Steady and unsteady pressure-flow relationships in central airways

Domestic cat nose functions as a highly efficient coiled parallel gas chromatograph

The peripheral structures of mammalian sensory organs often serve to support their functionality, such as alignment of hair cells to the mechanical properties of the inner ear. Here, we examined the structure-function relationship for mammalian olfaction by creating an anatomically accurate computational nasal model for the domestic cat (Felis catus) based on high resolution microCT and sequential histological sections. Our results showed a distinct separation of respiratory and olfactory flow regimes, featuring a high-speed dorsal medial stream that increases odor delivery speed and efficiency to the ethmoid olfactory region without compromising the filtration and conditioning purpose of the nose. These results corroborated previous findings in other mammalian species, which implicates a common theme to deal with the physical size limitation of the head that confines the nasal airway from increasing in length infinitely as a straight tube. We thus hypothesized that these ethmoid olfactory channels function as parallel coiled chromatograph channels, and further showed that the theoretical plate number, a widely-used indicator of gas chromatograph efficiency, is more than 100 times higher in the cat nose than an "amphibian-like" straight channel fitting the similar skull space, at restful breathing state. The parallel feature also reduces airflow speed within each coil, which is critical to achieve the high plate number, while feeding collectively from the high-speed dorsal medial stream so that total odor sampling speed is not sacrificed. The occurrence of ethmoid turbinates is an important step in the evolution of mammalian species that correlates to their expansive olfactory function and brain development. Our findings reveal novel mechanisms on how such structure may facilitate better olfactory performance, furthering our understanding of the successful adaptation of mammalian species, including F. catus, a popular pet, to diverse environments.

Respiratory Oscillometry in Newborn Infants: Conventional and Intra-Breath Approaches

BACKGROUND

Oscillometry has been employed widely as a non-invasive and standardized measurement of respiratory function in children and adults; however, limited information is available on infants.

AIMS

To establish the within-session variability of respiratory impedance (Zrs), to characterize the degree and profile of intra-breath changes in Zrs and to assess their impact on conventional oscillometry in newborns.

METHODS

109 healthy newborns were enrolled in the study conducted in the first 5 postpartum days during natural sleep. A custom-made wave-tube oscillometry setup was used, with an 8-48 Hz pseudorandom and a 16 Hz sinusoidal signal used for spectral and intra-breath oscillometry, respectively. A resistance-compliance-inertance (R-C-L) model was fitted to average Zrs spectra obtained from successive 30-s recordings. Intra-breath measures, such as resistance (Rrs) and reactance (Xrs) at the end-expiratory, end-inspiratory and maximum-flow points were estimated from three 90-s recordings. All natural and artifact-free breaths were included in the analysis.

RESULTS

Within-session changes in the mean R, C and L values, respectively, were large (mean coefficients of variation: 10.3, 20.3, and 26.6%); the fluctuations of the intra-breath measures were of similar degree (20-24%). Intra-breath analysis also revealed large swings in Rrs and Xrs within the breathing cycle: the peak-to-peak changes amounted to 93% (range: 32-218%) and 41% (9-212%), respectively, of the zero-flow Zrs magnitude.

DISCUSSION

Intra-breath tracking of Zrs provides new insight into the determinants of the dynamics of respiratory system, and highlights the biasing effects of mechanical non-linearities on the average Zrs data obtained from the conventional spectral oscillometry.

The impact of steady streaming and conditional turbulence on gas transport during high-frequency ventilation

High-frequency ventilation is a type of mechanical ventilation therapy applied on patients with damaged or delicate lungs. However, the transport of oxygen down, and carbon dioxide up, the airway is governed by subtle transport processes which hitherto have been difficult to quantify. We investigate one of these mechanisms in detail, nonlinear mean streaming, and the impact of the onset of turbulence on this streaming, via direct numerical simulations of a model 1:2 bifurcating pipe. This geometry is investigated as a minimal unit of the fractal structure of the airway. We first quantify the amount of gas recirculated via mean streaming by measuring the recirculating flux in both the upper and lower branches of the bifurcation. For conditions modeling the trachea-to-bronchi bifurcation of an infant, we find the recirculating flux is of the order of 3-5% of the peak flux . We also show that for conditions modeling the upper generations, the mean recirculation regions extend a significant distance away from the bifurcation, certainly far enough to recirculate gas between generations. We show that this mean streaming flow is driven by the formation of longitudinal vortices in the flow leaving the bifurcation. Second, we show that conditional turbulence arises in the upper generations of the airway. This turbulence appears only in the flow leaving the bifurcation, and at a point in the cycle centered around the maximum instantaneous flow rate. We hypothesize that its appearance is due to an instability of the longitudinal-vortices structure.

