An Automated Self‐Similarity Analysis of the Pulmonary Tree of the Sprague–Dawley Rat

Abstract

We present the results of an automated analysis of the morphometry of the pulmonary airway trees of the Sprague-Dawley rat. Our work is motivated by a need to inform lower-dimensional mathematical models to prescribe realistic boundary conditions for multiscale hybrid models of rat lung mechanics. Silicone casts were made from three age-matched, male Sprague-Dawley rats, immersed in a gel containing a contrast agent and subsequently imaged with magnetic resonance (MR). From a segmentation of this data, we extracted a connected graph, representing the airway centerline. Segment statistics (lengths and diameters) were derived from this graph. To validate this MR imaging/digital analysis method, airway segment measurements were compared with nearly 1,000 measurements collected by hand using an optical microscope from one of the rat lung casts. To evaluate the reproducibility of the MR imaging/digital analysis method, two lung casts were each imaged three times with randomized orientations in the MR bore. Diameters and lengths of randomly selected airways were compared among each of the repeated imaging datasets to estimate the variability. Finally, we analyzed the morphometry of the airway tree by assembling individual airway segments into structures that span multiple generations, which we call branches. We show that branches not segments are the fundamental repeating unit in the rat lung and develop simple mathematical relationships describing these structures for the entire lung. Our analysis shows that airway diameters and lengths have both a deterministic and stochastic character.