Thongchai A M Masilela

Yolanda Prezado
email: yolanda.prezado@curie.fr

Monte Carlo study of the free radical yields in minibeam radiation therapy

Keywords:

 He ions (HeMBRT), and 12 C ions (CMBRT). Primary yields at the end of the chemical stage were calculated in spheres of 20 𝜇m diameter, located in the peaks and valleys at various depths up to the Bragg peak. The chemical stage was limited to 1 ns to approximate biological scavenging, and the yield of ⋅ OH, H 2 O 2 , and e - aq was recorded. Results: Beyond 10 mm, there were no substantial differences in the primary yields between peaks and valleys of the pMBRT and HeMBRT modalities. For xMBRT, there was a lower primary yield of the radical species ⋅ OH and e - aq at all depths in the valleys compared to the peaks, and a higher primary yield of H 2 O 2 . Compared to the peaks, the valleys of the CMBRT modality were subject to a higher ⋅ OH and e - aq yield, and lower H 2 O 2 yield. This difference between peaks and valleys became more severe in depth. Near the Bragg peak, the increase in the primary yield of the valleys over the peaks was 6% and 4% for ⋅ OH and e - aq

respectively, while there was a decrease in the yield of H 2 O 2 by 16%. Given the similar ROS primary yields in the peaks and valleys of pMBRT and HeMBRT, the level of indirect DNA damage is expected to be directly proportional to the peak to valley dose ratio (PVDR). The difference in the primary yields implicates a lower level of indirect DNA damage in the valleys compared to the peaks than what would be suggested by the PVDR for xMBRT, and a higher level for CMBRT. Conclusions:These results highlight the notion that depending on the particle chosen, one can expect different levels of ROS in the peaks and valley that goes beyond what would be expected by the macroscopic PVDR. The combination of MBRT with heavier ions is shown to be particularly interesting as the primary yield in the valleys progressively diverges from the level observed in the peaks as the LET increases. While differences in the reported ⋅ OH yields of INTRODUCTION Minibeam radiation therapy (MBRT), is a subset of spatially fractionated radiotherapy (SFRT) in which the dose is delivered in narrow beamlets of 0.3 to 1 mm, 1 leading to highly heterogeneous dose distributions characterised by areas of high dose (peaks) and areas of low dose (valleys). The degree of heterogeneity can thus be quantified by the peak-to-valley dose ratio (PVDR), which is an important dosimetric quantity. High PVDR values ensure the sparing of healthy tissue. [START_REF] Dilmanian | Response of rat intracranial 9L gliosarcoma to microbeam radiation therapy[END_REF] Significant normal tissue sparing has been observed with both photon [START_REF] Deman | Monochromatic minibeams radiotherapy: from healthy tissue-sparing effect studies toward first experimental glioma bearing rats therapy[END_REF][START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] and proton [START_REF] Prezado | Proton minibeam radiation therapy widens the therapeutic index for high-grade gliomas[END_REF] minibeams, and this type of treatment has been shown to widen the therapeutic window. [START_REF] Prezado | Proton minibeam radiation therapy widens the therapeutic index for high-grade gliomas[END_REF][START_REF] Dilmanian | Interlaced x-ray microplanar beams: a radiosurgery approach with clinical potential[END_REF] Contrary to the traditional dogmas thought to govern the efficacy of conventional radiotherapy, namely temporally fractionated treatments with a homogeneous tumor dose coverage, [START_REF] Icru | Prescribing, Recording, and Reporting Photon-Beam Intensity-Modulated Radiation Therapy (IMRT)[END_REF] MBRT may signal a departure from these notions as it has been shown that high dose, single fractions are well tolerated [START_REF] Prezado | Tolerance to dose escalation in minibeam radiation therapy applied to normal rat brain: Longterm clinical, radiological and histopathological analysis[END_REF]9 and tumor control is still maintained with heterogeneous dose distributions. [9][10][START_REF] Bertho | First evaluation of temporal and spatial fractionation in proton minibeam radiation therapy of glioma-bearing rats[END_REF] It has been hypothesized that there are distinct radiobiological mechanisms at play in both the healthy and tumoral tissue's response to SFRT, which include -but may not necessarily be limited to -radiation induced non-targeted cell signaling effects (bystander/abscopal/cohort), differential effects depending on the tumor/healthy tissue vasculature, cell migration, as well as inflammation and immunomodulatory effects. 1,[START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF][START_REF] Meyer | Spatially fractionated proton minibeams[END_REF][START_REF] Mazal | FLASH and minibeams in radiation therapy: the effect of microstructures on time and space and their potential application to protontherapy[END_REF][START_REF] Yan | Spatially fractionated radiation therapy: history, present and the future[END_REF] Bystander effects have been observed in GRID [START_REF] Asur | Spatially fractionated radiation induces cytotoxicity and changes in gene expression in bystander and radiation adjacent murine carcinoma cells[END_REF] and microbeam radiation therapy (MRT), [START_REF] Lobachevsky | Synchrotron X-ray radiation-induced bystander effect: an impact of the scattered radiation, distance from the irradiated site and p53 cell status[END_REF] with the latter also being the subject of studies in which it was hypothesised to have a preferential damage inducing effect on immature blood vessels compared to the mature vasculature of healthy tissue. [START_REF] Sabatasso | Microbeam radiation-induced tissue damage depends on the stage of vascular maturation[END_REF] A distant abscopal effect was evident in LAT-TICE therapy, 19 and cell migration from valley regions may help repair damaged tissues in the peak, thus leading to an enhanced normal tissue sparing. [START_REF] Dilmanian | Response of rat intracranial 9L gliosarcoma to microbeam radiation therapy[END_REF][START_REF] Crosbie | Tumor cell response to synchrotron microbeam radiation therapy differs markedly from cells in normal tissues[END_REF] The recruitment of immune cells to the tumor microenvironment was observed in GRID, [START_REF] Johnsrud | Evidence for early stage anti-tumor immunity elicited by spatially fractionated radiotherapy-immunotherapy combinations[END_REF] MRT, 22,[START_REF] Sprung | Genome-wide transcription responses to synchrotron microbeam radiotherapy[END_REF] and MBRT, 24 which implicates the induction of immune regulated abscopal effects, themselves triggered by immunogenic cell death. [START_REF] Griffin | History and current perspectives on the biological effects of high-dose spatial fractionation and high dose-rate approaches: GRID, Microbeam & FLASH radiotherapy[END_REF] In this study, we therefore endeavoured to investigate the relative production of reactive oxygen species (ROS) between MB peak and valley regions due to their role, amongst various biological processes, in cell signalling, [START_REF] Hancock | Role of reactive oxygen species in cell signalling pathways[END_REF][START_REF] Azzam | Oxidative metabolism modulates signal transduction and micronucleus formation in bystander cells from alpha-particle-irradiated normal human fibroblast cultures[END_REF] vascular maturation, [START_REF] Zhou | Reactive oxygen species in vascular formation and development[END_REF] and the innate and adaptive immune response, [START_REF] Yang | Reactive oxygen species in the immune system[END_REF][START_REF] Weinberg | Reactive oxygen species in the tumor microenvironment: an overview[END_REF] [START_REF] Caër | Water radiolysis: influence of oxide surfaces on H2 production under ionizing radiation[END_REF] In this work, specific focus was given to the production of the hydroxyl radical ( ⋅ OH), the aqueous electron (e - aq ), and hydrogen peroxide (H 2 O 2 ). The ⋅ OH radical is an important species as it is primarily responsible for the indirect portion of DNA damage, [START_REF] Von Sonntag | Free-radical-induced DNA damage and its repair[END_REF] which itself accounts for approximately 70% of all DNA damage induced by low LET irradiations. [START_REF] Roots | Estimation of life times and diffusion distances of radicals involved in X-ray-induced DNA strand breaks or killing of mammalian cells[END_REF] Furthermore, this free radical is the primary mediator of the oxygen enhancement effect. [START_REF] Hirayama | OH radicals from the indirect actions of X-rays induce cell lethality and mediate the majority of the oxygen enhancement effect[END_REF] The aqueous electron reacts with dissolved oxygen during the early stages of water radiolysis, and therefore contributes to its depletion. This has an impact on target oxygenation, which is one of the indicators of the expected level of radiosensitivity of a biological system. [START_REF] Boscolo | Impact of target oxygenation on the chemical track evolution of ion and electron radiation[END_REF] H 2 O 2 is primarily formed from the recombination of ⋅ OH. At low physiological levels, it can contribute to non-targeted (bystander) effects through redox-sensitive cell signalling cascades, [START_REF] Azzam | Oxidative metabolism modulates signal transduction and micronucleus formation in bystander cells from alpha-particle-irradiated normal human fibroblast cultures[END_REF][START_REF] Gough | Hydrogen peroxide: a Jekyll and Hyde signalling molecule[END_REF] while at high physiological levels it can trigger cell death. [START_REF] Gough | Hydrogen peroxide: a Jekyll and Hyde signalling molecule[END_REF] It is distinct from other short-lived ROS in that it has a longer half life and can migrate across plasma membranes thus causing distant DNA damage. [START_REF] Desouky | Targeted and non-targeted effects of ionizing radiation[END_REF] Specific to minibeams, it has been hypothesized that a homogeneous coverage of the tumor by H 2 O 2 could be achieved during beam-on time, which could then be used as a chemical surrogate for MBRT efficacy. [START_REF] Bello | Proposal of a chemical mechanism for mini-beam and micro-beam efficacy[END_REF] To date, micro-and nano-scale investigations into the production of radiolytic species in the context of SFRT has been limited. Given their importance, not only to the traditionally thought of DNA damage, but also to some of the potential mechanisms of SFRT efficacy, this study was carried out in attempt to elucidate their relative production between MBRT peak and valley regions. Monte Carlo (MC) simulations were carried out using TOPAS-nBio, [START_REF] Schuemann | TOPAS-nBio: an extension to the TOPAS simulation toolkit for cellular and sub-cellular radiobiology[END_REF] which is the radiobiological extensions of TOPAS. [START_REF] Perl | TOPAS: an innovative proton Monte Carlo platform for research and clinical applications[END_REF][START_REF] Faddegon | The TOPAS tool for particle simulation, a Monte Carlo simulation tool for physics, biology and clinical research[END_REF] The primary yields of ⋅ OH, e - aq , and H 2 O 2 , were calculated for photon, proton, [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ion, and [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ion MBs and BBs, and each radiation modality was compared. While the majority of publications detailing the advantages of MBRT have focused on photon and proton beams due to their vastly increased clinical prevalence, these heavier ions were included in this study as there has been a renewed interest in their combination with MBRT in order to take advantage of their dosimetric properties. [START_REF] Prezado | A potential renewed use of very heavy ions for therapy: neon minibeam radiation therapy[END_REF] This work was therefore carried out in order establish a baseline level of knowledge on the presence of free radicals in MBRT, thus aiding future experiments/simulation studies.