Effect of nasal airway nonlinearities on oscillometric resistance measurements in infants

Oscillometric measurements of respiratory system resistance (R_rs) in infants are usually made via the nasal pathways, which not only significantly contribute to overall R_rs but also introduce marked flow (V')-dependent changes. We employed intrabreath oscillometry in casts of the upper airways constructed from head CT images of 46 infants. We examined oscillometric nasal resistance (R_n) in upper airway casts with no respiratory flow (R₀) and the effect of varying V' on R_n by simulating tidal breathing. A characteristic nonlinear relationship was found between R_n and V', exhibiting segmental linearity and a prominent breakpoint (V'_bp) after log-log transformation. V'_bp was linearly related to the preceding value of end-expiratory volume acceleration (V″_eE; on average r² = 0.96, P < 0.001). R_n depended on V', and R at end-expiration (R_eE) showed a strong dependence on V″_eE in every cast (r² = 0.994, P < 001) with considerable interindividual variability. The intercept of the linear regression of R_eE versus V″_eE was found to be a close estimate of R₀. These findings were utilized in reanalyzed R_rs data acquired in vivo in a small group of infants (n = 15). Using a graphical method to estimate R₀ from R_eE, we found a relative contribution of V'-dependent nonlinearity to total resistance of up to 33%. In conclusion, we propose a method for correcting the acceleration-dependent nonlinearity error in R_eE. This correction can be adapted to estimate R₀ from a single intrabreath oscillometric measurement, which would reduce the masking effects of the upper airways on the changes in the intrathoracic resistance.NEW & NOTEWORTHY Oscillometric measurements of respiratory system resistance (R_rs) in infants are usually made via the nasal pathways, which not only significantly contribute to overall R_rs but also introduce marked flow acceleration-dependent distortions. Here, we propose a method for correcting flow acceleration-dependent nonlinearity error based on in vitro measurements in 3D-printed upper airway casts of infants as well as in vivo measurements. This correction can be adapted to estimate R_rs from a single intrabreath oscillometric measurement.

In silico approaches to respiratory nasal flows: A review

The engineering discipline of in silico fluid dynamics delivers quantitative information on airflow behaviour in the nasal regions with unprecedented detail, often beyond the reach of traditional experiments. The ability to provide visualisation and analysis of flow properties such as velocity and pressure fields, as well as wall shear stress, dynamically during the respiratory cycle may give significant insight to clinicians. Yet, there remains ongoing challenges to advance the state-of-the-art further, including for example the lack of comprehensive CFD modelling on varied cohorts of patients. The present article embodies a review of previous and current in silico approaches to simulating nasal airflows. The review discusses specific modelling techniques required to accommodate physiologically- and clinically-relevant findings. It also provides a critical summary of the reported results in the literature followed by an outlook on the challenges and topics anticipated to drive research into the future.

Numerical investigation of transient transport and deposition of microparticles under unsteady inspiratory flow in human upper airways

In the present study, unsteady airflow patterns and particle deposition in healthy human upper airways were simulated. A realistic 3-D computational model of the upper airways including the vestibule to the end of the trachea was developed using a series of CT scan images of a healthy human. Unsteady simulations of the inhaled and exhaled airflow fields in the upper airway passages were performed by solving the Navier-Stokes and continuity equations for low breathing rates corresponding to low and moderate activities. The Lagrangian trajectory analysis approach was utilized to investigate the transient particle transport and deposition under cyclic breathing condition. Particles were released uniformly at the nostrils' entrance during the inhalation phase, and the total and regional depositions for various micro-particle sizes were evaluated. The transient particle deposition fractions for various regions of the human upper airways were compared with those obtained from the equivalent steady flow condition. The presented results revealed that the equivalent constant airflow simulation can approximately predict the total particle deposition during cyclic breathing in human upper airways. While the trends of steady and unsteady model predictions for local deposition were similar, there were noticeable differences in the predicted amount of deposition. In addition, it was shown that a steady simulation cannot properly predict some critical parameters, such as the penetration fraction. Finally, the presented results showed that using a detached nasal cavity (commonly used in earlier studies) for evaluation of total deposition fraction of particles in the nasal cavity was reasonably accurate for the steady flow simulations. However, in transient simulation for predicting the deposition fraction in a specific region, such as the nasal cavity, using the full airway system geometry becomes necessary.

Frictional resistance sheds light on the multicomponent nature of nasal obstruction: a combined in vivo and computational fluid dynamics study

Exploring nasal flow contributes to better understanding of pathophysiological functions of nasal cavities. We combined the rhinomanometry measurements of 11 patients and computational fluid dynamics (CFD) simulations in 3 nasal airway models to dissect the complex mechanisms that determine nasal flow obstruction: spatial complexity and pressure-dependent deformability of nasal airways. We quantified spatial complexity by calculating longitudinal variations of hydraulic diameter, perimeter and area of nasal cavities, and their impact on flow characteristics by examining the longitudinal variations of the kinetic energy coefficient and the kinetic to potential energy ratio. Airway distensibility variably affected in vivo pressure-flow relationships through the appearance of flow-limitation patterns characterized by maximum flow and/or flow plateau. We quantified deformability and spatial complexity effects on nasal airway resistance by normalizing all data with averaged reference parameters. The results show that discrepancies in nasal flow resistances reflect airway deformability and geometrical complexity, and thereby constitute a framework to better characterize nasal obstruction.

