A multi-scale model of gas transport in the lung to study heterogeneous lung ventilation during the multiple-breath washout test

Investigation of inert gas washout methods in a new numerical model based on an electrical analogy

Inert gas washout methods have been shown to detect pathological changes in the small airways that occur in the early stages of obstructive lung diseases such as asthma and COPD. Numerical lung models support the analysis of characteristic washout curves, but are limited in their ability to simulate the complexity of lung anatomy over an appropriate time period. Therefore, the interpretation of patient-specific washout data remains a challenge. A new numerical lung model is presented in which electrical components describe the anatomical and physiological characteristics of the lung as well as gas-specific properties. To verify that the model is able to reproduce characteristic washout curves, the phase 3 slopes (S3) of helium washouts are simulated using simple asymmetric lung anatomies consisting of two parallel connected lung units with volume ratios of1.25 0.75 ,1.50 0.50 , and1.75 0.25 and a total volume flow of 250 ml/s which are evaluated for asymmetries in both the convection- and diffusion-dominated zone of the lung. The results show that the model is able to reproduce the S3 for helium and thus the processes underlying the washout methods, so that electrical components can be used to model these methods. This approach could form the basis of a hardware-based real-time simulator.

Investigation of tracer gas transport in a new numerical model of lung acini

Obstructive pulmonary diseases are associated with considerable morbidity. For an early diagnosis of these diseases, inert gas washouts can potentially be used. However, the complex interaction between lung anatomy and gas transport mechanisms complicates data analysis. In order to investigate this interaction, a numerical model, based on the finite difference method, consisting of two lung units connected in parallel, was developed to simulate the tracer gas transport within the human acinus. Firstly, the geometries of the units were varied and the diffusion coefficients (D) were kept constant. Secondly, D was changed and the geometry was kept constant. Furthermore, simple monoexponential growth functions were applied to evaluate the simulated data. In 109 of the 112 analyzed curves, monoexponential function matched simulated data with an accuracy of over 90%, potentially representing a suitable numerical tool to predict transport processes in further model extensions. For total flows greater than 5 × 10−4 ml/s, the exponential growth constants increased linearly with linear increasing flow to an accuracy of over 95%. The slopes of these linear trend lines of 1.23 µl−1 (D = 0.6 cm2/s), 1.69 µl−1 (D = 0.3 cm2/s), and 2.25 µl−1 (D = 0.1 cm2/s) indicated that gases with low D are more sensitive to changes in flows than gases with high D.

Graphical abstract

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways

The complexity of the human respiratory system causes that one of the main methods of analyzing the dynamic pulmonary phenomena and interpreting experimental results are simulations of its computational models. Among the most compound elements of these models, apart from the bronchial tree structure, is the phenomenon of flow limitation in flexible bronchi, which causes them to collapse with increasing flow, thus their properties, such as resistance, compliance and inertance, are highly nonlinear and time-varying. Commonly, this phenomenon is ignored, or a distributed model for the airway pressure drop is applied, simulated with a modified numerical solver of this differential equation (ODE). The disadvantages of this solution are the problems with taking into account the inherent singularity of the model and the long computation time due to iterative nature of the ODE procedure. The aim of the work was to derive an algebraic approximation of this distributed model, suitable for implementation in continuous dynamic models, to validate it by comparing the results of simulations with the respiratory system model including approximate and original (ODE solver) numerical procedures, as well as to evaluate possible acceleration of calculations. All simulations, including spontaneous breathing, mechanical ventilation with the optimal ventilatory waveform and forced expiration, proved that algebraic approximation yielded results negligibly differing from the ODE solution, and shortened the computation time by an order. The proposed approach is an attractive alternative in the case of computer implementations of pulmonary models, where simulations of flows and pressures in the complex respiratory system are of primary importance.

