Researchers based in the US and Germany have published a paper in the Red Journal that details a multiscale approach to modelling the RBE of heavy ions. The results show the magnitude of spatial variation in RBE that can occur under clinically relevant conditions and highlight opportunities for the individualization of cancer treatments (Int. J. Radiat. Oncol. Biol. Phys. doi: 10.1016/j.ijrobp.2011.06.1983).

"The same physical dose delivered with different types of radiation will produce very different biological responses," David Carlson, an assistant professor at the Yale University School of Medicine (New Haven, CT), told medicalphysicsweb. "Radiobiological models provide a method to guide the optimization of physical dose to more effectively kill cancer cells and reduce damage to normal tissues."

Modelling methods

The foundation of the work carried out by Carlson and colleagues is the repair-misrepair-fixation (RMF) model. Developed by Carlson and his collaborator Robert Stewart at the University of Washington (Seattle, WA), the RMF model links reproductive cell death to the induction and biological processing of DNA double-strand breaks (DSBs).

"The RMF model incorporates the probability that a single particle track creates two separate DSBs, which in turn create an intra-track exchange-type chromosome aberration," commented Carlson. "The frequency of these events increases with increasing particle linear energy transfer (LET), so they become more important for heavy ions. The increase in intra-track exchanges with increasing LET is a distinguishing feature of our RBE model."

To reduce the number of ad hoc parameters, the team used the independently tested Monte Carlo Damage Simulation software (Radiat. Res. 176 587) to quantify the DSB yield as a function of particle type and energy.

"Formulas linking the α and β radiosensitivity parameters within the linear quadratic model to DSB induction and processing are then derived from the RMF model," explained Carlson. "The RMF model tells us how α and β change as we increase with depth in tissue, as a function of the radiation type and energy."

Validation and clinical application

To validate this approach, the team used an existing in vitro colony survival assay data set showing how three cell lines respond to three different radiation types: helium-3, carbon-12 and neon-20. The model predicted the observed trends in the measured data. Importantly, this process did not involve any model fitting to the data set.

Having shown that the method works well for measured conditions in vitro, the next step was to see what the model predicted for clinically relevant scenarios. The researchers considered a single pristine Bragg peak, as well as 17 individual pristine Bragg peaks spaced 3 mm apart, giving a 5 cm SOBP. For the same physical dose, the researchers predicted the number of DSBs for protons and carbon ions and used the RMF model to generate dose-averaged α and β parameters.

Using this information, they calculated RBE-weighted dose – a physical dose weighted for the biological effect of the particle type. For both protons and carbon ions, the RBE-weighted dose was found to increase from the proximal to the distal edge of the SOBP.

The authors found that for doses from 0.5–10 Gy, proton RBE values ranged from 1.02 at the proximal edge to 1.4 at the distal edge of the SOBP. For the same dose range, the RBE values for carbon ions were 1.5 and 6.7 from the proximal to distal edge, respectively.

"Clinically, it appears reasonable to assume an RBE of 1.1 for protons, but there is an opportunity to exploit these RBE effects and further optimize proton therapy plans," said Carlson. "Nobody debates that we have to take these effects into account for carbon ions. Our results suggest we should also consider this approach in proton radiotherapy."