Analytical modeling of depth-dose degradation in heterogeneous lung tissue for intensity-modulated proton therapy planning

•Heterogeneous lung tissue causes degradation of pristine proton pencil beams.•A degradation model was implemented into a treatment planning system.•For large tumor volumes, degradation was negligible.•The mean lung dose was not negatively affected in any of the investigated cases.•Small tumor volumes surrounded by lung tissue might get a local target underdose.