A mathematical programming approach to the fractionation problem in chemoradiotherapy

Salari, Ehsan; Unkelbach, Jan; Bortfeld, Thomas

doi:10.1080/19488300.2015.1017673

Cited by 6 publications

(9 citation statements)

References 48 publications

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“…It was found that some of these models give rise to more complex fractionation schemes, i.e. varying doses per fraction (Bertuzzi et al 2013, Salari et al 2015, Wein et al 2000, Yang & Xing 2005. However, the role of such models to guide fractionation decisions in clinical practice has been limited.…”

Section: Relation To Prior Workmentioning

confidence: 99%

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

Gaddy¹,

Yıldız²,

Unkelbach³

et al. 2018

Phys. Med. Biol.

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Abstract. Spatiotemporal fractionation schemes, that is, treatments delivering different dose distributions in different fractions, can potentially lower treatment side effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically effective dose (BED); however, this leads to computationally challenging nonconvex optimization problems. Optimization methods that are in current use yield only locally optimal solutions, and it has hitherto been unclear whether these plans are close to the global optimum. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue BED reduction for spatiotemporal plans.The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. The BED-based treatment plan optimization problems are formulated as quadratically constrained quadratic programming (QCQP) problems.First, a conventional, uniformly fractionated reference plan is computed using convex optimization. Then, a second, nonconvex, QCQP model is solved to local optimality to compute a spatiotemporally fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the reference plan with respect to all other planning goals. Finally, we derive a convex relaxation of the second model in the form arXiv:1712.03046v1 [physics.med-ph] 8 Dec 2017Spatiotemporal fractionation with bounds on the achievable benefit 2 of a semidefinite programming (SDP) problem, which provides a rigorous lower bound on the lowest achievable mean liver BED.The method is presented on 5 cases with distinct geometries. The computed spatiotemporal plans achieve 12-35 percent mean liver BED reduction over the optimal uniformly fractionated plans. This reduction corresponds to 79-97 percent of the gap between the mean liver BED of the uniform reference plans and our lower bounds on the lowest achievable mean liver BED. The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose and BED, and that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.

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Section: Relation To Prior Workmentioning

confidence: 99%

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

Gaddy¹,

Yıldız²,

Unkelbach³

et al. 2018

Phys. Med. Biol.

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“…However in the case of active radio-sensitization effect, optimal regimens use an escalated radiation dose on treatment sessions with chemotherapy administrations to benefit from the radiosensitization mechanism. This can be compared to an earlier work by Salari et al where it was shown that radio-sensitizers may alter the optimal radiation fractionation regimens in a similar fashion [48]. The benefits of accelerated hypo-fractionation schedules was established numerically, however radio-sensitizers may postpone delivering few radiotherapy sessions until the end of therapy.…”

Section: Resultsmentioning

confidence: 91%

“…A standard approach to solving Bellman's equations with forward recursion is to discretize the state space and use a linear interpolation of appropriate discretized values to increase the accuracy of cost-to-go function estimations at intermediate state values [3,48,5]. Depending on the size of the state space, a naive implementation of this approach may be computationally intractable due to the large number of possible discretized states, known as the curse of dimensionality.…”

Section: Developing Dp Solution Methodsmentioning

confidence: 99%

“…This is motivated by the observations that survival curves of cell lines that are exposed to chemotherapeutic agents follow an exponential form in terms of the drug's concentration [50,33]. To accommodate radio-sensitization, we use the approach suggested in [48] in which a multiplicative term of the radiation dose and chemotherapy drug's concentration is added to the exponent of the LQ model. This is based on clinical observations that radio-sensitizers increase the linear term of the LQ model without causing a considerable change in the quadratic term [12,19].…”

Section: Modeling Primary Tumor Population Growthmentioning

confidence: 99%

“…Second, the two modalities act independently (socalled additivity) or dependently (so-called radio-sensitization) to enhance tumor cell-kill at the primary site [51]. Recently, Salari et al [48] studied changes in optimal radiation fractionation regimens that result from adding chemotherapeutic agents to radiotherapy when maximizing TCP. More specifically, they incorporated additivity and radio-sensitization mechanisms into the radiation fractionation decision to identify corresponding changes in optimal radiation fractionation schemes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimizing Chemoradiotherapy to Target Metastatic Disease and Tumor Growth

Badri

Salari

Watanabe

et al. 2018

INFORMS Journal on Computing

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The majority of cancer-related fatalities are due to metastatic disease [22]. In chemoradiotherapy (CRT), chemotherapeutic agents are administered along with radiation to control the primary tumor and systemic disease such as metastasis. This work introduces a mathematical model of CRT treatment scheduling to obtain optimal drug and radiation protocols with the objective of minimizing metastatic cancer-cell populations at multiple potential sites while maintaining a desired level of control on the primary tumor. A dynamic programming (DP) framework is used to determine the optimal radiotherapy fractionation regimen and the drug administration schedule. We design efficient DP data structures and use structural properties of the optimal solution to reduce the complexity of the resulting DP algorithm. Also, we derive closed-form expressions for optimal chemotherapy schedules in special cases. The results suggest that if there is only an additive and spatial cooperation between the chemotherapeutic drug and radiation with no interaction between them, then radiation and drug administration schedules can be decoupled. In that case, regardless of the chemo-and radio-sensitivity parameters, the optimal radiotherapy schedule follows a hypo-fractionated scheme. However, the structure of the optimal chemotherapy schedule depends on model parameters such as chemotherapy-induced cell-kill at primary and metastatic sites, as well as the ability of primary tumor cells to initiate successful metastasis at different body sites. In contrast, an interactive cooperation between the drug and radiation leads to optimal split-course concurrent CRT regimens. Additionally, under dynamic radio-sensitivity parameters due to the re-oxygenation effect during therapy, we observe that it is optimal to immediately start the chemotherapy and administer few large radiation fractions at the beginning of the therapy, while scheduling smaller fractions in later sessions. We quantify the trade-off between the new and traditional objectives of minimizing the metastatic population size and maximizing the primary tumor control probability, respectively, for a cervical cancer case. The trade-off information indicates the potential for significant reduction in the metastatic population with minimal loss in the primary tumor control.

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Prospect for application of mathematical models in combination cancer treatments

Malinzi

Basita

Padidar

et al. 2021

Informatics in Medicine Unlocked

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A mathematical programming approach to the fractionation problem in chemoradiotherapy

Cited by 6 publications

References 48 publications

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

Optimization of spatiotemporally fractionated radiotherapy treatments with bounds on the achievable benefit

Optimizing Chemoradiotherapy to Target Metastatic Disease and Tumor Growth

Prospect for application of mathematical models in combination cancer treatments

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