Ws. Kendal, Technical report - The application of probability-generating functions to linear-quadratic radiation survival curves, INT J RAD B, 76(4), 2000, pp. 581-587
Purpose: To illustrate how probability-generating functions (PGFs) can be e
mployed to derive a simple probabilistic model for clonogenic survival afte
r exposure to ionizing irradiation.
Methods: Both repairable and irreparable radiation damage to DNA were assum
ed Co occur by independent (Poisson) processes, at intensities proportional
to the irradiation dose. Also, repairable damage was assumed to be either
repaired or further (lethally) injured according to a third (Bernoulli) pro
cess, with the probability of lethal conversion being directly proportional
to dose. Using the algebra of PGFs, these three processes were combined to
yield a composite PGF that described the distribution of lethal DNA lesion
s in irradiated cells.
Results: The composite PGF characterized a Poisson distribution with mean,
alpha D + beta D-2, where D was dose and alpha and beta were radiobiologica
l constants. This distribution yielded the conventional linear-quadratic su
rvival equation. To test the composite model, the derived distribution was
used to predict the frequencies of multiple chromosomal aberrations in irra
diated human lymphocytes. The predictions agreed well with observation. Thi
s probabilistic model was consistent with single-hit mechanisms, but it was
not consistent with binary misrepair mechanisms.
Conclusions: A stochastic model for radiation survival has been constructed
from elementary PGFs that exactly yields the linear-quadratic relationship
. This approach can be used to investigate other simple probabilistic survi
val models.