MATERIALS AND METHODS

Simulation details and associated geometries

All MC simulations were performed using TOPAS and TOPAS-nBio. A 5×5×10 cm [START_REF] Deman | Monochromatic minibeams radiotherapy: from healthy tissue-sparing effect studies toward first experimental glioma bearing rats therapy[END_REF] water tank (G4_WATER) was irradiated with beams of photons, protons, helium ions, and carbon ions, in both BB and MB configurations. Water spheres with a diameter of 20 𝜇m were placed along the peak and valley axes, at depths of 10, 30, 50, 70, and 76.5 mm (Bragg peak location). These spheres represented cellular targets, and the G-value of each chemical species resulting from water radiolysis was calculated in these targets. A schematic representation of the TOPAS/TOPAS-nBio simulation geometry is shown in Figure 1.

The distinct difference in scales involved introduced a multi-scalar element to the simulations. One of the challenges with such multi-scale simulations involves the reconciliation of the physical/biological consequences of realistic macroscopic-scale sources on microscopicscale targets with sufficient precision. One of the commonly employed approaches is to, in a first step, perform a macroscopic scale simulation to capture the radiation field, then in a second step switch to a cellscale simulation and replay this radiation field. [START_REF] Schuemann | A new standard DNA damage (SDD) data format[END_REF] There is precedent for the use of this technique in both Geant4-DNA, [START_REF] Santos | Minibeam radiation therapy: A micro-and nano-dosimetry Monte Carlo study[END_REF] as well as TOPAS-nBio. [START_REF] Ramos-Méndez | LET-Dependent intertrack yields in proton irradiation at ultra-high dose rates relevant for FLASH therapy[END_REF] The implementation of this technique can be visualized by the different panels in Figure 1, whereby panel A is representative of the full macro-scale simulation and panel B provides a more detailed view of how the physics surrounding/within the spherical targets is handled. Panel C, on the other hand, represents the fully microscopic portion of the simulations.

In the first step simulation of Panel A, condensed history (CH) physics was used -with the exact processes detailed in the relevant section below. In order to increase the statistics of particles reaching the targets and reduce the computational requirements, a physical collimator was not simulated, but rather rectangular sources of photons, 8 protons, 46,47 helium ions, [START_REF] Schneider | Monte Carlo comparison of proton and helium-ion minibeam generation techniques[END_REF] and carbon ions, [START_REF] González | Theoretical dosimetric evaluation of carbon and oxygen minibeam radiation therapy[END_REF] were generated at the surface of the water phantom.The size and energy of each source was taken from previous publications. Simulations were performed with sources in both a MB and BB configuration, in which three MB beamlets were simulated, and the BB width was equal to two times the MB centre-to-centre (c-t-c) distance plus the MB width.

The choice of physics models was changed from CH to track structure (TS) physics models within a 24 𝜇m 3 cube of water surrounding the cell, as shown in panel B. This was done in order to have a more detailed radiation field entering the cells, thereby resulting in a reduction in the eventual systematic and statistical uncertainties of our results. TOPAS facilitates this change by allowing the user to assign different physics models to different regions of the geometry.In a first step simulation,TOPAS phase space (PS) scorers were used to record the radiation field. In a second step simulation, as highlighted in panel C, the aforementioned PS scorer was then used as the particle source, and full TS physics and chemistry was enabled. Further details concerning the characteristics of the MC simulations are provided in Table 1 in accordance with the recommendation from AAPM TG-268, [START_REF] Sechopoulos | RECORDS: improved reporting of montE CarlO radiation transport studies: report of the AAPM research committee task group 268[END_REF] which attempts to standardize the reporting of MC simulations.

Physics and chemistry processes

TOPAS-nBio simulates the radiolysis of liquid water in three stages. The first of the three is called the 'physical stage' (< 10 -15 s), in which the interaction of ionizing radiation with matter is simulated through the application of specified physics processes, resulting in a collection of ionizations, and electronic and vibrational excitations. This collection of physical interactions is then used in the second stage, called the 'pre-chemical stage' (10 -15 -10 -12 s) whereby there is an initial creation of chemical species through dissociative decay, relaxation, and auto-ionisation processes, corresponding to the ionized/excited state of the water molecules. Finally, the non-homogeneous 'chemical stage' (10 -12 -10 -6 s) occurs, whereby the created species diffuse and react with one another. [START_REF] Ramos-Méndez | Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio[END_REF] The G-value describes the yield of chemical species per energy deposited, and the primary yield is representative of the G-value at the end of the non-homogeneous chemical stage. Further details concerning the physics and chemistry of the simulation are provided below.

Physics

The physics processes relevant to this work can be split into two categories, those used by the CH models and those used by the TS models. The physics modules used in the macroscopic, first step simulation were: g4h-phy_QGSP_BIC_HP, g4em-livermore, g4decay, g4ionbinarycascade, g4h-elastic_HP, and g4stopping. The hadronic physics interactions were specified by g4h-phy_QGSP_BIC_HP, which handles the inelastic interactions of protons and neutrons. Given the presence of hadron beams in this work, the BIC option was chosen due to its enhanced accuracy around the Bragg peak, [START_REF] Jarlskog | Physics settings for using the Geant4 toolkit in proton therapy[END_REF] and the HP option activates the high precision neutron model. Respectively, the remaining physics modules of the list handles electromagnetic processes down to 10 eV, decay physics, inelastic interactions for other types of ions, elastic hadronic physics, and stopping power physics. [START_REF]Geant4 physics reference manual release 11[END_REF] The microscopic TS portion of the simulations made use of g4em-dna_opt2. Although newer options exist, opt2 is still widely used as it covers the widest energy range (7.4 -1 MeV). [START_REF] Incerti | Geant4-DNA example applications for track structure simulations in liquid water: a report from the Geant4-DNA Project[END_REF] In addition to these electron interactions,TOPAS-nBio is able to simulate the interaction of photons, protons, ions from H through to O, Si, and Fe with liquid water. [START_REF] Schuemann | TOPAS-nBio: an extension to the TOPAS simulation toolkit for cellular and sub-cellular radiobiology[END_REF] It was inevitable that the radiation field saved in the PS files from the CH portion of the simulation contained certain particles which were not able to be handled by the TS part of simulation, due to greater wealth of interaction cross sections available for the CH simulations. Certain PS files contained positrons, neutrons, deuterons, tritons, as well as other elemental isotopes of He, up to and including C. Any particles not included in Table S1 of Incerti et al. [START_REF] Incerti | Geant4-DNA example applications for track structure simulations in liquid water: a report from the Geant4-DNA Project[END_REF] are not able to be handled by Geant4-DNA. Nevertheless, for the sake of completeness, no particles were removed from the PS files of the CH portion of the simulations for their use as sources in the TS portion of the simulations. In the case that an 'unrecognized' (from the point of view of the TS simulations) particle was launched from a PS source, it was simply transported by TOPAS through the volume without undergoing any interactions.

