title: Modelling the optimal radiotherapy regime for the control of T2 laryngeal carcinoma using parameters derived from several datasets.
abstract: OBJECTIVE
  A number of previous studies have used direct maximum-likelihood methods to derive the values of radiobiological parameters of the linear-quadratic model for head and neck tumors from large clinical datasets. Time factors for accelerated repopulation were included, along with a lag period before the start of this repopulation. This study was performed to attempt to utilise these results from clinical datasets to compare treatment regimes in common clinical use in the UK, along with other schedules used historically in a number of clinical series in North America and elsewhere, and to determine if an optimal treatment regime could be derived based on these clinical data.
  
  
  METHODS
  The biologically-based linear-quadratic model, applied to local tumor control and late morbidity, has been used to derive theoretical optimum (maximising tumor control whilst not exceeding tolerance for late reactions) radiotherapy schedules based on daily fractions. The specific case of T2 laryngeal carcinoma was considered as this is treated primarily by radiotherapy in many centers. Parameter values for local control were taken from previous analyses of several large single-center and national datasets. A time factor and a lag period were included in the modelling. Values for the alpha/beta ratio for late morbidity were used in the range 1-4 Gy, which is compatible with the limited range of values reported in the literature for particular complications following radiotherapy for head and neck cancer. Early reactions and their consequential late morbidity were not modelled in this study, but assumed to be within tolerance.
  
  
  RESULTS
  For treatments using daily fractions there was a broad optimum treatment time of between 3-6 weeks. The theoretical optimum depended to some extent on the value of the alpha/beta ratio for late morbidity, but in many cases was at or just beyond the end of the purported lag period of 3-4 weeks, although small values of alpha/beta between 1-2 Gy favour longer treatment times. Similar results were obtained using a range of parameter values derived from four independent clinical datasets.
  
  
  CONCLUSIONS
  The mathematical modelling of this broad range of once-daily treatments for most of which differences in local control and late morbidity are essentially undetectable (< 5%) has shown how this clinically-recognised phenomenon is interpreted in terms of the combination of dose-response slopes, fractionation sensitivities and time factors for both tumor control and normal tissue morbidity. Although the conclusions are inevitably tempered by a number of caveats concerning confounding factors in different centers; for example, the use of different treatment volumes, the present analysis provides a framework with which to explore the potential value of modifications to conventional treatment schedules, such as the use of multiple fractions per day.
authors.affiliation: CRC Biomathematics and Computing Unit, Christie Hospital NHS Trust, Manchester, UK.
authors.forename: S A
authors.initials: SA
authors.lastname: Roberts
authors.forename: J H
authors.initials: JH
authors.lastname: Hendry
authors.forename: N J
authors.initials: NJ
authors.lastname: Slevin
mesh_terms: D002277:Carcinoma / Q000473:pathology / Q000532:radiotherapy*; D006801:Humans; D007822:Laryngeal Neoplasms / Q000473:pathology / Q000532:radiotherapy*; D016014:Linear Models; D008954:Models, Biological; D011879:Radiotherapy Dosage; D013997:Time Factors