Effect of geometric variations on pressure loss for a model bifurcation of the human lung airway

Entropy generation in the human lung due to effect of psychrometric condition and friction in the respiratory tract

BACKGROUND AND OBJECTIVE

Entropy generation is associated with the irreversibility of any thermodynamic system. It provides an indication of lost energy and hence the efficiency of a system. In this paper, an attempt has been made to study the effects of specific humidity, relative humidity, ambient temperature change, breathing air friction with the respiratory tract on the entropy generation during the respiration process at different physiological conditions.

METHODS

To address the above issues, a human respiratory tract model with realistic length to diameter ratio at different branches has been considered. The analysis examines air flow rates of 6 lpm and 60 lpm during rest and exercise condition respectively; corresponding to breathing rates of 30 and 60 per minute, respectively. The body temperature has been considered at 36°C, and ambient condition of air has been taken at 25°C DBT and 50% RH. The respiratory tract geometry has been modelled on the basis of Weibel's experimental results.

RESULTS

It has been noticed that, at a particular Lewis number entropy generation per day decreases with the increase in specific humidity, again at a particular specific humidity entropy generation increases with the decrease in Lewis number. For a particular physical condition and Lewis number entropy generation decreases with the increase in relative humidity. In this work, it has been observed that negentropy increases with the increase in ambient temperature for a constant relative humidity, however the net entropy generation is always positive. This study reports that, maximum resistance of flow occurs where duct aspect ratio (i.e. tract diameter to length) is minimal. For a typical geometry of air passage, velocity of flow increases up to 3rd generation then it is decreases gradually till 23^rd generation. Amount of entropy generation goes on reducing as the duct goes on bifurcating except for the third generation where a local peak in entropy generation is observed. This is a consequence of typical geometry of human respiratory duct. This work reveals that, at rest entropy generation due to conditioning of breathing air is higher than its frictional component and during heavy physical activity, entropy generation due to breathing air friction with the respiratory tract is higher than its air conditioning component.

CONCLUSIONS

Entropy generation is significantly higher due to conditioning of breathing air than that of frictional effect with the tract. This is a preliminary attempt in quantifying this aspect and the authors believe that, these two components of entropy generation have a probable connection with the bronchial thermoplasty, which helps to treat the asthma.

A COMPARATIVE STUDY ON THE ENTROPY GENERATION IN THE HUMAN RESPIRATORY TRACT BASED ON HESS–MURRAY LAW AND WEIBEL EXPERIMENTED RESULT

Entropy generation ([Formula: see text]) is associated with the irreversibility of any thermodynamic system. It provides an indication of lost energy of a system. The main objective of this study is to show a method for calculating entropy generation in the human respiratory tract. In this work, human respiratory tract geometries from two different approaches are considered, first one is based on Hess–Murray theory and the second one is based on Weibel’s experimented result. The entropy generation has been calculated considering duct wall friction along with effect of bifurcation and diffusion. In this study, two different physiological conditions have been contemplated, i.e., at rest and at heavy physiological activities. It has shown that [Formula: see text] of human respiratory is lowest at 23rd level of bifurcation. The outcome of the study reveals that the entropy generation rates per day based on Hess–Murray theory at rest and under heavy physiological activities are [Formula: see text][Formula: see text]kJ/K and 0.013[Formula: see text]kJ/K, whereas the same based on Weibel’s experimented result at rest and under heavy physiological activities are [Formula: see text][Formula: see text]kJ/K and 0.05[Formula: see text]kJ/K, respectively.

Predicted airway obstruction distribution based on dynamical lung ventilation data: A coupled modeling-machine learning methodology

In asthma and chronic obstructive pulmonary disease, some airways of the tracheobronchial tree can be constricted, from moderate narrowing up to closure. Those pathological patterns of obstructions affect the lung ventilation distribution. While some imaging techniques enable visualization and quantification of constrictions in proximal generations, no noninvasive technique exists to provide the airway morphology and obstruction distribution in distal areas. In this work, we propose a method that exploits lung ventilation measures to access positions of airway obstructions (restrictions and closures) in the tree. This identification approach combines a lung ventilation model, in which a 0D tree is strongly coupled to a 3D parenchyma description, along with a machine learning approach. On the basis of synthetic data generated with typical temporal and spatial resolutions as well as reconstruction errors, we obtain very encouraging results of the obstruction distribution, with a detection rate higher than 85%.

