A mechanical approach to the longitudinal dispersion of gas flowing in human airways

The aim of this work is to contribute to elucidating the mechanism underlying gas mixing in the human pulmonary airways. For this purpose, a particular attempt is made to analyse the fluid mechanical aspects of gaseous dispersion using bolus response methods. The experiments were performed on five normal subjects by injection of 10 cm3 bolus of He, Ar and SF6 into the latter part of the inspired airstream, in such a way that the whole bolus entered the inspiratory flow and was recovered during the following expiration. The results, presented in a logarithmic plot of dimensionless variance (dispersion of the output bolus) against the Peclet number, show that gaseous dispersion is only slightly dependent on the nature of the tracer gas but is strongly related to flow velocity. This is in agreement with the theory of turbulent or disturbed dispersion; however, it seems that Taylor laminar dispersion does not play a significant role in the airways.     

A model of constant-flow ventilation in a dog lung

A semiempirical model of constant-flow ventilation (CFV) is developed to test the hypothesis that a three-zone serial model with the following characteristics can explain the adequate CO2 transport observed during CFV: 1) a zone of jet recirculation immediately downstream of the catheter in which convection dominates; 2) a zone influenced by turbulence but with little or no bulk flow; and 3) a peripheral zone, free of turbulence, in which transport is governed by molecular and augmented diffusion. Interactions between turbulent eddies and cardiogenic oscillations are included using a modification of Taylor dispersion theory according to the formulation of Kamm et al. Predicted values for arterial PCO2 are reasonably similar to experimental results for He-O2, air, and SF6-O2 mixtures for catheter flow rates from 0.2 to 1.6 l/s. Specific impedance to gas exchange was found to be largest immediately proximal to the end of turbulent mixing zone, where transport is governed by low-level eddy mixing and molecular diffusion. Simulations suggest that, during CFV, cardiogenic oscillations augment gas exchange primarily by promoting turbulent eddy dispersion in the distal airways and by extending the length of the turbulent mixing zone. Even small displacements of the catheter are shown to have a dramatic effect on gas exchange.     

Radial and longitudinal compartmental analysis of gas transport during high-frequency ventilation

A model of gas exchange by low-tidal-volume (VT), high-frequency ventilation (HFV) is presented, based on the physical principles of dispersion. These are the nonuniformity of the velocity profile and the nonreversible mixing of fluid components in a diffusive manner. A numerical method was used to incorporate these principles into a quantitative model. The airways of a symmetrically bifurcating bronchial-tree model were partitioned in the radial direction into two concentric layers representing the kinematic dispersion by nonuniformity of the velocity profile. Mixing between the layers was invoked in proportion to the diffusivity and local dimensions. The effects of frequency (f), VT, shape of the velocity profile, and bronchial-model configuration were tested in the model, with favorable comparison to available experimental data. The model predicts that for a frequency-dependent velocity profile, the rate of tracer exchange is proportional to the square root of f and to the square of VT-V0, where V0 is a constant small volume under which gas exchange was nil. Intracycle asymmetric mixing is predicted to have a stronger effect on gas exchange than asymmetric velocity profile. Gas exchange when turbulent-flow regime is assumed is predicted to be less for the higher VT values than with laminar flow and with mixing by molecular diffusivity. This model was found to be didactic, flexible, and capable of modeling combinations of factors affecting either one of the two fundamental processes of dispersion.     

Measurement of axial diffusivities in a model of the bronchial airways.

Values for the effective axial diffusivity D for laminar flow of a gas species in the bronchial airways have been obtained as a function of the mean axial gas velocity u by experiment measurements of benzene vapor dispersion in a five generation glass tube model of the bronchial tree. For both inspiration and expiration D is seen to be approximately a linear function of u over the range of Reynolds' numbers 30-2,000 corresponding to peak flows in bronchial generations 0-13 under resting breathing conditions. The diffusivity for expiration is seen to be approximately one-third that for inspiration due presumably to increased radial mixing at bifurcations during expiration. The effective diffusivities relative to the molecular diffusivity can be expressed by the formulas D/Dmol = 1 + 1.08 NPe for inspiration and D/Dmol = 1 + .37 N-Pe for expiration. These velocity dependent diffusivities help to explain the short transit times of gas boluses from mouth to alveoli and will aid in the analysis of airway gas mixing by mathematical transport equations.     

