External beam therapy is generally given over many sessions, spread-out over several weeks. Although certain rules as to number of fractions, total time, and dose per fraction have evolved empirically over several decades of clinical experience, these rules are ill-understood. The present project attempts to develop a simple mathematical description of the time course of the reactions of both normal tissue and tumor, as a function of these variables. The limiting factor for normal tissue is its short- term and long-term minimum acceptable functionality. The latter is assumed to be determined by the balance between attrition of the functioning cells and the production of replacement cells generated by the residual viable stem cells, whose population is highly radiation sensitive. Local tumor cure requires incapacitating every clonogenic cell in the tumor.
