Abstract 439: Mathematical modeling of cellular dose-response for radiation and radiation-drug combinations including cell cycle effects.
Authors: Williams Katherine S. , El-Kareh Ardith W. , Secomb Timothy W. 
Published: August 2014

Abstract
Thirty-six in vitro radiation dose-response data sets having 7 or more points, covering a variety of cell lines, were used to test four proposed models as alternatives to the linear-quadratic equation: the single-mechanism lognormal, the two-mechanism lognormal, the single-mechanism Hill and the two-mechanism Hill. All four models are forms of our general “damage model,” developed originally for drug dose-response. The lognormal models relate survival to damage using the cumulative lognormal density function, whereas the Hill models use a Hill equation. The models were ranked according to the Akaike Information Criterion, with the single-mechanism lognormal performing the best overall. A subset of the data showing 2-mechanism behavior was identified using the F-test method; for this subset, the two-mechanism lognormal model was superior. The lognormal model is therefore proposed as an alternative to the linear-quadratic.
The lognormal damage model is then extended to the case of radiochemotherapy using the concept of additive damage, which we previously developed for drugs with two mechanisms, and then applied to combination exposure. Previously, it was found that fixed-schedule, varying-dose exposures to drug and radiation could be described by the additive damage model. Here, the case of varying schedule is considered, for gemcitabine, which showed schedule-dependent radiosensitization in studies by Pauwels et al (2003, 2009). Cell cycle effects are included through a kinetic equation describing the evolution of the population distribution over the cell cycle. In contrast to some previous models where discrete phases of the cell cycle are treated as compartments, here the distribution is a continuous density function. Gemcitabine is assumed to cause a block at a single point, with dose-dependent duration. The cell cycle phase population density distribution then enters into the radiation damage term. The model thus includes radiation-drug interaction in two ways: through additive damage and through cell cycle effects. The case of fractionated doses of gemcitabine alone is also considered. Overall, the model provides a framework for understanding the complex effects of schedule and dose, as well as a method to potentially predict combination or fractionated dose-response from knowledge of a drug's perturbations to the cell cycle phase distribution. It is expected that these models will have application in preclinical optimization of combination therapy, as well as in computational simulation of anticancer therapy.
Citation Format: Katherine S. Williams, Ardith W. El-Kareh, Timothy W. Secomb. Mathematical modeling of cellular dose-response for radiation and radiation-drug combinations including cell cycle effects. [abstract]. In: Proceedings of the 104th Annual Meeting of the American Association for Cancer Research; 2013 Apr 6-10; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2013;73(8 Suppl):Abstract nr 439. doi:10.1158/1538-7445.AM2013-439