Moment Constraints in Radiation Therapy Planning Optimization Incorporating Patient-Specific Anatomical Geometry

Intensity-modulated proton therapy (IMPT) is an advanced cancer treatment technique, aimed at maximizing tumor control while minimizing collateral damage to surrounding healthy structures. In inverse planning, dose-volume histogram (DVH) is a key concept for measuring and restricting collateral radiation damage to healthy tissues. Interpreting the DVH as a probability distribution, a framework is proposed to assess the deviation from a reference dose-volume histogram when the so-called gEUD (generalized equivalent uniform dose) constraints are imposed to control the radiation dose. The underlying formulation is equivalent to devising sharp probability bounds subject to moment constraints. To evaluate these bounds numerically, a linear programming-based approach is proposed. Never-theless, such analysis may yield overly conservative bounds due to the base model lacking patient-specific anatomical or dosimetric information. To address that, an enhanced model is proposed that incorporates the so-called dose deposition matrix, thereby requiring reformulating the problem as a mixed-integer program (MIP). By embedding geometric considerations into the formulation, the objective is to produce dose–volume histogram approximations with greater clinical relevance. Computational results show that incorporating patient-specific anatomical geometry substantially enhances the accuracy of patient-specific DVH estima-tion, albeit at considerable computational expense. By evaluating the dose–volume histogram using the first dual bound reported by the MIP solver, clinically meaningful upper-bound approximations of the DVH are obtained within computationally feasible time frames, preserving mathematical validity while circumventing the need for full optimality certification.