title: Optimum overall times II: Extended modelling for head and neck radiotherapy.
abstract: OBJECTIVE
  A previous paper in this journal (part I) concluded that there was no pronounced optimum overall time, at least up to 70 fractions of 1.15 Gy at two fractions/day in 50 days. The maximum tolerable tumour doses increased only 2% from the best short schedules of 21 or 23 days to those of 50 days. Only this range was modelled in part I because it covered the fewest and the most fractions, and the longest overall times that will probably be used in practice. Most UK schedules, typically using five fractions a week, yield tumour effective doses about 10% less than the best schedules in other developed countries. The present paper covers a much wider range of fraction numbers from one to 115, and from 1 to 80 days. Some numerical errors in the Tables in part I are also corrected in the present appendix. These made no difference to the main conclusions just described.
  
  
  METHODS
  Standard linear quadratic modelling was used, assuming at first alpha/beta=10 Gy, alpha=0.35 ln/Gy, Tk=21 days, Tp=3 days for tumours, but with Tk=7 days, Tp=2.5 Gy for acute mucosal reactions, as before. A late complications constraint of 70 Gy was accepted, and an acute constraint of 51 Gy (both at 2 Gy fractions). Alternative values of more rapid or slower repopulation were also explored (Tp=2 days or Tp=5 days, respectively).
  
  
  RESULTS
  Optimal values were shown at 22-32 days for one fraction/day five times a week, and at 42-49 days for two fractions/day at 10 fractions/week. Repopulation caused a rapid fall in tumour dose after 30 days with one fraction/day, but not until after 50 days with two fractions/day, and so was not seen in part I with its too-practical end time.
  
  
  CONCLUSIONS
  Biological modelling can extrapolate calculations outside the borders of published treatment schedules to clarify borderline situations. Optimum schedules in radiotherapy can reliably give more tumour control if two fractions/day are used. The potential gains are equivalent to about two fractions of 2 Gy as given by this modelling. However, the late complications will be less with some nearly tumour equivalent shorter schedules if optimally designed.
authors.affiliation: Department of Human Oncology, University of Wisconsin Medical School, Madison, WI 53792, USA. jackfowler@btinternet.com
authors.forename: J F
authors.initials: JF
authors.lastname: Fowler
mesh_terms: D019583:Dose Fractionation, Radiation; D006801:Humans; D016014:Linear Models; D008432:Mathematical Computing; D008954:Models, Biological; D009369:Neoplasms / Q000532:radiotherapy*; D011879:Radiotherapy Dosage; D013997:Time Factors