Computational analysis of flow structure and particle deposition in a single asthmatic human airway bifurcation

This paper aims to improve current understanding of flow structure and particle deposition in asthmatic human airways. A single, symmetric airway bifurcation, corresponding to generations 10–11 of Weibel’s model, is investigated through validated numerical simulations. The parent airway segment is modelled as a smooth circular tube. The child segments are considered asthmatic and their cross-section is modelled as a constricted tube with sinusoidal folds uniformly distributed along the circumference. The flow structure and particle deposition pattern for normal (i.e., healthy) and asthmatic airway bifurcations are compared and discussed. The numerical results reveal that the secondary flow in the asthmatic airway bifurcation is much stronger than in the healthy one, resulting in higher particle deposition. The effects of size of the lumen area and number of folds on particle deposition and pressure drop are also investigated. It is found that particle deposition efficiency is significantly affected by lumen area of the asthmatic segment (the smaller the lumen area, the higher the particle deposition efficiency). The effect of number of folds is small. Particle deposition efficiency also increases with Reynolds number. The pressure drop in the asthmatic airway bifurcation depends mainly on size of the lumen area. The effect of number of folds becomes important for strongly collapsed airways.     

Blood flow downstream of a two-dimensional bifurcation

Many cardiovascular lesions such as aneurysms, intimal cushions, and atherosclerotic plaques tend to occur near bifurcations. This suggests that hemodynamic factors may be involved. Since measuring devices (such as anemometers) are still too large to allow local measurements of flow disturbances, we have attempted to predict the nature of these factors mathematically. Biological variables include pulsatile flow of a nonNewtonian fluid in distensible branching vessels with different angles and flow rates. Our initial analysis considers the flow in a two-dimensional bifurcation with a symmetrical flow divider perfused with steady flow at variable Reynolds numbers. At all flows, high shear forces develop on either side of the flow divider (i.e. at the apex of the bifurcation). With high flows, regions of sluggish or reverse flow develop near the outer walls of the bifurcation. The analysis confirms that the flow at the apex is quite different from that at the outer angles and that the latter varies more with flow rate than the former.     

Particle deposition in obstructed airways

One approach to tackle the particle deposition in human lungs in close proximity is to develop an understanding of the particle motion in bifurcation airways. Chronic obstructive pulmonary disease (COPD) is one of the most common diseases in humans. COPD always results in inflammation that leads to narrowing and obstructing of the airways. The obstructive airways can alter the respiratory flow and particle deposition significantly. In order to study the effect of obstruction on particle deposition, four three-dimensional four-generation lung models based on the 23-generation model of Weibel [1963. Morphometry of the Human Lung. New York Academic Press, Springer, Berlin.] have been generated. The fully three-dimensional incompressible laminar Navier-Stokes equations are solved using computational fluid dynamics (CFD) solver on structured hexahedral meshes. Subsequently, a symmetric four-generation airway model serves as the reference and the other three models are considered to be obstructed at each generation, respectively. The calculation results show that the obstructive airway has significant influence on the particle deposition down-stream of the obstruction. The skewed velocity profile in the bifurcation airway is modified by the throat; consequently, more particles impact on the divider which results in higher deposition efficiency.     

Inspiratory flow rate and dead space in dogs

It is generally accepted that a stationary concentration front is established in the tracheobronchial tree during the inspiratory phase of single- and multiple-breath washouts. The anatomic position of this front, which is determined by the balance between diffusive flux toward the airway opening and convective flux toward the periphery, is frequently used to predict the effects of molecular diffusivity and inspiratory flow rate on dead space. Although there is substantial experimental evidence supporting the predictive effect of molecular diffusivity, there is little evidence regarding the effect of convective flow. This study confirmed the predictions for the effects of molecular diffusivity but contradicted those for the effects of inspiratory flow. We measured dead space by multiple- and single-breath inert gas washout techniques and also measured physiological dead space in dogs for inspiratory flow rates of 10-71 ml.kg-1.s-1. None of the three measures of dead space increased over the entire range of flow rate, as predicted by contemporary gas transport models. A possible explanation for these findings is that axial dispersion coefficients in the anatomic region where stationary fronts are believed to develop (respiratory bronchioles and alveolar ducts) significantly increase with convective flow rate rather than remain equal to molecular diffusivity.     

