Mixed integer programming with dose‐volume constraints in intensity‐modulated proton therapy

Abstract Background In treatment planning for intensity‐modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed‐integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose‐volume constraints. In this study, we incorporated dose‐volume constraints in an MIP model to generate treatment plans for IMPT. Methods We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited‐memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) method while the other plan was derived with our MIP model with dose‐volume constraints. We then compared these two plans by dose‐volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose‐volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection. Results The MIP model with dose‐volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial‐and‐error process. Some notable reduction in the mean doses of OARs is observed. Conclusions The treatment plans from our MIP model with dose‐volume constraints can meet all dose‐volume constraints for OARs and targets without any tedious trial‐and‐error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.

[1]  Marita Falkinger,et al.  Prioritized optimization in intensity modulated proton therapy. , 2012, Zeitschrift fur medizinische Physik.

[2]  R Mohan,et al.  Algorithms and functionality of an intensity modulated radiotherapy optimization system. , 2000, Medical physics.

[3]  J. M. Dias,et al.  Discretization of optimal beamlet intensities in IMRT: A binary integer programming approach , 2012, Math. Comput. Model..

[4]  A L Boyer,et al.  Optimization of importance factors in inverse planning. , 1999, Physics in medicine and biology.

[5]  Robert R. Meyer,et al.  Radiation Treatment Planning: Mixed Integer Programming Formulations and Approaches , 2006 .

[6]  M. Urie,et al.  Proton beams in radiation therapy. , 1992, Journal of the National Cancer Institute.

[7]  H D Suit,et al.  Protons to replace photons in external beam radiation therapy? , 2003, Clinical oncology (Royal College of Radiologists (Great Britain)).

[8]  Wei Liu,et al.  An Automatic Approach for Satisfying Dose-Volume Constraints in Linear Fluence Map Optimization for IMPT. , 2014, Journal of cancer therapy.

[9]  J Dai,et al.  Selection and determination of beam weights based on genetic algorithms for conformal radiotherapy treatment planning. , 2000, Physics in medicine and biology.

[10]  Richard J. Giglio,et al.  Planning Electric Power Generation: A Nonlinear Mixed Integer Model Employing Benders Decomposition , 1977 .

[11]  Ronald L. Rardin,et al.  Strong valid inequalities for fluence map optimization problem under dose-volume restrictions , 2012, Ann. Oper. Res..

[12]  Radhe Mohan,et al.  Robust optimization of intensity modulated proton therapy. , 2012, Medical physics.

[13]  David Craft,et al.  A fast optimization algorithm for multicriteria intensity modulated proton therapy planning. , 2010, Medical physics.

[14]  Wei Liu,et al.  Uncertainty incorporated beam angle optimization for IMPT treatment planning. , 2012, Medical physics.

[15]  Arvind Kumar,et al.  A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems , 2006, Oper. Res..

[16]  Xiaodong Zhang,et al.  Beyond Gaussians: a study of single-spot modeling for scanning proton dose calculation , 2012, Physics in medicine and biology.