Modelling responses of the inert-gas washout and MRI to bronchoconstriction

Abstract

Many lung diseases lead to an increase in ventilation heterogeneity (VH). Two clinical practices for the measurement of patient VH are in vivo imaging, and the inert gas multiple breath washout (MBW). In this study computational modelling was used to compare the responses of MBW indices LCI and s and MRI measured global and local ventilation indices, σ and σ, to constriction of airways in the conducting zone of the lungs. The simulations show that s, LCI and σ behave quite similarly to each other, all being sensitive to increases in the severity of constriction, while exhibiting little sensitivity to the depth at which constriction occurs. In contrast, the local MRI index σ shows strong sensitivity to depth of constriction, but lowered sensitivity to constriction severity. We finish with an analysis of the sensitivity of MRI indices to grid sizes, showing that results should be interpreted with reference to the image resolution. Overall we conclude that the application of both local and global VH measures may help to classify different types of bronchoconstriction.

Modelling structural determinants of ventilation heterogeneity: a perturbative approach

“…The LCI values predicted by model M are low compared to those measured experimentally [38], but similar to those simulated in more detailed airway tree models [17,18]. The phase-III slopes are practically zero in the absence of constrictions, whereas in a healthy lung, airway asymmetry and acinar duct asymmetry both contribute to positive slopes [18].…”

“…The sharp response in simulated MBW indices is due to the inverse-fourth-power dependence of airway resistance (approximated here by Poiseuille flow) to changes in airway radius and has also been observed in studies using image-based models with non-linear pressure-drop relations [13,17]. Using a simple two-component model, we show in S1 File §5 that the ratio r DA /K lung τ (where r DA is the baseline resistance of the lower airways) is crucial to determining the constriction strength required to observe an increase in LCI.…”

“…Inter-regional heterogeneity [16,20]. This response was dominated by the resistance of the constricted airways (see S2 Figure) which resulted in under-ventilation of the affected regions, as well as asynchrony in emptying (see S1 Video and S2 Video).…”

“…According to cast estimates there are on the order of 10 4 − 10 5 branches in the conducting zone [8,9], and on the order of 10 7 including the acinar ducts. There have been numerous approaches to resolve this problem, such as using a symmetric description with an effective diffusion coefficient to account for heterogeneous ventilation [10], compartmental models with asynchronous or asymmetric ventilation [11,12,13], modelling a single heterogeneous acinus [14,15], and replacing the acini with well mixed units or symmetric models reducing the computation to ∼ 10 4 branches [16,17,18,19,20]. Models have considered both heterogeneity in healthy lungs (such that average diameters and lengths converge to the healthy lung data) and pathological heterogeneity (where branches are constricted on average).…”

Spectral graph theory efficiently characterises ventilation heterogeneity in lung airway networks

“…The networks generated are idealised examples of the effects of obstructive lung disease, with different networks for disease centred on proximal (g = 15), central (g = 10), or distal (g = 5) airways. This is similar to constrictions applied in models of CF and asthma [33,34,35]. In the constricted networks, we found that as the number of random constrictions is increased (either by increasing f or reducing g), the number of independent large-eigenvalue modes of the Maury matrix rises (figure 4(a)).…”