Contributions of Kinetic Energy and Viscous Dissipation to Airway Resistance in Pulmonary Inspiratory and Expiratory Airflows in Successive Symmetric Airway Models With Various Bifurcation Angles

The aim of this study was to investigate and quantify contributions of kinetic energy and viscous dissipation to airway resistance during inspiration and expiration at various flow rates in airway models of different bifurcation angles. We employed symmetric airway models up to the 20th generation with the following five different bifurcation angles at a tracheal flow rate of 20 L/min: 15 deg, 25 deg, 35 deg, 45 deg, and 55 deg. Thus, a total of ten computational fluid dynamics (CFD) simulations for both inspiration and expiration were conducted. Furthermore, we performed additional four simulations with tracheal flow rate values of 10 and 40 L/min for a bifurcation angle of 35 deg to study the effect of flow rate on inspiration and expiration. Using an energy balance equation, we quantified contributions of the pressure drop associated with kinetic energy and viscous dissipation. Kinetic energy was found to be a key variable that explained the differences in airway resistance on inspiration and expiration. The total pressure drop and airway resistance were larger during expiration than inspiration, whereas wall shear stress and viscous dissipation were larger during inspiration than expiration. The dimensional analysis demonstrated that the coefficients of kinetic energy and viscous dissipation were strongly correlated with generation number. In addition, the viscous dissipation coefficient was significantly correlated with bifurcation angle and tracheal flow rate. We performed multiple linear regressions to determine the coefficients of kinetic energy and viscous dissipation, which could be utilized to better estimate the pressure drop in broader ranges of successive bifurcation structures.

A tree-parenchyma coupled model for lung ventilation simulation

In this article, we develop a lung ventilation model. The parenchyma is described as an elastic homogenized media. It is irrigated by a space-filling dyadic resistive pipe network, which represents the tracheobronchial tree. In this model, the tree and the parenchyma are strongly coupled. The tree induces an extra viscous term in the system constitutive relation, which leads, in the finite element framework, to a full matrix. We consider an efficient algorithm that takes advantage of the tree structure to enable a fast matrix-vector product computation. This framework can be used to model both free and mechanically induced respiration, in health and disease. Patient-specific lung geometries acquired from computed tomography scans are considered. Realistic Dirichlet boundary conditions can be deduced from surface registration on computed tomography images. The model is compared to a more classical exit compartment approach. Results illustrate the coupling between the tree and the parenchyma, at global and regional levels, and how conditions for the purely 0D model can be inferred. Different types of boundary conditions are tested, including a nonlinear Robin model of the surrounding lung structures.

Calculated ventilation and effort distribution as a measure of respiratory disease and Heliox effectiveness

In spite of numerous clinical studies, there is no consensus on the benefit Heliox mixtures can bring to asthmatic patients in terms of work of breathing and ventilation distribution. In this article we use a 3D finite element mathematical model of the lung to study the impact of asthma on effort and ventilation distribution along with the effect of Heliox compared to air. Lung surface displacement fields extracted from computed tomography medical images are used to prescribe realistic boundary conditions to the model. Asthma is simulated by imposing bronchoconstrictions to some airways of the tracheo-bronchial tree based on statistical laws deduced from the literature. This study illuminates potential mechanisms for patient responsiveness to Heliox when affected by obstructive pulmonary diseases. Responsiveness appears to be function of the pathology severity, as well as its distal position in the tracheo-bronchial tree and geometrical position within the lung.

Secondary motion in three-dimensional branching networks

A major aim of the present work is to understand and thoroughly document the generation, the three-dimensional distribution, and the evolution of the secondary motion as the fluid progresses downstream through a branched network. Six generations (G0-G5) of branches (involving 63 straight portions and 31 bifurcation modules) are computed in one go; such computational challenges are rarely taken in the literature. More than 30 × 10⁶ computational elements are employed for high precision of computed results and fine quality of the flow visualization diagrams. The study of co-planar vis-à-vis non-planar space-filling configurations establishes a quantitative evaluation of the dependence of the fluid dynamics on the three-dimensional arrangement of the same individual branches. As compared to the secondary motion in a simple curved pipe, three distinctive features, viz., the change of shape and size of the flow-cross-section, the division of non-uniform primary flow in a bifurcation module, and repeated switchover from clockwise to anticlockwise curvature and vice versa in the flow path, make the present situation more complex. It is shown that the straight portions in the network, in general, attenuate the secondary motion, while the three-dimensionally complex bifurcation modules generate secondary motion and may alter the number, arrangement, and structure of vortices. A comprehensive picture of the evolution of quantitative flow visualizations of the secondary motion is achieved by constructing contours of secondary velocity [Formula: see text], streamwise vorticity [Formula: see text], and [Formula: see text] iso-surfaces. It is demonstrated, for example, that for in-plane configuration, the vortices on any plane appear in pair (i.e., for each clockwise rotating vortex, there is an otherwise identical anticlockwise vortex), whereas the vortices on a plane for the out-of-plane configuration may be dissimilar, and there may even be an odd number of vortices. We have formulated three new parameters (E_S/P , [Formula: see text], and [Formula: see text]) for a quantitative description of the overall features of the secondary flow field. [Formula: see text] represents a non-uniformity index of the secondary flow in an individual branch, E_S/P represents the mass-flow-averaged relative kinetic energy of the secondary motion in an individual branch, and [Formula: see text] provides a measure of the non-uniformity of the secondary flow between various branches of the same generation Gn. The repeated enhancement of the secondary kinetic energy in the bifurcation modules is responsible for the occurrence of significant values of E_S/P even in generation G5. For both configurations, it is found that for any bifurcation module, the value of E_S/P is greater in that daughter branch in which the mass-flow rate is greater. Even though the various contour plots of the complex secondary flow structure appear visually very different from one another, the values of [Formula: see text] are found to lie within a small range ([Formula: see text]) for the six-generation networks studied. It is shown that [Formula: see text] grows as the generation number Gn increases. It is established that the out-of-plane configuration, in general, creates more secondary kinetic energy (higher E_S/P ), a similar level of non-uniformity in the secondary flow in an individual branch (similar [Formula: see text]), and a significantly lower level of non-uniformity in the distribution of secondary motion among various branches of the same generation (much lower [Formula: see text]), as compared to the in-plane arrangement of the same branches.

