"As an immediate result, our findings can help radiation oncologists decide the number and orientation of carbon ion beams," said Till Böhlen, first author and PhD candidate at CERN in Geneva. "In the medium term, we hope that optimizations for radiobiological robustness will be incorporated in treatment planning software for carbon ion radiotherapy and, more generally, that inverse planning can be guided not only by dose, but also by other parameters such as dose-averaged LET."

RBE: a complex parameter

For ion beams, RBE is more than a simple definition describing radiobiological effects in tissue compared to a reference radiation type. Rather, it depends on multiple factors including: tissue type; the biological endpoint in question; beam properties, such as energy and linear energy transfer (LET); and parameters in the linear quadratic model, including α and β. Consequently, the calculation of RBE-weighted dose in clinical ion treatment plans requires the modelling of RBE, where the accuracy of estimates for input parameters and the model itself can have significant consequences for calculation accuracy.

The researchers' approach was to assess the effect of various input parameters by varying the values for each in models of chordoma, prostate, liver and salivary gland cancers. The RBE models were interfaced to a Monte Carlo treatment planning tool based on the FLUKA code and were used to calculate RBE, cell survival and RBE-weighted dose for planning target volumes (PTVs) in a homogeneous water phantom.

The team analysed the effects of variations in input parameters in clinically representative single and opposed beam arrangements. Inverse planning was used to optimize the dose distributions, with strategies that prioritized several dosimetric and biological goals.

"The carbon ion treatment fields were relatively robust to uncertainties in the model input parameters and for the investigated scenarios, resulted mostly in RBE-weighted dose variations well below 15%," said Böhlen.

A strategy identified by the researchers for reducing the sensitivity of RBE-weighted dose to uncertainties was to optimize treatment fields to achieve a more uniform radiation quality in the PTV. By minimizing variations in radiation quality, variations in energy deposition (a determinant of RBE) are also minimized. It's thought that the approach could help achieve steeper dose-response curves for treatment protocols, improving clinical outcomes.

However, while plan optimization did help reduce RBE uncertainty, the approach also involved trade-offs with the integral dose to the patient and the robustness of a plan to physical uncertainties, such as particle range and set up uncertainties.

Opposed fields reduce uncertainty

Opposed treatment fields, as commonly used in clinical practise with ion beams, were also found to reduce the risk of inaccurate estimates of RBE-weighted dose. By superimposing two opposing RBE profiles the steep gradients in each are smoothed out in the composite profile, resulting in a more uniform distribution of RBE and RBE-weighted dose across the PTV.

A more radical strategy investigated by the researchers was the use of two ion species. "Dual ion fields can help to decrease relative uncertainties in RBE as a function of the field size," said Böhlen. "However, such possible advantages could be more than counter-balanced by the additional treatment complexity and time, as well as by the dilution of the potentially advantageous high-LET component."

In ongoing research, the group is further investigating the efficacy of single and dual ion beam treatment plans, working with protons and helium, carbon and oxygen ions.

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