged as a simple approach to proton beam dosimetry. The source of the signal in this method has been attributed to Cerenkov radiation. The aim of this work was a phenomenological study of the nature of the visible light responsible for the signal in bare fiber optic dosimetry of proton therapy beams. METHODS: Plastic fiber optic probes embedded in solid water phantoms were irradiated with proton beams of energies 100, 180, and 225 MeV produced by a proton therapy cyclotron. Luminescence spectroscopy was performed by a CCD-coupled spectrometer. The spectra were acquired at various depths in phantom to measure the percentage depth dose (PDD) for each beam energy. For comparison, the PDD curves were acquired using a standard multilayer ion chamber device. In order to further analyze the contribution of the Cerenkov radiation in the spectra, Monte Carlo simulation was performed using fluka Monte Carlo code to stochastically simulate radiation transport, ionizing radiation dose deposition, and optical emission of Cerenkov radiation. RESULTS: The measured depth doses using the bare fiber are in agreement with measurements performed by the multilayer ion chamber device, indicating the feasibility of using bare fiber probes for proton beam dosimetry. The spectroscopic study of proton-irradiated fibers showed a continuous spectrum with a shape different from that of Cerenkov radiation. The Monte Carlo simulations confirmed that the amount of the generated Cerenkov light does not follow the radiation absorbed dose in a medium. CONCLUSIONS: The source of the optical signal responsible for the proton dose measurement using bare optical fibers is not Cerenkov radiation. It is fluorescence of the plastic material of the fiber.

Monte Carlo simulations of ³He ion physical characteristics in a water phantom and evaluation of radiobiological effectiveness.

PURPOSE: (3)He ions may hold great potential for clinical therapy because of both their physical and biological properties. In this study, the authors investigated the physical properties, i.e., the depth-dose curves from primary and secondary particles, and the energy distributions of helium ((3)He) ions. A relative biological effectiveness (RBE) model was applied to assess the biological effectiveness on survival of multiple cell lines. METHODS: In light of the lack of experimental measurements and cross sections, the authors used Monte Carlo methods to study the energy deposition of (3)He ions. The transport of (3)He ions in water was simulated by using three Monte Carlo codes-FLUKA, GEANT4, and MCNPX-for incident beams with Gaussian energy distributions with average energies of 527 and 699 MeV and a full width at half maximum of 3.3 MeV in both cases. The RBE of each was evaluated by using the repair-misrepair-fixation model. In all of the simulations with each of the three Monte Carlo codes, the same geometry and primary beam parameters were used. RESULTS: Energy deposition as a function of depth and energy spectra with high resolution was calculated on the central axis of the beam. Secondary proton dose from the primary (3)He beams was predicted quite differently by the three Monte Carlo systems. The predictions differed by as much as a factor of 2. Microdosimetric parameters such as dose mean lineal energy (y(D)), frequency mean lineal energy (y(F)), and frequency mean specific energy (z(F)) were used to characterize the radiation beam quality at four depths of the Bragg curve. Calculated RBE values were close to 1 at the entrance, reached on average 1.8 and 1.6 for prostate and head and neck cancer cell lines at the Bragg peak for both energies, but showed some variations between the different Monte Carlo codes. CONCLUSIONS: Although the Monte Carlo codes provided different results in energy deposition and especially in secondary particle production (most of the differences between the three codes were observed close to the Bragg peak, where the energy spectrum broadens), the results in terms of RBE were generally similar.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.

PURPOSE: The motivation of this study was to find and eliminate the cause of errors in dose-averaged linear energy transfer (LET) calculations from therapeutic protons in small targets, such as biological cell layers, calculated using the geant 4 Monte Carlo code. Furthermore, the purpose was also to provide a recommendation to select an appropriate LET quantity from geant 4 simulations to correlate with biological effectiveness of therapeutic protons. METHODS: The authors developed a particle tracking step based strategy to calculate the average LET quantities (track-averaged LET, LETt and dose-averaged LET, LETd) using geant 4 for different tracking step size limits. A step size limit refers to the maximally allowable tracking step length. The authors investigated how the tracking step size limit influenced the calculated LETt and LETd of protons with six different step limits ranging from 1 to 500 µm in a water phantom irradiated by a 79.7-MeV clinical proton beam. In addition, the authors analyzed the detailed stochastic energy deposition information including fluence spectra and dose spectra of the energy-deposition-per-step of protons. As a reference, the authors also calculated the averaged LET and analyzed the LET spectra combining the Monte Carlo method and the deterministic method. Relative biological effectiveness (RBE) calculations were performed to illustrate the impact of different LET calculation methods on the RBE-weighted dose. RESULTS: Simulation results showed that the step limit effect was small for LETt but significant for LETd. This resulted from differences in the energy-deposition-per-step between the fluence spectra and dose spectra at different depths in the phantom. Using the Monte Carlo particle tracking method in geant 4 can result in incorrect LETd calculation results in the dose plateau region for small step limits. The erroneous LETd results can be attributed to the algorithm to determine fluctuations in energy deposition along the tracking step in geant 4. The incorrect LETd values lead to substantial differences in the calculated RBE. CONCLUSIONS: When the geant 4 particle tracking method is used to calculate the average LET values within targets with a small step limit, such as smaller than 500 µm, the authors recommend the use of LETt in the dose plateau region and LETd around the Bragg peak. For a large step limit, i.e., 500 µm, LETd is recommended along the whole Bragg curve. The transition point depends on beam parameters and can be found by determining the location where the gradient of the ratio of LETd and LETt becomes positive.

