The "Goldilocks" Pulse: Mechanistic Constraints on Dose-per-Pulse and Repetition Rate for Flash Sparing
Abstract
Purpose
To mechanistically define the beam parameter space required for FLASH radioprotection, moving beyond Mean Dose Rate (MDR) to identify critical constraints in pulse structure (dose-per-pulse and frequency).
Methods
We utilized a Mechanistic Lethal-Potentially Lethal (M-LPL) model extended with oxygen-dependent fixation kinetics to simulate pulsed delivery. We analyzed 10 Gy irradiation across three microenvironments: Perinecrotic Tumor (0.2 mmHg), Normal Stem-Cell Niche (3.0 mmHg), and Perivascular Tissue (30 mmHg). A "Split-Step" solver performed sensitivity analysis, sweeping pulse counts from n = 1 to 320 across frequencies of 5–320 Hz to quantify differential sparing (Λ = ln [SFFLASH/SFCONV]).
Results
Simulations identified three response regimes. (1) Invariance of Extremes: Perinecrotic (0.2 mmHg) and Perivascular (30 mmHg) targets exhibited negligible sparing (Λ ≈ 0) regardless of beam structure, constrained physically by the OER "floor" and "plateau," respectively. (2) Conditional MDR Validity: For Normal Niches (3.0 mmHg), MDR predicts sparing only when repetition frequency exceeds tissue reoxygenation rates (>> 80 Hz). (3) Dose-per-Pulse Dominance: At low frequencies (< 20 Hz), MDR fails to predict survival. Instead, maximal sparing is achieved with a small number of pulses (low n) due to the extremely high dose-per-pulse, which drives deep transient hypoxia. Increasing n at low frequencies allows inter-pulse reoxygenation, rapidly abolishing the effect.
Conclusion
The M-LPL model demonstrates that MDR is an insufficient metric for FLASH efficacy. Clinical translation must prioritize high dose-per-pulse delivery, particularly for low-frequency sources (e.g., standard linacs), to ensure protection of the stem-cell niche.