The influence of the α/β ratio on treatment time iso-effect relationships in the central nervous system

Abstract

Purpose: To investigate the influence of changes in α/β ratio (range 1.5–3 Gy) on iso-effective doses, with varying treatment time, in spinal cord and central nervous system tissues with comparable radio-sensitivity. It is important to establish if an α/β ratio of 2 Gy, the accepted norm for neuro-oncology iso-effect estimations, can be used.

Methods: The rat spinal cord irradiation data of Pop et al. provided ED₅₀ values for radiation myelopathy for treatment times that varied from minutes to ∼6 days. Analysis using biphasic repair kinetics, allowing for variable dose-rates, provided the best fit with repair half-times of 0.19 and 2.16 hr, each providing ∼50% of overall repair; with an α/β ratio 2.47 Gy (CI 1.5–3.95 Gy). Using the above data set, graphical methods were used to investigate changes in the repair parameters for differing fixed α/β ratios between 1.5 and 3.0 Gy. Two different intermittent dose delivery equations were used to evaluate the implications in a radiosurgery setting.

Results: Changes in the α/β ratio (1.5–3.0 Gy) have a minor effect on equivalent doses for radiation myelopathy for treatment durations of a few hours. Changing the α/β value from 2 Gy to 2.47 Gy, modified equivalent single doses by < 1% when overall treatment times ranged from 0.1 to 5.0 hr. Significant changes were only found for treatment times longer than 5–10 hr. These two α/β ratios were also compared in a practical radiosurgery situation, using two different models for estimating BED, again there was no significant loss of accuracy.

Conclusions: It is reasonable to use an α/β ratio of 2 Gy for CNS tissue, with the same repair half-times as published in the original publication by Pop et al., in situations where the assessment of the BED in radiosurgery is used with other form of radiotherapy. In radiosurgery, the variation in BED with treatment duration (for a fixed physical dose) is very similar, but absolute BED values depend on the α/β value. In radiosurgery, clinical recommendations obtained using BED calculations using the originally proposed α/β ratio of 2.47 Gy are still appropriate. For calculations involving a combination of radiosurgery and other modalities, such as fractionated radiotherapy, it would be appropriate in all cases to apply a value of 2 Gy, the accepted norm in neuro-oncology, without significant loss of accuracy in the radio-surgical component. This may have important applications in retreatment situations.

Keywords:

• Radiosurgery
• treatment time
• biologically effective dose (BED)
• α/β ratio

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of one of us (TK) is supported by the EPSRC-funded UCL Centre for Doctoral Training in Medical Imaging with funding from the Engineering and Physical Sciences Research Council (EPSRC) [EP/L016478/1], the Wellcome/EPSRC Centre for Interventional and Surgical Sciences [NS/A000050/1], the Wellcome/EPSRC Centre for Medical Engineering [WT 203148/Z/16/Z] and by the NIHR BRC based at Guys and St Thomas Trust.

Notes on contributors

Bleddyn Jones

Bleddyn Jones is a medically qualified radiobiologist and Professor of Clinical Radiobiology at The University of Oxford. He has made many contributions to explicit mathematical models of radiotherapy, particle therapy, radiosurgery and chemotherapy, as well as their application in the clinic.

Thomas Klinge

Thomas Klinge holds degrees in physics (MSc, Ruprecht-Karls-Universität, Heidelberg) and medical imaging (MRes, University College London) and is currently working on a PhD project with the UCL Center for Doctoral Training in Medical Imaging. His research has focused on treatment plan optimization for radiotherapy, particle therapy and radiosurgery.

John W. Hopewell

John W. Hopewell was the Director of Radiobiological Research, University of Oxford, between 1980 and 2001. His primary research interest has been the study of different aspects of normal tissue toxicity related to radiotherapy: pathogenesis, dose fractionation, radiosurgery, dose-rate, volume effects and retreatment.