VOL. 1, No. 1, January 2004

T. Radivoyevitch, et al. [2004] Med Hypotheses Res 1: 23-28.

The Linear-Quadratic Log-Survival Radiation Dose
Response Model: Confidence Ellipses, Drug-Drug
Interactions, and Brachytherapeutic Gains

Tomas Radivoyevitch, Pietro Taverna, Jane E. Schupp, and
Timothy J. Kinsella*

Departments of Epidemiology and Biostatistics (T.R.) and Radiation Oncology (P.T., J.E.
S., T.J.K.), Ireland Cancer Center, Case Western Reserve University School of Medicine
and University Hospitals of Cleveland, BRB-3, 10900 Euclid Avenue, Cleveland,
OH 44106, USA

Abstract. A method for detecting drug-drug interactions with respect to a linear-
quadratic (LQ) log-survival radiation dose response curve has been proposed by
Lindstrom et al. [Radiation Research 135: 269, 1993]. In this method, clonogenic survival
data are first converted into estimates of the LQ cell killing parameters alpha and beta,
and two drugs are then defined as interacting if they cause significant deviations from an
a priori expectation of additive effects in the parameter space. At least for alpha and beta
individually, this expectation leads naturally to definitions of synergy and antagonism.
Our goal, however, is therapeutic gain. This can be achieved either through antagonism
that is greater in normal tissue than in malignant tissue, or through synergism that is
greater in malignant tissue than in normal tissue. Using clonogenic survival data in which
mismatch repair deficient HCT116 cells serve as a model of malignant tissue and
mismatch repair competent HCT116 3-6 cells serve as a model of the adjacent normal
tissue, we compute expected brachytherapeutic gains (defined as either the ratio or
difference of malignant and normal LQ alpha's) for various pretreatment scenarios. We
suggest that the difference in α is preferable over the ratio as a metric of
brachytherapeutic gain.

*Address all correspondence to: Dr. Timothy J. Kinsella, Department of Radiation
Oncology, University Hospitals of Cleveland/Ireland Cancer Center, 11100 Euclid
Avenue, Cleveland, OH 44106 (USA).  E-Mail:

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