Spatial mapping of the biologic effectiveness of scanned particle beams: towards biologically optimized particle therapy.

The physical properties of particles used in radiation therapy, such as protons, have been well characterized, and their dose distributions are superior to photon-based treatments. However, proton therapy may also have inherent biologic advantages that have not been capitalized on. Unlike photon beams, the linear energy transfer (LET) and hence biologic effectiveness of particle beams varies along the beam path. Selective placement of areas of high effectiveness could enhance tumor cell kill and simultaneously spare normal tissues. However, previous methods for mapping spatial variations in biologic effectiveness are time-consuming and often yield inconsistent results with large uncertainties. Thus the data needed to accurately model relative biological effectiveness to guide novel treatment planning approaches are limited. We used Monte Carlo modeling and high-content automated clonogenic survival assays to spatially map the biologic effectiveness of scanned proton beams with high accuracy and throughput while minimizing biological uncertainties. We found that the relationship between cell kill, dose, and LET, is complex and non-unique. Measured biologic effects were substantially greater than in most previous reports, and non-linear surviving fraction response was observed even for the highest LET values. Extension of this approach could generate data needed to optimize proton therapy plans incorporating variable RBE.

DSB repair model for mammalian cells in early S and G1 phases of the cell cycle: application to damage induced by ionizing radiation of different quality.

The purpose of this work is to test the hypothesis that kinetics of double strand breaks (DSB) repair is governed by complexity of DSB. To test the hypothesis we used our recent published mechanistic mathematical model of DSB repair for DSB induced by selected protons, deuterons, and helium ions of different energies representing radiations of different qualities. In light of recent advances in experimental and computational techniques, the most appropriate method to study cellular responses in radiation therapy, and exposures to low doses of ionizing radiations is using mechanistic approaches. To this end, we proposed a 'bottom-up' approach to study cellular response that starts with the DNA damage. Monte Carlo track structure method was employed to simulate initial damage induced in the genomic DNA by direct and indirect effects. Among the different types of DNA damage, DSB are known to be induced in simple and complex forms. The DSB repair model in G1 and early S phases of the cell cycle was employed to calculate the repair kinetics. The model considers the repair of simple and complex DSB, and the DSB produced in the heterochromatin. The inverse sampling method was used to calculate the repair kinetics for each individual DSB. The overall repair kinetics for 500 DSB induced by single tracks of the radiation under test were compared with experimental results. The results show that the model is capable of predicting the repair kinetics for the DSB induced by radiations of different qualities within an accepted range of uncertainty.

Radiation induced base excision repair (BER): a mechanistic mathematical approach.

This paper presents a mechanistic model of base excision repair (BER) pathway for the repair of single-stand breaks (SSBs) and oxidized base lesions produced by ionizing radiation (IR). The model is based on law of mass action kinetics to translate the biochemical processes involved, step-by-step, in the BER pathway to translate into mathematical equations. The BER is divided into two subpathways, short-patch repair (SPR) and long-patch repair (LPR). SPR involves in replacement of single nucleotide via Pol ß and ligation of the ends via XRCC1 and Ligase III, while LPR involves in replacement of multiple nucleotides via PCNA, Pol δ/ɛ and FEN 1, and ligation via Ligase I. A hallmark of IR is the production of closely spaced lesions within a turn of DNA helix (named complex lesions), which have been attributed to a slower repair process. The model presented considers fast and slow component of BER kinetics by assigning SPR for simple lesions and LPR for complex lesions. In the absence of in vivo reaction rate constants for the BER proteins, we have deduced a set of rate constants based on different published experimental measurements including accumulation kinetics obtained from UVA irradiation, overall SSB repair kinetic experiments, and overall BER kinetics from live-cell imaging experiments. The model was further used to calculate the repair kinetics of complex base lesions via the LPR subpathway and compared to foci kinetic experiments for cells irradiated with γ rays, Si, and Fe ions. The model calculation show good agreement with experimental measurements for both overall repair and repair of complex lesions. Furthermore, using the model we explored different mechanisms responsible for inhibition of repair when higher LET and HZE particles are used and concluded that increasing the damage complexity can inhibit initiation of LPR after the AP site removal step in BER.

Ionizing radiation and genetic risks. XVII. Formation mechanisms underlying naturally occurring DNA deletions in the human genome and their potential relevance for bridging the gap between induced DNA double-strand breaks and deletions in irradiated germ cells.