Chemistry

The chemistry processes used in this work are those from one of the default options available in TOPAS-nBio, namely TsEmDNAChemistry, which was the module of choice in recent TOPAS-nBio publications. [START_REF] Ramos-Méndez | Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio[END_REF][START_REF] Zhu | Cellular response to proton irradiation: a simulation study with TOPAS-nBio[END_REF] The full list of pre-chemical processes and chemical stage reactions activated by TsEmDNAChemistry is shown in Table 2. Henceforth, the chemical stage reactions of Table 2 are referred to by the letter R and the corresponding reaction number, that is, R6 refers to the reaction ⋅ OH + ⋅ OH → H 2 O 2 . There are two main numerical techniques for computing the diffusion and reaction of species in the chemical stage of water radiolysis, namely the step-by-step (SBS) method and the independent reaction time (IRT) approximation, which are both based on solutions to the Smoluchowski equation. TOPAS-nBio v1.0 uses the SBS method, in which the reactions are said to be totally diffusion controlled, fully detailed elsewhere. 56 In brief, the Brownian diffusion of particles is described by the solution to the Smoluchowski equation in three dimensions, as shown below. This is the probability density of the particle's TA B L E 1 Summary of the main characteristics of the MC simulations, in accordance with the recommendation of AAPM TG-268. 50

Item Description

Codes All simulations were performed using TOPAS [START_REF] Perl | TOPAS: an innovative proton Monte Carlo platform for research and clinical applications[END_REF][START_REF] Faddegon | The TOPAS tool for particle simulation, a Monte Carlo simulation tool for physics, biology and clinical research[END_REF] version 3.6.1 released on the 1st of February 2021, and TOPAS-nBio [START_REF] Schuemann | TOPAS-nBio: an extension to the TOPAS simulation toolkit for cellular and sub-cellular radiobiology[END_REF] version 1.0 released on the 19th of May 2021. Timing All computing jobs were sent to the Joliot Curie-SKL supercomputer, which uses 2 × 24-core Intel Skylake@2.7GHz (AVX512) CPUs, with 1656 computing nodes in total, and 48 cores per node. The simulation times contained here refer to the full use of all 48 cores of a node. The total time consumed for phase space simulations was as follows:

• Photons: 65 520 h (xBB) and 94 380 h (xMBRT)

• Protons: 44 h (pBB) and 177 h (pMBRT)

• 4 He: 47 h (HeBB) and 407 h (HeMBRT)

• 12 C: 120 h (CBB) and 1994 h (CMBRT)

The total time consumed for G-value simulations was as follows:

• Photons: 720 h (xBB) and 360 h (xMBRT)

• Protons: 45 h (pBB) and 44 h (pMBRT)

• 4 He: 480 h (HeBB) and 422 h (HeMBRT)

• 12 C: 430 h (CBB) and 5 016 h (CMBRT) Sources Each source was simulated as monodirectional and monoenergetic, with the exception of the photon source in which the effective energy of the SARRP (small animal radiation research platform) was used. The total number of histories were varied in order to have a satisfactory compromise between statistical uncertainty and computational expense. Cross-sections Standard Geant4 and Geant4-DNA physics cross section data files were used from the physics modules g4em-livermore, g4h-phy_QGSP_BIC_HP, g4decay, g4ion-binarycascade, g4h-elastic_HP, g4stopping, and g4em-dna_opt2.

Transport parameters

In the first step simulation, the CH approach was used with a default cut of 0.05 mm for all particles. In the second step simulation, g4em-dna_opt2 was activated which uses the TS approach, explicitly simulating all interactions down to the low energy limit of the corresponding physics model. Chemical species were transported step by step by Brownian motion, according to the Smoluchowski equation, described elsewhere. [START_REF] Kyriakou | Review of the Geant4-DNA simulation toolkit for radiobiological applications at the cellular and DNA level[END_REF]

Scored quantities

Doses were scored using the DoseToMedium discretized volume scorer. All particles crossing the surface of the 20 µm spheres were recorded using TOPAS's PhaseSpace scorer. Primary yields were calculated using the gvalue scorer. And finally, chemical reactions were counted using the ReportOriginOfMoleculesToAsciiFile string parameter.

Post-processing

Post-processing of the raw data was performed using python scripts to generate the relevant figures.

position after a time lapse of t.

p(⃗ r) = 4𝜋r 2 (4𝜋Dt) 3∕2 . exp

( - r 2 4Dt
)

After each simulation time step, the positions of all the chemical species are recorded and whenever the separation distance between two species is smaller than their reaction radius R, a reaction is assumed to TA B L E 2 Pre-chemical processes and non-homogeneous chemical stage reactions considered in TOPAS-nBio. Adapted from Tables 2 and3 in Ramos-Méndez et al. [START_REF] Ramos-Méndez | Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio[END_REF]

Pre-chemical stage processes Process Probability [%]

Ionised state Dissociative decay

H 3 O + + • OH 100 A 1 B 1 excitation Dissociative decay • OH + H • 65 Relaxation H 2 O + ΔE 3 5 B 1 A 1 excitation Auto-ionisation H 3 O + + • OH + e - aq 55
Auto-ionisation

• OH + • OH + H 2 15 Relaxation H 2 O + ΔE 3 0 Rydberg, diffuse bands Auto-ionisation H 3 O + + • OH + e - aq 50 Relaxation H 2 O + ΔE 5 0 Chemical stage reactions (1) e - aq + e - aq → H 2 + 2OH - (2) e - aq + • OH → OH - (3) e - aq + H • → H 2 + OH - (4) e - aq + H 3 O + → H • (5) e - aq + H 2 O 2 → OH -+ • OH (6) • OH + • OH → H 2 O 2 (7) • OH + H • → H 2 O ( 8 ) H • + H • → H 2 (9) H 3 O + + OH -→ H 2 O
immediately occur and both species are replaced with their products. If the separation distance between two species is greater than R, they continue diffusing in the next simulation step. The IRT approximation is a more computationally efficient method of calculating the chemical yields from water radiolysis, and has been shown to generate comparable chemical yields to the SBS method while reducing the computation time by a factor of ∼145. [START_REF] Schuemann | TOPAS-nBio: an extension to the TOPAS simulation toolkit for cellular and sub-cellular radiobiology[END_REF] However, TOPAS-nBio v1.0 is limited to the use of the SBS method up to 1 𝜇s (the end of the chemical stage). Both the SBS method and IRT approximation assume that each chemical species is a spherical volume, they diffuse independently of one another, and the medium within which they diffuse is a continuum (isotropic). 56 A more detailed simulation would have to take into account various factors linked with the complex cellular microenvironment. One of those factors is the intracellular radical scavenging which affects the evolution of the chemical stage. [START_REF] Kreipl | Time-and space-resolved Monte Carlo study of water radiolysis for photon, electron and ion irradiation[END_REF] As the inclusion of a scavenging capacity was not yet incorporated into TOPAS-nBio v1.0, the accepted approach is to limit the duration of the chemical stage. [START_REF] Kyriakou | Review of the Geant4-DNA simulation toolkit for radiobiological applications at the cellular and DNA level[END_REF] Recent publications from the TOPAS development team made use of a 1 ns cut-off, at which point the chemical stage was terminated. [START_REF] Schuemann | TOPAS-nBio: an extension to the TOPAS simulation toolkit for cellular and sub-cellular radiobiology[END_REF][START_REF] Zhu | Cellular response to proton irradiation: a simulation study with TOPAS-nBio[END_REF] This was the same approach used in this work.

TOPAS and TOPAS-nBio scorers

TOPAS is capable of recording a variety of quantities (dose, LET, fluence, chemical yield, etc.) through the use of dedicated scorers. [START_REF] Perl | TOPAS: an innovative proton Monte Carlo platform for research and clinical applications[END_REF] This section highlights the different TOPAS scorers used in this work.

PS scorer

The PS scorer accumulates the quantity of interest on the surface of some specified component. As previously mentioned, the surface assigned was that of a 20 𝜇m sphere, representative of our cellular targets, located at various depths along both the peak and valley axes of the simulation. The OnlyIncludeParticlesGoing = "In" filter was applied to only record those particles entering into the cell. As highlighted in panels A and B of Figure 1, the first step CH simulation was run, and the physics of the region immediately surrounding the PS scorer was changed to TS physics in order to record a more detailed radiation field. In the second, fully TS simulation shown in panel C of Figure 1, each cellular target was simulated independently of one another using the recorded PS as a source. The disparity in size between the microscopic targets and simulated sources meant that a large number of primaries needed to be launched in order to have sufficient statistics in the PS files and limit both the statistical and systematic uncertainty. As seen in the 'Sources' section of Table 1, the number of primaries simulated for certain beams surpasses the 10 9 primary history limit imposed per single TOPAS simulation. To overcome this limit, multiple simulations were launched in parallel, and the resulting PS files were combined to later be used as sources in the TS simulations.

G-value scorer

Scoring of the chemical yield in TOPAS-nBio was accomplished through the use of the dedicated F I G U R E 2 pMBRT and pBB primary yields in the peak (solid line) and valley (dashed line) for the species: G-value scorer gvalue, which was assigned to each spherical target, and which recorded the evolution of the yield of each species from 1 ps up to 1 ns in 100 logarithmic bins. TS simulations are computationally very expensive, and given that 'rich' PS sources were necessary to limit the amount of statistical and systematic uncertainty, multiple simulations involving the high LET particles were split and run in parallel in order to achieve a reasonable computation time. The G-value outputs of these multiple simulations were later re-combined. This parallelisation is permitted because TOPAS-nBio simulates the three stages of water radiolysis history by history, independent of subsequent histories. [START_REF] Ramos-Méndez | Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio[END_REF] The statistical uncertainties on primary yields reported in this work are representative of the standard deviation of the mean, and in the case where the simulations were first split before subsequently re-combining the G-value outputs, the statistical uncertainties were propagated through the summation in quadrature method.

