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.     

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.     

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.     

Gas exchange in healthy rabbits during high-frequency oscillatory ventilation

We examined the effects of oscillatory frequency (f), tidal volume (VT), and mean airway pressure (Paw) on respiratory gas exchange during high-frequency oscillatory ventilation of healthy anesthetized rabbits. Frequencies from 3 to 30 Hz, VT from 0.4 to 2.0 ml/kg body wt (approximately 20-100% of dead space volume), and Paw from 5 to 20 cmH2O were studied. As expected, both arterial partial pressure of O2 and CO2 (PaO2 and PaCO2, respectively) were found to be related to f and VT. Changing Paw had little effect on blood gas tensions. Similar values of PaO2 and PaCO2 were obtained at many different combinations of f and VT. These relationships collapsed onto a single curve when blood gas tensions were plotted as functions of f multiplied by the square of VT (f. VT2). Simultaneous tracheal and alveolar gas samples showed that the gradient for PO2 and PCO2 increased as f. VT2 decreased, indicating alveolar hypoventilation. However, venous admixture also increased as f. VT2 decreased, suggesting that ventilation-perfusion inequality must also have increased.     

Augmentation of axial dispersion by intermittent oscillatory flow.

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.     

Physiological dead space during high-frequency ventilation in dogs

Tidal volumes used in high-frequency ventilation (HFV) may be smaller than anatomic dead space, but since gas exchange does take place, physiological dead space (VD) must be smaller than tidal volume (VT). We quantified changes in VD in three dogs at constant alveolar ventilation using the Bohr equation as VT was varied from 3 to 15 ml/kg and frequency (f) from 0.2 to 8 Hz, ranges that include normal as well as HFV. We found that VD was relatively constant at tidal volumes associated with normal ventilation (7-15 ml/kg) but fell sharply as VT was reduced further to tidal volumes associated with HFV (less than 7 ml/kg). The frequency required to maintain constant alveolar ventilation increased slowly as tidal volume was decreased from 15 to 7 ml/kg but rose sharply with attendant rapid increases in minute ventilation as tidal volumes were decreased to less than 7 ml/kg. At tidal volumes less than 7 ml/kg, the data deviated substantially from the conventional alveolar ventilation equation [f(VT - VD) = constant] but fit well a model derived previously for HFV. This model predicts that gas exchange with volumes smaller than dead space should vary approximately as the product of f and VT2.     

Comparison of axisymmetric and three-dimensional models for gas uptake in a single bifurcation during steady expiration

Reactive gas uptake is predicted and compared in a single bifurcation at steady expiratory flow in terms of Sherwood number using an axisymmetric single-path model (ASPM) and a three-dimensional computational fluid dynamics model (CFDM). ASPM is validated in a two-generation geometry by comparing the average gas-phase mass transfer coefficients with the experimental values. ASPM predicted mass transfer coefficients within 20% of the experimental values. The flow and concentration variables in the ASPM were solved using Galerkin finite element method and in the CFDM using commercial finite element software FIDAP. The simulations were performed for reactive gas flowing at Reynolds numbers ranging from 60 to 350 in both symmetric bifurcation for three bifurcation angles, 30 deg, 70 deg, and 90 deg, and in an asymmetric bifurcation. The numerical models compared with each other qualitatively but quantitatively they were within 0.4-8% due to nonfully developed flow in the parent branch predicted by the CFDM. The radially averaged concentration variation along the axial location matched qualitatively between the CFDM and ASPM but quantitatively they were within 32% due to differences in the flow field. ASPM predictions compared well with the CFDM predictions for an asymmetric bifurcation. These results validate the simplified ASPM and the complex CFDM. ASPM predicts higher Sherwood number with a flat velocity inlet profile compared to a parabolic inlet velocity profile. Sherwood number increases with the inlet average velocity, wall mass transfer coefficient, and bifurcation angle since the boundary layer grows slower in the parent and daughter branches.     

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)     

Regional mapping of gas transport during high-frequency and conventional ventilation

The effects of changing tidal volume (VT) and frequency (f) on the distribution of ventilation during high-frequency ventilation (HFV) were assessed from the washout of nitrogen-13 by positron emission tomography. Six dogs, anesthetized and paralyzed, were studied in the supine position during conventional ventilation (CV) and during HFV at f of 3, 6, and 9 Hz. In CV and HFV at 6 Hz, VT was selected to achieve eucapnic arterial partial pressure of CO2 (37 +/- 3 Torr). At 3 and 9 Hz, VT was proportionally changed so that the product of VT and f remained constant and equal to that at 6 Hz. Mean residence time (MRT) of nitrogen-13 during washout was calculated for apical, midheart, and basal transverse sections of the lung and further analyzed for gravity-dependent, cephalocaudal and radial gradients. An index of local alveolar ventilation per unit of lung volume, or specific ventilation (spV), was calculated as the reciprocal of MRT. During CV vertical gradients of regional spV were seen in all sections with ventral (nondependent) regions less ventilated than dorsal (dependent) regions. Regional nonuniformity in gas transport was greatest for HFV at 3 and 6 Hz and lowest at 9 Hz and during CV. During HFV, a central region at the base of the lungs was preferentially ventilated, resulting in a regional time-averaged tracer concentration equivalent to that of the main bronchi. Because the main bronchi were certainly receiving fresh gas, the presence of this preferentially ventilated area, whose ventilation increased with VT, strongly supports the hypothesis that direct convection of fresh gas is an important mechanism of gas transport during eucapnic HFV. Aside from the local effect of increasing overall lung ventilation, this central area probably served as an intermediate shuttle station for the transport of gas between mouth and deeper alveoli when VT was less than the anatomic dead space.     