Airflow and nanoparticle deposition in rat nose under various breathing and sniffing conditions: a computational evaluation of the unsteady effect

Accurate prediction of nanoparticle (1~100 nm) deposition in the rat nasal cavity is important for assessing the toxicological impact of inhaled nanoparticles as well as for potential therapeutic applications. A quasi-steady assumption has been widely adopted in the past investigations on this topic, yet the validity of such simplification under various breathing and sniffing conditions has not been carefully examined. In this study, both steady and unsteady computational fluid dynamics (CFD) simulations were conducted in a published rat nasal model under various physiologically realistic breathing and sniffing flow rates. The transient airflow structures, nanoparticle transport and deposition patterns in the whole nasal cavity and the olfactory region were investigated and compared with steady state simulation of equivalent flow rate. The results showed that (1) the quasi-steady flow assumption for cyclic flow was valid for over 70% of the cycle period during all simulated breathing and sniffing conditions in the rat nasal cavity, or the unsteady effect was only significant during the transition between the respiratory phases; (2) yet the quasi-steady assumption for nanoparticle transport was not valid, except in the vicinity of peak respiration. In general, the total deposition efficiency of nanoparticle during cyclic breathing would be lower than that of steady state due to the unsteady effect on particle transport and deposition, and further decreased with the increase of particle size, sniffing frequency, and flow rate. In the contrary, previous study indicated that for micro-scale particles (0.5~4μm), the unsteady effect would increase deposition efficiencies in rat nasal cavity. Combined, these results suggest that the quasi-steady assumption of nasal particle transport during cycling breathing should be used with caution for an accurate assessment of the toxicological and therapeutic impact of particle inhalation. Empirical equations and effective steady state approximation derived in this study are thus valuable to estimate such unsteady effects in future applications.

Micron particle deposition in a tracheobronchial airway model under different breathing conditions

Effective management of asthma is dependent on achieving adequate delivery of the drugs into the lung. Inhalers come in the form of dry powder inhalers (DPIs) and metered dose inhalers (pMDIs) with the former requiring a deep fast breath for activation while there are no restrictions on inhalation rates for the latter. This study investigates two aerosol medication delivery methods (i) an idealised case for drug particle delivery under a normal breathing cycle (inhalation-exhalation) and (ii) for an increased effort during the inhalation with a breath hold. A computational model of a human tracheobronchial airway was reconstructed from computerised tomography (CT) scans. The model's geometry and lobar flow distribution were compared with experimental and empirical models to verify the current model. Velocity contours and secondary flow vectors showed vortex formation downstream of the bifurcations which enhanced particle deposition. The velocity contour profiles served as a predictive tool for the final deposition patterns. Different spherical aerosol particle sizes (3-10μm, 1.55g/cm(3)) were introduced into the airway for comparison over a range of Stokes number. It was found that a deep inhalation with a breath hold of 2s did not necessarily increase later deposition up to the sixth branch generation, but rather there was an increase in the deposition in the first few airway generations was found. In addition the breath hold allows deposition by sedimentation which assists in locally targeted deposition. Visualisation of particle deposition showed local "hot-spots" where particle deposition was concentrated in the lung airway.

Comparison of micron- and nanoparticle deposition patterns in a realistic human nasal cavity

Knowledge regarding particle deposition processes in the nasal cavity is important in aerosol therapy and inhalation toxicology applications. This paper presents a comparative study of the deposition of micron and submicron particles under different steady laminar flow rates using a Lagrangian approach. A computational model of a nasal cavity geometry was developed from CT scans and the simulation of the fluid and particle flow within the airway was performed using the commercial software GAMBIT and FLUENT. The air flow patterns in the nasal cavities and the detailed local deposition patterns of micron and submicron particles were presented and discussed. It was found that the majority of micron particles are deposited near the nasal valve region and some micron particles are deposited on the septum wall in the turbinate region. The deposition patterns of micron particles in the left cavity are different compared with that in the right one especially in the turbinate regions. In contrast, the deposition for nanoparticles shows a moderately even distribution of particles throughout the airway. Furthermore the particles releasing position obviously influences the local deposition patterns. The influence of the particle releasing position is mainly shown near the nasal valve region for micron particle deposition, while for submicron particles deposition, both the nasal valve and turbinate region are influenced. The results of the paper are valuable in aerosol therapy and inhalation toxicology.

