INTRODUCTION

Theoretically, all types of malignant tumors could be eradicated if treated with sufficiently high doses of radiation. However, radiation also damages normal tissue making normal tissue toxicity the main limitation in the administration of curative radiation doses in cancer treatment (1). In FLASH radiation therapy (FLASH-RT), ultra-high dose rates are used to deliver large doses of radiation to tumors almost instantaneously (a few milliseconds), while unexpectedly sparing normal tissue (2, 3). Recently published work reporting on this relative protection of normal tissues sparked great interest in the use of FLASH for cancer treatment. However, there exists a lack of understanding of the underlying mechanism(s) of this effect (4).

For more than 50 years, dose-rate effects have been an important topic in radiobiology and radiotherapy (5, 6). Since fundamental radiobiological processes, even if they are numerous and complex, are commonly triggered in an aqueous environment, a thorough knowledge of the radiation chemistry of water is essential in addressing this topic. Indeed, pulsed radiation in water radiolysis has been useful in identifying the short-term chemical species that trigger the biological consequences of radiation exposure. In particular, it has been shown that in ∼1 ps after initial energy deposition, radiolytic products formed in pure, deaerated water, exposed to either low- or high-linear energy transfer (LET) radiation, include the hydrated electron (e^–_aq), H^•, H₂, ^•OH, H₂O₂, H₃O⁺ and OH^–, among others (7, 8). In an aerobic cellular environment under normal irradiation conditions (i.e., low absorbed dose rate), e^–_aq and H^• atoms produced in localized spurs or tracks are scavenged by dissolved molecular oxygen on a time scale of a few microseconds (assuming a typical intracellular O₂ concentration of ∼30 µM) and converted to superoxide anions (O₂^•–) and hydroperoxyl (HO₂^•) radicals, respectively. At physiological pH, HO₂^• dissociates to O₂^•– [pK_a(HO₂^•/O₂^•–) ≈ 4.8 in water at 25°C] (9). In contrast to the relatively low dose rates used in conventional therapeutic irradiations, the energy of the ionizing radiation can be considered as evenly distributed over the entire irradiated volume in ultra-high-dose-rate FLASH (10). In this case, the overall physicochemical situation changes significantly due to the overlap between the adjacent spurs or tracks, which occur quickly after the absorption of the radiation. This interaction between neighboring spurs and tracks results in an increased initial concentration of radicals (e^–_aq, H^• and ^•OH), comparable to, or even higher than that of intracellular O₂. Under these conditions, radical-radical combination reactions in which molecular products are formed (mainly H₂O₂ and H₂O, H₂ being relatively inert) are favored, and the effect of radiolytic oxygen depletion (or consumption) becomes important (1, 2, 10). Translated to basic cellular radiobiological research, both of these mechanisms could significantly reduce radiation effects and thus explain the protection of normal tissues in FLASH-RT (4, 11–16). Finally, worthy of mention here is a third mechanism that was recently advanced, which could also play a role in FLASH, namely the generation of early, transient, strongly acidic pH spikes that result from the formation of hydronium ions (H₃O⁺) during the initial stages of water radiolysis (17, 18).

Currently used in several countries (notably Japan and Germany), carbon ions have a characteristic dose deposition profile in which energy is released inversely to the velocity of the ions (19, 20). Therapeutically, the carbon ions enter tissue at a high energy (e.g., ∼290 MeV/nucleon) and an LET in the lower range (∼13 keV/µm for 290 MeV/nucleon ¹²C⁶⁺), but they deposit energy as they penetrate the tissue, which leads to their having less energy and a higher LET, particularly towards the end of their path. They therefore deliver a lower entry dose and deposit most of their energy in the tumor near the end of the flight path (the “Bragg peak”). In other words, if the Bragg peak occurs in the tumor, there is potential for increased sparing of the normal tissue. A similar dose distribution is not possible with low-LET conventional irradiation methods. Radiobiologically, carbon ions are also two- to threefold more effective at killing cells than protons and conventional radiation modalities (21). Moreover, compared to photon radiation, carbon ions produce complex DNA damage that is not easily repaired, and cells exposed to carbon ions have a lower “oxygen enhancement ratio” (OER) and are less affected by variations in radiosensitivity related to the cell cycle (22). Compared to protons, they also have a higher LET and lower lateral dose distribution. In short, carbon ions improve tumor cell killing compared to conventional photons or protons at a given dose of radiation. Determining whether carbon ions delivered at ultra-high dose rates can provide clinically relevant FLASH-RT could dramatically improve cancer management (23). It may also accelerate the development of laser acceleration for heavy ions, which could be delivered at dose rates of ∼10¹¹ Gy/s (24), as it may be difficult to achieve the necessary dose rates with current carbon-ion therapy facilities.

