Spatial patterns and frequency distributions of regional deformation in the healthy human lung

Understanding regional deformation in the lung has long attracted the medical community, as parenchymal deformation plays a key role in respiratory physiology. Recent advances in image registration make it possible to noninvasively study regional deformation, showing that volumetric deformation in healthy lungs follows complex spatial patterns not necessarily shared by all subjects, and that deformation can be highly anisotropic. In this work, we systematically study the regional deformation in the lungs of eleven human subjects by means of in vivo image-based biomechanical analysis. Regional deformation is quantified in terms of 3D maps of the invariants of the right stretch tensor, which are related to regional changes in length, surface and volume. Based on the histograms of individual lungs, we show that log-normal distributions adequately represent the frequency distribution of deformation invariants in the lung, which naturally motivates the normalization of the invariant fields in terms of the log-normal score. Normalized maps of deformation invariants allow for a direct intersubject comparison, as they display spatial patterns of deformation in a range that is common to all subjects. For the population studied, we find that lungs in supine position display a marked gradient along the gravitational direction not only for volumetric but also for length and surface regional deformation, highlighting the role of gravity in the regional deformation of normal lungs under spontaneous breathing.