Multivariate statistical modelling enhances the predictive power of Prompt Gamma-Ray Timing for proton treatment verification

Given its sensitivity to anatomical variations, proton therapy is expected to benefit strongly from reliable on-line treatment verification. As a light-weight, collimator-free technique that can be easily integrated into existing systems, Prompt Gamma-Ray Timing is a promising candidate for this purpose. The development of such a system is challenging, as the proton range delivered in the patient needs to be reconstructed with high accuracy from the temporal distribution of a very limited number of gamma-rays. So far, this reconstruction has been based on the mean and standard deviation of the distribution, but the accuracy of this method was found to be insufficient. We therefore developed multivariate statistical models based on additional histogram characteristics to improve proton range reconstruction.

Prompt Gamma-Ray Timing distributions acquired during pencil beam irradiation of an acrylic glass phantom with air cavities of different thicknesses were analysed. Relevant histogram features were chosen using forward selection and the Least Absolute Shrinkage and Selection Operator (LASSO) from a feature assortment based on recommendations of the Image Biomarker Standardisation Initiative. Candidate models were defined by multivariate linear regression and evaluated based on their coefficient of determination R2 and root mean square error RMSE on an independent dataset.

The newly developed models showed a strongly improved predictive power (R2 > 0.6) compared to the previously used models (R2 < 0.1). These results demonstrate that elaborate statistical modelling is a valuable tool to enhance the Prompt Gamma-Ray Timing method and increase its potential to be used for proton treatment verification.