Biomechanical analysis and regional volumetric strain maps

The image-based biomechanical analysis was performed following the approach introduced by our group in previous publications [16, 17]. In brief, the NiftyReg library [18] was employed to perform image registration between aerated-lung masks of EE and EI to obtain the displacements between the expiratory and inspiratory states of the lung. A 3D tetrahedral finite-element mesh was created from the aerated-lung mask at EI for each lung of all subjects. The displacement of the mesh from EE to EI allowed for the calculation of local volumetric strain. The biomechanical approach used in this work has been summarized in non-technical terms elsewhere [2]. Additional file 2: Figure S2 shows a schematic diagram of the sequential steps performed for obtaining the 3D regional lung strain maps, which are indicative of local parenchymal stretching [19, 20]. To allow for regional comparison between groups, lungs in each subject were divided into ten segments with approximately equal volumes along the apical–basal (AB) direction and into ten segments along the dorsal–ventral (DV) direction. By intersecting all AB and DV segments, we constructed a matrix of 10 × 10 regions of interest (ROIs) that are independent of one another. During this procedure, some AB and DV segments did not intersect, and therefore some of the ROIs were void. Weighted mean and standard deviation values of regional volumetric strain were computed for each ROI, where the sample includes tetrahedra contained in each ROI, and weighting is performed according to each tetrahedron volume. The time evolution of the regional volumetric strain at each ROI was studied by means of the regional strain progression index (SPI), defined for each ROI as SPI = (1 + ROI-mean strain at T3)/(1 + ROI-mean strain at T1). We note that SPI is a relative measure of deformation progression. An SPI = 1 implies no evolution of regional strain, an SPI > 1 is related to temporal progression (amplification) of regional strain, and SPI < 1 implies a reduction of regional strain over time. To evaluate the dispersion of regional strain in an ROI, we defined the regional strain heterogeneity index (SHI) as the coefficient of variation of the ROI strain distribution, which is expressed in terms of volumetric change, i.e., SHI = (1 + ROI standard deviation)/(1 + ROI-mean).