title: A comprehensive formulation for volumetric modulated arc therapy planning.
abstract: OBJECTIVE
  Volumetric modulated arc therapy (VMAT) is a widely employed radiation therapy technique, showing comparable dosimetry to static beam intensity modulated radiation therapy (IMRT) with reduced monitor units and treatment time. However, the current VMAT optimization has various greedy heuristics employed for an empirical solution, which jeopardizes plan consistency and quality. The authors introduce a novel direct aperture optimization method for VMAT to overcome these limitations.
  
  
  METHODS
  The comprehensive VMAT (comVMAT) planning was formulated as an optimization problem with an L2-norm fidelity term to penalize the difference between the optimized dose and the prescribed dose, as well as an anisotropic total variation term to promote piecewise continuity in the fluence maps, preparing it for direct aperture optimization. A level set function was used to describe the aperture shapes and the difference between aperture shapes at adjacent angles was penalized to control MLC motion range. A proximal-class optimization solver was adopted to solve the large scale optimization problem, and an alternating optimization strategy was implemented to solve the fluence intensity and aperture shapes simultaneously. Single arc comVMAT plans, utilizing 180 beams with 2° angular resolution, were generated for a glioblastoma multiforme case, a lung (LNG) case, and two head and neck cases-one with three PTVs (H&N3PTV) and one with foue PTVs (H&N4PTV)-to test the efficacy. The plans were optimized using an alternating optimization strategy. The plans were compared against the clinical VMAT (clnVMAT) plans utilizing two overlapping coplanar arcs for treatment.
  
  
  RESULTS
  The optimization of the comVMAT plans had converged within 600 iterations of the block minimization algorithm. comVMAT plans were able to consistently reduce the dose to all organs-at-risk (OARs) as compared to the clnVMAT plans. On average, comVMAT plans reduced the max and mean OAR dose by 6.59% and 7.45%, respectively, of the prescription dose. Reductions in max dose and mean dose were as high as 14.5 Gy in the LNG case and 15.3 Gy in the H&N3PTV case. PTV coverages measured by D95, D98, and D99 were within 0.25% of the prescription dose. By comprehensively optimizing all beams, the comVMAT optimizer gained the freedom to allow some selected beams to deliver higher intensities, yielding a dose distribution that resembles a static beam IMRT plan with beam orientation optimization.
  
  
  CONCLUSIONS
  The novel nongreedy VMAT approach simultaneously optimizes all beams in an arc and then directly generates deliverable apertures. The single arc VMAT approach thus fully utilizes the digital Linac's capability in dose rate and gantry rotation speed modulation. In practice, the new single VMAT algorithm generates plans superior to existing VMAT algorithms utilizing two arcs.
authors.affiliation: Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California 90024.
authors.forename: Dan
authors.initials: D
authors.lastname: Nguyen
authors.affiliation: Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California 90024.
authors.forename: Qihui
authors.initials: Q
authors.lastname: Lyu
authors.affiliation: Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California 90024.
authors.forename: Dan
authors.initials: D
authors.lastname: Ruan
authors.affiliation: Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California 90024.
authors.forename: Daniel
authors.initials: D
authors.lastname: O'Connor
authors.affiliation: Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California 90024.
authors.forename: Daniel A
authors.initials: DA
authors.lastname: Low
authors.affiliation: Department of Radiation Oncology, University of California Los Angeles, Los Angeles, California 90024.
authors.forename: Ke
authors.initials: K
authors.lastname: Sheng
mesh_terms: D000465:Algorithms; D001932:Brain Neoplasms / Q000532:radiotherapy; D005909:Glioblastoma / Q000532:radiotherapy; D006258:Head and Neck Neoplasms / Q000532:radiotherapy; D006801:Humans; D008175:Lung Neoplasms / Q000532:radiotherapy; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*