While FLASH-RT has been studied in the context of electron, photon and proton therapies, the efficacy of heavy ions, such as energetic carbon ions, under FLASH conditions remains unclear (23). Regardless of the radiation modality, basic biology experiments and clinical trials will be required to demonstrate the safety and efficacy of FLASH radiotherapy. However, physicochemical modeling can help describe the underlying mechanisms by which FLASH radiotherapy achieves its beneficial effects, and may suggest whether these ultra-high-dose-rate techniques would be favorable in the context of carbon-ion therapy. Here, based on pure radiation chemistry, we present the additive or even synergistic advantages of integrating the FLASH dose rates into therapy with energetic heavy ions, using the example of carbon ions. These benefits result from the ability of heavy ions at high LET to generate an oxygenated microenvironment around their track [for low-LET radiation, O₂ is not considered to be a primary radiolytic product (7, 8)], due to the occurrence of multiple (mainly double) ionization of water (25–28). This early O₂ generation is shown to occur preferentially in the Bragg peak region where the LET of carbon ions is highest. In carbon-ion therapy, this Bragg peak region is targeted to the tumor volume.

Here, we sought to determine how the physicochemical changes occurring under FLASH dose rates may alter oxygen generation for irradiations with energetic carbon ions. We use Monte Carlo track chemistry simulations of the radiolysis of pure, deaerated water to calculate the early yields (or G values) and concentrations of O₂ for irradiating carbon ions of different initial energies, with and without the inclusion of the mechanism of multiple ionization of water molecules at 25°C. A brief presentation of our simulation approach is given below.

MONTE CARLO TRACK CHEMISTRY SIMULATION

The carbon-ion radiolysis of pure, deaerated liquid water at high LET was modeled using our Monte Carlo track chemistry simulation code IONLYS-IRT. A detailed description of this code has been provided elsewhere [see (26) and references therein]. In short, the sequence of all individual stochastic events of the early physical (<10^–15 s) and physicochemical (∼10^–15–10^–12 s) stages in the track development is handled by our IONLYS event-by-event simulation program. The energy deposition by the multiply-charged incident ion and by all secondary electrons generated by it takes place through the slowing down of these particles. This is done via a variety of elastic and inelastic scattering processes and thus by generating a large number of ionized and electronically excited water molecules. To take into account the effects of direct multiple ionization of the outer (loosely bound) electron shells of the target under the impact of high-LET heavy ions, the model incorporates double and triple ionization processes in single ion-water collisions. Ionizations of higher multiplicity are neglected since they are much less likely to occur in the LET range of interest here. Theoretically, it is difficult to acquire a detailed description of multiple ionization, due to the complex, quantum-mechanical many-body nature of the scattering mechanisms involved. Nevertheless, some attempts have been made to simulate the role of multiple ionization in liquid water to assess its consequences for the heavy-ion radiation chemistry of water [for a review, see (25)]. The carbon-ion cross-section values that were used for the double and triple ionizations of water in our track structure simulation modeling have been described in detail elsewhere (25–28) and are therefore not discussed further here.

The consequences of multiple ionization with two, three or more outgoing electrons in the final state have often not been considered in the models of water radiation chemistry and biology. Yet, this hypothesis goes back to Platzman (29), who came to the conclusion more than 60 years ago that these processes, although rare compared to single ionization events, should be “extremely effective chemically” due to the high instability of the multiply-ionized molecules produced. Only recently has this earlier hypothesis been reconsidered to explain the production of HO₂^•/O₂^•– that has been experimentally observed in heavy-ion radiolysis of water at high LET (30–32).

