On mixed electron–photon radiation therapy optimization using the column generation approach

Purpose: Despite considerable increase in the number of degrees of freedom handled by recent radiotherapy optimisation algorithms, treatments are still typically delivered using a single modality. Column generation is an iterative method for solving large optimisation problems. It is well suited for mixed‐modality (e.g., photon–electron) optimisation as the aperture shaping and modality selection problem can be solved rapidly, and the performance of the algorithm scales favourably with increasing degrees of freedom. We demonstrate that the column generation method applied to mixed photon–electron planning can efficiently generate treatment plans and investigate its behaviour under different aperture addition schemes. Materials and methods: Column generation was applied to the problem of mixed‐modality treatment planning for a chest wall case and a leg sarcoma case. 6 MV beamlets (100 cm SAD) were generated for the photon components along with 5 energies for electron beamlets (6, 9, 12, 16 and 20 MeV), simulated as shortened‐SAD (80 cm) beams collimated with a photon MLC. For the chest wall case, IMRT‐only, modulated electron radiation therapy (MERT)‐only, and mixed electron–photon (MBRT) treatment plans were created using the same planning criteria. For the sarcoma case, MBRT and MERT plans were created to study the behaviour of the algorithm under two different sets of planning criteria designed to favour specific modalities. Finally, the efficiency and plan quality of four different aperture addition schemes was analysed by creating chest wall MBRT treatment plans which incorporate more than a single aperture per iteration of the column generation loop based on a heuristic aperture ranking scheme. Results: MBRT plans produced superior target coverage and homogeneity relative to IMRT and MERT plans created using the same optimisation criteria, all the while preserving the normal tissue‐sparing advantages of electron therapy. Adjusting the planning criteria to favour a specific modality in the sarcoma case resulted in the algorithm correctly emphasizing the appropriate modality. As expected, adding a single aperture per iteration yielded the lowest (best) cost function value per aperture included in the treatment plan. However, a greedier scheme was able to converge to approximately the same cost function after 125 apertures in one third of the running time. Electron apertures were on average 50–100% larger than photon apertures for all aperture addition schemes. The distribution of intensities among the available modalities followed a similar trend for all schemes, with the dominant modalities being 6 MV photons along with 6, 9 and 20 MeV electrons. Conclusion: The column generation method applied to mixed modality treatment planning was able to produce clinically realistic treatment plans and combined the advantages of photon and electron radiotherapy. The running time of the algorithm depended heavily on the choice of mixing scheme. Adding the highest ranked aperture for each modality provided the best trade‐off between running time and plan quality for a fixed number of apertures. This work contributes an efficient methodology for the planning of mixed electron–photon treatments.