The potential for mathematical modelling in the assessment of the radiation dose equivalent of cytotoxic chemotherapy given concomitantly with radiotherapy

Abstract

The linear quadratic (LQ) concept of biological effective dose (BED) is used with Poisson statistics to estimate the radiation equivalent BED of cytotoxic chemotherapy (CBED) that would provide improvements in tumour control probability (TCP) typically achieved in randomized clinical trials of chemoradiation. The concepts of pure radio-sensitization and independent chemotherapy cell kill are represented by mathematical equations. Small values of sensitizer enhancement ratios (s) can provide modest increases in TCP when large numbers of radiotherapy fractions are sensitized; larger s values are required if only a small number of radiotherapy fractions are sensitized. Independent chemotherapy induced cell kill is sufficient to explain the benefits achieved with concomitant chemoradiotherapy in situations where a sufficiently high chemotherapy dose intensity is used (i.e. the dose-time intensity of cytotoxic chemotherapy without radiation is considered to be sufficient to cause significant tumour regression although not cure). Care is required in the use of the Poisson cure probability model because of the associated steep dose-response curves that may underestimate both s and the CBED. By use of random sampling methods and estimation over a theoretical population of different tumours, more robust results are obtained with dose-response curves that correspond better to those in clinical data sets. These predict a 2-4 Gy(10) equivalent for each pulse of chemotherapy such as single agent Cis-Platinum when used weekly during radiotherapy for a maximum of 4 cycles. This preliminary paper does not consider normal tissue complication probabilities, of which there are relatively few mature results for modern chemoradiotherapy. The BED concept can be used to estimate the equivalent dose of radiotherapy that will achieve the same cell kill as concomitant cytotoxic chemotherapy. Relatively simple radiobiological modelling can be used to guide decision-making regarding the assessment of the most appropriate combined modality schedules, and has important implications in the design of clinical trials.