[Paper Review] Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

R. Davidi, Y. Censor+3 more|arXiv (Cornell University)|Feb 6, 2014

Spectroscopy Techniques in Biomedical and Chemical Research4 citations

TL;DR

This paper proposes using the superiorization methodology (SM) to improve inverse treatment planning in intensity-modulated radiation therapy (IMRT), replacing computationally intensive minimization with a perturbation-resilient feasibility-seeking algorithm that reduces the total variation (TV) of beamlet intensities. SM achieved clinically acceptable dose distributions in fewer iterations than standard feasibility-seeking methods, with improved conformality and reduced hotspots in a prostate cancer case study using RTOG 0815 criteria.

ABSTRACT

We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking for the constraints and full-fledged constrained minimization of the objective function subject to these constraints. It is based on the discovery that many feasibility-seeking algorithms (of the projection methods variety) are perturbation-resilient, and can be proactively steered toward a feasible solution of the constraints with a reduced, thus superiorized, but not necessarily minimal, objective function value.

Motivation & Objective

• To address the high computational cost of current IMRT inverse planning methods that use full constrained minimization.
• To investigate whether superiorization can produce clinically acceptable treatment plans with reduced computational burden.
• To evaluate if SM can improve solution quality (lower objective function value) while maintaining constraint feasibility.
• To compare SM with standard feasibility-seeking algorithms in terms of convergence speed and dose distribution quality.
• To demonstrate the feasibility of using TV-superiorization for generating deliverable, piecewise-constant intensity maps in IMRT.

Proposed method

• The inverse treatment planning problem is formulated as a constrained minimization of total variation (TV) over a large system of two-sided linear inequalities.
• The superiorization methodology (SM) is applied to the Algebraic Reconstruction Technique (ART) for inequalities, which is known to be bounded perturbation resilient.
• SM introduces controlled perturbations during feasibility iterations to steer the solution toward lower TV values without requiring full minimization.
• The method uses a projection-based algorithm that alternates between feasibility-seeking steps and objective function reduction via TV minimization.
• The algorithm is initialized with zero or uniform beamlet intensities and iteratively updates solutions while enforcing dose constraints.
• The final solution is evaluated using dose-volume histogram (DVH) analysis and compliance with RTOG 0815 clinical acceptance criteria.

Experimental results

Research questions

• RQ1 Can superiorization produce clinically acceptable IMRT plans faster than standard feasibility-seeking algorithms?
• RQ2 Does superiorization reduce the total variation of beamlet intensities while maintaining dose constraints?
• RQ3 Can SM improve plan quality (e.g., reduced hotspots, better conformality) without increasing computational cost?
• RQ4 How does the choice of initial beamlet intensity affect convergence speed and plan quality in superiorized algorithms?
• RQ5 Is SM robust enough to achieve clinical goals when standard feasibility-seeking methods fail within the same iteration limit?

Key findings

• In experiment 1 (zero initialization), the TV-superiorized algorithm met RTOG 0815 criteria in 12 iterations, while the feasibility-seeking algorithm failed to meet the minimum PTV dose (56.13 Gy vs. required 75.24 Gy).
• In experiment 2 (uniform initialization), the TV-superiorized algorithm achieved acceptable plans in 7 iterations, with a PTV minimum dose of 77.80 Gy, compared to 76.15 Gy in the non-superiorized version.
• The rectum volume exceeding 60 Gy was reduced to 34.50% (TV-superiorized) vs. 8.50% (non-superiorized) in experiment 1, indicating better OAR sparing.
• In experiment 2, the rectum volume exceeding 60 Gy was 36.90% with superiorization versus 40.50% without, showing improved OAR protection.
• The maximum dose to the rectum was 82.64 Gy (TV-superiorized) and 82.71 Gy (non-superiorized) in experiment 1, indicating comparable OAR sparing.
• DVH curves demonstrated that superiorized solutions achieved better conformality and homogeneity, particularly in PTV coverage and OAR sparing, within fewer iterations.