Effects of gas properties and waveform asymmetry on gas transport in a branching tube network

Local gas transport coefficients, quantifying longitudinal dispersion through a symmetrical constant-diameter tube network, have been measured during oscillation with both symmetrical and nonsymmetrical waveforms. Experiments were carried out over a range of conditions that would prevail in the central to lower airways during high-frequency ventilation at moderate frequency (5 Hz) and tidal volume (15-80 ml). Gas transport coefficients resulting from oscillation of three different resident-trace gas pairs were measured using a new analytic technique. This technique allowed rapid determination of the transport coefficient distribution along the entire network. Results demonstrate a small but significant influence attributable to changes in gas properties that is similar to that found in a straight tube and indicate that augmented dispersion is an important mechanism of axial transport. Gas transport coefficients were found to be unaffected by changes in flow waveform symmetry, suggesting that previously reported improvements in gas exchange associated with decreasing inspiratory to expiratory time ratios are not due to a change in local conditions such as asymmetry in the velocity profile.     

Gas mixing in the airways of dog lungs during high-frequency ventilation

Washout of insoluble inert test gases of different diffusivity (He and SF6 or He and Ar) from dog lungs was studied during high-frequency ventilation (HFV). Test gas equilibrium and subsequent washout were performed with HFV, succeeding measurements being performed at different stroke volumes (1.5-2.5 ml/kg body wt), oscillation frequencies (10-30 Hz), and with different lung volumes (32-74 ml X kg-1). Test gas concentrations were continuously measured by a mass spectrometer. The time course of washout could be described as the sum of two exponentials. There were no consistent differences in the time courses of washout between He and SF6 or between He and Ar. It is concluded that gas mixing in the airways during HFV is not significantly limited by diffusion, and this is suggested to apply during HFV to steady-state transport of respiratory gases (e.g., O2 and CO2) as well as to the transient state of inert gas washout.     

Simulation of gas transport due to cardiogenic oscillations

We simulated gas transport due to cardiogenic oscillations (CO) using a model developed to quantify the gas mixing due to high-frequency ventilation (16). The basic components of the model are 1) gas mixing by augmented transport, 2) symmetrical lung morphometry, and 3) a Lagrangian (moving) reference frame. The theoretical predictions of the model are in general agreement with published experimental studies that have examined the effect of CO on the nitrogen concentration obtained by intrapulmonary gas sampling and the effect of CO on regional and total anatomical dead space. Further, the model predicts that augmentation of gas transport due to CO is less, nearer to the alveolar regions of the lung, and that the effect of CO during normal tidal breathing is negligible, but that CO may contribute up to approximately 10% of the alveolar ventilation in patients with severe hypoventilation. The agreement between experimental and theoretical results suggests that it may not be necessary to invoke gas transport mechanisms specific to an asymmetrical bronchial tree to explain the major proportion of gas transport due to CO.     

Intra-airway gas mixing during high-frequency ventilation

We examined the intra-airway gas transport mediated by high-frequency oscillations (HFO) in 10 nonintubated healthy volunteers using a method based on comparisons of single-breath N2-washout curves obtained after various durations of breath hold or high-frequency oscillations. With a mathematical analysis based on Fick's law of diffusion we computed the local transport parameter, effective diffusivity, during oscillations of frequency 2-24 Hz and tidal volume 10-120 ml and during breath hold alone. Local effective diffusivity increased with both oscillatory frequency and tidal volume at all levels in the tracheobronchial tree; the enhancing effect of tidal volume on local effective diffusivity was more pronounced than that of frequency so that effective diffusivity was greater with larger tidal volume at fixed frequency-tidal volume product (f . VT). The greatest enhancement of gas mixing within the lung during HFO (over breath hold) was seen in the central airways. In previous studies examining CO2 removal rate during HFO (J. Clin. Invest. 68: 1475, 1981), we found that CO2 output was also greater with larger tidal volume at fixed f . VT, and we attributed this to an end constraint imposed by a fresh gas bias flow. Results of the current study, performed without a bias flow, indicate that bias flow end constraint does not solely account for the observed dependence of CO2 output on frequency and tidal volume.     

