Dynamic Modulation of Radiotherapy Fractionation: A Simulation Study

Article Outline

• Purpose/Objective(s)
• Materials/Methods
• Results
• Conclusions
• Copyright

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Purpose/Objective(s) 

Biological image feedback and adaptive radiotherapy has been proposed to manage biological image guided radiotherapy. In this approach, tumor bioactivities, measured using multiple PET images during the radiotherapy course, are described using a nonlinear and dynamical system. This study utilized the dynamic programming methodology on this dynamical system to determine the optimal control strategy for dynamic modulation of radiotherapy fractionation.

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Materials/Methods 

Tumor cell survival fraction characterized using a nonlinear and dynamic state transformation was used as the objective function for optimal control of treatment fractionation; meanwhile the normal tissue biological effective dose was used as a constraint. The optimal control problem was solved applying the dynamic programming numerically on the Lagrange equation for both the objective and the constraint. Given an initial tumor proliferation fraction gf₁ and hypoxic fraction hf₁, two key parameters in the dynamical system were selected to simulate the dose responses of tumor cell proliferation and hypoxia during the therapy course. These are the ratio of tumor cell re-proliferation, R_g, and the ratio of tumor cell re-oxygenation, R_h. Simulating individual tumor bioactivities with the given initial values and parameters, the dynamic modulation of treatment fractionation was determined using the dynamic programming method, and compared to the standard fractionation 2 Gy × 35.

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Results 

Inter-patient heterogeneities in tumor proliferation and hypoxia were simulated by selecting the four parameters in the ranges of [3%, 30%] for gf₁, [3, 10] for R_g, [3%, 80%] for hf₁, and [3, 10] for R_h. Tumor cell survival fractions accomplished using the optimal control of dynamically modulated fractionation were about 10⁻¹ to 10⁻³ smaller than those achieved by the standard fractionation. Individual tumor, which appears fast response on cell repopulation and reoyxgenation, achieves a higher gain from the optimal control. Figure shows a typical dynamic fractionation to provide the optimal management for the individual tumor with corresponding gf₁ = 3%, R_g = 3, hf₁ = 20% and R_h = 10. In this example, the tumor survival fraction achieved from the optimal and dynamic fractionation is about 5% smaller than the one from the standard fractionation.

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Conclusions 

Individual tumor radiobiological response during the treatment course can be most likely determined using advanced biological imaging, and provides new horizon for adaptive treatment optimization. Dynamic modulation of radiotherapy fractionation determined using the dynamic program shows great potentials in optimizing individual treatment based on biological image feedback.

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