Minimum dose rate estimation for pulsed FLASH radiotherapy: A dimensional analysis

Abstract

Purpose/objectives: To provide an order of magnitude estimate of the minimum dose rate (R min ) required by pulsed ultra-high dose rate radiotherapy (FLASH RT) using dimensional analysis. Materials/methods: In this study, we postulate that radiation-induced transient hypoxia inside normal tissue cells during FLASH RT results in better normal tissue sparing over conventional dose rate radiotherapy. We divide the process of cell irradiation by an ultra-short radiation pulse into three sequential phases: (a) The radiation pulse interacts with the normal tissue cells and produces radiation-induced species. (b) The radiation-induced species react with oxygen molecules and reduce the cell environmental oxygen concentration ( O 2 ½ ). (c) Oxygen molecules, from nearest capillaries, diffuse slowly back into the resulted low O 2 ½ regions. By balancing the radiation-induced oxygen depletion in phase II and diffusion-resulted O 2 ½ replenishment in phase III, we can estimate the maximum allowed pulse repetition interval to produce a pulse-to-pulse superimposed O 2 ½ reduction against the baseline O 2½ . If we impose a threshold in radiosensitivity reduction to achieve clinically observable radiotherapy oxygen effect and combine the processes mentioned above, we could estimate the R min required for pulsed FLASH RT through dimensional analysis. Results: The estimated R min required for pulsed FLASH RT is proportional to the product of the oxygen diffusion coefficient and O 2 ½ inside the cell, and inversely proportional to the product of the square of the oxygen diffusion distance and the drop of intracellular O 2 ½ per unit radiation dose. Under typical conditions, our estimation matches the order of magnitude with the dose rates observed in the recent FLASH RT experiments. Conclusions: The R min introduced in this paper can be useful when designing a FLASH RT system. Additionally, our analysis of the chemical and physical processes may provide some insights into the FLASH RT mechanism.

Determining the parameter space for effective oxygen depletion for FLASH radiation therapy

“…The other contribution to the overall reaction rate is the radiation-induced consumption of oxygen. Similar to the approach taken by Zhou et al ( 2020 ), this model uses a two-stage lumped reaction: During the first stage, radiation interacts with the cells to produce radiolytic species A : The cell here is modelled as a water-like system, where species A accounts for the lumped products of the physico-chemical stage of the radiolysis of water (Draganic and Draganic 1971 , Ling 1975 , Zhou et al 2020 ). It is assumed that the concentration of A produced is proportional to the radiation dose (in Gy), such that where r A is the rate of production of A (in mol m −3 s −1 ) and is the dose rate (in Gy s −1 ).…”

“…It is assumed that the concentration of A produced is proportional to the radiation dose (in Gy), such that where r A is the rate of production of A (in mol m −3 s −1 ) and is the dose rate (in Gy s −1 ). During the second stage, species A reacts with intracellular oxygen to produce species B via the 2nd-order chemical reaction (Ling 1975 , Zhou et al 2020 ): where species B is likely a very reactive peroxide-type compound (Draganic and Draganic 1971 ). …”

“…During the second stage, species A reacts with intracellular oxygen to produce species B via the 2nd-order chemical reaction (Ling 1975 , Zhou et al 2020 ): where species B is likely a very reactive peroxide-type compound (Draganic and Draganic 1971 ).…”

“…This present work aims to expand upon some of the simplifications in their model, and explore additional variation of the parameters involved. Conversely, a study by Zhou et al ( 2020 ) used a dimensional analysis approach to determine that a clinically-observable change in radiosensitivity from FLASH-induced oxygen depletion would be possible for normal tissue given a minimum dose rate of ∼60 Gy s −1 . It is clear then that, while oxygen depletion remains a widely-accepted explanation for FLASH, there is a lack of understanding of the parameters at play which influence the possibility of a sparing effect.…”

Dosimetry for FLASH Radiotherapy: A Review of Tools and the Role of Radioluminescence and Cherenkov Emission

“…Most radiotherapy sources are pulsed with a repetition rate that varies depending on the source of particle acceleration used, spanning between ∼100 MHz in cyclotron sources to ∼100 Hz in linac-based sources, which however can be broken down into ∼GHz bunching repetition rates. More importantly, the temporal resolution should be driven by the dynamics of underlying biological and chemical changes driving FLASH effect, which itself is currently a topic being intensively investigated [38][39][40][41]. The time resolution requirement shall therefore be specified in terms of temporal division of machine output, which most closely matches the biochemical dynamics of FLASH.…”