Analytical simulation of lingitudinal gas mixing in the human central airways

In order to study gaseous mixing in the proximal respiratory airways during stationary breathing, a simple mathematical model with an analytical solution of the corresponding equation is presented. Calculations were carried out by solving the differential equation analytically according to the system response to a unit impulse combined with the convolution method. It seems that this analytical method gives similar results to those obtained by the numerical ones; however, our method is computationally simple and can provide a reasonable tool to study gas transport in the airways.     

Bolus contaminant dispersion in oscillating flow in curved tubes.

The investigation of longitudinal dispersion of tracer substances in unsteady flows has biomechanical application in the study of heat and mass transport within the bronchial airways during normal, abnormal, and artificial pulmonary ventilation. To model the effects of airway curvature on intrapulmonary gas transport, we have measured local gas dispersion in axially uniform helical tubes of slight pitch during volume-cycled oscillatory flow. Following a small argon bolus injection into the flow field, the time-averaged effective diffusion coefficient (Deff/Dmol) for axial transport of the contaminant was evaluated from the time-dependent local argon concentration measured with a mass spectrometer. The value of (Deff/Dmol) is extracted from the curve of concentration versus time by two techniques yielding identical results. Experiments were conducted in two helical coiled tubes (delta = 0.031, lambda = 0.022 or delta = 0.085, lambda = 0.060) over a range of 2 < alpha < 15, 3 < A < 15, where delta is the ratio of tube radius to radius of curvature, lambda is the ratio of pitch height to radius of curvature, alpha is the Womersley parameter or dimensionless frequency, and A is the stroke amplitude or dimensionless tidal volume. Experimental results show that, when compared to transport in straight tubes, the effective diffusivity markedly increases in the presence of axial curvature. Results also compare favorably to mathematical predictions of bolus dispersion in a curved tube over the ranges of frequency and tidal volume studied.     

Oscillatory flow and gas transport through a symmetrical bifurcation

Axial gas transport due to the interaction between radial mixing and radially nonuniform axial velocities is responsible for gas transport in thick airways during High-frequency oscillatory ventilation (HFO). Because the airways can be characterized by a bifurcating tube network, the secondary flow in the curved portion of a bifurcating tube contributes to cross-stream mixing. In this study the oscillatory flow and concentration fields through a single symmetrical airway bifurcating tube model were numerically analyzed by solving three-dimensional Navier-Stokes and mass concentration equations with the SIMPLER algorithm. The simulation conditions were for a Womersley number, alpha = 9.1 and Reynolds numbers in the parent tube between 200 and 1000, corresponding to Dn2/alpha 4 in the curved portion between 2 and 80, where Dn is Dean number. For comparison with the results from the bifurcating tube, we calculated the velocity and concentration fields for fully developed oscillatory flow through a curved tube with a curvature rate of 1/10, which is identical to the curved portion of the bifurcating tube. For Dn2/alpha 4 < or = 10 in the curved portion of the bifurcating tube, the flow divider and area changes dominate the axial gas transport, because the effective diffusivity is greater than in either a straight or curved tube, in spite of low secondary velocities. However, for Dn2/alpha 4 > or = 20, the gas transport characteristics in a bifurcation are similar to a curved tube because of the significant effect of secondary flow.     

Further considerations in a theoretical description of gas transport in lung airways

A discrete one-dimensional model of convection-diffusion in branching alveolar ducts is described and it is shown that, for a suitable choice of effective axial dispersion, the solution closely approximates that for an axially symmetric representation, at least for Peclet numbers Pe<1. Following earlier work a composite model of a uniform lung is formed by matching such a respiratory pathway (now having the more convenient one-dimensional form) onto a trumpet representation of the conducting airways. Enhanced mixing due to heart action, and isotropic volume changes of trumpet (in addition to the pathway) during breathing are additional factors included. Calculations are made of O₂ concentrations during steady-state breathing and of the concentration of inert gas during single breath wash-out of a gas mixture containing it. Predicted alveolar levels in each case agree extremely well with published data, although no alveolar slope is obtained for the inert gas.     