While much is known about radiation-induced DNA double-strand breaks (DSBs) and their repair, the question of how deletions of different sizes arise as a result of the processing of DSBs by the cell's repair systems has not been fully answered. In order to bridge this gap between DSBs and deletions, we critically reviewed published data on mechanisms pertaining to: (a) repair of DNA DSBs (from basic studies in this area); (b) formation of naturally occurring structural variation (SV) - especially of deletions - in the human genome (from genomic studies) and (c) radiation-induced mutations and structural chromosomal aberrations in mammalian somatic cells (from radiation mutagenesis and radiation cytogenetic studies). The specific aim was to assess the relative importance of the postulated mechanisms in generating deletions in the human genome and examine whether empirical data on radiation-induced deletions in mouse germ cells are consistent with predictions of these mechanisms. The mechanisms include (a) NHEJ, a DSB repair process that does not require any homology and which functions in all stages of the cell cycle (and is of particular relevance in G0/G1); (b) MMEJ, also a DSB repair process but which requires microhomology and which presumably functions in all cell cycle stages; (c) NAHR, a recombination-based DSB repair mechanism which operates in prophase I of meiosis in germ cells; (d) MMBIR, a microhomology-mediated, replication-based mechanism which operates in the S phase of the cell cycle, and (e) strand slippage during replication (involved in the origin of small insertions and deletions (INDELs). Our analysis permits the inference that, between them, these five mechanisms can explain nearly all naturally occurring deletions of different sizes identified in the human genome, NAHR and MMBIR being potentially more versatile in this regard. With respect to radiation-induced deletions, the basic studies suggest that those arising as a result of the operation of NHEJ/MMEJ processes, as currently formulated, are expected to be relatively small. However, data on induced mutations in mouse spermatogonial stem cells (irradiation in G0/G1 phase of the cell cycle and DSB repair presumed to be via NHEJ predominantly) show that most are associated with deletions of different sizes, some in the megabase range. There is thus a 'discrepancy' between what the basic studies suggest and the empirical observations in mutagenesis studies. This discrepancy, however, is only an apparent but not a real one. It can be resolved by considering the issue of deletions in the broader context of and in conjunction with the organization of chromatin in chromosomes and nuclear architecture, the conceptual framework for which already exists in studies carried out during the past fifteen years or so. In this paper, we specifically hypothesize that repair of DSBs induced in chromatin loops may offer a basis to explain the induction of deletions of different sizes and suggest an approach to test the hypothesis. We emphasize that the bridging of the gap between induced DSB and resulting deletions of different sizes is critical for current efforts in computational modeling of genetic risks.

Biochemical DSB-repair model for mammalian cells in G1 and early S phases of the cell cycle.

The paper presents a model of double strand breaks (DSB) repair in G1 and early S phases of the cell cycle. The model is based on a plethora of published information on biochemical modification of DSB induced by ionizing radiation. So far, three main DSB repair pathways have been identified, including nonhomologous end-joining (NHEJ), homologous recombination (HR), and microhomology-mediated end-joining (MMEJ). During G1 and early S phases of the cell cycle, NHEJ and MMEJ repair pathways are activated dependent on the type of double strand breaks. Simple DSB are a substrate for NHEJ, while complex DSB and DSB in heterochromatin require further end processing. Repair of all DSB start with NHEJ presynaptic processes, and depending on the type of DSB pursue simple ligation, further end processing prior to ligation, or resection. Using law of mass action the model is translated into a mathematical formalism. The solution of the formalism provides the step by step and overall repair kinetics. The overall repair kinetics are compared with the published experimental measurements. Our calculations are in agreement with the experimental results and show that the complex types of DSBs are repaired with slow repair kinetics. The G1 and early S phase model could be employed to predict the kinetics of DSB repair for damage induced by high LET radiation.

The non-homologous end-joining (NHEJ) mathematical model for the repair of double-strand breaks: II. Application to damage induced by ultrasoft X rays and low-energy electrons.

We investigated the kinetics of simple and complex types of double-strand breaks (DSB) using our newly proposed mechanistic mathematical model for NHEJ DSB repair. For this purpose the simulated initial spectrum of DNA DSB, induced in an atomistic canonical model of B-DNA by low-energy single electron tracks, 100 eV to 4.55 keV, and the electrons generated by ultrasoft X rays (CK, AlK and TiK), were subjected to NHEJ repair processes. The activity elapsed time of sequentially independent steps of repair performed by proteins involved in NHEJ repair process were calculated for separate DSB. The repair kinetics of DSBs were computed and compared with published data on repair kinetics obtained by pulsed-field gel electrophoresis method. The comparison shows good agreement for V79-4 cells irradiated with ultrasoft X rays. The average times for the repair of simple and complex DSB confirm that double-strand break complexity is a potential explanation for the slow component of DSB repair observed in V79-4 cells irradiated by ultrasoft X rays.