Dynamic flow characteristics in normal and asthmatic lungs

Complex flow patterns exist within the asymmetric branching airway network in the lungs. These flow patterns are known to become increasingly heterogeneous during disease as a result of various mechanisms such as bronchoconstriction or alterations in lung tissue compliance. Here, we present a coupled model of tissue deformation and network airflow enabling predictions of dynamic flow properties, including temporal flow rate, pressure distribution, and the occurrence of reverse flows. We created two patient-specific airway geometries, one for a healthy subject and one for a severe asthmatic subject, derived using a combination of high-resolution CT data and a volume-filling branching algorithm. In addition, we created virtually constricted airway geometry by reducing the airway radii of the healthy subject model. The flow model was applied to these three different geometries to solve the pressure and flow distribution over a breathing cycle. The differences in wave phase of the flows in parallel airways induced by asymmetric airway geometry and bidirectional interaction between intra-acinar and airway network pressures were small in central airways but were more evident in peripheral airways. The asthmatic model showed elevated ventilation heterogeneity and significant flow disturbance. The reverse flows in the asthmatic model not only altered the local flow characteristics but also affected total lung resistance. The clinical significance of temporal flow disturbance on lung ventilation in normal airway model is obscure. However, increased flow disturbance and ventilation heterogeneity observed in the asthmatic model suggests that reverse flow may be an important factor for asthmatic lung function.

Validation of airway resistance models for predicting pressure loss through anatomically realistic conducting airway replicas of adults and children

This work describes in vitro measurement of the total pressure loss at varying flow rate through anatomically realistic conducting airway replicas of 10 children, 4 to 8 years old, and 5 adults. Experimental results were compared with analytical predictions made using published airway resistance models. For the adult replicas, the model proposed by van Ertbruggen et al. (2005. J. Appl. Physiol. 98, 970-980) most accurately predicted central conducting airway resistance for inspiratory flow rates ranging from 15 to 90 L/min. Models proposed by Pedley et al. (1970. J. Respir. Physiol. 9, 371-386) and by Katz et al. (2011. J. Biomech. 44, 1137-1143) also provided reasonable estimates, but with a tendency to over predict measured pressure loss for both models. For child replicas, the Pedley and Katz models both provided good estimation of measured pressure loss at flow rates representative of resting tidal breathing, but under predicted measured values at high inspiratory flow rate (60 L/min). The van Ertbruggen model, developed based on flow simulations performed in an adult airway model, tended to under predict measured pressure loss through the child replicas across the range of flow rates studied (2 to 60 L/min). These results are intended to provide guidance for selection of analytical pressure loss models for use in predicting airway resistance and ventilation distribution in adults and children.

Quantifying morphological parameters of the terminal branching units in a mouse lung by phase contrast synchrotron radiation computed tomography

An effective technique of phase contrast synchrotron radiation computed tomography was established for the quantitative analysis of the microstructures in the respiratory zone of a mouse lung. Heitzman’s method was adopted for the whole-lung sample preparation, and Canny’s edge detector was used for locating the air-tissue boundaries. This technique revealed detailed morphology of the respiratory zone components, including terminal bronchioles and alveolar sacs, with sufficiently high resolution of 1.74 µm isotropic voxel size. The technique enabled visual inspection of the respiratory zone components and comprehension of their relative positions in three dimensions. To check the method’s feasibility for quantitative imaging, morphological parameters such as diameter, surface area and volume were measured and analyzed for sixteen randomly selected terminal branching units, each consisting of a terminal bronchiole and a pair of succeeding alveolar sacs. The four types of asymmetry ratios concerning alveolar sac mouth diameter, alveolar sac surface area, and alveolar sac volume are measured. This is the first ever finding of the asymmetry ratio for the terminal bronchioles and alveolar sacs, and it is noteworthy that an appreciable degree of branching asymmetry was observed among the alveolar sacs at the terminal end of the airway tree, despite the number of samples was small yet. The series of efficient techniques developed and confirmed in this study, from sample preparation to quantification, is expected to contribute to a wider and exacter application of phase contrast synchrotron radiation computed tomography to a variety of studies.