Compromised Cardiopulmonary Function in Fibulin-5 Deficient Mice

Competent elastic fibers are critical to the function of the lung and right circulation. Murine models of elastopathies can aid in understanding the functional roles of the elastin and elastin-associated glycoproteins that constitute elastic fibers. Here, we quantify together lung and pulmonary arterial structure, function, and mechanics with right heart function in a mouse model deficient in the elastin-associated glycoprotein fibulin-5. Differences emerged as a function of genotype, sex, and arterial region. Specifically, functional studies revealed increased lung compliance in fibulin-5 deficiency consistent with a histologically observed increased alveolar disruption. Biaxial mechanical tests revealed that the primary branch pulmonary arteries exhibit decreased elastic energy storage capacity and wall stress despite only modest differences in circumferential and axial material stiffness in the fibulin-5 deficient mice. Histological quantifications confirm a lower elastic fiber content in the fibulin-5 deficient pulmonary arteries, with fragmented elastic laminae in the outer part of the wall - likely the reason for reduced energy storage. Ultrasound measurements confirm sex differences in compromised right ventricular function in the fibulin-5 deficient mice. These results reveal compromised right heart function, but opposite effects of elastic fiber dysfunction on the lung parenchyma (significantly increased compliance) and pulmonary arteries (trend toward decreased distensibility), and call for further probing of ventilation-perfusion relationships in pulmonary pathologies. Amongst many other models, fibulin-5 deficient mice can contribute to our understanding of the complex roles of elastin in pulmonary health and disease.

Towards a multi-scale computer modeling workflow for simulation of pulmonary ventilation in advanced COVID-19

Physics-based multi-scale in silico models offer an excellent opportunity to study the effects of heterogeneous tissue damage on airflow and pressure distributions in COVID-19-afflicted lungs. The main objective of this study is to develop a computational modeling workflow, coupling airflow and tissue mechanics as the first step towards a virtual hypothesis-testing platform for studying injury mechanics of COVID-19-afflicted lungs. We developed a CT-based modeling approach to simulate the regional changes in lung dynamics associated with heterogeneous subject-specific COVID-19-induced damage patterns in the parenchyma. Furthermore, we investigated the effect of various levels of inflammation in a meso-scale acinar mechanics model on global lung dynamics. Our simulation results showed that as the severity of damage in the patient's right lower, left lower, and to some extent in the right upper lobe increased, ventilation was redistributed to the least injured right middle and left upper lobes. Furthermore, our multi-scale model reasonably simulated a decrease in overall tidal volume as the level of tissue injury and surfactant loss in the meso-scale acinar mechanics model was increased. This study presents a major step towards multi-scale computational modeling workflows capable of simulating the effect of subject-specific heterogenous COVID-19-induced lung damage on ventilation dynamics.

Using a Human Circulation Mathematical Model to Simulate the Effects of Hemodialysis and Therapeutic Hypothermia

Background: We developed a hemodynamic mathematical model of human circulation coupled to a virtual hemodialyzer. The model was used to explore mechanisms underlying our clinical observations involving hemodialysis. Methods: The model consists of whole body human circulation, baroreflex feedback control, and a hemodialyzer. Four model populations encompassing baseline, dialysed, therapeutic hypothermia treated, and simultaneous dialysed with hypothermia were generated. In all populations atrial fibrillation and renal failure as co-morbidities, and exercise as a treatment were simulated. Clinically relevant measurables were used to quantify the effects of each in silico experiment. Sensitivity analysis was used to uncover the most relevant parameters. Results: Relative to baseline, the modelled dialysis increased the population mean diastolic blood pressure by 5%, large vessel wall shear stress by 6%, and heart rate by 20%. Therapeutic hypothermia increased systolic blood pressure by 3%, reduced large vessel shear stress by 15%, and did not affect heart rate. Therapeutic hypothermia reduced wall shear stress by 15% in the aorta and 6% in the kidneys, suggesting a potential anti-inflammatory benefit. Therapeutic hypothermia reduced cardiac output under atrial fibrillation by 12% and under renal failure by 20%. Therapeutic hypothermia and exercise did not affect dialyser function, but increased water removal by approximately 40%. Conclusions: This study illuminates some mechanisms of the action of therapeutic hypothermia. It also suggests clinical measurables that may be used as surrogates to diagnose underlying diseases such as atrial fibrillation.

