Optimal fractionation in radiotherapy with multiple normal tissues

We present a formulation of the optimal fractionation problem that includes multiple normal tissues. Our model can tackle any combination of maximum dose, mean dose and dose-volume type constraints for serial and parallel normal tissues as this is characteristic of most treatment protocols. We also allow for a spatially heterogeneous dose distribution within each normal tissue. Furthermore, we do not a priori assume that the doses are invariant across fractions. Finally, our model uses a spatially optimized treatment plan as input and hence can be seamlessly combined with any treatment planning system. Our formulation is a mixed-integer, non-convex, quadratically constrained quadratic programming problem. In order to simplify this computationally challenging problem without loss of optimality, we establish sufficient conditions under which equal-dosage or single-dosage fractionation is optimal. Based on the prevalent estimates of tumour and normal tissue model parameters, these conditions are expected to hold in many types of commonly studied tumours, such as those similar to head-and-neck and prostate cancers. This motivates a simple reformulation of our problem that leads to a closed-form formula for the dose per fraction. We then establish that the tumour-BE is quasiconcave in the number of fractions; this ultimately helps in identifying the optimal number of fractions. We perform extensive numerical experiments using 10 head-and-neck and prostate test cases to uncover sev...
Source: Mathematical Medicine and Biology - Category: Biomedical Science Authors: Tags: Articles Source Type: research