Optimization of radiation therapy: integral-response of a model biological system.

Several radiotherapy treatment planning criteria have been proposed for dose distribution optimization. Here we present a simple mathematical model of an idealized biological system. From it we have derived an objective function designed to achieve an extremum for that particular plan which minimizes the probabilities of occurrence of unacceptable complications in healthy tissue and of recurrence or spread of disease. The model assumes that an organism is separable into physiologically discrete compartments or organs, each consisting of a set of microscopic functional units with their own dose-response characteristics. In analogy to the integral-dose, we define an integral-response parameter v as a measure of radiation-induced damage; the value of this v may be calculated for any given spatial distribution of dose in a compartment or organ. A Probability of Serious Complications function, PSC(v), then provides an estimate of the likelihood of occurrence of unacceptable complications. Special problems arising with paired organs (kidneys), "series" organs (spinal cord), and the recurrence and spread of disease are addressed. The PSC for the various organs and neoplasia can be combined to form a compound Complication Factor (CF) objective function; the lower the value of the CF, the better the overall plan. Prospects for making the model explicitly time/fractionation dependent, and for incorporating utility theoretic ideas, are discussed.