Chemical reaction scorer

While TOPAS-nBio version 1.0 provides the user a way to access the yield and spatio-temporal information of the chemical species created, there is no dedicated scorer to track the frequency of specific chemical reactions in the non-homogeneous chemical stage. However, the user is able to obtain raw data detailing the species' event and track IDs, name, and track IDs of both parents by using the ReportOriginOfMoleculesToAsciiFile string parameter which outputs a .chem ASCII file.It was therefore possible, through the use of this string parameter, to create a Python script which took these .chem files as an input, and matched the reported parent track IDs of a species with the corresponding parent names, which could then be used to determine which of the nine chemical reactions listed in Table 2 occurred. This 'chemical reaction scorer' was used to create histograms detailing the relative frequency of the chemical reactions, as a way to interpret the differences/similarities in the primary yields recorded. These histograms are visualized in Figures 5 and7 for the photon and carbon ion beams respectively. One of the drawbacks of this scorer is that it does not account for the occurrence of reactions R7 and R9. This is because the product of these reactions, H 2 O, is not involved in any other chemical process and is not able to be irradiated given the nature of how water radiolysis in TOPAS-nBio is handled. One of the other limitations is that statistical uncertainty information is not provided in the .chem output files. This was overcome by using all 48 available cores of the computing node to calculate the diffusion and reaction of chemical species. This resulted in 48 .chem files, each with a certain reaction count, from which the standard deviation of the 48 reaction counts could then be calculated. These standard deviations were taken to represent the statistical uncertainty of each reaction and are depicted as the error bars in Figures 5 and7. uncertainties were maintained below 0.38%, which corresponds with the statistical uncertainty of the yield of H 2 O 2 in the MB valley at 10 mm. We observed a progressive increase in the primary yield of H 2 O 2 with depth, which corresponds with a decrease in the yields of ⋅ OH and e - aq . This is an expected trend due to the fact that the proton LET increases towards the end of its range, resulting in an increased rate of radical-radical reactions, thereby causing a decrease in radical yields and an increase in molecular products such as H 2 O 2 . [START_REF] Wasselin-Trupin | Hydrogen peroxide yields in water radiolysis by high-energy ion beams at constant LET[END_REF] Beyond the first few centimetres in the water phantom, there is no statistically significant difference between the primary yields in the BB modality compared to the MB peaks and valleys. In the MB peaks, the ⋅ OH primary yield decreased by approximately 5% between 10 and 76.5 mm, while the H 2 O 2 primary yield increased by approximately 17% over the same range. Similarly to ⋅ OH, the e - aq primary yield decreased by approximately 4% between 10 mm and the Bragg peak depth.

RESULTS

Protons

There was however, a difference in the primary yield between peak and valley regions at the entrance of the water phantom. Figure 2 depicts an increase in the H 2 O 2 primary yield of approximately 3% and a decrease in the ⋅ OH and e - aq yields of approximately 1% from the peaks to the valleys. This was attributed to the difference in the composition of the PS sources used, which arose due to the lack of lateral scattering at shallow depths, compounded by the fact that the sources were generated flush at the surface of the water phantom. The particle composition of the PS sources can be seen in Figure S7. The most striking difference observed was the percentage composition of protons in the peaks (69%) compared to the valleys (38%) at the 10 mm depth, which is due to the lack of lateral scattering. Furthermore, the minimum proton energy in the peak at this depth was 1.50 MeV, compared to the 0.12 MeV in the valleys. This difference is consistent with observations that the valleys of proton minibeam radiation therapy (pMBRT) are filled with particles of a higher LET than the peaks. [START_REF] Schneider | Improving the dose distributions in minibeam radiation therapy: helium ions vs protons[END_REF][START_REF] Lansonneur | First proton minibeam radiation therapy treatment plan evaluation[END_REF] Despite the lower proportion of protons, the higher LET in the valleys led to a greater recombination of ⋅ OH through R6 (see Figure S8 and Table S1) which explains the differences observed in the entrance regions of Figure 2.

Helium ions

Figure 3 depicts the primary yield as a function of depth for the [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ion beam. Statistical uncertainties were maintained below 0.73%, which corresponds to the statistical uncertainty of the yield of H 2 O 2 on-axis in the BB modality at the Bragg peak depth of 76.5 mm. As with the beam of protons in Figure 2, beyond the depth of 10 mm there are similar primary yields between the BB modality and the MB peaks and valleys.

Another similarity with the proton beam yields is the increasing trend in H 2 O 2 and decreasing trends in ⋅ OH and e - aq . However, given that [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ions minibeam radiation therapy (HeMBRT) has a higher ionization density (increased LET) in both peaks and valleys compared to the corresponding regions in pMBRT, [START_REF] Schneider | Improving the dose distributions in minibeam radiation therapy: helium ions vs protons[END_REF] there is a greater proportion of radical-radical reactions with [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He than there are for protons, leading to an increase in the proportion of molecular products. Correspondingly, for the BB modality, MB peak, and MB valley regions at each F I G U R E 4 xMBRT and xBB primary yields in the peak (solid line) and valley (dashed line) for the species: • OH, H 2 O 2 , and e - aq , depicted as a function of depth in the water phantom. depth,we observed a lower primary yield of ⋅ OH and e - aq , and a higher yield of H 2 O 2 compared to the beams of protons, visualized in Figure 8. In the MB peaks, Figure 3 depicts a decrease of about 13% and 9% respectively for the ⋅ OH and e - aq species, while the primary yield of H 2 O 2 increased by approximately 30% over the same range. The increase/decrease of the primary yields of each species with depth for the [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ion beams represents, on average, a factor of two augmentation over the increases/decreases observed for the primary yields for protons. There was a further parallel between the pMBRT and HeMBRT modalities, in that Figure 3 also depicts a divergence in the primary yields between the peak and valley regions at 10 mm.There was a decrease in ⋅ OH yields of approximately 1% from the peak to the valley, and a corresponding increase in H 2 O 2 yields of approximately 4%. This was due to similar differences in the composition and particle energies present in the PS sources used, as highlighted in Figure S9. The presence of higher LET particles in the MB valleys, specifically at shallow depths, led to a greater recombination of ⋅ OH to form H 2 O 2 .

Photons

The primary yield results as a function of depth for the beam of photons is depicted in Figure 4, in which significant differences between the BB modality/MB peaks and the MB valleys can be observed. The difference across all depths between the peaks and valleys appeared to be approximately constant, and an average difference of 0.93% and 2.46% was found for ⋅ OH and H 2 O 2 respectively. It should be noted that obtaining statistically relevant results in microscopic targets for a macroscopic source of photons is particularly challenging, given the low interaction probability of a beam of photons over microscopic distances. While statistical uncertainties were maintained below 0.1% at all depths, the seemingly erratic trend in depth (particularly for e - aq ) has two explanations. The first is a matter of scale. Given the change of LET in depth for the beam of protons and [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ions, the primary yield changes substantially from the entrance region to the Bragg peak. This is not the case for the beam of photons, where if the same scale was used, the primary yield would appear approximately constant (as seen in Figure 8). Compared to Figures 2 and3, the scale of the primary yields for photons is approximately a factor of 5 and 10 smaller respectively. The second explanation has to do with composition of the PS sources. As can be seen in Table 1, the number of photon primaries simulated were several orders of magnitude greater than any of the other modalities evaluated in this work, however the computing time required to calculate the G-values corresponding to the resulting PS source was not representative of this substantial gap. This is due to the PS sources at all depths being composed of approximately 99% photons and 1% secondary electrons. According to the NIST database, the mean free path for 69 keV photons (effective energy of the spectrum used in this work) is about 0.2 cm. [START_REF] Berger | NIST Standard Reference Database 8 (XGAM)[END_REF] It is therefore evident that the photons present in the PS sources, with energies of a similar magnitude, are unlikely to interact within the 20 𝜇m diameter spherical target volume. Ultimately, the statistical integrity hinges solely on the distribution of electrons within the PS source. In spite of the systematic uncertainties, it appears that there is a difference in the primary yields of the BB modality/MB peaks and the MB valleys, particular for ⋅ OH and H 2 O 2 . As can be seen in Figure S12, the valley PS sources are composed of both a higher proportion of low energy electrons compared with the peak, as well as electrons with lower maximum energies. This difference could have an impact on the pre-chemical processes and resulting chemical reactions depicted in Table 2, therefore the chemical reactions were counted according to the methodology outlined in the Materials and methods section. This resulted in the bar graphs depicted in Figure 5.