Indirect assessment of mucosal surface temperatures in the airways: theory and tests

We developed and tested a method, based on conduction heat transfer analysis, to infer airway mucosal temperatures from airstream temperature-time profiles during breath-hold maneuvers. The method assumes that radial conduction of heat from the mucosal wall to inspired air dominates heat exchange during a breath-hold maneuver and uses a simplified conservation of energy analysis to extrapolate wall temperatures from air temperature vs. time profiles. Validation studies were performed by simultaneously measuring air and wall temperatures by use of a retractable basket probe in the upper airways of human volunteers and intrathoracic airways of paralyzed intubated dogs during breath holding. In both protocols, a good correlation was demonstrated between directly measured wall temperatures and those calculated from adjacent airstream temperature vs. time profiles during a breath hold. We then calculated intrathoracic bronchial wall temperatures from breath-hold airstream temperature-time profiles recorded in normal human subjects after cold air hyperpnea at 30 and 80 l/min. The calculations show airway wall temperatures in the upper intrathoracic airways that are below core body temperature during hyperpnea of frigid air and upper thoracic airways that are cooler than more peripheral airways. The data suggest that the magnitude of local intrathoracic heat/water flux is not represented by heat/water loss measurements at the airway opening. Both the magnitude and locus of heat transport during cold gas hyperventilation vary with changes in inspired gas temperature and minute ventilation; both may be important determinants of airway responses.     

Convective dispersion during steady flow in the conducting airways of the human lung

The adverse health effects of inhaled particulate matter from the environment depend on its dispersion, transport, and deposition in the human airways. Similarly, precise targeting of deposition sites by pulmonary drug delivery systems also relies on characterizing the dispersion and transport of therapeutic aerosols in the respiratory tract. A variety of mechanisms may contribute to convective dispersion in the lung; simple axial streaming, augmented dispersion, and steady streaming are investigated in this effort. Flow visualization of a bolus during inhalation and exhalation, and dispersion measurements were conducted during steady flow in a three-generational, anatomically accurate in vitro model of the conducting airways to support this goal. Control variables included Reynolds number, flow direction, generation, and branch. Experiments illustrate transport patterns in the lumen cross section and map their relation to dispersion metrics. These results indicate that simple axial streaming, rather than augmented dispersion, is the dominant steady convective dispersion mechanism in symmetric Weibel generations 7-13 during normal respiration. Experimental evidence supports the branching nature of the airways as a possible contributor to steady streaming in the lung.     

Pressure change and gas mixing induced by oscillations in a closed system

In an attempt to delineate some mechanical behaviors found in branching airways, pressure transmission, gas motion, and mixing were studied during high-frequency oscillation (HFO) in an idealized system consisting of a large straight tube and a rigid sphere linked together by a small straight tube. Depending on the frequency f, and on the unsteadiness dimensionless parameter alpha, pressure amplitude in the large tube is either strongly attenuated or amplified in the sphere. This finding may provide a theoretical basis for the pressure resonance phenomenon observed in the lung by previous investigators. Gas compression in the closed volume causes convective mixing throughout the system. The measured dispersion was found to be proportional to f(VT/A)2, in agreement with a recent report. However, bulk convective mixing was sufficient to explain the dispersion for oscillatory volumes (VT) as small as 80 percent of the small tube volume, as has been previously suggested.     

Effects of respiratory variables on regional gas transport during high-frequency ventilation

The regional effects of tidal volume (VT), respiratory frequency, and expiratory-to-inspiratory time ratio (TE/TI) during high-frequency ventilation (HFV) were studied in anesthetized and paralyzed dogs. Regional ventilation per unit of lung volume (spVr) was assessed with a positron camera during the washout of the tracer isotope 13NN from the lungs of 12 supine dogs. From the washout data, functional images of the mean residence time (MRT) of 13NN were produced and spVr was estimated as the inverse of the regional MRT. We found that at a constant VT X f product (where f represents frequency), increasing VT resulted in higher overall lung spV through the local enhancement of the basal spVr and with little effect in the apical spVr. In contrast, increasing VT X f at constant VT increased overall ventilation without significantly affecting the distribution of spVr values. TE/TI had no substantial effect in regional spVr distribution. These findings suggest that the dependency of gas transport during HFV of the form VT2 X f is the result of a progressive regional transition in gas transport mechanism. It appears, therefore, that as VT increases, the gas transport mechanism changes from a relative inefficient dispersive mechanism, dependent on VT X f, to the more efficient mechanism of direct fresh gas convection to alveoli with high regional tidal volume-to-dead-space ratio. A mathematical model of gas transport in a nonhomogeneous lung that exhibits such behavior is presented.     