Periodic flow at airway bifurcations. III. Energy dissipation

We measured the energy dissipation associated with large-amplitude periodic flow through airway bifurcation models. Each model consisted of a single asymmetric bifurcation with a different branching angle and area ratio, with each branch terminated into an identical elastic load. Sinusoidal volumetric oscillations were applied at the parent duct so that the upstream Reynolds number (Re) varied from 30 to 77,000 and the Womersley parameter (alpha) from 4 to 30. Pressures were measured continuously at the parent duct and at both terminals, and instantaneous branch flow rates were calculated. Time-averaged energy dissipation in the bifurcation was computed from an energy budget over a control volume integrated over a cycle and was expressed as a friction factor, F. We found that when tidal volume was small [ratio of tidal volume to resident (dead space) volume, VT/VD less than 1], F was independent of branching angle and fell with increasing alpha and VT/VD. When tidal volume was large (VT/VD greater than 1), F increased with increasing branching angle and varied less strongly with alpha and VT/VD. No simple benchmark flow represented the data well over the entire experimental range. This study demonstrates that only two nondimensional parameters, alpha and VT/VD, are necessary and are sufficient to describe time-averaged energy dissipation in a given bifurcation geometry during sinusoidal flow.     

Influence of bifurcations on forced oscillations in an airway model.

Forced oscillations is a technique to determine respiratory input impedance from small amplitude sinusoidal pressure excursions introduced at the airway opening. Models used to predict respiratory input impedance typically ignore the direct effect of bifurcations on the flow, and treat airway branches as individual straight tubes placed appropriately in parallel and series. The flow within the individual tubes is assumed equivalent to that which would occur in infinitely long tubes. In this study we examined the influence of bifurcations on impedance for conditions of the forced oscillatory technique. We measured input impedance using forced oscillations in straight tubes and in an anatomically-relevant, four generation physical model of a human airway network. The input impedance measured experimentally compared well to that obtained theoretically using model predictions. The predictive scheme was based on appropriate parallel and series combinations of theoretically computed individual tube impedances, which were computed from solutions to oscillatory flow of a compressible gas in an infinitely long rigid tube. The agreement between experimental measurements and predictions indicates that bifurcations play a relatively minor direct role on the flow impedance for conditions of the forced oscillations technique. These results are explained in terms of the small tidal volumes used, whereby the axial distance traveled by a fluid particle during an oscillation cycle is appreciably smaller than branch segment lengths. Accordingly, only a small fraction of fluid particles travel through the bifurcation region, and the remainder experience an environment approaching flow in an infinite straight tube. The relevance of the study to the prediction of impedances in the human lung during forced oscillations is discussed.     

Resistance of intrathoracic airways of healthy subjects during periodic flow.

The resistance and reactance of lower airways were measured as functions of the frequency and amplitude of periodic flow in three healthy subjects by relating flow, produced with a piston pump, to the difference between lateral tracheal and alveolar pressure, estimated plethysmorgraphically. Resistance consistently increased with frequency; reactance was small never exceeding resistance. This result cannot be explained by distortion of velocity profiles by inertia because, in long pipes, resistance increases only when inertial forces are large and reactance exceeds resistance. Theoretical analyses of airway resistance suggested that the results reflected inhomogeneity. In lung models which considered airway wall distensibility and inertial reactance of airways, resistance increased with frequency and inertial reactance was small. These results imply that in health, as in lung disease, resistance is determined by the distribution of resistance and reactance within the lung and is not simply the total resistance of the individual airways. As flow amplitude increased at constant frequency, flow-pressure relationships became distorted and resistance increased, due probably to motion of airway walls and further distortion of velocity profiles     