The frequencies of reactions R2, R5, and R6 were evaluated for the depths of 10, 30, 50, and 70 mm in the water phantom. The frequency of each reaction was normalized according to the total amount of chemical reactions counted for that specific location within the water phantom. Note that the normalized frequency of R5 is displayed on the second y-axis, on the right hand side of each graph. Statistical uncertainties were maintained below the maximum of 0.03%, which corresponds with the statistical uncertainty of R5 in the valley at 70 mm. Throughout this work, analysis of the frequency of chemical reactions focused on the production and consumption of ⋅ OH and H 2 O 2 due to their involvement in a limited number of reactions, thereby easing the interpretation of results. H 2 O 2 is involved in two reactions, R5 and R6, where it is consumed and produced respectively. ⋅ OH is involved in R2, R5, R6, and R7, where it is consumed in all the reactions barring R5. In all cases, the ⋅ OH recombination reaction of R6 was the most occurring reaction in both peak and valley regions regardless of depth. While Figure 4 depicts a decreased ⋅ OH primary yield and increased H 2 O 2 primary yield, the increased frequency of R5 at all depths in the valleys, shown in Figure 5, seems to indicate the contrary effect (i.e., an increase in ⋅ OH and decrease in H 2 O 2 ). However, R5 occurs much less frequently than R6, which appears to be the reaction that dictates the presence/lack of ⋅ OH and H 2 O 2 in the water phantom. All the results are summarized in Table 3, which depicts the frequencies of Figure 5 as percentages.

While, according to the statistical uncertainties, there were statistically significant differences between most peak and valley values, this was not the case for the peak and valley values of R6 at 70 mm. As previously mentioned, R5 seems to contradict the results of Figure 4 in that the values of Table 3 show a lower expected primary yield of H 2 O 2 in the valleys, while the figure depicts a higher yield. However, the proportion of R6 reactions is much greater and therefore appears to dominate the behavior of the ⋅ OH and H 2 O 2 species. The proportion of R6 in the valleys is consistent with Figure 4, in that there is a higher primary yield of H 2 O 2 in the valleys compared to the peaks. Table 3 also depicts the difference between R6 and R5 in the peaks and valleys. Given that H 2 O 2 is only involved in these two reactions, these values are indicative of the combined impact of the chemical stage reactions on the primary yield of H 2 O 2 . We observed that at the depths of 10, 30, and 50 mm the difference between R6 and R5 in the peaks and valleys is consistent with what is depicted in Figure 4, that is, that there is a higher primary yield of H 2 O 2 in the valleys. At 70 mm the peak and valley values for the difference between R6 and R5 seem to contradict the graph, however as noted in Table 3, the values obtained for R6 in the peak and valley don't exhibit a statistically significant difference. Upon evaluating the peak and valley proportions of R2, it was also observed that at all depths there was a lower proportion of R2 in the valleys, which implies an increased presence of ⋅ OH due to it not being consumed in a reaction with an e - aq . We hypothesise, therefore, that the behavior of R2 is complementary to the behavior of R6, in that the lower the consumption of ⋅ OH through R2 in the valleys, the higher the recombination probability through R6. While the behavior of R2 (increased presence of ⋅ OH in the valleys) itself seems to contradict the reduced primary yield of ⋅ OH observed in Figure 4, we believe that the large proportion of R6 overcomes this contradiction and reduces the presence of ⋅ OH through its consumption.

It appears that for photons minibeam radiation therapy (xMBRT), there is an increased recombination of ⋅ OH at all depths in the valleys through R6, leading to the increased primary yield of H 2 O 2 observed in Figure 4. The behavior of R6 in the valleys compared to the peaks is complemented by R2, and appears to overcome the behavior of R5, which itself is not consistent with what is depicted in the primary yield graphs. As a final note for the beam of photons, subtracting the combined H 2 O 2 producing proportions of the valleys from those of the peaks yields negative values for 10, 30, and 50 mm, which is representative of the gap between peaks and valleys observed in Figure 4.

Carbon ions

The primary yields for the [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ion beams are shown in Figure 6. The trend in depth for each of the species was similar to those of the proton and [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ion beams, whereby there was a decrease in the primary yields of ⋅ OH and e - aq , and an increase in the primary yield of H 2 O 2 . One of the challenges with water radiolysis simulations of the [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C beams is the exceptionally high number of chemical species produced in very small volumes due to the high ionization density. Previous publications have highlighted that water radiolysis simulations of heavy ions around the Bragg peak are particularly challenging when using CPU-based computer architectures. [START_REF] Baba | Quantitative estimation of track segment yields of water radiolysis species under heavy ions around Bragg peak energies using Geant4-DNA[END_REF] Correspondingly, all the results for the Carbon beams were limited to a depth of 70 mm.

Given the increased LET of [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ions over protons and [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ions, there is a greater proportion of radicalradical interactions, leading to a sharper decrease in the F I G U R E 6 CMBRT and CBB primary yields in the peak (solid line) and valley (dashed line) for the species: • OH, H 2 O 2 , and e - aq , depicted as a function of depth in the water phantom.

primary yields of both ⋅ OH and e - aq in depth, and a sharper increase in H 2 O 2 primary yields in depth, as depicted in Figure 8. We observed similar entrance region behavior when compared to the beams of protons or [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ions, in that there was an increase in the primary yield of ⋅ OH between 10 and 30 mm, and a corresponding decrease in the primary yield of H 2 O 2 between the same depths. However, what differentiates Carbon from these other two beams is that the primary yields in the valleys of each species are significantly different from those in the BB modality/MB peak at all depths. This was attributed to the presence of nuclear fragments in the [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ions minibeam radiation therapy (CMBRT) valleys, which is expanded upon later in this section. All statistical uncertainties were maintained below 0.15%, which corresponds with the highest statistical uncertainty obtained -that of the e - aq primary yield at 10 mm in the MB valley.

Figure 6 depicts a decrease in the primary yields of ⋅ OH and e - aq in the MB peak of approximately 6% and 4% respectively, between 10 and 70 mm, while the primary yield of H 2 O 2 in the MB peaks increased by 17% over the same range. As previously mentioned, there were significant differences between the primary yields in the MB peaks and those of the MB valleys, which became progressively larger with increasing depth. For ⋅ OH, the percentage increase of the primary yield in the valleys compared to the peaks was approximately 0.5% at 10 mm and 6% at 70 mm. We observed no statistically significant difference in the primary yield of H 2 O 2 in the MB valley at 10 mm compared to the peak, however at 70 mm the percentage decrease was found to be approximately 16%. At 10 mm the percentage increase of the e - aq primary yield in the valleys compared to the peaks was 0.5% which increased to 4% at 70 mm. Compared to the other irradiation modalities investigated, the beams of [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ions appear to be the only ones in which there is a statistically significant difference between the primary yields in the MB peaks compared to those on-axis in the BB case.

The sharp increase/decrease in the primary yields were predominantly observed in the MB peaks due to the high LET of the primary particles. In the MB valleys we observe a quasi-plateau up to 50 mm, beyond which the primary yields begin to follow the same increasing/decreasing trend as is observed in the peak region. As previously mentioned, we postulated that the difference between peak and valley primary yields arose as a result of a more varied radiation field induced by the nuclear reactions of [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ions as they travel through the water phantom. From the work of González et al., [START_REF] González | Theoretical dosimetric evaluation of carbon and oxygen minibeam radiation therapy[END_REF] it was shown that in the MB peaks, the main contributor to the dose is delta rays up until the Bragg peak region where the nuclear fragments begin to take over. However in the MB valleys at all depths, nuclear fragments are the main contributors to the dose. These observations were corroborated by an evaluation of the composition of the PS sources, as shown in Figure S13. Given the dominance of these nuclear fragments to the dose deposited in MB valleys, preliminary expectations were that there would be an increased proportion of ionizations in the MB valleys, since the only physical process available for ions is the G4DNAIonisation process class. [START_REF] Incerti | Geant4-DNA example applications for track structure simulations in liquid water: a report from the Geant4-DNA Project[END_REF] In order to investigate the consequences F I G U R E 7 Normalised frequencies for the chemical reactions R2, R5, and R6, in CMBRT peak and valley regions at 10 mm, 30 mm, 50 mm, and 70 mm. of these nuclear fragments on the resulting chemistry, the frequencies of chemical reactions were counted and are depicted in Figure 7. Statistical uncertainties were maintained below 1.2%, which corresponded with R5 in the valley at 10 mm.

