Spectral graph theory efficiently characterizes ventilation heterogeneity in lung airway networks

This paper introduces a linear operator for the purposes of quantifying the spectral properties of transport within resistive trees, such as airflow in lung airway networks. The operator, which we call the Maury matrix, acts only on the terminal nodes of the tree and is equivalent to the adjacency matrix of a complete graph summarizing the relationships between all pairs of terminal nodes. We show that the eigenmodes of the Maury operator have a direct physical interpretation as the relaxation, or resistive, modes of the network. We apply these findings to both idealized and image-based models of ventilation in lung airway trees and show that the spectral properties of the Maury matrix characterize the flow asymmetry in these networks more concisely than the Laplacian modes, and that eigenvector centrality in the Maury spectrum is closely related to the phenomenon of ventilation heterogeneity caused by airway narrowing or obstruction. This method has applications in dimensionality reduction in simulations of lung mechanics, as well as for characterization of models of the airway tree derived from medical images.

Spectral graph theory efficiently characterises ventilation heterogeneity in lung airway networks

This paper introduces a linear operator for the purposes of quantifying the spectral properties of transport within resistive trees, such as airflow in lung airway networks. The operator, which we call the Maury matrix, acts only on the terminal nodes of the tree and is equivalent to the adjacency matrix of a complete graph summarising the relationships between all pairs of terminal nodes. We show that the eigenmodes of the Maury operator have a direct physical interpretation as the relaxation, or resistive, modes of the network. We apply these findings to both idealised and image-based models of ventilation in lung airway trees and show that the spectral properties of the Maury matrix characterise the flow asymmetry in these networks more concisely than the Laplacian modes, and that eigenvector centrality in the Maury spectrum is closely related to the phenomenon of ventilation heterogeneity caused by airway narrowing or obstruction. This method has applications in dimensionality reduction in simulations of lung mechanics, as well as for characterisation of models of the airway tree derived from medical images.

Directional preference of airway smooth muscle mass increase in human asthmatic airways

Airway smooth muscle (ASM) orientation and morphology determine the ability of the muscle to constrict the airway. In asthma, ASM mass is increased, but it is unknown whether ASM orientation and morphology are altered as well or whether the remodeling at the source of the mass increase is ongoing. We dissected human airway trees from asthmatic and control lungs. Stained, intact airway sections were imaged in axial projection to show ASM bundle orientation, whereas cross-sectional histological slides were used to assess ASM area, bundle thickness, and ASM bundle-to-basement membrane distance. We also used these slides to assess cell size, proliferation, and apoptosis. We showed that ASM mass increase in cartilaginous airways is primarily the result of an increase of ASM bundle thickness (as measured radially in an airway cross section) and coincides with an increased distance of the ASM bundles to the airway perimeter. ASM orientation was unchanged in all airways. Apoptosis markers and cell size did not show differences between asthmatics and controls. Our findings show that ASM mass increase likely contributes to the airway-constricting capacity of the muscle. Both the increased bundle thickness and increased thickness of the airway wall inwards of the ASM bundles could further enhance this capacity. Turnover of ASM appears to be the same in airways and biopsies, but the lack of correlation between different markers of proliferation casts doubt on the specificity of markers generally used to assess proliferation.

A Conjugate Fluid–Porous Approach for Simulating Airflow in Realistic Geometric Representations of the Human Respiratory System

Simulation of flow in the human lung is of great practical interest as a means to study the detailed flow patterns within the airways for many physiological applications. While computational simulation techniques are quite mature, lung simulations are particularly complicated due to the vast separation of length scales between upper airways and alveoli. Many past studies have presented numerical results for truncated airway trees, however, there are significant difficulties in connecting such results with respiratory airway models. This article presents a new modeling paradigm for flow in the full lung, based on a conjugate fluid–porous formulation where the upper airway is considered as a fluid region with the remainder of the lung being considered as a coupled porous region. Results are presented for a realistic lung geometry obtained from computed tomography (CT) images, which show the method's potential as being more efficient and practical than attempting to directly simulate flow in the full lung.