Robust optimization of dose schedules in radiotherapy

A major diculty of choosing an optimal radiation schedule is the uncertainty of model parameters due to geometric and patient specic uncertainties. This paper proposes a method for determining the optimal fractionation schedule in the Linear Quadratic (LQ) model with multiple normal tissue toxicity constraints in the presence of uncertainties in model parameters. To this end, we assumed uncertainty in the LQ model can take two forms: (i) estimation errors for parameters of constant but unknown value, and (ii) stochasticity of random variables. For the unknown parameters, we formulated our problem as a conservative model whose solution is immune to the parameter drifts. When the underlying distributions of uncertain parameters are known, we developed a model which required the decision maker to specify a probability that determined the feasibility of normal tissues constraints and risk factor in the objective function. We proved that our problem can be solved eciently through a decision variable transformation with a few nonlinear constraints and implementing several iterative optimization algorithms. We performed substantial numerical experiments for head-and-neck tumor including six normal tissues, spinal cord, brain stem, skin, oral cavity, mandible and larynx to reveal the eect of