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.     

Transit time dispersion in pulmonary and systemic circulation: effects of cardiac output and solute diffusivity

We present an in vivo method for analyzing the distribution kinetics of physiological markers into their respective distribution volumes utilizing information provided by the relative dispersion of transit times. Arterial concentration-time curves of markers of the vascular space [indocyanine green (ICG)], extracellular fluid (inulin), and total body water (antipyrine) measured in awake dogs under control conditions and during phenylephrine or isoproterenol infusion were analyzed by a recirculatory model to estimate the relative dispersions of transit times across the systemic and pulmonary circulation. The transit time dispersion in the systemic circulation was used to calculate the whole body distribution clearance, and an interpretation is given in terms of a lumped organ model of blood-tissue exchange. As predicted by theory, this relative dispersion increased linearly with cardiac output, with a slope that was inversely related to solute diffusivity. The relative dispersion of the flow-limited indicator antipyrine exceeded that of ICG (as a measure of intravascular mixing) only slightly and was consistent with a diffusional equilibration time in the extravascular space of approximately 10 min, except during phenylephrine infusion, which led to an anomalously high relative dispersion. A change in cardiac output did not alter the heterogeneity of capillary transit times of ICG. The results support the view that the relative dispersions of transit times in the systemic and pulmonary circulation estimated from solute disposition data in vivo are useful measures of whole body distribution kinetics of indicators and endogenous substances. This is the first model that explains the effect of flow and capillary permeability on whole body distribution of solutes without assuming well-mixed compartments.     

CO2 elimination as a function of frequency and tidal volume in rabbits during HFO

CO2 elimination (VCO2) was monitored during high-frequency oscillation (HFO) over a frequency (f) range of 2-30 Hz in anesthetized and paralyzed rabbits to determine whether effective gas exchange could be achieved in this species, to determine the f and tidal volume (VT) dependence of gas exchange in this species, and to compare these results with those from dog and human studies. We were able to produce VCO2 levels during HFO that exceeded normal steady-state levels of CO2 production with VT's less than the total dead space volume. VCO2 was related to f in a curvilinear fashion, whereas in some rabbits VCO2 became independent of f at higher frequencies. This curvilinear relationship between f and VCO2 is similar to data from humans but contrasts with the linear relationship found in dogs. Evidence is presented indicating frequency-dependent behavior of gas exchange is correlated with a frequency-dependent decrease in respiratory system resistance. We propose that the frequency-dependent mechanical properties of the rabbit lung may also account for the species differences in HFO gas exchange.     

Stochastic modelling of axial dispersion in external-loop airlift bioreactors

The paper presents a model of the motion of a particle subjected to several transport processes in connection with mixing in two phase flow. A residence time distribution technique coupled with a one-dimensional dispersion model was used to obtain the axial dispersion coefficient in the liquid phase, D_ax. The proposed model of D_ax for an external-loop airlift bioreactor is based on the stochastic analysis of the two-phase flow in a cocurrent bubble column and modified for the specific flow in the airlift reactor. The model takes into account the riser gas superficial velocity, the riser liquid superficial velocity, the Sauter bubble diameter, the riser gas hold-up, the downcomer-to-riser cross sectional area ratio. The proposed model can be applied with an average error of ᆨ.     

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.     

The influence of vessel height and top-section size on the hydrodynamic characteristics of airlift fermentors

Fermentations of the yeast Saccharomyces cerevisiae were carried out in a 90 to 250-L working volume concentric tube airlift fermentor. Measurements of liquid circulation velocity, gas hold-up, and liquid mixing were made under varying conditions of gas flowrate, vessel height, and top-section size. Both liquid circulation velocity and mixing time increased with vessel height. Liquid velocity varied approximately in proportion to the square root of column height, supporting a theoretically based relationship. The effect of vessel height on gas hold-up was negligible. The height of the top-section had a significant effect on liquid mixing. Mixing time decreased with increasing size of the top-section up to a critical height. As the top-section was expanded beyond this height, little improvement in mixing was seen. This indicated the presence of a two-zone flow pattern in the top-section. Liquid velocity and gas hold-up were essentially independent of top-section height. (c) 1994 John Wiley & Sons, Inc.     

