Modelling the effect of gravity on inert-gas washout outputs

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

BACKGROUND

Indices of ventilation heterogeneity (VH) from multiple breath washout (MBW) have been shown to correlate well with VH indices derived from hyperpolarised gas ventilation MRI. Here we report the prediction of ventilation distributions from MBW data using a mathematical model, and the comparison of these predictions with imaging data.

METHODS

We developed computer simulations of the ventilation distribution in the lungs to model MBW measurement with 3 parameters: σ_V, determining the extent of VH; V₀, the lung volume; and V_D, the dead-space volume. These were inferred for each individual from supine MBW data recorded from 25 patients with cystic fibrosis (CF) using approximate Bayesian computation. The fitted models were used to predict the distribution of gas imaged by ³He ventilation MRI measurements collected from the same visit.

RESULTS

The MRI indices measured (I_1/3, the fraction of pixels below one-third of the mean intensity and I_CV, the coefficient of variation of pixel intensity) correlated strongly with those predicted by the MBW model fits (r=0.93,0.88 respectively). There was also good agreement between predicted and measured MRI indices (mean bias ± limits of agreement: I_1/3:-0.003±0.118 and I_CV:-0.004±0.298). Fitted model parameters were robust to truncation of MBW data.

CONCLUSION

We have shown that the ventilation distribution in the lung can be inferred from an MBW signal, and verified this using ventilation MRI. The Bayesian method employed extracts this information with fewer breath cycles than required for LCI, reducing acquisition time required, and gives uncertainty bounds, which are important for clinical decision making.

In asthma positive phase III slopes result from structural heterogeneity of the bronchial tree

We have previously identified bronchial generations 5-7 as the locus of maximum contribution to the convective portion of the phase III slope in CT-based lung models of asthma patients. In the present study, we examined how exactly phase III slope is generated locally, by specifically interrogating at individual branch points, the necessary condition for a phase III slope to occur : some degree of convective flow sequencing between any two daughter branches that have a heterogeneity in gas washout concentration between them. Flow sequencing at individual branch points showed a wide range of values, including branch points where flow sequencing was such that phase III slopes were negative locally. Yet, the net effect in the 24 bronchial trees that we studied was that flow sequencing between least and best ventilated units was of the correct sign to generate a positive phase III slope in generations 5-7. By investigating the link of local flow sequencing between any two daughter branches to the corresponding heterogeneity of mechanical lung properties, heterogeneity of compliance was seen to be a major determinant of flow sequencing. In these structures bronchial structures, compliance heterogeneity was essentially brought about by volume asymmetry resulting from terminating pathways within the 3D confines of the lung contours. We conclude that the serial and parallel combination of lung mechanical properties at individual branch points in an asymmetrical branching network generate flow sequencing in mid-range conductive airways, so as to obtain positive at-mouth phase III slopes.

Various reduced-order surrogate models for fluid flow and mass transfer in human bronchial tree

The bronchial tree plays a main role in the human respiratory system because the air distribution throughout the lungs and gas exchange with blood occur in the airways whose dimensions vary from several centimeters to micrometers. Organization of about 60,000 conducting airways and 33 million respiratory airways in a limited space results in a complex structure. Due to this inherent complexity and a high number of airways, using target-oriented dimensional reduction is inevitable. In addition, there is no general reduced-order model for various types of problems. This necessitates coming up with an appropriate model from a variety of different reduced-order models to solve the desired problem. Lumped formulation, trumpet, or typical path model of whole or parts of bronchial tree are frequently used reduced-order models. On the other hand, using any of these models results in underestimation of flow heterogeneity leading to inaccurate prediction of the systems whose mechanisms depend on the fluid heterogeneity. In this study, a simple robust model combining mechanistic and non-mechanistic modeling approaches of the bronchial tree is proposed which overcomes the limitations of the previous reduced-order models and gives the same results of a detailed mechanistic model for the first time. This model starts from an accurate multi-branching model of conducting and respiratory airways (i.e., the base model) and suggests a proxy model of conducting airway and reduced-order model of respiratory airways based on the base model to significantly reduce computational cost while retaining the accuracy. The combination of these models suggests various reduced-order surrogate models of the human bronchial tree for different problems. The applications and limitations of each reduced-order model are also discussed. The accuracy of the proposed model in the prediction of fluid heterogeneity has been examined by the simulation of multi-breath inert gas washout because the alveolar slope is the reflection of fluid heterogeneity where the computational time decreases from 121 h (using the base model) to 4.8 s (using the reduced-order model). A parallel strategy for solving the equations is also proposed which decreases run time by 0.18 s making the model suitable for real-time applications. Furthermore, the ability of the model has been evaluated in the modeling of asthmatic lung as an instance of abnormal lungs, and in the modeling of O2-CO2 exchange as an instance of nonlinear reacting systems. The results indicate that the proposed model outperforms previous models based on accuracy, robustness, and run time.

