A model for optimizing normal tissue complication probability in the spinal cord using a generalized incomplete repair scheme

The authors determined the dose fraction sizes and interfraction intervals (IFIs) that minimize the Normal Tissue Complication Probability (NTCP) in the spinal cord, for given total treatment dose and time. They generalize the concept of incomplete repair in the Linear Quadratic (LQ) model, allowing for arbitrary dose fractions and IFIs. This is incorporated in a previously presented model for NTCP in the spinal cord. Equations are derived, regarding each dose fraction and IFI as independent parameters, subject to the constraints of fixed total treatment dose and time. An exact solution is found for the case when the IFIs are all equal. The general problem is nonlinear, and is solved numerically using simulated annealing. The authors find that optimal NTCP is obtained by two large and equal dose spikes at the start and finish of the treatment, with the rest of the doses equal to each other, and smaller than the dose spikes. This is valid both for constant and arbitrary IFIs. As the IFI is decreased the NTCP decreases, indicating that optimal NTCP obtained In the continuum limit, where “middle” fractions, between the two edge doses, are given continuously at a low dose rate. In conclusion, continuous low dose rate irradiation with dose spikes at the start and end of treatment yields the lowest NTCP in the spinal cord, given a fixed total dose and total treatment time