Mathematical optimization in intensity modulated radiation therapy

Ehrgott, Matthias; Güler, Çiğdem; Hamacher, Horst W.; Shao, Lei

doi:10.1007/s10288-008-0083-7

Cited by 81 publications

(72 citation statements)

References 192 publications

(192 reference statements)

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“…In particular, they focused on the linear models in detail. Furthermore, Ehrgott et al (2008) gave an extensive survey of the optimisation models, methods and theories concerning IMRT design.…”

Section: Healthcare Practicementioning

confidence: 99%

Operations Research in Healthcare: a survey

Rais

Viana

2010

International Transactions in Operational Research

294

130

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Optimisation problems in Healthcare have received considerable attention for more than three decades. More recently, however, with decreasing birth rates in nearly all of the developed countries and increasing average longevity globally, optimisation issues in Healthcare have become noticeably important and attract keen interest from the Operations Research community. Over the years, attention has gradually expanded from resource allocation and strategic planning to include operational issues such as resource scheduling and treatment planning. This paper surveys several applications of Operations Research in the domain of Healthcare. In particular, the paper reviews key contributions addressing contemporary optimisation issues in this area. It highlights current research activities, focusing on a variety of optimisation problems as well as solution techniques used for solving the optimisation problems.

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Section: Healthcare Practicementioning

confidence: 99%

Operations Research in Healthcare: a survey

Rais

Viana

2010

International Transactions in Operational Research

294

130

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“…Nowadays, also commercial treatment planning systems start to support dosimetric constraints (see, e.g., [50]). For an extensive recent review of IMRT planning from a mathematical perspective, we refer the reader to Ehrgott et al [28]. …”

Section: Imrt Inverse Planning As An Optimization Problemmentioning

confidence: 99%

“…Exact approaches that aim at truly finding an optimal subset of beam directions from a larger set of candidate beams are based on Mixed Integer Programming (MIP) methods [61]. See also the mathematically oriented review by Ehrgott et al [28]. …”

Section: The Full Imrt Problem Versus Limited Angle Imrtmentioning

confidence: 99%

From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

Censor

Unkelbach

2012

Physica Medica

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In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT).

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“…Another work of note was put forth by Romeijin et al by approximating DVC as a “mean‐tail‐dose” that refers to the mean dose of either the high or low‐dose voxels. Ehrgott et al provided a comprehensive review of the optimization methods used for IMRT including DVC‐based models.…”

Section: Introductionmentioning

confidence: 99%

Integrating soft and hard dose‐volume constraints into hierarchical constrained IMRT optimization

et al. 2019

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Purpose Dose‐volume constraints (DVCs) continue to be common features in intensity‐modulated radiation therapy (IMRT) prescriptions, but they are non‐convex and difficult to incorporate. We propose computationally efficient methods to incorporate dose‐volume constraints (DVCs) into automated IMRT planning. Methods We propose a two‐phase approach: in phase‐1, we solve a convex approximation with DVCs. Although this convex approximation does not guarantee DVC satisfaction, it provides crucial initial information about voxels likely to receive doses below DVC thresholds. Subsequently, phase‐2 solves an optimization problem with maximum dose constraints imposed on those subthreshold voxels. We further categorize DVCs into hard‐ and soft‐DVCs, where hard‐DVCs are strictly enforced by the optimization and soft‐DVCs are encouraged in the objective function. We tested this approach in our automated treatment planning system which is based on hierarchical constrained optimization. Performance is demonstrated on a series of paraspinal, lung, oligometastasis, and prostate cases as well as a small paraspinal case for which we can computationally afford to obtain a ground‐truth by solving a non‐convex optimization problem. Results The proposed algorithm successfully meets all the hard‐DVCs while increasing the overall computational time of the baseline planning process (without DVCs) by 20%, 10%, and 11% for paraspinal, oligometastasis, and prostate cases, respectively. For a soft‐DVC applied to the lung case, the dose‐volume histogram curve moves toward the desired direction and the computational time is increased by 11%. For a low‐resolution paraspinal case, the ground‐truth solution process using mixed‐integer programming methods required 15 h while the proposed algorithm converges in only 2 min with a proximal solution. Conclusions A computationally tractable algorithm to handle hard‐ and soft‐DVCs is developed which is capable of satisfying DVCs without any parameter tweaking. Although the algorithm is demonstrated in our in‐house developed automated treatment planning system, it can potentially be used in any constrained optimization framework.

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Mathematical optimization in intensity modulated radiation therapy

Cited by 81 publications

References 192 publications

Operations Research in Healthcare: a survey

Operations Research in Healthcare: a survey

From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

Integrating soft and hard dose‐volume constraints into hierarchical constrained IMRT optimization

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