Computational Modelling of Gas-Particle Flows with Different Particle Morphology in the Human Nasal Cavity

This paper summarises current studies related to numerical gas-particle flows in the human nasal cavity. Of interest are the numerical modelling requirements to consider the effects of particle morphology for a variety of particle shapes and sizes such as very small particles sizes (nanoparticles), elongated shapes (asbestos fibres), rough shapes (pollen), and porous light density particles (drug particles) are considered. It was shown that important physical phenomena needed to be addressed for different particle characteristics. This included the Brownian diffusion for submicron particles. Computational results for the nasal capture efficiency for nano-particles and various breathing rates in the laminar regime were found to correlate well with the ratio of particle diffusivity to the breathing rate. For micron particles, particle inertia is the most significant property and the need to use sufficient drag laws is important. Drag correlations for fibrous and rough surfaced particles were investigated to enable particle tracking. Based on the simulated results, semi-empirical correlations for particle deposition were fitted in terms of Peclet number and inertial parameter for nanoparticles and micron particles respectively.

Modeling the bifurcating flow in a CT-scanned human lung airway

The inspiratory flow characteristics in a CT-scanned human lung model were numerically investigated using low Reynolds number (LRN) kappa-omega turbulent model. The five-generation airway is extracted from the trachea to segmental bronchi of a 60-year-old Chinese male patient. Computations were carried out in the Reynolds number range of 900-2100, corresponding to mouth-air breathing rates of 190-440 ml/s. Flow patterns on the Re=2100 and flow rate distribution were presented. In this model, the flow pattern is very complex. To count the effect of laryngeal jet on trachea inlet, the trachea was extended and modified to simulate the larynx, consequently the inlet velocity profile is biased towards the rear wall. In the inferior lobar bronchi, there are two stems in which the axial velocity is stronger but secondary velocity is weaker. Secondary flow in the lateral bronchi is stronger than the medial ones. With increasing Re, the air flow increases in the middle, inferior lobes and left main bronchus, i.e., flow biases to left and downward.

Optimising nasal spray parameters for efficient drug delivery using computational fluid dynamics

Experimental images from particle/droplet image analyser (PDIA) and particle image velocimetry (PIV) imaging techniques of particle formation from a nasal spray device were taken to determine critical parameters for the study and design of effective nasal drug delivery devices. The critical parameters found were particle size, diameter of spray cone at a break-up length and a spray cone angle. A range of values for each of the parameters were ascertained through imaging analysis which were then transposed into initial particle boundary conditions for particle flow simulation within the nasal cavity by using Computational Fluid Dynamics software. An Eulerian-Lagrangian scheme was utilised to track mono-dispersed particles (10 and 20 microm) at a breathing rate of 10 L/min. The results from this qualitative study aim to assist the pharmaceutical industry to improve and help guide the design of nasal spray devices.

Numerical simulations for detailed airflow dynamics in a human nasal cavity

Nasal physiology is dependent on the physical structure of the nose. Individual aspects of the nasal cavity such as the geometry and flow rate collectively affect nasal function such as the filtration of foreign particles by bringing inspired air into contact with mucous-coated walls, humidifying and warming the air before it enters the lungs and the sense of smell. To better understand the physiology of the nose, this study makes use of CFD methods and post-processing techniques to present flow patterns between the left and right nasal cavities and compared the results with experimental and numerical data that are available in literature. The CFD simulation adopted a laminar steady flow for flow rates of 7.5 L/min and 15 L/min. General agreement of gross flow features were found that included high velocities in the constrictive nasal valve area region, high flow close to the septum walls, and vortex formations posterior to the nasal valve and olfactory regions. The differences in the left and right cavities were explored and the effects it had on the flow field were discussed especially in the nasal valve and middle turbinate regions. Geometrical differences were also compared with available models.

Fluid-dynamic optimality in the generation-averaged length-to-diameter ratio of the human bronchial tree

It is shown in this paper that the nearly constant length-to-diameter ratio observed with conducting airways of human bronchial tree can be explained based on the fluid dynamic optimality principle. In any branched tube there are two pressure loss mechanisms, one for wall friction in the tube section and the other for flow division in the branching section, and there exists an optimal length-to-diameter ratio which minimizes the total pressure loss for a branched tube in laminar flow condition. The optimal length-to-diameter ratio predicted by the pressure loss minimization shows an excellent agreement with the length-to-diameter ratios found in the human conducting airways.

Respiratory flow in obstructed airways

Chronic obstructive pulmonary disease (COPD) is one of the most common diseases in human community. The COPD always results in inflammation that leads to narrowing and obstruction of the airways. The obstructive airways have significant effect on respiratory flow. In order to understand the flow phenomenon in such obstructive airways, four three-dimensional four-generation lung models based on the 23-generation model of Weibel [1963. Morphometry of the Human Lung. Springer, Academic Press, Berlin, New York] are generated. The fully three-dimensional incompressible laminar Navier-Stokes equations are solved using computational fluid dynamics (CFD) solver on unstructured tetrahedral meshes. Therein, a symmetric four-generation airway model is served as the reference, 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 air flow in both up- and down-stream airways and it even results in flow separation in the conjunction region. The re-circulation cell blocks the air from entering the downstream branches. This may be the reason why COPD patients should breathe gently, and this also provides some valuable information for medicine powder deposition.