Pulmonary acini exhibit complex changes during postnatal rat lung development

Pulmonary acini represent the functional gas-exchanging units of the lung. Due to technical limitations, individual acini cannot be identified on microscopic lung sections. To overcome these limitations, we imaged the right lower lobes of instillation-fixed rat lungs from postnatal days P4, P10, P21, and P60 at the TOMCAT beamline of the Swiss Light Source synchrotron facility at a voxel size of 1.48 μm. Individual acini were segmented from the three-dimensional data by closing the airways at the transition from conducting to gas exchanging airways. For a subset of acini (N = 268), we followed the acinar development by stereologically assessing their volume and their number of alveoli. We found that the mean volume of the acini increases 23 times during the observed time-frame. The coefficients of variation dropped from 1.26 to 0.49 and the difference between the mean volumes of the fraction of the 20% smallest to the 20% largest acini decreased from a factor of 27.26 (day 4) to a factor of 4.07 (day 60), i.e. shows a smaller dispersion at later time points. The acinar volumes show a large variation early in lung development and homogenize during maturation of the lung by reducing their size distribution by a factor of 7 until adulthood. The homogenization of the acinar sizes hints at an optimization of the gas-exchange region in the lungs of adult animals and that acini of different size are not evenly distributed in the lungs. This likely leads to more homogeneous ventilation at later stages in lung development.

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.

Hypoxic pulmonary vasoconstriction as a regulator of alveolar-capillary oxygen flux: A computational model of ventilation-perfusion matching

The relationship between regional variabilities in airflow (ventilation) and blood flow (perfusion) is a critical determinant of gas exchange efficiency in the lungs. Hypoxic pulmonary vasoconstriction is understood to be the primary active regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply. However, it is not understood how the integrated action of hypoxic pulmonary vasoconstriction affects oxygen transport at the system level. In this study we develop, and make functional predictions with a multi-scale multi-physics model of ventilation-perfusion matching governed by the mechanism of hypoxic pulmonary vasoconstriction. Our model consists of (a) morphometrically realistic 2D pulmonary vascular networks to the level of large arterioles and venules; (b) a tileable lumped-parameter model of vascular fluid and wall mechanics that accounts for the influence of alveolar pressure; (c) oxygen transport accounting for oxygen bound to hemoglobin and dissolved in plasma; and (d) a novel empirical model of hypoxic pulmonary vasoconstriction. Our model simulations predict that under the artificial test condition of a uniform ventilation distribution (1) hypoxic pulmonary vasoconstriction matches perfusion to ventilation; (2) hypoxic pulmonary vasoconstriction homogenizes regional alveolar-capillary oxygen flux; and (3) hypoxic pulmonary vasoconstriction increases whole-lobe oxygen uptake by improving ventilation-perfusion matching.

The relationship between regional ventilation (airflow) and perfusion (blood flow) is a major determinant of gas exchange efficiency. Atelactasis and pulmonary vascular occlusive diseases, such as acute pulmonary embolism, are characterized by ventilation-perfusion mismatching and decreased oxygen in the bloodstream. Despite the physiological and medical importance of ventilation-perfusion matching, there are gaps in our knowledge of the regulatory mechanisms that maintain adequate gas exchange under pathological and normal conditions. Hypoxic pulmonary vasoconstriction is understood to be the primary regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply, yet it is not understood how this mechanism affects oxygen transport at the system level. In this study we present a computational model of the ventilation-perfusion matching and hypoxic pulmonary vasoconstriction to better understand how physiological regulation at the regional level scales to affect oxygen transport at the system level. Our model simulations predict that this regulatory mechanism improves the spatial overlap of airflow and blood flow, which serves to increase the uptake of oxygen into the bloodstream. This improved understanding of ventilation-perfusion matching may offer insights into the etiology of, and therapeutic interventions for diseases characterized by ventilation-perfusion mismatching.

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.

AVATREE: An open-source computational modelling framework modelling Anatomically Valid Airway TREE conformations

This paper presents AVATREE, a computational modelling framework that generates Anatomically Valid Airway tree conformations and provides capabilities for simulation of broncho-constriction apparent in obstructive pulmonary conditions. Such conformations are obtained from the personalized 3D geometry generated from computed tomography (CT) data through image segmentation. The patient-specific representation of the bronchial tree structure is extended beyond the visible airway generation depth using a knowledge-based technique built from morphometric studies. Additional functionalities of AVATREE include visualization of spatial probability maps for the airway generations projected on the CT imaging data, and visualization of the airway tree based on local structure properties. Furthermore, the proposed toolbox supports the simulation of broncho-constriction apparent in pulmonary diseases, such as chronic obstructive pulmonary disease (COPD) and asthma. AVATREE is provided as an open-source toolbox in C++ and is supported by a graphical user interface integrating the modelling functionalities. It can be exploited in studies of gas flow, gas mixing, ventilation patterns and particle deposition in the pulmonary system, with the aim to improve clinical decision making.