Some features of oscillatory flow in a model bifurcation

Oscillatory flow in the lung is studied using an order-of-magnitude analysis and flow visualization experiments in a single bifurcation with lung-like geometry. The results are used to obtain a classification scheme that identifies three major flow regimes, distinguished on the basis of whether the flow is dominated by unsteadiness, viscous effects, or the effects of convective acceleration. The unsteady regime is found to exist for values of a dimensionless stroke length (L/a, i.e., stroke volume/local cross-sectional area) less than or equal to 3 and for values of a dimensionless frequency (alpha 2 = alpha 2 omega/nu, where alpha is airway radius, omega the oscillatory frequency, and nu the kinematic viscosity) less than or equal to 10 in basic agreement with previous studies. The viscous regime is found when alpha 2(L/a)(a/R)1/2 less than 10 and alpha 2 less than 10 where R is the local radius of curvature in the bifurcation; the convective regime is found when alpha 2(L/a)(a/R)1/2 greater than 10 and L/a greater than 3. This same approach yields scaling laws for the magnitude of secondary flow velocities and shows that the ratio of secondary-to-axial velocity is small everywhere outside of the convective regime where it scales with (a/R)1/2. Comparison of these results to related simple flows shows that many of the features observed can be attributed to the effects of curvature, suggesting that the influence of the flow divider and of area change may be of lesser importance than previously thought.     

Computational model of airway narrowing: mature vs. immature rabbit.

Immature rabbits have greater maximal airway narrowing and greater maximal fold increases in airway resistance during bronchoconstriction than mature animals. We have previously demonstrated that excised immature rabbit lungs have more distensible airways, a lower shear modulus, and structural differences in the relative composition and thickness of anatomically similar airways. In the present study, we incorporated anatomic and physiological data for mature and immature rabbits into a computational model of airway narrowing. We then investigated the relative importance of maturational differences in these factors as determinants of the greater airway narrowing that occurs in the immature animal. The immature model demonstrated greater sensitivity to agonist, as well as a greater maximal fold increase in airway resistance. Exchanging values for airway compliance between the mature and immature models resulted in the mature model exhibiting a greater maximal airway response than the immature model. In contrast, exchanging the shear moduli or the composition of the airway wall relative to the airway size produced relatively small changes in airway reactivity. Our results strongly suggest that the mechanical properties of the airway, i.e., greater compliance of the immature airway, can be an important factor contributing to the greater airway narrowing of the immature animal.     

Aerosol transport and deposition in sequentially bifurcating airways

Deposition patterns and efficiencies of a dilute suspension of inhaled particles in three-dimensional double bifurcating airway models for both in-plane and 90 deg out-of-plane configurations have been numerically simulated assuming steady, laminar, constant-property air flow with symmetry about the first bifurcation. Particle diameters of 3, 5, and 7 microns were used in the simulation, while the inlet Stokes and Reynolds numbers varied from 0.037 to 0.23 and 500 to 2000, respectively. Comparisons between these results and experimental data based on the same geometric configuration showed good agreement. The overall trend of the particle deposition efficiency, i.e., an exponential increase with Stokes number, was somewhat similar for all bifurcations. However, the deposition efficiency of the first bifurcation was always larger than that of the second bifurcation, while in general the particle efficiency of the out-of-plane configuration was larger than that of the in-plane configuration. The local deposition patterns consistently showed that the majority of the deposition occurred in the carinal region. The distribution pattern in the first bifurcation for both configurations were symmetric about the carina, which was a direct result of the uniaxial flow at the inlet. The deposition patterns about the second carina showed increased asymmetry due to highly nonuniform flow generated by the first bifurcation and were extremely sensitive to bifurcation orientation. Based on the deposition variations between bifurcation levels and orientations, the use of single bifurcation models was determined to be inadequate to resolve the complex fluid-particle interactions that occur in multigenerational airways.     

