title: Reduced-order constrained optimization in IMRT planning.
abstract: This paper presents a new algorithm for constrained intensity-modulated radiotherapy (IMRT) planning, made tractable by a dimensionality reduction using a set of plans obtained by fast, unconstrained optimizations. The main result is to reduce planning time by an order of magnitude, producing viable five field prostate IMRT plans in about 5 min. Broadly, the algorithm has three steps. First, we solve a series of independent unconstrained minimization problems based on standard penalty-based objective functions, 'probing' the space of reasonable beamlet intensities. Next, we apply principal component analysis (PCA) to this set of plans, revealing that the high-dimensional intensity space can be spanned by only a few basis vectors. Finally, we parameterize an IMRT plan as a linear combination of these few basis vectors, enabling the fast solution of a constrained optimization problem for the desired intensities. We describe a simple iterative process for handling the dose-volume constraints that are typically required for clinical evaluation, and demonstrate that the resulting plans meet all clinical constraints based on an approximate dose calculation algorithm.
authors.affiliation: Electrical, Computer, and Systems Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
authors.forename: Renzhi
authors.initials: R
authors.lastname: Lu
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Radke
authors.forename: Jie
authors.initials: J
authors.lastname: Yang
authors.forename: Laura
authors.initials: L
authors.lastname: Happersett
authors.forename: Ellen
authors.initials: E
authors.lastname: Yorke
authors.forename: Andrew
authors.initials: A
authors.lastname: Jackson
mesh_terms: D000465:Algorithms; D006801:Humans; D008297:Male; D009010:Monte Carlo Method; D025341:Principal Component Analysis; D011471:Prostatic Neoplasms / Q000532:radiotherapy; D011829:Radiation Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*