Little, in fact, is known about the fate of multiply-ionized water molecules in solution. Here, the rearrangement of these thermodynamically unstable charged water cations is treated according to the general mechanism proposed by Ferradini and Jay-Gerin (30), which assumes that, in liquid water, H₂Oⁿ⁺ (n=1–10; the molecule of water has 10 bound electrons) dissociates by acid-base re-equilibration processes [see Table 14.3 of (25)]. Among these processes, it is assumed that the chemical production of O₂ (mainly) results from the doubly-ionized water molecules through the intervention of oxygen atoms formed in their ³P ground state, according to the overall dissociation reaction (28):

followed by

or

at a very early stage in the expansion of the tracks. We should recall here that the O(³P) atoms in the ground state are rather inert to water and, due to the very high-local concentration of radicals, react efficiently with themselves or with ^•OH in the heavy-ion track core (26, 30). As for the triple-charged water cations, we have:

The complex spatial distribution of reactants at the end of the physicochemical stage, which is provided as an output of the IONLYS program, is then used directly as the starting point for the “chemical stage” (>10^–12 s). This third stage, in which the different radiolytic species diffuse and react with themselves or with dissolved solutes (if any) present at the time of irradiation, is covered by our IRT program. This program uses the “independent reaction times” (IRT) method (33) to model chemical development in this stage and to simulate the formation of measurable yields. It is a computer-efficient stochastic simulation technique that simulates reaction times without having to follow the trajectories of the diffusing species. The IRT method is based on the approximation that the reaction time of each pair of reactants is independent of the presence of other reactants in the system. Its detailed implementation has previously been described elsewhere [see (26) and references therein]. The reaction scheme and parameters used in our IRT program for pure liquid water at 25°C are the same as those used previously, as described elsewhere [see Table 1 in (34)], except that they now include some newly measured or recently reevaluated reaction rates by Elliot and Bartels (35). The values for the diffusion coefficients of the various reactive species involved in the simulations are listed elsewhere [see table 6 in (36)].

The O₂ yields generated by the radiolysis of liquid water were calculated as a function of time in the interval ∼10^–12 to 10^–6 s for three representative incident carbon-ion energies, namely, 4.1, 290 and 400 MeV/nucleon. This was done by simulating short (∼2–40 µm) carbon-ion track segments, over which the energy and LET of the ion are well defined and remain nearly constant. Typically, approximately 5,000 to 4 × 10⁵ reactive chemical species are generated during the chemical development of these simulated track segments (depending on the LET), whereby the average chemical yields can be calculated with acceptable statistical reliability.

RESULTS AND DISCUSSION

Figure 1 shows the time profiles of G(O₂) at 25°C, over the range of ∼10^–12–10^–6 s, obtained from our Monte Carlo track chemistry simulations (with or without multiple ionization of water) for the three irradiating carbon ions: 4.1, 290 and 400 MeV/nucleon (LET ∼ 330, 11.3 and 10 keV/µm, respectively). The O₂ yield for 300-MeV protons, which mimic the low-LET limiting case of ⁶⁰Co γ or fast-electron irradiation (LET ∼0.3 keV/µm) (28), is also shown in the figure for comparison. As can be seen, these yields remain low in the absence of multiple ionization of water, with G(O₂) showing only a slight gradual increase with increasing LET, similar to the other molecular yields of the radiolysis (7, 8). In contrast, our calculations show that G(O₂) increases sharply considering the mechanism of multiple ionization of water. This is clearly shown in Fig. 1 for 4.1 MeV/nucleon ¹²C⁶⁺ ions, i.e., for the highest LET studied, where G(O₂) increases early (∼10^–12 s) from ∼0.0009 molecule/100 eV in the absence of multiple ionization to ∼0.074 molecule/100 eV when multiple ionization is included in the simulations (an increase of approximately two orders of magnitude). Interestingly, the curve of G(O₂) reaches a maximum of ∼0.113 molecule/100 eV around 4 × 10^–10 s, after which it drops to finally stabilize at approximately 0.068 molecule/100 eV at 1 µs.

FIG. 1

Time dependence of the O₂ yields calculated from our IONLYS-IRT Monte Carlo track chemistry simulations of the radiolysis of pure, air-free liquid water at 25°C, in the interval of 10^–12–10^–6 s, for the three incident carbon ions considered here: 4.1 (with and without multiple ionization of water molecules), 290 and 400 MeV per nucleon (LET: ∼330, 11.3, and 10 keV/µm, respectively). Note that multiple ionization plays no significant role on the values of G(O₂) for the lower-LET 290 and 400 MeV/nucleon ¹²C⁶⁺ ions (represented by dash-dot and dot-dot lines, respectively). The short-dot line corresponds to our calculated G(O₂) values for 300-MeV protons (which mimic the low-LET limiting case of ⁶⁰Co γ or fast electron irradiation, LET ∼ 0.3 keV/µm) and is shown here for comparison. Radiation chemical yields are expressed in units of molecule per 100 eV. For conversion into SI units (mol/J), 1 molecule/100 eV ≈ 0.10364 µmol/J (7, 8). MI = multiple ionization.

