“…Especially for pencil beam scanned (PBS) proton therapy, the interplay between the patient's motion and the dynamic beam delivery can result in complex dose degradation with dose inhomogeneities occurring within the target (Phillips et al 1992, Bert et al 2008. Using 4D dose calculations (4DDC), the dosimetric effects of motion on the planned dose distributions have been comprehensively investigated in various simulation studies (Bert et al 2008, Seco et al 2009, Zhang et al 2012, Grassberger et al 2013, Ammazzalorso and Jelen 2014, Zou et al 2014, Batista et al 2018, Dolde et al 2019, Meijers et al 2020, Steinsberger et al 2021, Lebbink et al 2022. The effectiveness of different motion mitigation techniques, such as breath hold, beam gating, rescanning and tracking, have also been analyzed extensively (Li et al 2006, Bert and Rietzel 2007, Knopf et al 2011, Grassberger et al 2015, Zhang et al 2015, Gorgisyan et al 2017, Ishihara et al 2017, Engwall et al 2018, Dolde et al 2019, Gorgisyan et al 2019.…”