Three-dimensional visualization and morphometry of small airways from microfocal X-ray computed tomography

Physiological morphometry is a critical factor in the flow dynamics in small airways. In this study, we visualized and analyzed the three-dimensional structure of the small airways without dehydration and fixation. We developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomographic (CT) system. To verify the applicability of this staining and CT imaging (SCT) method, we used the method to visualize small airways in excised rat lungs. By using the SCT method to obtain continuous CT images, three-dimensional branching and merging bronchi ranging from 500 to 150 microm (the airway generation=8-16) were successfully reconstructed. The morphometry of the small airways (diameter, length, branching angle and gravity angle between the gravity direction and airway vector) was analyzed using the three-dimensional thinning algorithm. The diameter and length exponentially decreased with the airway generation. The asymmetry of the bifurcation decreased with generation and one branching angle decided the other pair branching angle. The SCT method is the first reported method that yields faithful high-resolution images of soft tissue geometry without fixation and the three-dimensional morphometry of small airways is useful for studying the biomechanical dynamics in small airways.     

Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles

Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method, which has been developed recently. The non-Newtonian behaviour of blood is modelled using Casson's relation, based on measured dynamic viscosity. The study concentrates on flow and stress characteristics in the carotid sinus. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation.     

Biomechanical Aspects of Compliant Airways due to Mechanical Ventilation

Without proper knowledge of mechanical ventilation effects, physicians can aggravate an existing lung injury. A better understanding of the interaction between airflow and airway tissue during mechanical ventilation will be helpful to physicians so that they can provide appropriate ventilator parameters for intubated patients. In this study, a computational model incorporating the interactions between airflow and airway walls was developed to investigate the effects of airway tissue flexibility on airway pressure and stress. Two flow rates, 30 and 60 l/min, from mechanical ventilation were considered. The transient waveform was active inhalation with a constant flow rate and passive exhalation. Results showed that airway tissue flexibility decreased airway pressure at bifurcation sites by approximately 25.06% and 16.91% for 30 and 60 l/min, respectively, and increased wall shear stress (WSS) by approximately 74.00% and 174.91% for 30 and 60 l/min, respectively. The results from the present study suggested that it is very important to consider the interaction between airflow and airway walls when computational models are developed. Results of this study help to better quantify how the airflow rate used in mechanical ventilation, in conjunction with airway tissue flexibility, affects airway pressure and stresses.     

Effects of tumors on inhaled pharmacologic drugs

Lung carcinomas are now the most common form of cancer. Clinical data suggest that tumors are found preferentially in upper airways, perhaps specifically at carina within bifurcations. The disease can be treated by aerosolized pharmacologic drugs. To enhance their efficacies site-specific drugs must be deposited selectively. Since inhaled particles are transported by air, flow patterns will naturally affect their trajectories. Therefore, in Part I of a systematic investigation, we focused on tumor-induced effects on airstreams, in Part II (the following article [p. 245]), particle trajectories were determined. To facilitate the targeted delivery of inhaled drugs, we simulated bifurcations with tumors on carinas using a commercial computational fluid dynamics (CFD) software package (FIDAP) with a Cray T90 supercomputer and studied effects of tumor sizes and ventilatory parameters on localized flow patterns. Critical tumor sizes existed; e.g., tumors had dominant effects when r/R > or = 0.8 for bifurcation 3-4 and r/R > or = 0.6 for bifurcation 7-8 (r = tumor radius and R = airway radius). The findings suggest that computer modeling is a means to integrate alterations to airway structures caused by diseases into aerosol therapy protocols.     

Activation of smooth muscle in the airway wall, force production, and airway narrowing.

