A unified approach to dose-effect relationships in radiotherapy. II: Inhomogeneous dose distributions

Conventional dose-effect relationships, such as those based upon the NSD or linear-quadratic concepts, do not account for dose inhomogeneities. Only a single "dose" value can be used in these equations and this can give rise to significant errors in the estimation of the "tolerance" dose in situations where dose distributions are inhomogeneous. This paper presents a method of "integrating" the biologically effective dose over the entire volume of each organ or tissue irradiated. Integral forms of the variable-exponent TDF and linear quadratic factor (LQF) models (ITDF and ILQF, respectively) can be used to determine whether or not any organ or tissue in an irradiated volume has exceeded tolerance, regardless of dose distribution non-uniformity. Several examples are given with comparisons to solutions obtained by conventional dose-effect models.