Using state-of-the-art X-ray tomographic microscopy we can image lung tissue in three dimensions in intact animals down to a micrometer precision. The structural complexity and hierarchical branching scheme of the lung at this level of details, however, renders the extraction of biologically relevant quantities particularly challenging. We have developed a methodology for a detailed description of lung inflation patterns by measuring the size and the local curvature of the parenchymal airspaces. These quantitative tools for morphological and topological analyses were applied to high-resolution murine 3D lung image data, inflated at different pressure levels under immediate post mortem conditions. We show for the first time direct indications of heterogeneous intra-lobar and inter-lobar distension patterns at the alveolar level. Furthermore, we did not find any indication that a cyclic opening-and-collapse (recruitment) of a large number of alveoli takes place.