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-O₁ 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.     

High-frequency ventilation of ducks and geese

We studied gas exchange in anesthetized ducks and geese artificially ventilated at normal tidal volumes (VT) and respiratory frequencies (fR) with a Harvard respirator (control ventilation, CV) or at low VT-high fR using an oscillating pump across a bias flow with mean airway opening pressure regulated at 0 cmH2O (high-frequency ventilation, HFV). VT was normalized to anatomic plus instrument dead space (VT/VD) for analysis. Arterial PCO2 was maintained at or below CV levels by HFV with VT/VD less than 0.5 and fR = 9 and 12 s-1 but not at fR = 6 s-1. For 0.4 less than or equal to VT/VD less than or equal to 0.85 and 3 s-1. less than or equal to fR less than or equal to 12 s-1, increased VT/VD was twice as effective as increased fR at decreasing arterial PCO2, consistent with oscillatory dispersion in a branching network being an important gas transport mechanism in birds on HFV. Ventilation of proximal exchange units with fresh gas due to laminar flow is not the necessary mechanism supporting gas exchange in HFV, since exchange could be maintained with VT/VD less than 0.5. Interclavicular and posterior thoracic air sac ventilation measured by helium washout did not change as much as expired minute ventilation during HFV. PCO2 was equal in both air sacs during HFV. These results could be explained by alterations in aerodynamic valving and flow patterns with HFV. Ventilation-perfusion distributions measured by the multiple inert gas elimination technique show increased inhomogeneity with HFV. Elimination of soluble gases was also enhanced in HFV as reported for mammals.(ABSTRACT TRUNCATED AT 250 WORDS)     

Convective and diffusive gas transport in canine intrapulmonary airways.

The significance of convective and diffusive gas transport in the respiratory system was assessed from the response of combined inert gas and particle boluses inhaled into the conducting airways. Particles, considered as "nondiffusing gas," served as tracers for convection and two inert gases with widely different diffusive characteristics (He and SF6) as tracers for convection and diffusion. Six-milliliter boluses labeled with monodisperse di-2-ethylhexyl sebacate droplets of 0.86-microns aerodynamic diameter, 2% He, and 2% SF6 were inspired by three anesthetized mechanically ventilated beagle dogs to volumetric lung depths up to 170 ml. Mixing between inspired and residual air caused dispersion of the inspired bolus, which was quantified in terms of the bolus half-width. Dispersion of particles increased with increasing lung depth to which the boluses were inhaled. The increase followed a power law with exponents less than 0.5 (mean 0.39), indicating that the effect of convective mixing per unit volume was reduced with depth. Within the pulmonary dead space, the behavior of the inert gases He and SF6 was similar to that of the particles, suggesting that gas transport was almost solely due to convection. Beyond the dead space, dispersion of He and SF6 increased more rapidly than dispersion of particles, indicating that diffusion became significant. The gas and particle bolus technique offers a suitable approach to differential analysis of gas transport in intrapulmonary airways of lungs.     

Spatial and temporal variation of secondary flow during oscillatory flow in model human central airways

Axial and secondary velocity profiles were measured in a model human central airway to clarify the oscillatory flow structure during high-frequency oscillation. We used a rigid model of human airways consisting of asymmetrical bifurcations up to third generation. Velocities in each branch of the bifurcations were measured by two-color laser-Doppler velocimeter. The secondary velocity magnitudes and the deflection of axial velocity were dependent not only on the branching angle and curvature ratio of each bifurcation, but also strongly depended on the shape of the path generated by the cascade of branches. Secondary flow velocities were higher in the left bronchus than in the right bronchus. This spatial variation of secondary flow was well correlated with differing gas transport rates between the left and right main bronchus.