Demystifying the radiobiology of hypofractionation: Simple equations to determine tumour alpha beta ratio

Abstract

Introduction

The radiobiological basis of hypofractionation pivots on two fundamental tumour characteristics - low α/β ratio and high repopulation factor. In our work, we present novel yet simple equations to derive the tumour α/β ratio assuming non-inferiority of two fractionation regimens.

Methods

A simple equation was derived to determine the α/β ratio of tumours assuming non-inferiority of shorter fractionation regimen with longer regimen, by applying the concept of biological effective dose as shown below. $\left(\alpha /\beta \right)=\left[\frac{H.h-\left\{c.\left(C-R\right)\right\}}{C-H-R}\right]$.

Where H = total dose of the short regimen, h = dose per fraction of the short regimen, C = total dose of the long regimen and c = dose per fraction of the long regimen, R = dose lost due to repopulation.

Based on this equation, the actual α/β ratio of tumour is determined by substituting regimen of each individual clinical trial, using an iterative and non-iterative approach.

Results

Using this equation, in prostate cancer, the α/β ratio is in the range of 2–3 Gy. For urothelial muscle invasive bladder cancer, there is a wide range of probable values for the α/β ratio from 6 Gy to 15 Gy. Assuming the conventional value of 10 Gy for the α/β ratio for bladder cancer, the equivalence of 55 Gy in 20 fractions with 64 Gy in 32 fractions is consistent with a repopulation rate of 0.4 Gy/day.

Conclusion

Tumour α/β ratio can be easily derived using simple equations assuming non-inferiority of fractionation regimen.

Advances in knowledge

In this work we present simple equations to derive the tumour α/β ratio when a hypofractionated regimen has proven to be non-inferior to a conventional regimen.