Radiotoxic model for three-dimensional treatment planning. Part 1: Theoretical basis.

Since recent treatment planning systems calculate volumetric dose distribution, an objective evaluation of potential toxicity in the main critical organs may be helpful in treatment optimization. Modeling the toxicity of radiotherapy must at least account for: (a) specific risks in every critical organ; (b) total dose and dose per fraction; (c) partial irradiation of critical organs; (d) heterogeneous dose distribution. The Radiation Damage Factor formula is aimed at estimating the delayed toxicity of a given treatment plan on every critical organ concerned. The formulation uses a double exponential function: RDF = 100 e-Ke-(a+bd)DVc, where: D is the total dose, and d the dose per fraction; a and b are coefficients representing the radiosensitivity of the critical organ, according to the linear-quadratic model, with a/b = alpha/beta. K represents the theoretical critical unit content of the organ, these critical units being groups of functionally related stem cells. The avoidance of a complication depends on the ability of surviving critical units to preserve organ function. V is the ratio:irradiated volume/total volume of the organ. Exponent c accounts for tissue organization: c is equal to or near 1 in "parallel organs" like the liver or the lung, where localized hot spots are tolerated; c is lower in "series organs" like the spinal cord where hot spots, even in a small portion, are dangerous. Heterogeneous irradiation, summarized by dose cumulative-volume histograms, is accounted for by calculating step by step the dose D' considered as having an equivalent effect when given in the largest irradiated volume ratio. Preliminary calibration of the RDF formula is attempted for radiation myelitis and radiation hepatitis.