Using the G values for O₂ obtained from our Monte Carlo simulations, we can estimate the corresponding oxygen concentrations of the ion track as a function of time, using the general relationship C = ρDG, where C is the concentration of species, ρ is the density, D is the radiation dose and G is the chemical yield (37). In fact, assuming that the oxygen molecules are generated evenly in axially homogeneous cylinders with a length of L = 1 µm and initial radius r_c equal to the radius of the physical “core” of the impacting ion tracks (at ∼10^–13 s) (38, 39), the track concentrations of O₂ can be derived from (17, 26):

where

represents the change with time of r_c due to the two-dimensional (2D) diffusive expansion of the tracks. Here, t is the time and D is the diffusion coefficient of O₂ [D= 2.42 × 10^–9 m²/s at 25°C (40)]. r_c corresponds to the tiny radial region within the first few nanometers around the ion trajectories. In this study, an r_c of ∼2 nm was assumed for the three carbon ions under consideration (26, 28). Figure 2 shows typical 3D representations of track segments of a 300-MeV/nucleon carbon ion (LET ∼ 10 keV/µm), 4.1-MeV/nucleon carbon ion (LET ∼ 330 keV/µm), and a 300-MeV proton (LET ∼ 0.3 keV/µm) traversing through liquid water using calculations from our IONLYS simulation code. As is evident here, the energy density of the deposition in the core area is very high for the high-LET 4.1-MeV/nucleon ¹²C⁶⁺ ions.

FIG. 2

Three-dimensional representations of track segments for the following impacting ions: (panel A) 4.1-MeV/nucleon ¹²C⁶⁺ (LET ∼ 330 keV/µm, 2-µm track length), (panel B) 300-MeV/nucleon ¹²C⁶⁺ (LET ∼ 11 keV/µm, 30-µm track length), and (panel C) 300-MeV ¹H⁺ (LET ∼ 0.3 keV/µm, 30-µm track length) traversing through liquid water at 25°C, calculated (at ∼10^–13 s) with our IONLYS Monte Carlo simulation code. Ions are generated at the origin and start traveling along the y-axis. Each dot represents an interaction where energy deposition occurred. Surrounding the “core” of the track is a much larger region (named the “penumbra”) in which all of the energy is deposited by energetic secondary electrons (δ rays) that result from knock-on collisions with the primary carbon ion.

Figure 3 shows the time profiles of the O₂ concentrations (referred to as [O₂]) at 25°C in the three considered carbon-ion tracks, 4.1, 290 and 400 MeV/nucleon in the interval of ∼10^–12–10^–6 s, calculated directly from Eqs. (6) and (7) using the G(O₂) values given in Fig. 1 (with and without multiple ionization of water). For comparison purposes, the figure also shows the corresponding values of [O₂] for 300-MeV incident protons (28). As shown, carbon ions with higher LET lead to increased production of nascent oxygen compared to those with lower LET over the studied time range. Interestingly, our results for the 4.1-MeV/nucleon ¹²C⁶⁺ ions (LET ∼ 330 keV/µm) showed a steep increase in the values of [O₂] when the multiple ionization of water molecules was incorporated compared to those obtained in the absence of multiple ionization. For example, the initial value of [O₂] (at ∼10^–12 s) increases from ∼0.4 to 32.2 mM when the multiple ionization of water is included in the calculations. This value is approximately three orders of magnitude higher than the oxygen levels in most normal human cells (∼30 µM), and a fortiori in normally oxygenated tumor regions (which vary considerably, from zero to more than 20 µM) as well as in hypoxic tumor regions (a large part of which have almost no oxygenation) (22, 28, 41, 42). The results found in Fig. 3 also show that, for the 290- and 400-MeV/nucleon ¹²C⁶⁺ ions (i.e., of much lower LET, ∼11.3 and 10 keV/µm, respectively), the O₂ concentrations generated are significantly lower, not more than ∼20 µM (at ∼4 × 10^–10 s). Our results clearly show a substantial production of “radiolytic” molecular oxygen in the tracks of high-LET carbon ions immediately after the passage of the ion. Interestingly, however, this level of O₂ production is not observed in low-LET-irradiating ions.