Mathematical model for a three-phase fluidized bed biofilm reactor in wastewater treatment

A mathematical model for a three phase fluidized bed bioreactor (TFBBR) was proposed to describe oxygen utilization rate, biomass concentration and the removal efficiency of Chemical Oxygen Demand (COD) in wastewater treatment. The model consisted of the biofilm model to describe the oxygen uptake rate and the hydraulic model to describe flow characteristics to cause the oxygen distribution in the reactor. The biofilm model represented the oxygen uptake rate by individual bioparticle and the hydrodynamics of fluids presented an axial dispersion flow with back mixing in the liquid phase and a plug flow in the gas phase. The difference of settling velocity along the column height due to the distributions of size and number of bioparticle was considered. The proposed model was able to predict the biomass concentration and the dissolved oxygen concentration along the column height. The removal efficiency of COD was calculated based on the oxygen consumption amounts that were obtained from the dissolved oxygen concentration. The predicted oxygen concentration by the proposed model agreed reasonably well with experimental measurement in a TFBBR. The effects of various operating parameters on the oxygen concentration were simulated based on the proposed model. The media size and media density affected the performance of a TFBBR. The dissolved oxygen concentration was significantly affected by the superficial liquid velocity but the removal efficiency of COD was significantly affected by the superficial gas velocity. An erratum to this article can be found online at .     

A simplified model of hydrodynamics in airlift loop reactors

As a function of the gas throughput the following parameters were measured in an external loop reactor with a riser diameter of 0.6 m and a gassed liquid height of 8.6 m: integral and local values of gas hold-up; liquid velocities; mixing times and axial dispersion coefficients of the liquid phase. The height of the reactor could be altered by reconstruction. Measurements were also carried out with lower heights than 8.6 m. Besides pure water, aqueous solutions of coalescing, non-coalescing and viscosity-increasing substances were used as model systems. With the results a general relationship between superficial gas velocity, gas hold-up and liquid velocity was established. This hydrodynamic model uses the relative velocity between gas and liquid phase as the fundamental parameter. The generally valid model consists of one term for the homogeneous and of two additional terms for the heterogeneous flow regime.     

Compliance, blood gases, and acid-base balance in guinea pigs artificially ventilated with different IPPV patterns

In order to estimate optimum parameters for artificial ventilation of adult guinea pigs, the effect of four hours intermittent positive pressure ventilation (IPPV) was studied using different tidal volumes (VT), respiratory frequencies (f), and minute volumes (Ve). Total compliance was measured by placing the animal in a whole body plathysmograph, the arterial blood gases, pH and base excess by catheterizing the carotid artery. In Series I 9 guinea pigs were ventilated at parameters adapted to the spontaneous breathing pattern (VT = 2 ml, f = 70 breaths.min-1). This ventilatory pattern resulted in severe disorders in compliance, gas exchange, and acid-base balance. In Series II 3 different VT (2, 6, 10 ml) were studied by changing f so that Ve was kept constant. The results demonstrated a favourable effect of slow and deep ventilation upon lung mechanics and oxygenation. In Series III 3 different Ve (300, 250, 200 ml.min-1) were tested using a constant VT = 10 ml. Optimum parameters for artificial ventilation of adult guinea pigs were: VT = 10 ml and f = 20 breath--min-1 which resulted in stable compliance, good O2-saturation, normocapnia and normal acid-base balance.     

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

Local gas transport in eucapnic ventilation: effects of gravity and breathing frequency

The effects of body position and respiratory frequency (f) on regional gas transport during eucapnic conventional ventilation (CV) and high-frequency ventilation (HFV) were assessed from the washout of nitrogen 13 (13NN) using positron-emission tomography. In one protocol, six dogs were ventilated with CV or HFV at f = 6 Hz and tidal volume (VT) selected supine for eucapnia. A coronal cross section of the lung base was studied in the supine, prone, and right and left lateral decubitus positions. In a second protocol, six dogs were studied prone: apical and basal cross sections were studied in CV and in HFV with f = 3 and 9 Hz at eucapnic VT. Regional alveolar ventilation per unit of lung volume (spVr) was calculated for selected regions and analyzed for gravity-dependent cephalocaudal and right-to-left gradients. In both CV and HFV, nonuniformity in spVr was highest supine and lowest prone. In CV there were vertical gradients of spVr in all body positions: nondependent less ventilated than dependent regions, particularly in the supine position. In HFV there was a moderate vertical gradient in spVr in addition to a preferentially ventilated central region in all body positions. Overall lung spV was unaffected by body position in CV but in HFV was highest supine and lowest prone. Nonuniformity in eucapnic prone HFV was unaffected by f and always higher than in CV.(ABSTRACT TRUNCATED AT 250 WORDS)