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.
(α /β) =
[
H.h− {c.(C− R)}
C− H− R
]
.
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 frac
tionation regimen.
Advances in knowledge: In this work we present simple equations to derive the tumour α/β ratio when a hypo
fractionated regimen has proven to be non-inferior to a conventional regimen.