It is evident from Figure 7 that at the depths of 30, 50, and 70 mm, there is a reduced proportion of R5 (i.e., a lower consumption of H 2 O 2 ) in the valleys compared to the peaks. The exact values are provided in Table 4. This seems to contradict what was observed in Figure 6, which depicts a lower primary yield of H 2 O 2 . Similarly to the beam of photons, the occurrence of R5 is substantially lower than R6, which in fact dominates the behavior of ⋅ OH and H 2 O 2 . Figure 7 shows a decreased proportion of R6 in the valleys compared to the peaks, which is consistent with the primary yield graphs of Figure 6. This lower recombination of ⋅ OH through R6 is evident in Table 4. Given that H 2 O 2 is only involved in two reactions, R5 and R6, the difference in the proportion of each of these reactions in the peaks and valleys was also displayed in Table 4. As previously noted, this difference is representative of the combined behavior of H 2 O 2 due to its consumption in R5 and production in R6. At the depths of 30, 50, and 70 mm, this combined effect is consistent with the primary yields of Figure 6. It implies that there is a lower recombination of ⋅ OH in the MB valleys, leading to a reduction in the primary yields of H 2 O 2 when compared with the peaks. Results for the combined effect at 10 mm are not as conclusive, given that there was no statistically significant difference between the peak and valley proportions for both R5 and R6. Table 4 also presents the proportion of R2 in both peaks and valleys. At depths of 30 mm and beyond, there was an increased proportion of R2 in the valleys compared to the peaks, indicating an increased consumption of ⋅ OH. This is complementary to the behavior of R6 in the valleys, in that it takes away some ⋅ OH species which would otherwise recombine to form H 2 O 2 . As depicted in Figure 6 the differences in the primary yield of H 2 O 2 between the MB peaks and MB valleys appears to increase in depth. This trend is also represented in Table 4 by the row of values in which the combined peak proportion is subtracted from the valley proportion, leading to values of 0.37%, 0.89%, and 1.49%, for 30, 50, and 70 mm respectively. These values represent the increase in the proportion of H 2 O 2 producing reactions in the peaks over the valleys. Given the increased presence of nuclear fragments in the valleys, it seems counter-intuitive that there would be a higher primary yield of ⋅ OH in the valleys, combined with a lower proportion of ⋅ OH recombinations to yield H 2 O 2 , since high LET particles are known to induce more radical-radical reactions, thereby reducing the yield of radical species and increasing the molecular products. Preliminarily, it was believed that since the only physical process process available to nuclear fragments (a majority constituent of the PS sources in the valleys) in Geant4-DNA is the G4DNAIonisation process, there would be an increased amount of ⋅ OH through dissociative decays from the ionized state, as depicted in Table 2. However, it should be remembered that the composition of these PS sources is only descriptive of the particles entering into the 20 𝜇m volume, and not representative of the distribution of ionizations and excitations occurring within the actual volume. We hypothesise, therefore, that given the high LET of the nuclear fragments entering into the volume there are indeed a large number of dissociative decays from the ionized state, but in conjunction there is a substantial creation of other secondary particles such as protons and electrons within the actual volume, which themselves are able to cause both excitations and ionizations due to the presence of appropriate Geant4-DNA physics processes. The excited water molecules, in thermalising, would produce ⋅ OH and e - aq , among other species. It is therefore possible that the excess creation of these radical species led to the increased primary yields observed in Figure 6 due to the fact that a large proportion of these species weren't consumed in chemical reactions before the end of the chemical stage at 1 ns. An excess of these species would also be consistent with the observation in Figure 7 and Table 4 that there is an increased proportion of R2 -the second most common reaction after R6, and most occurring reaction involving e - aq -in the MB valleys.

DISCUSSION

Despite the advantages that MBRT offers in terms of normal tissue sparing, [START_REF] Deman | Monochromatic minibeams radiotherapy: from healthy tissue-sparing effect studies toward first experimental glioma bearing rats therapy[END_REF][START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF][START_REF] Prezado | Proton minibeam radiation therapy widens the therapeutic index for high-grade gliomas[END_REF] tumor control, [9][10][START_REF] Bertho | First evaluation of temporal and spatial fractionation in proton minibeam radiation therapy of glioma-bearing rats[END_REF][START_REF] Sotiropoulos | X-rays minibeam radiation therapy at a conventional irradiator: pilot evaluation in F98-glioma bearing rats and dose calculations in a human phantom[END_REF] and seeming flexibility in the of particles/energies able to be used in conjunction with this technique, [START_REF] Prezado | A potential renewed use of very heavy ions for therapy: neon minibeam radiation therapy[END_REF][START_REF] González | Theoretical dosimetric evaluation of carbon and oxygen minibeam radiation therapy[END_REF][START_REF] Schneider | Improving the dose distributions in minibeam radiation therapy: helium ions vs protons[END_REF][START_REF] Martínez-Rovira | Carbon and oxygen minibeam radiation therapy: an experimental dosimetric evaluation[END_REF] the exact biological mechanisms of action are still not fully understood, [START_REF] Griffin | History and current perspectives on the biological effects of high-dose spatial fractionation and high dose-rate approaches: GRID, Microbeam & FLASH radiotherapy[END_REF] and therefore warranted further investigation. These investigations were performed through the lens of radical and molecular species produced from water radiolysis, where the interest was two-fold. Firstly, they are involved in both non-targeted cell signalling effects,and have an impact on the immune system. H 2 O 2 in particular can act as second messengers for certain signalling pathways, [START_REF] Gough | Hydrogen peroxide: a Jekyll and Hyde signalling molecule[END_REF][START_REF] Forman | An overview of mechanisms of redox signaling[END_REF] which may contribute to the bystander effect. [START_REF] Azzam | Oxidative metabolism modulates signal transduction and micronucleus formation in bystander cells from alpha-particle-irradiated normal human fibroblast cultures[END_REF] It is known that the anti-tumor immune response triggered by immunogenic cell death is weakened for elevated levels of H 2 O 2 due to the oxidation of HMGB1, an important mediator of inflammation and immunity, thereby neutralizing its biologic activity. [START_REF] Lennicke | Hydrogen peroxide -production, fate and role in redox signaling of tumor cells[END_REF][START_REF] Deng | Targeted scavenging of extracellular ROS relieves suppressive immunogenic cell death[END_REF] It has been shown that decreasing the levels of extracellular ROS increased the infiltration of T lymphocytes. [START_REF] Deng | Targeted scavenging of extracellular ROS relieves suppressive immunogenic cell death[END_REF] This highlights the idea that ROS modulation is important in prolonging the survival of T cells. [START_REF] Chen | Reactive oxygen species regulate T cell immune response in the tumor microenvironment[END_REF] Secondly, From a more traditional, targeted DNA damage point of view, an evaluation of the level of ROS, particularly ⋅ OH, would allow insights into the level of indirect DNA damage expected in MBRT peaks and valleys. This represents a continuation of a previous micro-and nano-dosimetric study,in which the direct DNA strand breaks were evaluated for different MBRT modalities, however the impact of indirect DNA damages in peak and valley regions was not considered. The work carried out in this article is therefore representative of a first microdosimetric study using MC simulations, into the implications of water radiolysis in the peaks and valleys of MBRT, using beams of photons, protons, [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ions, and [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C ions. With regards to the primary yields of protons and 4 He ions, we observed very similar results, in that there was a decreasing yield of ⋅ OH and e - aq in depth which corresponded with an increasing yield of H 2 O 2 . These trends in depth were due to the increased radical-radical reactions which arose as a consequence of the increase in LET. When comparing HeMBRT to pMBRT, at all depths in the water phantom and in both peaks and valleys, there is a lower primary yield of ⋅ OH and e - aq , and a higher primary yield of H 2 O 2 , as depicted in Figure 8. Beyond the entrance depth of 10 mm, neither modality exhibited substantial differences between the primary yields in the peaks and valleys. By taking a PVDR of 10 at a specific depth in the water phantom as an example, the implication is that for both modalities there would be an approximately 10-fold increase in the amount of ⋅ OH produced in the peaks compared to the valleys at that depth. We hypothesise therefore that for the case of protons and [START_REF] Prezado | Transfer of minibeam radiation therapy into a cost-effective equipment for radiobiological studies: a proof of concept[END_REF] He ions,at depths where there is no significant difference between the primary yields of the peak compared to the valley, both modalities can expect a level of indirect DNA damage which is directly correlated to the PVDR. This extrapolation of microsecond yields of ⋅ OH to an irradiation dose delivered over seconds/minutes is coherent due to the fact that ⋅ OH is rapidly scavenged and does not diffuse long distances. In order to simulate this biological scavenging, the chemical stage was limited to 1 ns, which is in line with the seminal work by Roots and Okada [START_REF] Roots | Estimation of life times and diffusion distances of radicals involved in X-ray-induced DNA strand breaks or killing of mammalian cells[END_REF] who calculated an average ⋅ OH lifetime of approximately 4 ns. This rapid scavenging implies a lack of background reactions beyond the spur that would otherwise need to be taken into account when performing such an extrapolation.

While the levels of ⋅ OH are indicative of the indirect DNA damage, [START_REF] Von Sonntag | Free-radical-induced DNA damage and its repair[END_REF] the level of H 2 O 2 is implicated in non-targeted effects [START_REF] Azzam | Oxidative metabolism modulates signal transduction and micronucleus formation in bystander cells from alpha-particle-irradiated normal human fibroblast cultures[END_REF][START_REF] Gough | Hydrogen peroxide: a Jekyll and Hyde signalling molecule[END_REF] and the potential immune response [START_REF] Yang | Reactive oxygen species in the immune system[END_REF] observed in MBRT. Figures S3 andS4 highlight the lateral dose profiles of pMBRT and HeMBRT respectively, in which we observe that due to lateral scattering the pMBRT dose profile rapidly homogenises in depth, which isn't the case for the HeMBRT dose profile. It has been shown that in conventional radiotherapy, ionizing radiation could potentially deplete a substantial proportion of circulating naïve T cells, therefore hindering the activation of anti-tumor immunity and abscopal effects. However, the quality of spatial fractionation 'may create interspersed areas of intratumoral immune cell sparing and vascular access with the potential for better immune system activation'. [START_REF] Johnsrud | Evidence for early stage anti-tumor immunity elicited by spatially fractionated radiotherapy-immunotherapy combinations[END_REF] Consequently, the H 2 O 2 primary yields for these two MB modalities, in combination with the behavior of their lateral dose profiles, would suggest that the valley regions of HeMBRT in the Bragg peak (where a heterogeneous dose is delivered) would be more beneficial to an anti-tumor immune response than the valley regions of pMBRT (where the dose is quasi-homogeneous). However, this hypothesis is contingent on two very important aspects, which are as of yet not considered in this study. First of all, in comparison to ⋅ OH which is rapidly scavenged, H 2 O 2 has a longer lifetime and its yield would therefore be affected by background reactions beyond 1 𝜇s. Secondly, the impact of diffusion of this species would also need to be evaluated. If there was limited diffusion of this species during beam-on time this hypothesis may still hold, however a previously published study has hypothesised a possible homogeneous distribution of H 2 O 2 in the tumor. [START_REF] Bello | Proposal of a chemical mechanism for mini-beam and micro-beam efficacy[END_REF] This highlights the need for further research in understanding the behavior of H 2 O 2 in relation to MBRT.

