A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning

Abstract

We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (> 95%), target homogeneity (< 10% overdosing and < 7% underdosing) and organ sparing using at least one of the two models.

Evaluating Target Cold Spots By the use of Tail EUDs

“…Many articles have shown that underdosing even small fractions of the target volume can lead to a drastic reduction of the tumor control probability (see, for example, [9,14,18,24]). Hence, the common practice to prescribe dose to the D 95% , i.e., the dose value at the 95% volume level in the dose volume histogram (DVH), is problematic, unless the dose tail below the D 95% is somehow limited [22].…”

Benders decomposition and an IP-based heuristic for selecting IMRT treatment beam angles

“…Ehrgott et al (2008) present an extensive survey. When the objective function is linear or can be linearized, the program can be solved with standard commercial software (Lim et al 2007, Romeijn et al 2003, Saka et al 2011, Saka et al 2014. Otherwise, researchers have developed their own the problem-specific algorithms.…”

IMRT Beam Angle Optimization Using Non-descent Pattern Search Methods

“…Many mathematical optimization models and algorithms have been proposed for the FMO problem, including linear models [20], mixed integer linear models [11] and nonlinear models [2]. Here, we will use this later approach that penalizes each voxel according to the square difference of the amount of dose received by the voxel and the amount of dose desired/allowed for the voxel.…”

“…Here, we will use this later approach that penalizes each voxel according to the square difference of the amount of dose received by the voxel and the amount of dose desired/allowed for the voxel. This formulation yields a quadratic programming problem with only linear non-negativity constraints on the fluence values [20]:…”