Accounting for overdispersion of lethal lesions in the linear quadratic model improves performance at both high and low radiation doses

Abstract

Purpose

The linear-quadratic (LQ) model represents a simple and robust approximation for many mechanistically-motivated models of radiation effects. We believe its tendency to overestimate cell killing at high doses derives from the usual assumption that radiogenic lesions are distributed according to Poisson statistics.

Materials and methods

In that context, we investigated the effects of overdispersed lesion distributions, such as might occur from considerations of microdosimetric energy deposition patterns, differences in DNA damage complexities and repair pathways, and/or heterogeneity of cell responses to radiation. Such overdispersion has the potential to reduce dose response curvature at high doses, while still retaining LQ dose dependence in terms of the number of mean lethal lesions per cell. Here we analyze several irradiated mammalian cell and yeast survival data sets, using the LQ model with Poisson errors, two LQ model variants with customized negative binomial (NB) error distributions, the Padé-linear-quadratic, and Two-component models. We compared the performances of all models on each data set by information-theoretic analysis, and assessed the ability of each to predict survival at high doses, based on fits to low/intermediate doses.

Results

Changing the error distribution, while keeping the LQ dose dependence for the mean, enables the NB LQ model variants to outperform the standard LQ model, often providing better fits to experimental data than alternative models.

Conclusions

The NB error distribution approach maintains the core mechanistic assumptions of the LQ formalism, while providing superior estimates of cell survival following high doses used in radiotherapy. Importantly, it could also be useful in improving the predictions of low dose/dose rate effects that are of major concern to the field of radiation protection.

Keywords:

• Linear quadratic model
• lethal lesions
• chromosomal aberrations
• overdispersion
• Poisson distribution
• cell survival
• mathematical modeling

Acknowledgements

We are grateful to Dr. Halim E. Lehtihet for instructive comments and feedback on the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Igor Shuryak

Igor Shuryak, MD, PhD, is an Assistant Professor of Radiation Oncology in the Center for Radiological Research, Department of Radiation Oncology, Columbia University Irving Medical Center. His research focuses on quantitative modeling of a variety of biological effects of ionizing radiation. In particular, he works on modeling and prevention of radiation-induced carcinogenesis, radioresistance, non-targeted effects, and quantification of risks of radiation-induced cancer and other diseases. This work relies on implementation of applied mathematics, programming, statistics and machine learning.

Michael N. Cornforth

Michael N. Cornforth, PhD, is a tenured Professor in the Department of Radiation Oncology, where he serves as director of the Biology Division and holds the Vincent P. Collins Distinguished Professorship. His main interests are in experimental radiation cytogenetics and biophysical approaches applied to fundamental models of radiation action, most recently as it relates to DNA repair and the formation large-scale structural variants in the human genome.