Spectral graph theory efficiently characterizes ventilation heterogeneity in lung airway networks

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 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.

Locating Nidi for High-Frequency Chest Wall Oscillation Smart Therapy via Acoustic Imaging of Lung Airways as a Spatial Network

“…2(b). The airway network is then resolved by the acoustic pressure at each segment induced by the pressure distribution from bronchi breathing and the airway network [24], [25]. Merging the acoustic power over a predetermined period of time during each breathing cycle, a plane image is generated by the projected network as a subset of the acoustic lung image Q(x, y) ∈ ℝ m×n (discussed in Section III-C).…”

“…3, and ( 1)-( 5). Thus, we have the following annotation shown in ( 6) from the theory of network topology [24], [25].…”

Model-based Bayesian inference of the ventilation distribution in patients with Cystic Fibrosis from multiple breath washout, with comparison to ventilation MRI

“…Future refinement will be required to include more realistic acinar mixing effects and lung mechanics. To achieve this in a computationally efficient way, we may need to employ new approaches to dimensionality reduction 49 and homogenisation 50 of acinar and airway transport simulations. The Bayesian framework laid out here will also aid in these developments, since Bayesian model selection 32 (which the algorithm 51 is programmed to perform) can be used to compare the ability of different models to adequately explain the data independently of external verification.…”

The role of mathematical models in designing mechanopharmacological therapies for asthma

“…Recently graph-theoretic perspectives have proven useful in characterizing transport in various examples of biological networks. Whitfield et al (2020) use concepts from spectral graph theory to demonstrate that the resistive properties of realistic tree networks are characterized by a tree-specific operator called the Maury matrix, first introduced in (Maury, 2013) which provides a complete description of linear resistance relations on the network. They demonstrate how ventilation heterogeneity can be evaluated for four realistic airway network models (based on CT imaging) and how the Maury operator efficiently captures spatial patterns of ventilation heterogeneity, providing a new method for dimensionality reduction in these systems.…”