FIG. 3

Time dependence of the corresponding track concentrations of O₂ (in mM) (with and without multiple ionization of water molecules) calculated as explained in the text for the three incident carbon ions under consideration, using the G(O₂) values reported in Fig. 1. As in Fig. 1, the [O₂] values for the lower-LET 290 and 400 MeV/nucleon ¹²C⁶⁺ ions are represented by the dash-dot and dot-dot lines, respectively. The short-dot line corresponds to our calculated [O₂] values for 300-MeV protons (which mimic the low-LET limiting case of ⁶⁰Co γ or fast electron irradiation, LET ∼ 0.3 keV/µm), shown in the figure for comparison. Typical O₂ concentrations in normal human cells (∼30 µM) are indicated by the arrow on the right side. MI = multiple ionization.

To understand the role of FLASH ultra-high dose rates with energetic heavy ions, we must first recall the change in LET with the penetration depth of the ions. This is shown in Fig. 4 for the three irradiating carbon ions studied. As mentioned above, the energy distribution of carbon ions over the treatment field is highly inhomogeneous. Carbon ions deliver a lower entry dose (i.e., in the “plateau” region where the LET is rather low) and deposit most of their energy towards the end of their flight path (i.e., at the Bragg peak, where they have their highest LET). Clinically, carbon-ion radiotherapy is performed in such a way that the Bragg peak is contained in the tumor, resulting in a therapeutic index superior to conventional photon irradiation and a reduction in toxicity to normal tissue.

FIG. 4

Changes in LET with the penetration depth in liquid water at 25°C for carbon ions at the three energies considered in this study, as obtained using the SRIM software (43). Total ions calculated = 1,000. The arrows on the left side show the entry LET of the ions: ∼330, 11.3 and 10 keV/µm, corresponding to the incident ion energies of 4.1, 290 and 400 MeV per nucleon, respectively.

It is well established that molecular oxygen can be a strong radiation sensitizer (22, 44) with the biological response to radiation being greater under oxygenated conditions than under hypoxic conditions. The radiolytic formation of O₂ (due to the occurrence of multiple ionization of water) in the Bragg peak (i.e., in the tumor region), where the LET of the carbon ions is very high, should therefore convert initially hypoxic (i.e., radioresistant) tumor cells into an “oxygenated” environment around the relevant cellular target molecules, which leads to a strong improvement in cell killing (22, 45). In contrast, this level of oxygen generation would not occur in normal tissue because it is in the “plateau” region of the depth-dose distribution of ions where the LET is lower (see Fig. 4).

In the context of FLASH irradiation used to date [e.g., instantaneous dose rates of ∼10⁶–10⁷ Gy/s were used by Favaudon et al. (2)], the average distance between adjacent tracks is small enough that they overlap to a certain degree at early times (10, 18). Under these conditions, the energy of the impinging carbon ions can be considered as being relatively evenly distributed over the irradiated volume. In that case, the early, transient generation of O₂ at the Bragg peak described above should thus occur in all track regions and then, due to their close proximity, extend evenly over the entire irradiated tumor volume. Radiobiologically, this highly oxygenated environment throughout the entire tumor volume should considerably improve tumor cell killing by causing damage from which cancer cells cannot recover.

Taken together, our results provide critical insights into the additive or even synergistic benefits of combining carbon-ion therapy with FLASH-RT, not only to eliminate tumors but also to protect surrounding normal tissues and thus alleviate potential long-term adverse effects.

CONCLUSION

This study highlights the potential biological effect of nascent oxygen formation associated with heavy ions at ultra-high dose rates. This is of particular importance for improving assessment of the clinical potential of FLASH-RT with heavy ions. It has been shown that FLASH, using low-LET electrons, is a promising new method that damages the tumor while protecting normal tissue. Here we found that ultra-high-dose-rate carbon ions increasingly generate molecular oxygen towards the end of their trajectory at the Bragg peak, which is located within the tumor in clinical radiotherapy with heavy ions. This finding indicates increased cell killing potential through the use of carbon ions. Taken together, our results suggest with the use of energetic carbon-ion FLASH-RT, an even better therapeutic ratio can be achieved due to the creation of an oxygenated environment in the tumor, which contributes to increased cell killing efficacy while simultaneously protecting normal tissue.