Ventilation heterogeneity imaged by multibreath wash-ins of hyperpolarized 3 He and 129 Xe in healthy rabbits

KEY POINTS

Multibreath imaging to estimate regional gas mixing efficiency is superior to intensity-based single-breath ventilation markers, as it is capable of revealing minute but essential measures of ventilation heterogeneity which may be sensitive to subclinical alterations in the early stages of both obstructive and restrictive respiratory disorders. Large-scale convective stratification of ventilation in central-to-peripheral directions is the dominant feature of observed ventilation heterogeneity when imaging a heavy/less diffusive xenon gas mixture; smaller-scale patchiness, probably originating from asymmetric lung function at bronchial airway branching due to the interaction of convective and diffusive flows, is the dominant feature when imaging a lighter/more diffusive helium gas mixture. Since detecting low regional ventilation is crucial for characterizing diseased lungs, our results suggest that dilution with natural abundance helium and imaging at higher lung volumes seem advisable when imaging with hyperpolarized ¹²⁹ Xe; this will allow the imaging gas to reach slow-filling and/or non-dependent lung regions, which might otherwise be impossible to distinguish from total ventilation shunt regions. The ability to differentiate these regions from those of total shunt is worse with typical single-breath imaging techniques.

ABSTRACT

The mixing of freshly inhaled gas with gas already present in the lung can be directly assessed with heretofore unachievable precision via magnetic resonance imaging of signal build-up resulting from multiple wash-ins of a hyperpolarized (HP) gas. Here, we used normoxic HP ³ He and ¹²⁹ Xe mixtures to study regional ventilation at different spatial scales in five healthy mechanically ventilated supine rabbits at two different inspired volumes. To decouple the respective effects of density and diffusion rates on ventilation heterogeneity, two additional studies were performed: one in which ³ He was diluted with an equal fraction of natural abundance xenon, and one in which ¹²⁹ Xe was diluted with an equal fraction of ⁴ He. We observed systematic differences in the spatial scale of specific ventilation heterogeneity between HP ³ He and ¹²⁹ Xe. We found that large-scale, central-to-peripheral convective ventilation inhomogeneity is the dominant cause of observed heterogeneity when breathing a normoxic xenon gas mixture. In contrast, small-scale ventilation heterogeneity in the form of patchiness, probably originating from asymmetric lung function at bronchial airway branching due to interactions between convective and diffusive flows, is the dominant feature when breathing a normoxic helium gas mixture, for which the critical zone occurs more proximally and at an imageable spatial scale. We also showed that the existence of particular underventilated non-dependent lung regions when breathing a heavy gas mixture is the result of the density of that mixture - rather than, for example, its diffusion rate or viscosity. Finally, we showed that gravity-dependent ventilation heterogeneity becomes substantially more uniform at higher inspired volumes for xenon gas mixtures compared to helium mixtures.

Proning reduces ventilation heterogeneity in patients with elevated BMI: implications for COVID-19 pneumonia management?

Coronavirus disease 2019 (COVID-19) is caused by a novel zoonotic coronavirus known as severe acute respiratory syndrome coronavirus 2 and has been identified as a pandemic by the World Health Organization (WHO) [1]. Several risk factors have been identified for severe COVID-19-associated pneumonia, with obesity identified as a significant and independent risk factor for death [2].

Simulations of patient-based lungs suggest that proning reduces ventilation heterogeneity in overweight and obese subjects but increases heterogeneity in non-overweight subjects. This suggests proning may be beneficial for overweight #COVID19 patients.https://bit.ly/2MfCiyk

Unraveling Disease Pathophysiology with Mathematical Modeling

Modeling has enabled fundamental advances in our understanding of the mechanisms of health and disease for centuries, since at least the time of William Harvey almost 500 years ago. Recent technological advances in molecular methods, computation, and imaging generate optimism that mathematical modeling will enable the biomedical research community to accelerate its efforts in unraveling the molecular, cellular, tissue-, and organ-level processes that maintain health, predispose to disease, and determine response to treatment. In this review, we discuss some of the roles of mathematical modeling in the study of human physiology and pathophysiology and some challenges and opportunities in general and in two specific areas: in vivo modeling of pulmonary function and in vitro modeling of blood cell populations.