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Optimal fractionation in radiotherapy with multiple normal tissues.

Fatemeh Saberian1, Archis Ghate2, Minsun Kim3

  • 1Industrial and Systems Engineering, University of Washington, Box 352650, Seattle, WA 98195, USA saberian@uw.edu.

Mathematical Medicine and Biology : a Journal of the IMA
|May 19, 2015
PubMed
Summary
This summary is machine-generated.

Optimizing radiotherapy fractionation requires considering multiple normal tissues, not just one. This study introduces a new model to find the best radiation dose and session number for improved cancer treatment outcomes.

Keywords:
intensity modulated radiation therapylinear-quadratic cell survival modelquadratically constrained quadratic programming

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Area of Science:

  • Radiation Oncology
  • Medical Physics
  • Computational Biology

Background:

  • Radiotherapy aims to maximize tumor biological effect (BE) while minimizing normal tissue toxicity.
  • Fractionation, or dividing treatment into sessions, allows normal tissues to repair radiation damage.
  • Current models often simplify by including only one normal tissue, potentially leading to suboptimal treatment plans.

Purpose of the Study:

  • To develop an optimal radiotherapy fractionation model that incorporates multiple normal tissues.
  • To address limitations of existing models that consider only a single normal tissue.
  • To determine optimal radiation dosing schedules and number of fractions for improved treatment efficacy and safety.

Main Methods:

  • Formulated an optimal fractionation problem including multiple normal tissues with various dose constraints (max, mean, dose-volume) for serial and parallel tissues.
  • Allowed for spatially heterogeneous dose distributions and non-invariant doses across fractions.
  • Developed a mixed-integer, non-convex, quadratically constrained quadratic programming model.
  • Established conditions for equal-dosage or single-dosage fractionation optimality and derived a closed-form formula for dose per fraction.
  • Analyzed tumor-BE quasiconcavity in relation to the number of fractions.

Main Results:

  • The new model can handle complex dose constraints and heterogeneous dose distributions across multiple normal tissues.
  • Sufficient conditions were identified for simplified fractionation strategies (equal or single dose) to be optimal.
  • A closed-form solution for dose per fraction was derived under specific conditions.
  • Extensive numerical experiments on head-and-neck and prostate cancer cases provided clinically relevant insights.

Conclusions:

  • The developed model offers a more realistic approach to radiotherapy fractionation by including multiple normal tissues.
  • The findings suggest that simplified fractionation schedules may be optimal in many common cancer types.
  • This work provides a framework for optimizing radiotherapy treatment planning, potentially improving outcomes for patients undergoing radiation therapy.