Equivalent constant dose rate as a unifying dose rate concept for FLASH across all beam time structures

Area of Science:

• Medical physics
• Radiation oncology
• Radiobiology

Background:

• FLASH effects vary significantly with different beam time structures (pulsed electron, pencil beam scanning proton).
• Direct comparison of experimental FLASH data is challenging due to these structural differences.
• A unified, biologically founded dose rate concept is needed for consistent FLASH effect analysis.

Purpose of the Study:

• To define and develop a mathematical framework for the equivalent constant dose rate ($\dot{D}$ _eq,const).
• To investigate $\dot{D}$ _eq,const across various beam time structures.
• To establish a basis for comparing FLASH sparing effects regardless of delivery method.

Main Methods:

• Utilized a phenomenological oxygen enhancement ratio (OER) weighted dose model for FLASH sparing.
• Developed analytical equations to calculate $\dot{D}$ _eq,const for piecewise constant dose rates.
• Systematically characterized $\dot{D}$ _eq,const for pulsed beams and proton pencil beam scanning (PBS).

Main Results:

• For pulsed beams, $\dot{D}$ _eq,const was approximated by n/(n+1)⋅ $\dot{D}$ _mean.
• $\dot{D}$ _eq,const values varied significantly with PBS parameters (e.g., 155 Gy/s without repainting, 7.7 Gy/s with split delivery).
• Calculated $\dot{D}$ _eq,const correlated with observed acute skin toxicity in mice, confirming radiobiological relevance.

Conclusions:

• The equivalent constant dose rate ($\dot{D}$ _eq,const) is a universally applicable, biologically founded concept.
• This concept facilitates direct comparisons of FLASH dose rates across diverse beam time structures.
• It provides a robust metric for understanding FLASH radiobiology and optimizing treatments.