Dependence of the Radical Dynamics on the Beam Temporal Profile in FLASH Radiotherapy

Purpose: This study aims to investigate the impact of the beam temporal profile on the radical dynamics and inter-track interactions of FLASH radiotherapy, supporting parameter optimization for the equipment development and clinical implementation. Methods: MonteCarlo simulations based on the IRT method were performed to analyze the dynamics after irradiation, including single-pulse or multi-pulses irradiation, pulse repetition rate, width and dose. The physicochemical experiments were performed to measure the eaq-lifetimes for validation. The generation and recombination of OH and eaq-radicals were recorded under 6 MeV electron irradiation with varying beam temporal profiles. The radial distributions of the radicals were statistically analyzed, and the corresponding LETd and LETt were calculated. The inter-track interactions were assessed through a mathematical model. Results: The spatial distribution and temporal evolution of radicals were significantly affected by the beam time profiles. Compared with multi-pulses irradiation, single-pulse mode with a width less than 1/10 of the radical lifetime, a repetition interval longer than the radical lifetime, and a dose exceeding 1 Gy/pulse can lead to radicals rapid consumption, reducing the residual content. Instantaneous high dose rates induced radical tracks overlaps. When the single-pulse dose exceeded 1 Gy, the overlap probability approached 100%, aligning with the threshold for radical instantaneous combination. Conclusion: Under a low-duty cycle and high instantaneous dose-rate time profile, the radicals were rapidly consumed through track overlap hence reduced damage to normal tissues, inducing FLASH effect. The optimized time profile can be used to guide the development of equipment and parameter settings in clinical practice to maximize the FLASH effect, such as the laser accelerators and superconducting photocathode guns.

💡 Research Summary

Flash radiotherapy (FLASH‑RT) has emerged as a promising technique that delivers ultra‑high dose rates within extremely short time intervals, thereby sparing normal tissue while maintaining tumor control. Although several biological hypotheses have been proposed, the influence of the beam’s temporal profile on the underlying chemical stage—particularly the generation, diffusion, and recombination of reactive radicals—remains poorly quantified. This study addresses this gap by combining Monte‑Carlo (MC) simulations based on the Independent Reaction Time (IRT) formalism with experimental validation of hydrated‑electron (e⁻_aq) lifetimes.

Using the OpenTOPAS v4.0.0 platform together with the TOPAS‑nBio v3.0 extension, the authors modeled 6 MeV electron irradiation of water and tracked the full cascade from physical energy deposition to the chemical stage (·OH, e⁻_aq, H·, etc.). Key beam parameters—pulse width (10 ps to 1 ms), pulse repetition frequency (1 kHz to 100 MHz), dose per pulse (0.1–5 Gy), and total dose (0.1–10 Gy)—were varied independently. For each configuration, 10 random seeds (for 1 Gy) or 30 seeds (for lower doses) were used to ensure statistical robustness. The simulations incorporated published reaction rate constants and diffusion coefficients, allowing the calculation of time‑dependent radical concentrations, spatial distributions, and two forms of linear energy transfer: dose‑averaged LET_d and track‑averaged LET_t.

Experimental verification employed a 6 MeV electron beam (pulse width ≈3 µs) and a 715 nm helium‑neon laser to monitor the transient absorption of e⁻_aq in a sealed water cell. Oxygen was removed by nitrogen bubbling and maintained at 1.7 mg L⁻¹ (≈5 × 10⁻⁵ M), reproducing physiological pO₂ levels. The measured e⁻_aq decay curves matched the MC predictions across a range of oxygen concentrations, confirming the model’s accuracy.

The results reveal several critical insights:

1. Pulse width relative to radical lifetime is decisive. When the pulse duration is less than one‑tenth of the radical lifetime (·OH ≈10 ms, e⁻_aq ≈10 µs), radicals are generated almost instantaneously and are consumed within the first ~30 % of their natural lifetime. This rapid consumption is driven by immediate recombination among densely packed radicals.

2. Inter‑pulse interval matters only if it exceeds the radical lifetime. If the interval between successive pulses is longer than the radical lifetime, each pulse behaves essentially as an isolated event, leading to lower residual radical concentrations compared with multi‑pulse delivery. Conversely, when the interval is shorter than the lifetime, radical concentrations increase stepwise, but the overall effect on peak concentrations is modest.

3. Dose per pulse governs track overlap. A simple geometric model of track overlap predicts the probability that N tracks intersect within a radius r (track radius) inside a target radius R. Simulations show that when the dose per pulse exceeds ~1 Gy, the overlap probability approaches 100 % for the number of electrons typical of clinical FLASH beams (≈10⁴–10⁵ particles). This “instantaneous radical combination” effectively annihilates radicals before they can diffuse to biological targets.

4. Electron energy (1–100 MeV) has negligible impact on radical yields. LET_d and LET_t remain essentially constant across this energy range because electron stopping power varies little, indicating that the temporal profile, not the beam energy, dominates radical production.

5. Spatial analysis confirms extreme concentration within a narrow cylindrical track. Energy deposition profiles for 10–10 000 electrons show overlapping radial distributions, yielding LET_d values of 0.12–0.144 keV µm⁻¹ and LET_t of 0.096–0.102 keV µm⁻¹, reflecting a highly localized energy burst that promotes radical crowding and rapid recombination.

Collectively, these findings support the hypothesis that the FLASH effect arises from rapid radical consumption facilitated by high instantaneous dose rates and low duty cycles. An optimal beam temporal profile for clinical FLASH‑RT should therefore satisfy three conditions: (i) pulse width < 1/10 of the relevant radical lifetime, (ii) pulse‑to‑pulse interval > radical lifetime, and (iii) dose per pulse ≥ 1 Gy. Under such conditions, normal tissue experiences markedly reduced oxidative damage, while tumor cells—often hypoxic and less reliant on radical‑mediated killing—retain therapeutic response.

The authors discuss the practical implications for accelerator design. Laser‑driven electron sources, superconducting photocathode guns, and other ultrafast accelerators can be tuned to deliver the required sub‑nanosecond to picosecond pulses with high repetition rates, while maintaining the necessary per‑pulse dose. The study thus provides concrete, physics‑based guidelines for equipment developers and clinicians aiming to maximize the therapeutic window of FLASH‑RT. Future work should extend these findings to in‑vivo tumor models, explore tissue‑specific oxygen dynamics, and integrate the chemical‑stage insights into comprehensive radiobiological models.