Figure 3
Generation of RL distributions from FN and PG production data. The figure illustrates the procedures utilized to obtain RL distributions. First, the true FN points of origin in the patient, (a), are mapped onto a 1D histogram along the incident proton beam direction. Examples of such histograms are shown in (b) for true proton beam range shifts of \({0}\,\hbox {mm}\) and \({1}\,\hbox {mm}\) at proton intensities of \(10^8\) and \(10^7\). From these distributions, individual RLs are calculated. Then, sub-sampling bootstrapping is used to obtain a distribution of RLs at varying proton intensities. Example RL distributions are shown in (c) for proton intensities of \(10^8\) and \(10^7\). The distributions get wider at lower proton intensities with a resulting increase in overlapping portions. Although the example illustrates the use of FN data, the procedure is the same for PG data. Note also that the procedure is similar for reconstructed FN and PG distributions with the difference being the mapping of reconstructed FN and PG production distributions in 2D onto a 1D histogram.