Modeling the bifurcating flow in an asymmetric human lung airway

In a former paper, the inspiratory flow characteristics in a three-generation symmetric bifurcation airway have been numerically investigated using a control volume method to solve the fully three-dimensional laminar Navier-Stokes equations. The present paper extends the work to deal with asymmetric airway extracted from the 5th-11th branches of the model of Weibel (Morphometry of the Human Lung. New York Academic Press, Verlag, 1963) in order to more appropriately model human air passage. Computations are carried out in the Reynolds number range 200-1600, corresponding to mouth-air breathing rates ranging from 0.27 to 2.16l/s, representative for an averaged height man breathing from quiet to vigorous state. Particular attentions are paid to establishing relations between the Reynolds number and the overall flow characteristics, including flow patterns and pressure drop. The study shows that the ratios of airflow rate through the medial branches to that of their mother branches are the same, and this is also true for the ratios of airflow rate through the lateral branches. This partially explains why regular human breathing is not affected by airways of different sizes.

Modeling the bifurcating flow in a human lung airway

The inspiratory flow characteristics in a three-generation lung airway have been numerically investigated using a control volume method to solve the fully three-dimensional laminar Navier-Stokes equations. The three-generation airway is extracted from the fifth to seventh branches of the model of Weibel (Morphometry of the Human Lung, Academic Press, New York, Springer, Berlin, 1963) with in-plane and 90 degrees off-plane configurations. Computations are carried out in the Reynolds number range of 200-1600, corresponding to mouth-air breathing rates ranging from 0.27 to 2.16l/s, or an averaged height of a man breathing from quiet to vigorous state. Particular attention is paid to establishing relations between the Reynolds number and the overall flow characteristics, including flow patterns and pressure drop. The ratio of airflow rate through the medial branch to that of the lateral branch for an in-plane airway increases as Re(0.227). However, the total pressure drop coefficient varies as Re(-0.497) for an in-plane airway and as Re(-0.464) for an off-plane airway. These pressure drop results are in good agreement with the experimentally measured behavior of Re(-0.5) and are more accurate than the numerically determined behavior of Re(-0.61) assuming the airways to be approximated by two-dimensional channels.

Noninvasive ventilation with helium-oxygen in acute exacerbations of chronic obstructive pulmonary disease

The use of helium-oxygen (HeO(2)) was tested in combination with noninvasive ventilation (NIV) in 10 patients with acute exacerbation of chronic obstructive pulmonary disease (COPD). Effort to breathe as assessed by the respiratory muscle pressure-time index (PTI), work of breathing (WOB), and gas exchange were the main endpoints. Results of NIV-HeO(2) were compared with those obtained with standard NIV (AirO(2)), at two levels of pressure-support ventilation (PSV), 9 +/- 2 cm H(2)O and 18 +/- 3 cm H(2)O. Significant reductions in PTI were observed between HeO(2) and AirO(2) at both the low PSV level (n = 9; 160 +/- 58 versus 198 +/- 78 cm H(2)O/s/ min; p < 0.05) and the high PSV level (n = 10; 100 +/- 45 versus 150 +/- 82 cm H(2)O/s/min; p < 0.01). WOB also differed significantly between HeO(2) and AirO(2) (7.8 +/- 4.1 versus 10.9 +/- 6.1 J/min at the low PSV level, p < 0.05; and 5.7 +/- 3.3 versus 9.2 +/- 5. J/min, p < 0.01 at the high PSV level). HeO(2) reduced Pa(CO(2)) at both the low PSV level (61 +/- 13 versus 64 +/- 15 mm Hg; p < 0.05) and the high PSV level (56 +/- 13 versus 58 +/- 14 mm Hg; p < 0.05), without significantly changing breathing pattern or oxygenation. We conclude that use of HeO(2) during NIV markedly enhances the ability of NIV to reduce patient effort and to improve gas exchange.

Estimation of inspiratory pressure drop in neonatal and pediatric endotracheal tubes

Endotracheal tubes (ETTs) constitute a resistive extra load for intubated patients. The ETT pressure drop (DeltaP(ETT)) is usually described by empirical equations that are specific to one ETT only. Our laboratory previously showed that, in adult ETTs, DeltaP(ETT) is given by the Blasius formula (F. Lofaso, B. Louis, L. Brochard, A. Harf, and D. Isabey. Am. Rev. Respir. Dis. 146: 974-979, 1992). Here, we also propose a general formulation for neonatal and pediatric ETTs on the basis of adimensional analysis of the pressure-flow relationship. Pressure and flow were directly measured in seven ETTs (internal diameter: 2.5-7.0 mm). The measured pressure drop was compared with the predicted drop given by general laws for a curved tube. In neonatal ETTs (2.5-3.5 mm) the flow regime is laminar. The DeltaP(ETT) can be estimated by the Ito formula, which replaces Poiseuille's law for curved tubes. For pediatric ETTs (4.0-7.0 mm), DeltaP(ETT) depends on the following flow regime: for laminar flow, it must be calculated by the Ito formula, and for turbulent flow, by the Blasius formula. Both formulas allow for ETT geometry and gas properties.

