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Spatiotemporally Optimal Fractionation in Radiotherapy

Author

Listed:
  • Fatemeh Saberian

    (Department of Industrial and Systems Engineering, University of Washington, Seattle, Washington 98195)

  • Archis Ghate

    (Department of Industrial and Systems Engineering, University of Washington, Seattle, Washington 98195)

  • Minsun Kim

    (Department of Radiation Oncology, University of Washington, Seattle, Washington 98195)

Abstract

We present a spatiotemporally integrated formulation of the optimal fractionation problem using the standard log-linear-quadratic survival model. Our objective is to choose a fluence map and a number of fractions to maximize the biological effect of tumor dose averaged over its voxels subject to maximum dose, mean dose, and dose-volume constraints for various normal tissues. Constraints are expressed in biologically effective dose equivalents. We propose an efficient convex programming method to approximately solve the resulting computationally difficult model. Through extensive computer simulations on 10 head-and-neck and prostate cancer test cases with a broad range of radiobiological parameters, we compare the biological effect on tumors obtained by our integrated approach relative to that from two other models. The first is a traditional intensity modulated radiation therapy (IMRT) fluence map optimization model that does not optimize the number of fractions. The second assumes that a fluence map is available a priori from a traditional IMRT optimization model and then optimizes the number of fractions, thus separating the spatial and temporal components. The improvements in tumor biological effect over IMRT were 9%–52%, with an average of 22% for head-and-neck, and 53%–108%, with an average of 69% for prostate. The improvements in tumor biological effect over the spatiotemporally separated model were 15%–45%, with an average of 27%, and 17%–23%, with an average of 21%, for head-and-neck and prostate, respectively. This suggests that integrated optimization of the fluence map and the number of fractions could improve treatment efficacy, as measured within the linear-quadratic framework.

Suggested Citation

  • Fatemeh Saberian & Archis Ghate & Minsun Kim, 2017. "Spatiotemporally Optimal Fractionation in Radiotherapy," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 422-437, August.
  • Handle: RePEc:inm:orijoc:v:29:y:2017:i:3:p:422-437
    DOI: 10.1287/ijoc.2016.0740
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    References listed on IDEAS

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    1. Ehsan Salari & H. Edwin Romeijn, 2012. "Quantifying the Trade-off Between IMRT Treatment Plan Quality and Delivery Efficiency Using Direct Aperture Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 518-533, November.
    2. Kim, Minsun & Ghate, Archis & Phillips, Mark H., 2012. "A stochastic control formalism for dynamic biologically conformal radiation therapy," European Journal of Operational Research, Elsevier, vol. 219(3), pages 541-556.
    3. H. Edwin Romeijn & Ravindra K. Ahuja & James F. Dempsey & Arvind Kumar, 2006. "A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems," Operations Research, INFORMS, vol. 54(2), pages 201-216, April.
    4. H. Romeijn & James Dempsey, 2008. "Rejoinder on: Intensity modulated radiation therapy treatment plan optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 256-257, December.
    5. H. Romeijn & James Dempsey, 2008. "Intensity modulated radiation therapy treatment plan optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 215-243, December.
    6. Thomas Bortfeld & Jagdish Ramakrishnan & John N. Tsitsiklis & Jan Unkelbach, 2015. "Optimization of Radiation Therapy Fractionation Schedules in the Presence of Tumor Repopulation," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 788-803, November.
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    Cited by:

    1. Ali Adibi & Ehsan Salari, 2022. "Scalable Optimization Methods for Incorporating Spatiotemporal Fractionation into Intensity-Modulated Radiotherapy Planning," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1240-1256, March.
    2. Danielle A. Ripsman & Thomas G. Purdie & Timothy C. Y. Chan & Houra Mahmoudzadeh, 2022. "Robust Direct Aperture Optimization for Radiation Therapy Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2017-2038, July.
    3. Ali Ajdari & Fatemeh Saberian & Archis Ghate, 2020. "A Theoretical Framework for Learning Tumor Dose-Response Uncertainty in Individualized Spatiobiologically Integrated Radiotherapy," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 930-951, October.

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