Whitfield, C.A. orcid.org/0000-0001-5913-735X, Latimer, P., Horsley, A. orcid.org/0000-0003-1828-0058 et al. (3 more authors) (Submitted: 2020) Spectral graph theory efficiently characterises ventilation heterogeneity in lung airway networks. [Preprint - bioRxiv] (Submitted)
Abstract
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.
Metadata
Item Type: | Preprint |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 The Author(s). This preprint is made available under the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Lung; Respiratory |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > Department of Infection, Immunity and Cardiovascular Disease The University of Sheffield > Faculty of Medicine, Dentistry and Health (Sheffield) > School of Medicine and Population Health |
Funding Information: | Funder Grant number MEDICAL RESEARCH COUNCIL MR/M008894/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 07 Sep 2023 16:02 |
Last Modified: | 07 Sep 2023 16:04 |
Published Version: | http://dx.doi.org/10.1101/2020.04.15.042416 |
Status: | Submitted |
Publisher: | Cold Spring Harbor Laboratory |
Identification Number: | 10.1101/2020.04.15.042416 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202832 |
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Licence: CC-BY-NC-ND 4.0