A simple α/β-independent method to derive fully isoeffective schedules following changes in dose per fraction

Purpose: Dosimetric errors in delivering the prescribed dose per fraction made early in a treatment can be corrected by modifying the dose per fraction and total dose given subsequently to discovery of the error, using the linear-quadratic model to calculate the correcting doses which should be completed within the same overall time as originally prescribed. This study shows how these calculations can be carried out independently of any alpha/beta ratios to bring the treatment back exactly to planned tolerance simultaneously for all tissues and tumor involved. Methods: Planned treatment is defined as p Gy per fraction to a total dose P Gy; the initial error is e Gy per fraction given to a total of E Gy. The linear-quadratic formula is assumed to describe all isoeffect relationships between total dose and dose per fraction. Results and Conclusion: An exact solution is found that describes a compensating dose of d Gy per fraction to a total of D Gy. The formulae are: D = P - E d = Pp - Ee/P - E Thus the total dose for the complete treatment (error plus compensation) remains as originally prescribed, with hyperfractionation being used to correct an initial hypofractionation error and hypofractionation being used to correct an initial hyperfractionation error. Incomplete repair is shown to perturb this exact solution. Thus compensating treatments calculated with these formulae should not be scheduled in such a manner that would introduce incomplete repair. (C) 2004 Elsevier Inc.