The xMBRT and CMBRT modalities represent a divergence from pMBRT and HeMBRT in the sense that at all depths there was a difference in the primary yields of ⋅ OH, H 2 O 2 , and e - aq between peak and valley regions. For xMBRT,the reduced primary yield of ⋅ OH could imply a lower amount of indirect DNA damage in the valleys of xMBRT than what is suggested by the PVDR. However, it is still unclear if the unit level difference in the yields can be decoupled from the experimental uncertainty to realistically observe the biological consequence of this difference. The beam of [START_REF] Billena | A current review of spatial fractionation: back to the future?[END_REF] C is particularly interesting as the increased prevalence of low-fractionated high-dose protocols in clinics has prompted the notion that the production of ROS from these high LET beams may need to be re-investigated. [START_REF] Matsumoto | Heavy-ion beaminduced reactive oxygen species and redox reactions[END_REF] This could be even more relevant for minibeams, given the high peak doses involved when prescribing to achieve the same average dose as in conventional radiotherapy.

For CMBRT at all depths in the water phantom, there is a higher primary yield of ⋅ OH and e - aq , and a lower primary yield of H 2 O 2 in the valleys compared to the peaks. What is interesting is that the primary yield observed in the CMBRT valleys is most comparable to the pMBRT yields, as seen in Figure 8. In fact, amongst the charged particle beams, beyond 10 mm the primary yield of H 2 O 2 in the CMBRT valleys was the lowest, while simultaneously being the highest in the peaks. Performing the same extrapolation to a total absorbed dose, these results point to an increased level of indirect DNA damage in the CMBRT valleys than what would be suggested by the PVDR. This difference in the primary yield between between peaks and valleys was attributed to the unique radiation field in the MB valleys, which was composed of a large proportion of nuclear fragments, which in turn induced a different set of pre-chemical processes and chemical reactions than was observed in the peaks. The results presented in this work implicate a lower proportion of ⋅ OH recombination reactions (R6) to form H 2 O 2 , which was in part due to the consumption of ⋅ OH with e - aq (R2). In addition to the results obtained through our MC simulations, there is a theoretical basis for the decrease in the primary yield of H 2 O 2 in the MB valleys. It was previously found that in the very high LET regions of Carbon, Nitrogen, and Neon ions, a decrease in the yield of H 2 O 2 begins. [START_REF] Wasselin-Trupin | Hydrogen peroxide yields in water radiolysis by high-energy ion beams at constant LET[END_REF] 7 and Table 4, the decreased proportion of this reaction in the valleys compared to the peaks seems to contradict the findings of Wasselin-Trupin et al., [START_REF] Wasselin-Trupin | Hydrogen peroxide yields in water radiolysis by high-energy ion beams at constant LET[END_REF] however the increased proportion of R2 seems to support it. As previously stated, this increased proportion of R2 in the valleys implicates a greater consumption of ⋅ OH which in turn would lead to a reduction in R6.

From the point of view of ROS, it is evident that the valley regions of MBs are of particular importance,given that the largest divergence in the primary yield from the BB case of each modality always occurred in the valley regions. This divergence goes beyond the naïve notion that the level of local ROS can be directly correlated with the PVDR, which, in this study, was not the case for xMBRT, CMBRT, and the pMBRT and HeMBRT modalities in the entrance region. Various studies have already pinpointed the importance of MB valley regions in the investigation of the driving forces behind the efficacy of spatially fractioned treatments. When survival curves of cells located in SFRT valley regions have been analyzed, they have been found to have lower survival rates than what would normally be expected of the scattered dose in those regions. [START_REF] Asur | Spatially fractionated radiation induces cytotoxicity and changes in gene expression in bystander and radiation adjacent murine carcinoma cells[END_REF] Furthermore, it has also been shown that the valley dose, as opposed to the peak dose, is the better correlating dosimetric parameter to the treatment response. [START_REF] Fernandez-Palomo | Should peak dose be used to prescribe spatially fractionated radiation therapy?-a review of preclinical studies[END_REF] There are, nevertheless, some limitations to the work carried out in this study. First of all, in part due to the limitation on the cross sections available in Geant4-DNA, and in part due to the fact that the SBS method assumes that the diffusion of chemical species occurs in an isotropic volume, all simulations were performed in liquid water. This is a limitation as these 20 𝜇m spheres of liquid water are not fully representative of the microenvironment of the cell, and heterogeneous media may affect water radiolysis. [START_REF] Caër | Water radiolysis: influence of oxide surfaces on H2 production under ionizing radiation[END_REF] Although all efforts were taken in this work to limit the statistical uncertainty of the results, there are still some systematic uncertainties in the simulations. Previously, a combined statistical and systematic uncertainty of approximately 6% was estimated for ⋅ OH and e - aq . [START_REF] Ramos-Méndez | Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio[END_REF] There also exists some systematic uncertainty arising from a difference in the choice of chemical reactions between simulation codes. In Geant4-DNA, the reaction

⋅ OH + H 2 O 2 → H 2 O + HO ⋅ 2
is not included as one of the default reactions, however it is partly responsible for a reduction in the primary yield of H 2 O 2 at much higher LET values. Additionally, discrepancies between simulated yields of H 2 O 2 and experimental yields have been attributed to the fact that multiple ionizations of the same water molecule have no process in Geant4-DNA. It was found that at high LET there was a reduction in the yield of H 2 O 2 due to these multiple ionizations. [START_REF] Baba | Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License beams with multiple ionization using Geant4-DNA[END_REF] The available H 2 O 2 is also implicated in the Fenton reaction, given by H 2 O 2 + Fe 2+ → ⋅ OH + OH -+ Fe 3+ which, at the time the simulations were ran, could not be included due to the lack of appropriate chemical species, as well as time scale limitations in TOPAS-nBio. It's importance lies not only in the modification of the yield of H 2 O 2 , but also in the fact that the potential high levels of H 2 O 2 in the MB peaks may catalyze this reaction, thereby producing cytotoxic ⋅ OH. The catalysis of this reaction is a strategy that has already been investigated in conjunction with the use of nanoparticles, [START_REF] Ranji-Burachaloo | Cancer treatment through nanoparticle-facilitated fenton reaction[END_REF] and the newly released TOPAS-nBio v2.0 facilitates its inclusion. [START_REF] Ramos-Méndez | LET-Dependent intertrack yields in proton irradiation at ultra-high dose rates relevant for FLASH therapy[END_REF] Furthermore, through this reaction there could be an induction of distant DNA damage by ⋅ OH depending on the diffusion of H 2 O 2 from the MB peaks.

Looking to the future, TOPAS-nBio v2.0 could be used to study the diffusion of H 2 O 2 [START_REF] Bello | Proposal of a chemical mechanism for mini-beam and micro-beam efficacy[END_REF] thanks to the inclusion of background reactions, as well as longer timescale simulations made possible by the more computationally efficient IRT approximation. The addition of nanoparticles and organelle geometries also opens up new and exciting avenues of investigation. Preliminary studies combining BB irradiations with manganese dioxide nanoparticles [START_REF] Meng | Tumor oxygenation and hypoxia inducible factor-1 functional inhibition via a reactive oxygen species responsive nanoplatform for enhancing radiation therapy and abscopal effects[END_REF] and hafnium oxide nanoparticles [START_REF] Zhang | Radiotherapy-activated hafnium oxide nanoparticles produce abscopal effect in a mouse colorectal cancer model[END_REF] have shown an enhanced abscopal effect. While these specific cross sections are still not available in the TS physics processes of Geant4-DNA, a recent study using TOPAS-nBio v2.0 has demonstrated the implementation of a cell model containing organelles, and investigated the dose enhancement in these organelles due to radioactive gold nanoparticles. [START_REF] Hahn | Combined cell and nanoparticle models for TOPAS to study radiation dose enhancement in cell organelles[END_REF] These recent advancements in the MC modeling of radiobiological processes facilitates the investigation of more complex cellular microenvironments, at biologically relevant temporal scales, thereby bridging the gap between the currently reported nano-and microsecond quantities observed in homogeneous media. In the context of SFRT, there appears to be as of yet unexplored avenues of research, namely multi-modality cancer treatments looking at the combination of SFRT with nanoparticles, or organelle-targeted therapies. [START_REF] Yang | Organelle-targeted therapies: a comprehensive review on system design for enabling precision oncology[END_REF] Concerning the former, there could be an interest in further exploiting the abscopal effects, which represent an intersection between both techniques. With regards to the latter, destabilization of organelles such as mitochondria are a major source of ROS for the cell, and this mitochondrial ROS is able to stimulate various signalling pathways, and is also critical for the activation of Tcells. [START_REF] Weinberg | Reactive oxygen species in the tumor microenvironment: an overview[END_REF] The higher levels of H 2 O 2 in the MB peaks may also be implicated in the increased production of extracellular vesicles, which themselves contain mitochondrial proteins. [START_REF] Miller | Hydrogen peroxide promotes the production of radiation-derived EVs containing mitochondrial proteins[END_REF] Taking all of this into consideration, it is clear that the capabilities of state of the art MC codes opens the door to further investigations looking at the bio/physico-chemical hallmarks of non-targeted effects,and the associated immune response.The differential ROS production between peaks and valleys may be one of the contributors to the distinct radiobiological mechanisms involved in MBRT which allows it to elicit an anti-tumor immune response. 24 This is particularly important from the point of view of the clinical translation of this technique, as one of the challenges currently facing radiotherapy treatments with conventional BB irradiations, is the difficulty to reliably elicit an anti-tumor immune response to its effects being both immunostimulatory and immunosuppressive. [START_REF] Rückert | Radiotherapy and the immune system: more than just immune suppression[END_REF]

