Browsing by Author "Merritt, Michael"

Now showing 1 - 5 of 5
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    A Geometric Approach to Fluence Map Optimization in IMRT Cancer Treatment Planning
    (2004-07) Zhang, Yin; Merritt, Michael
    Intensity-modulated radiation therapy (IMRT) is a state-of-the-art technique for administering radiation to cancer patients. The goal of a treatment is to deliver a prescribed amount of radiation to the tumor, while limiting the amount absorbed by the surrounding healthy and critical organs. Planning an IMRT treatment requires determining fluence maps, each consisting of hundreds or more beamlet intensities. Since it is difficult or impossible to deliver a sufficient dose to a tumor without irradiating nearby critical organs, radiation oncologists have developed guidelines to allow tradeoffs by introducing so-called dose-volume constraints (DVCs), which specify a given percentage of volume for each critical organ that can be sacrificed if necessary. Such constraints, however, are of combinatorial nature and pose significant challenges to the fluence map optimization problem. In this paper, we describe a new geometric approach to the fluence map optimization problem. Contrary to the traditional view, we regard dose distributions as our primary independent variables, while treating beamlet intensities as secondary ones. We consider two sets in the dose space: (i) the physical set consisting of physically realizable dose distributions, and (ii) the prescription set consisting of dose distributions meeting the prescribed tumor doses and satisfying the given dose-volume constraints. We seek a suitable dose distribution by successively projecting between these two sets. A crucial observation is that the projection onto the prescription set, which is non-convex, can be properly defined and easily computed. The projection onto the physical set, on the other hand, requires solving a nonnegative least squares problem. We show that this alternating projection algorithm is actually equivalent to a greedy algorithm driven by local sensitivity information readily available in our formulation. Moreover, the availability of such local sensitivity information will enable us to devise greedy algorithms to search for a desirable plan even when a "good and achievable" prescription is unknown.
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    A Sensitivity-Driven Greedy Approach to Fluence Map Optimization in Intensity-Modulated Radiation Therapy
    (2006-05) Merritt, Michael
    Intensity-modulated radiation therapy (IMRT) is a state-of-the-art technique for administering radiation to cancer patients. The goal of a treatment is to maximize the radiation absorbed by the tumor and minimize that absorbed by the surrounding critical organs. Since a plan can almost never be found that both kills the tumor and completely avoids irradiating critical organs, the medical physics community has quantified the sacrifices that can be tolerated in so-called dose-volume constraints. Efficiently imposing such constraints, which are fundamentally combinatorial in nature, poses a major challenge due to the large amount of data. Also, the IMRT technology limits which dose distributions are actually deliverable. So, we seek a physically deliverable dose distribution that at the same time meets the minimum tumor dose prescription and satisfies the dose-volume constraints. We propose a new greedy algorithm and show that it converges to a local minimum of the stated formulation of the fluence map problem. Numerical comparison is made to an approach representative of the leading commercial software for IMRT planning. We find our method produces plans of competitive quality with a notable improvement in computational performance. Our efficiency gain is most aptly attributed to a new interior-point gradient algorithm for solving the nonnegative least squares subproblem every iteration. Convergence is proven and numerical comparisons are made to other leading methods demonstrating this solver is well-suited for the subproblem.
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    A Successive Linear Programming Approach to IMRT Optimization Problem
    (2002-12) Merritt, Michael; Zhang, Yin; Liu, Helen; Mohan, Radhe
    We propose to solve the IMRT optimization problem through a successive linear programming approach. Taking advantage of the sensitivity information in linear programming and the re-optimization ability of simplex methods, the proposed approach provides an affordable methodology to efficiently solve problems with dose-volume constraints. Preliminary computational results indicate that, compared to the standard weighted least squares approach, the new approach leads to higher tumor dosage escalation and better conformation.
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    An Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems
    (2004-05) Merritt, Michael; Zhang, Yin
    We study an interior-point gradient method for solving a class of so-called totally nonnegative least squares problems. At each iteration, the method decreases the residual norm along a diagonally scaled negative gradient direction with a special scaling. We establish the global convergence of the method, and present some numerical examples to compare the proposed method with some existing methods including the affine scaling method.
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    Dose-Volume-Based IMRT Fluence Optimization: A Fast Least-Squares Approach With Differentiability
    (2006-08) Zhang, Yin; Merritt, Michael
    In intensity-modulated radiation therapy (IMRT) for cancer treatment, the most commonly used metric for treatment prescriptions and evaluations is the so-called dose volume constraint (DVC). These DVCs induce much needed flexibility but also non-convexity into the fluence optimization problem, which is an important step in the IMRT treatment planning. Currently, the models of choice for fluence optimization in clinical practice are weighted least-squares models. When DVCs are directly incorporated into the objective functions of least-squares models, these objective functions become not only non-convex but also non-differentiable. This non-differentiability makes it problematic that software packages designed for minimizing smooth functions are routinely applied to these non-smooth models in commercial IMRT planning systems. In this paper, we formulate and study a new least-squares model that allows a monotone and differentiable objective function. We devise a greedy approach for approximately solving the resulting optimization problem. We report numerical results on several clinical cases showing that, compared to a widely used existing model, the new approach is capable of generating clinically relevant plans at a much faster speed, with speedups above one-order of magnitude for some large-scale problems.