Endotracheal cuff pressure as an index of airway smooth muscle activity: comparison with total lung resistance

Pressure changes in the cuff of an endotracheal tube (Pcuff) were measured as an index of the tracheal smooth muscle activity and compared with total lung resistance (RL) in anesthetized, paralyzed and artificially ventilated dogs. After obtaining passive pressure-volume relationships of the cuff in situ, we activated the airway smooth muscle by electrical stimulation of the right vagus nerve, intravenous acetylcholine, and airway mechanical stimulation. The responses elicited by vagal stimulation and airway probing affected predominantly the tracheal smooth muscle, whereas acetylcholine administration caused homogeneous responses in Pcuff and RL, suggesting involvement of the smooth muscle of the entire airway. Pcuff cannot represent the whole airway smooth muscle activity, but it is more sensitive than RL for detecting vagally mediated smooth muscle responses. We conclude that the combination of Pcuff and RL may provide a better evaluation of smooth muscle response to various stimuli.

Computational model of oscillatory airflow in a bronchial bifurcation

Airflow distribution in the bronchial tree is an important factor that controls gas mixing in the lungs, especially, in diseased lungs or during high frequency ventilation. A nonlinear analog model has been developed to investigate the dependency of airflow distribution in asymmetric bronchial bifurcations on structural and physiological parameters. The system parameters (electrical analogs) are time-dependent and were extracted from laboratory studies of airway models and physiological measurements. The model was used to study flow distribution in peripheral pathways of normal and pathological airways during different modes of quiet breathing as well as high frequency ventilation. Model simulations revealed that (i) increasing of ventilation frequency or stroke volume increases the time and percentage of pendelluft in each cycle, (ii) diameter asymmetry between parallel pathways is more dominant than length asymmetry and enhances the degree of asynchronous ventilation to peripheral pathways, and (iii) asymmetry in the compliance of peripheral airways and lung parenchyma greatly increases the degree of asynchronous ventilation.

Numerical modeling of steady inspiratory airflow through a three-generation model of the human central airways

Two-dimensional steady inspiratory airflow through a three-generation model of the human central airways is numerically investigated, with dimensions corresponding to those encountered in the fifth to seventh generations of the Weibel's model. Wall curvatures are added at the outer walls of the junctions for physiological purposes. Computations are carried out for Reynolds numbers in the mother branch ranging from 200 to 1200, which correspond to mouth air breathing at flow rates ranging from 0.27 to 1.63 liters per second. The difficulty of generating grids in a so complex configuration is overcome using a nonoverlapping multiblock technique. Simulations demonstrate the existence of separation regions whose number, location, and size strongly depend on the Reynolds number. Consequently, four different flow configurations are detected. Velocity profiles downstream of the bifurcations are shown to be highly skewed, thus leading to an important unbalance in the flow distribution between the medial and lateral branches of the model. These results confirm the observations of Snyder et al. and Tsuda et al. and suggest that a resistance model of flow partitioning based on Kirchhoff's laws is inadequate to simulate the flow behavior accurately within the airways. When plotted in a Moody diagram, airway resistance throughout the model is shown to fit with a linear relation of slope -0.61. This is qualitatively in good agreement with the experimental investigations of Pedley et al, and Slutsky et al.

Mathematical model for the selective deposition of inhaled pharmaceuticals

To accurately assess the potential therapeutic effects of airborne drugs, the deposition sites of inhaled particles must be known. Herein, an original theory is presented for physiologically based pharmacokinetic modeling and related prophylaxis of airway diseases. The mathematical model describes the behavior and fate of particles in the lungs of adult human subjects under various breathing conditions. Their deposition patterns are calculated via superposition of the separate but not independent processes of inertial impaction, sedimentation, and diffusion. The related computer code is designed to calculate total and compartmental (tracheobronchial and pulmonary) distributions of inhaled aerosols. In this manuscript, the model is first tested via comparisons of predicted deposition patterns with laboratory data from human inhalation exposure experiments and then it is applied to determine which factors most influence the dosimetry of inhaled particles. In this format, deposition patterns are explicitly related to particle characteristics, ventilatory parameters, and intersubject variabilities of lung morphologies. The dosimetric model was developed to improve the efficacy of aerosol therapy via the selective deposition of inhaled pharmaceuticals at prescribed lung locations to elicit optimum effects.

