[en] Purpose: To develop a 4D treatment optimization approach for Pencil Beam Scanned (PBS) proton therapy that includes breathing variability. Method: PBS proton therapy delivers a pattern of proton pencil beams (PBs), distributed to cover the target volume and optimized such as to achieve a homogenous dose distribution across the target. In this work, this optimization step has been enhanced to include advanced 4D dose calculations of liver tumors based on motion extracted from either 4D-CT (representing a single and averaged respiratory cycle) or 4D-CT(MRI) (including breathing variability). The 4D dose calculation is performed per PB on deforming dose grid, and according to the timestamp of each PB, a displacement due to patient’s motion and a change in radiological depth.Three different treatment fields have been optimized in 3D on the end-exhale phase of a 4D-CT liver data set (3D-opt) and then in 4D using the motion extracted from either 4D-CT or 4D-CT(MRI) using deformable image registration. All plans were calculated directly on the PTV without the use of an ITV. The delivery characteristics of the PSI Gantry 2 have been assumed for all calculations. Results: Dose inhomogeneities (D5-D95) in the CTV for the 3D optimized plans recalculated under conditions of variable motion were increased by on average 19.8% compared to the static case. These differences could be reduced by 4D-CT based 4D optimization to 10.5% and by 4D-CT(MRI) based optimization to only 2.3% of the static value. Liver V25 increased by less than 1% using 4D optimization. Conclusion: 4D optimized PBS treatment plans taking into account breathing variability provide for significantly improved robustness against motion and motion variability than those based on 4D-CT alone, and may negate the need of motion specific target expansions. Swiss National Fund Grant (320030-1493942-1)