Quantification of the uncertainties of a biological model and their impact on variable RBE proton treatment plan...

In proton radiation therapy, a relative biological effectiveness (RBE) equal to 1.1 is currently assumed, although biological experiments show that it is not constant. The purpose of this study was to quantify the uncertainties of a published biological model and explore their impact on variable RBE treatment plan (TP) optimization.

Two patient cases with a high and a low (α/β)_x tumor were investigated. Firstly, intensity modulated proton therapy TPs assuming constant RBE were derived, and subsequently the variable RBE weighted dose (RWD), including the uncertainty originating in the fit to the experimental data and the uncertainty of the (α/β)_x, were calculated. Secondly, TPs optimized for uniform biological effect assuming a variable RBE were created using the worst case tissue specific (α/β)_x.

For the nasopharyngeal cancer patient, the uncertainty of (α/β)_x corresponded to a CTV D₉₈ confidence interval (CI) of (-2, +4)% while for the fit parameter CI was (-2,+1)%. For the standard fractionation prostate case the (α/β)_x CI was (-7,+5)% and the fit parameter CI was (-3,+3)%. For the hypofractionated case both CIs were (-1,+1)%. In both patient cases, the RBE in most organs at risk (OARs) was significantly underestimated by the constant RBE approximation, whereas the situation was not as definite in the target volumes. Overdosage of OARs was reduced by using the biological effect optimization.

For the two patient cases, the RWD uncertainty from the fit parameter in the biological model contributed non-negligibly to the total uncertainty, depending on the patient case and the organ. The presented optimization strategy is a basic method for robust biological effect optimization to reduce potential consequences caused by the (α/β)_x uncertainty.