Dynamic lung inflation during high frequency oscillation in neonates

The effects of high frequency oscillation (HFO) on dynamic lung inflation were examined in 22 neonates ventilated for respiratory disease. HFO was combined with conventional ventilation and a series of frequencies from 2-25 Hz was tested. Dynamic lung inflation was measured using a jacket plethysmograph which was converted to a measure of alveolar pressure using the compliance of the respiratory system obtained during conventional ventilation. The results showed an increase in dynamic lung inflation with frequency such that volume increased by 0.4 ml for each increase of 10 Hz. Alveolar pressure increased by 1.2 cm H2O for each increase of 10 Hz. Dynamic lung inflation also increased with increased volumes of oscillation.

Gas physical properties and respiratory system resistance measured by flow interruption

If the flow of gas at the airway opening of a tracheostomized dog is suddenly interrupted during expiration, the airway pressure exhibits a sudden very rapid rise, called delta Pinit, which has been shown previously to equal the resistive pressure drop across the airways in open-chest dogs, and to have a significant additional contribution from the tissues of the chest wall in intact dogs. In the present study we attempted to separate the contributions of airways and tissues to delta Pinit in intact dogs by performing flow interruptions with the lungs full of gas mixtures having different physical properties. A Moody plot (the Friction coefficient calculated using delta Pinit versus the Reynolds number) had a marked negative slope at Reynolds numbers up to 5 x 10(4), whereas the plot is predicted to have a slope close to zero at Reynolds numbers greater than 4 x 10(3) on the basis of purely fluid dynamic considerations. Assuming delta Pinit to be the result of a linear dependence of airway resistance on flow and a constant tissue resistance, we were able to account for the negative slope of the Moody plot. We also found that the values of airway and tissue resistances estimated from the data were very close to those estimated by more direct means in a previous study of delta Pinit. We conclude that it is possible to discern the separate effects of airway and tissue resistances in delta Pinit at high Reynolds numbers.

Flow distribution in a single bifurcation during high-frequency oscillation

The distribution of flow in a single bifurcation was studied to examine what factors played a critical role. Flow was preferentially directed down the straightest pathway when higher frequencies and/or larger tidal volumes were used, but otherwise followed the pattern dictated by the distal impedance regardless of bifurcation geometry. In a symmetrical model, the observed flow distribution was in good agreement with a mathematical prediction based on linear impedance theory, though this was not the case when tidal volumes were increased. The difference in mean pressure between the two terminal units was also a strong function of branching angle and the Reynolds number. These findings suggest that the geometrical factors and local flow conditions contribute to both the flow and mean pressure distribution in an inertia-induced nonlinear manner. Consequently, linear impedance theory can be applied only to the limited situation of low tidal volume and symmetric configuration.

Gas exchange during constant flow ventilation with different gases

To investigate the mechanisms of CO2 transport during constant flow ventilation, we measured arterial blood gases using air, 80% He-20% O2 (He) or 80% SF6-20% O2 (SF6) as the insufflating gas. At any given flow rate (0.2 to 1.0 L/s), PaCO2 was greatest with He and lowest with SF6. Data for all gases could be described by the equation PaCO2/Pb = 0.044 V-0.64 v0.23, where Pb = barometric pressure, PaCO2 is in mm Hg, V = insufflated flow in L/s, and v = kinematic viscosity (cm2/s). At any given flow rate, the AaPO2 was greater using SF6 than using He. These results are consistent with a 2-zone model of gas transport in which the enhancement of gas transport as V increases may be due to an increase in the turbulent diffusivity in zone I (the region affected by the jet). The decreased gas transport with He compared to air and SF6 at any V may be due to either the decreased penetration depth of zone I caused by the greater kinematic viscosity of He, or the decreased rate of gas transport in the region affected by cardiogenic oscillations (zone II) secondary to the higher molecular diffusivity of He.

Steady pressure-flow relationship in a cast of the upper and central human airways

Pressure drops across the upper (larynx) and central airways of a human lung cast were measured at steady state inspiratory and expiratory flows. Air, He-O2 and SF6-O2 gas mixtures were used at tracheal Reynolds' numbers ranging from 145 to 30,000. The pressure-flow characteristics of the model were analysed using standard pressure-flow diagrams and Moody plots. We found that the asymmetry between inspiratory and expiratory resistances, observed in the central airways (larynx excluded), was markedly reduced in the presence of the larynx. However, static pressure differences were greater across the entire model of the upper and central airways than across the model of the five generations of the tracheo-bronchial tree (without larynx) at the same flow-rates. In addition, our results showed that the presence of the larynx tended to reduce the zone of fully developed laminar flow in the Moody diagram with the higher density gas, while extending the zone of turbulent flow even for the low density gas at low Reynold's numbers.