Airway narrowing depends on smooth muscle force production and muscle shortening, but the structural and geometric properties exhibited by individual generations of the bronchial tree largely determine the extent and characteristics of airway narrowing. Properties of major importance include the nature and integrity of the epithelium, the structural and mechanical properties of the airway wall, as well as airway diameter. The influence of these properties on airway narrowing measured as flow or flow resistance in large and small diameter segments of airways from pig lung is described using a novel preparation, the perfused bronchial segment.     

Low Reynolds number equi-bifurcation flow in a two-dimensional channel

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.     

Zero-stress state of intra- and extraparenchymal airways from human, pig, rabbit, and sheep lung.

Alterations in airway wall anatomic properties and the consequential effects on airway narrowing have been assessed by use of computational models. In these models, it is generally assumed that at zero transmural pressure the airway wall exists in a zero-stress state. Many studies have shown that this is often not the case, as evidenced by a nonzero opening angle. In this study, we measured the opening angle of airway rings at zero transmural pressure to test this assumption. The airway tree was dissected from human, pig, sheep, and rabbit lungs. Airways were excised from the tree, and the opening angle was measured. There were obvious species and regional differences in opening angle. Rabbit airways from both extraparenchymal and intraparenchymal sites exhibited marked opening angles (7-82 degrees). Extraparenchymal airways from sheep had large opening angles (up to 50 degrees), but ovine intraparenchymal airways had small opening angles. Measurable opening angles were rarely observed in human and porcine airways of any size. The assumption of a stable zero-stress state at zero transmural pressure is therefore valid for human and porcine, but not rabbit and sheep, airways.     

Immediate sensory nerve-mediated respiratory responses to irritants in healthy and allergic airway-diseased mice.

The immediate responses of the upper respiratory tract (URT) to the irritants acrolein and acetic acid were examined in healthy and allergic airway-diseased C57Bl/6J mice. Acrolein (1.1 ppm) and acetic acid (330 ppm) vapors induced an immediate increase in flow resistance, as measured in the surgically isolated URT of urethane-anesthetized healthy animals. Acrolein, but not acetic acid, induced a small URT vasodilatory response. In awake spontaneously breathing mice, both vapors induced a prolonged pause at the start of expiration (a response mediated via stimulation of nasal trigeminal nerves) and an increase in total respiratory specific airway flow resistance, the magnitude of which was similar to that observed in the isolated URT. Both responses were significantly reduced in animals pretreated with large doses of capsaicin to defunctionalize sensory nerves, strongly suggesting a role for sensory nerves in development of these responses. The breathing pattern and/or obstructive responses were enhanced in mice with ovalbumin-induced allergic airway disease. These results suggest that the primary responses to acrolein and acetic acid vapors are altered breathing patterns and airway obstruction, that sensory nerves play an important role in these responses, and that these responses are enhanced in animals with allergic airway disease.     

Periodic flow at airway bifurcations. I. Development of steady pressure differences

In studies of large-amplitude periodic flows at an airway bifurcation, we found an appreciable steady-state pressure difference between the terminal units. To elucidate the fluid dynamic origins of such steady-state pressure differences, we studied single asymmetric bifurcation models with various area ratios and branching angles. The daughter ducts were identical in size and were terminated into identical elastic loads. Sinusoidal flow oscillations were applied at the parent duct so that the upstream Reynolds number ranged from 30 to 77,000 and the Womersley parameter from 2 to 30. The steady-state component (time averaged) of the pressure measured at the terminal with the smaller branching angle was found to be consistently higher than that at the other terminal. This steady-state pressure difference scaled approximately as a fixed fraction of the parent duct dynamic head. Guided by the results of flow-visualization studies, we modeled such behavior based on the temporal and spatial differences of head loss between the two branches of the bifurcation. Our results suggest that interlobar heterogeneity of mean alveolar-pressure observed in excised canine lungs during high frequency oscillation (Allen et al., J. Appl. Physiol. 62: 223-228, 1987) arises solely from fluid dynamic origins: differential head loss due to asymmetry of central airway branching structure.