Variable Relative Biological Effectiveness of Protons in the Rat Spinal Cord: Measurements and Comparison With Model Calculations

Purpose

To determine the relative biological effectiveness (RBE) in the rat spinal cord after 6 fractions of protons as a function of linear energy transfer (LET) and dose.

Methods and Materials

The rat spinal cord was irradiated at 4 different positions of a 6 cm spread-out Bragg peak using 6 fractions of protons (LET: 1.4, 2.7, 3.9, and 5.5 keV/µm). Dose-response curves were established for the endpoint paresis grade 2, and the RBE was calculated based on the dose at 50% effect probability. Including data with single and split doses, the measured RBE values were compared with predictions from 4 mechanistic, 3 phenomenological, and 2 patient-derived variable RBE models.

Results

With increasing LET, the dose at 50% effect probability decreased from 51.3 Gy to 43.3 Gy, resulting in a rise in the RBE from 1.11 to 1.32. The biologically equivalent dose decreased markedly between the 2 proximal and 2 distal spinal cord positions, resulting in extrapolated maximum RBE values of up to 1.87 in the limit of zero dose per fraction. The α/β values ranged between 1.5 Gy and 4.2 Gy. At 3.9 and 5.5 keV/µm, the RBE increased with decreasing dose, and at 1.8 Gy per fraction, the RBE was extrapolated to 1.40 and 1.42, respectively. The agreement between predicted and measured RBE varied between the different models.

Conclusions

A fixed RBE of 1.1 provides a good approximation up to the center of the spread-out Bragg peak; however, at 3 mm from the distal end, the RBE increases markedly and may reach values above 1.4 at clinical fraction schedules. Using predictions from a variable RBE model may, therefore, be reasonable; however, the model and model parameters should be carefully selected, ideally as a consensus among the proton therapy centers.