Turbulence in pulsatile flows

Turbulence during pulsatile flow has been suggested as a possible mechanism to enhance the transport of gases during high-frequency ventilation. Experimental studies on oscillatory flow in straight, circular tubes have identified three types of flow: (a) laminar; (b) conditionally turbulent, in which high-frequency disturbances occur during the decelerating phase of the flow cycle but relaminarize by the beginning of the subsequent accelerating phase; and (c) fully turbulent flow, in which disturbances occur throughout the flow cycle. Fully turbulent flow has been observed only when a mean flow is present, and only laminar or conditionally turbulent flow has been observed for purely oscillatory flow. A critical Reynolds number based on the Stokes layer can be defined, and transition Reynolds numbers between 400 and 550 have been experimentally determined for purely oscillatory flow in a circular tube, although lower values are expected for physiological flows. There are some indications that the structure of oscillating turbulent flow is similar to steady turbulent flow, and preliminary work in our laboratory shows that the spectral content of flows during high-frequency ventilation is similar to that in steady turbulent flow.

Model study of flow dynamics in human central airways. Part III: Oscillatory velocity profiles

Measurements of oscillatory velocity were made in a 3:1 model of the human central airways. The model was built of acrylic plastic and mounted vertically. A reciprocating pump connected to the upper end of the model privided oscillatory flow frequencies of 0.25, 1, 2 and 4 Hz (equivalent to 2.25, 9, 18 and 36 Hz in the actual airways) and tidal volumes of 300, 500 and 1500 ml. A hot-wire anemometer probe was used to measure velocities along two perpendicular diameters and at six stations distributed through the model. The flow distribution through the five lobar bronchi was controlled by distally positioned linear resistors . The measurements indicate that the entry flow profile into the model during oscillatory flow was essentially flat. At low frequencies, the velocity profiles attained at peak flow rate resemble the profiles seen under steady flow conditions at the corresponding Reynolds number. In the frontal plant these profiles are asymmetric with a maximum in velocity directed towards the outer wall of the bend. In the sagittal plane the velocity profiles are symmetric and have the characteristic bi-peak (M-shaped) structure seen in the steady flows. However, as the frequency increases the velocity profiles throughout most branches tend to flatten except in the right upper lobar bronchus where the skewed velocity profiles persist even at the highest frequencies studied. As in steady flows the nature of the velocity profile is strongly influenced by the airway geometry. Furthermore, the peak velocity profiles resemble steady flow profiles at comparable Reynolds numbers up to a Womersley number of 16.

Mass transport in mammalian lungs: comparative physiology

Comparative physiology of mass transport of gases in mammalian lungs is surveyed in terms of the use of experimental mammals in inhalation toxicology. Principles of similarity, scaling, and the relationship of metabolism to body size are touched on, with reference to the wide variability among mammals of similar size. Mechanisms that influence the magnitude and distribution of pulmonary ventilation are reviewed, including mechanical differences associated with variation in body size. More systematic and complete descriptions and understanding are needed. Recent advances in the understanding of gas mixing and transport in airways and in the pulmonary acinus have applications in comparative physiology and inhalation toxicology that are worth exploring.

A model study of flow dynamics in human central airways. Part I: axial velocity profiles

We measured detailed steady inspiratory and expiratory velocity profiles in a 3:1 scale model of the human central airways. The model was constructed out of acrylic plastic, mounted vertically, and connected to a specially designed steady-flow system. Laterally introduced hot-wire anemoneter probes were used to record axial velocities along 4 diameters at each of the 12 pre-drilled stations of measurement; the flow distribution among the five lobar bronchi was controlled by distally positioned linear resistors. Whether with a flat entrance profile or entering as a narrow jet, the inspiratory flow velocity profiles in the frontal plane showed a high degree of asymmetry in all branches, with peak velocities near the inner wall of the bifurcation. In the sagittal plane the velocity profiles were nearly symmetric, exhibiting a single peak near the center in the frontal plane and almost flat in the sagittal plane. Overall, the velocity profiles were more sensitive to airway geometry than to flow rate. The only site of flow separation was observed in the right upper lobar bronchus. The most evident modification of axial velocity profiles in a single branch was found in the left main bronchus during expiratory flow.

Effects of unequal pressure swings and different waveforms on distribution of ventilation: a non-linear model simulation

In an attempt to understand the role of unequal pleural pressure swings and of different waveforms of pleural pressure variation in the distribution of ventilation during cyclic breathing, a mathematical model simulation was performed. The computer model which incorporates non-linear resistances and compliances as well as sinusoidal, square, and triangular waveforms of pleural pressure variations indicates that the distribution of ventilation is insensitive to the waveform of the pleural pressure. The distribution is also little changed by the depth of breathing (amplitude), but it is affected significantly by the pattern of different pressures over the regions of the model. For sinusoidal, triangular, and low amplitude square wave pleural pressures with equal amplitudes on both compartments, air was distributed preferentially to the lower compartment under the influence of the static pressure difference. With unequal amplitudes, more air flowed to the compartment experiencing the larger pressure swing. This was virtually independent of the waveform and of the amplitudes of the pleural pressure variation. Comparison of the present results with a constant flow model reveals that the overall distribution of tidal air during cyclic breathing is very different from the results obtained in constant rate inspiration experiments or in bolus distribution experiments. New experiments performed under cyclic breathing conditions are thus indicated.