CONCLUSION

This work investigated the difference in the primary yields of ⋅ OH, H 2 O 2 , and e - aq , at the end of nonhomogeneous chemical stage of water radiolysis, for the xMBRT, pMBRT, HeMBRT, and CMBRT irradiation modalities. For both pMBRT and HeMBRT, there were no substantial differences observed in the primary yields of each species beyond the entrance depth of 10 mm. Given the rapidly scavenged, and short diffusion distances of ⋅ OH, it was concluded that for these two modalities one can expect a level of indirect DNA damage which is directly proportional to the PVDR. The divergence in the entrance region was due to differences in the composition of the PS sources, which resulted in a greater proportion of ⋅ OH recombinations and a corresponding increase in H 2 O 2 . The CMBRT modality exhibited higher primary yields of the radical species ⋅ OH, and e - aq in the valleys compared to the peaks, and lower primary yields of the molecular species H 2 O 2 . This was due to a lower ⋅ OH recombination in the valleys through R6, complimented by the higher proportion of ⋅ OH consumption through R2, brought about due to the presence of nuclear fragments in the valleys. Correspondingly, one expects a higher level of indirect DNA damage in the valleys than would be suggested by the PVDR. The opposite conclusions were reached for the xMBRT modality. The H 2 O 2 yields in this study will act as a reference for future works in which the impact of H 2 O 2 diffusion, resulting distribution, and ultimately implications on non-targeted cell signalling effects will be investigated.

AC K N OW L E D G E M E N T S

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 817908). T.A.M.M. received funding from the Imperial College London-CNRS PhD grant programme. Furthermore, we acknowledge PRACE for awarding us access to the Joliot Curie-SKL (France) computational cluster under TGCC projects 2021240006 and A0130313736, as well as HPC Vega under proposal number EHPC-REG-2022R02-177.

C O N F L I C T O F I N T E R E S T S TAT E M E N T

The authors have have no relevant conflicts of interest to disclose.

R E F E R E N C E S

  U R E 1 TOPAS simulation schematic drawing. The legend in the top left indicates which physics/chemistry processes are being applied. Panel A depicts the water phantom in which CH physics was used during the first simulation. The black circles are representative of the 20 𝜇m diameter spherical water cells, located in the peak and valley regions, and at the depths of 10, 30, 50, 70, and 76.5 mm. Panel B depicts the 24 𝜇m 3 cubic volume which surrounds the cell, within which Geant4-DNA physics was used. All particles crossing the surface of the sphere were saved and replayed as a source in a second simulation -shown in panel C. In this second simulation full chemistry processes were enabled in order to track the chemical species. CH, condensed history.

Figure 2

 2 Figure 2 depicts the primary yield in species/100 eV as a function of depth for the proton beams. Statistical

F I G U R E 5

 5 Normalised frequencies for the chemical reactions R2, R5, and R6, in xMBRT peak and valley regions at 10 mm, 30 mm, 50 mm, and 70 mm.

44

 44

F I G U R E 8

 8 Primary yield comparisons between xMBRT, pMBRT, HeMBRT, and CMBRT in the peaks (solid lines) and valleys (dashed lines), up to a depth of 70 mm in the water phantom. Each modality is represented by a colour. The left panel depicts • OH yields, while the right panel represents the yields of H 2 O 2 .

  thereby implicating them in the aforementioned mechanisms of SFRT efficacy.One of the mechanisms of exogenous ROS production is water radiolysis, which refers to the decomposition of H 2 O into various radiolytic products as a result of ionizing radiation, and can be expressed as fol-

	lows: H 2 O H 2 O 2 , H 2 .	ionizing radiation → e -aq , ⋅ OH, H ⋅ , HO ⋅ 2 , H 3 O + , OH -,

Source characteristics c-t-c distance MB size BB size Beam energy

	Photons	1200 µm	600 µm × 5 mm	3000 µm × 5 mm	69 keV effective
	Protons	3200 µm	400 µm × 5 mm	6800 µm × 5 mm	100 MeV
	4 He ions	3500 µm	600 µm × 5 mm	7600 µm × 5 mm	99.3 MeV/u
	12 C ions	3500 µm	600 µm × 5 mm	7600 µm × 5 mm	185.8 MeV/u

Number of primaries simulated Broad beam simulations Minibeam simulations

Photons 4.8 × 10 12 -2.4 × 10 13 2.4 × 10 12 -4.8 × 10 13 Protons 4.5 × 10 8 -1.35 × 10 9 4.5 × 10 8 -3.6 × 10 10 4 He ions 5.4 × 10 7 -4.95 × 10 8 1.8 × 10 7 -1.62 × 10 10 12 C ions 1.8 × 10 8 1.8 × 10 7 -1.08 × 10 10

  • OH, H 2 O 2 , and e - aq , depicted as a function of depth in the water phantom.

  Proportion of chemical reactions R2, R5, and R6 in xMBRT, expressed as a percentage of the total occurring chemical reactions at the corresponding depth and lateral location. Values highlighted in blue indicate a lower expected yield of H 2 O 2 in the valleys compared to the peaks for that specific reaction, while values highlighted in grey indicate the contrary; a higher expected yield of H 2 O 2 in the valleys compared to the peaks indicates that there is no statistically significant difference between the peak and valley values for this reaction at this location.

	Reaction	Lateral location	10 mm	30 mm	50 mm	70 mm
	R2	Peak	28.616	28.626	28.614	28.621
		Valley	28.514	28.515	28.559	28.595
	R5	Peak	0.776	0.781	0.778	0.777
		Valley	0.782	0.783	0.784	0.783
	R6	Peak	55.114	55.095	55.115	55.108 a
		Valley	55.176	55.175	55.150	55.109
	Difference between H 2 O 2 production, and consumption: R6 -R5
		Peak	54.338	54.314	54.337	54.331
		Valley	54.394	54.392	54.366	54.326
	Peak -Valley		-0.056	-0.078	-0.029	0.005

TA B L E 3

a

  Proportion of chemical reactions R2, R5, and R6 in CMBRT, expressed as a percentage of the total occurring chemical reactions at the corresponding depth and lateral location. Values highlighted in blue indicate a lower expected yield of H 2 O 2 in the valleys compared to the peaks for that specific reaction, while values highlighted in grey indicate the contrary; a higher expected yield of H 2 O 2 in the valleys compared to the peaks indicates that there is no statistically significant difference between the peak and valley values for this reaction at this location.

	TA B L E 4 Reaction	Lateral location	10 mm	30 mm	50 mm	70 mm
	R2	Peak	28.05	27.69	27.10	25.12
		Valley	27.84	28.91	28.94	27.77
	R5	Peak	0.83 a	0.85	0.88	1.00
		Valley	0.84	0.75	0.79	0.86
	R6	Peak	54.84 a	55.06	55.42	56.69
		Valley	55.10	54.59	54.44	55.06
	Difference between H 2 O 2 production, and consumption: R6 -R5
		Peak	54.01	54.21	54.54	55.69
		Valley	54.26	53.84	53.65	54.20
	Peak -Valley		-0.25	0.37	0.89	1.49

a

  It was postulated that this decrease occurs due to the increased reactions of H 2 O 2 with ⋅ OH and e - aq through ⋅ OH + H 2 O 2 → H 2 O + HO

	⋅ 2 and e -aq + H 2 O 2 → OH -+ ⋅ OH respectively, there-
	fore leading to a situation whereby there is a smaller
	concentration of H 2 O 2 escaping the track. We therefore
	hypothesise that a similar effect is occurring in the MB
	valleys. The first reaction was not included in TOPAS-
	nBio v1.0, but the second reaction is depicted by R5 in
	this work. As highlighted in Figure

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European Research Council, Grant/Award Number: 87195

S U P P O R T I N G I N F O R M AT I O N

Additional supporting information can be found online in the Supporting Information section at the end of this article.