Interior point algorithms: guaranteed optimality for fluence map optimization in IMRT

Abstract

One of the most widely studied problems of the intensity-modulated radiation therapy (IMRT) treatment planning problem is the fluence map optimization (FMO) problem, the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. For a given set of beams, the fluences of the beamlets can drastically affect the quality of the treatment plan, and thus it is critical to obtain good fluence maps for radiation delivery. Although several approaches have been shown to yield good solutions to the FMO problem, these solutions are not guaranteed to be optimal. This shortcoming can be attributed to either optimization model complexity or properties of the algorithms used to solve the optimization model. We present a convex FMO formulation and an interior point algorithm that yields an optimal treatment plan in seconds, making it a viable option for clinical applications.

A Novel Region Reconstruction Method for Fluorescence Molecular Tomography

“…In this formulation, the unknown values are assumed as the constant concentration values of the anomaly (object of interest) and background, c 1 and c 2 , respectively [34], [35]. The characteristic function H(φ) is defined as a smooth approximation of the step function and the Dirac delta function…”

“…Various methods based on convex optimization have been proposed, such as the conjugated gradient method, Gauss-Newton method, and interior-point method, etc. [33]- [35]. Recently, the quadratic penalty (i.e., L2 regularization) is widely used, since it is simple and can be efficiently solved by a large range of standard minimization algorithms, such as Tikhonov method.…”

A Two-Stage Programming Approach to Fluence Map Optimization for Intensity-Modulated Radiation Therapy Treatment Planning

“…Romeijn et al [9] demonstrated that most of the treatment plan evaluation criteria proposed in the medical physics literature are equivalent to convex penalty function criteria when viewed as a multi-criteria optimization problem. Here, we will use a convex penalty function voxel-based nonlinear model [7]. The conclusions drawn regarding this particular model embedded in the proposed two-stage programming strategy are valid also if different FMO formulations are considered.…”

“…This nonlinear formulation implies that a very small amount of underdose or overdose may be accepted in clinical decision making, but larger deviations from the desired/allowed doses are decreasingly tolerated [7]. The optimal solutions obtained ensure that the resulting treatment is the best possible with respect to the weighting parameters (λ ) used.…”

“…After deciding what beam angles should be used, a patient will be treated using an optimal plan obtained by solving the fluence map (or intensity) optimization problem -the problem of determining the optimal beamlet weights for the fixed beam angles. Many mathematical optimization models and algorithms have been proposed for the intensity problem, including linear models [3,4], mixed integer linear models [5,6], nonlinear models [7,8], and multiobjective models [9,10]. After an acceptable set of fluence maps is produced, one must find a suitable way for delivery (realization problem).…”