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.     

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.     

A biomechanical model of the upper airways for simulating laryngoscopy

This paper describes a three-dimensional finite element model of the human upper airways during rigid laryngoscopy. In this procedure, an anaesthetist uses a rigid blade to displace and compress the tongue of the patient, and then inserts a tube into the larynx to allow controlled ventilation of the lungs during an operation. A realistic model of the main biomechanical aspects involved would help anaesthetists in training and in predicting difficult cases in advance. For this purpose, the finite element method was used to model structures such as the tongue, ligaments, larynx, vocal cords, bony landmarks, laryngoscope blade, and their inter-relationships, based on data extracted from X-ray, MRI, and photographic records. The model has been used to investigate how the tongue tissue behaves in response to the insertion of the laryngoscope blade, when it is subjected to a variety of loading conditions. In particular, the mechanical behaviour of the soft tissue of the tongue was simulated, from simple linear elastic material to complex non-linear viscoelastic material. The results show that, within a specific set of tongue material parameters, the simulated outcome can be successfully related to the view of the vocal cords achieved during real laryngoscopies on normal subjects, and on artificially induced difficult laryngoscopy, created by extending the upper incisors teeth experimentally.     

Velocity profiles in central airways with endotracheal intubation: a model study

Steady inspiratory velocity profiles were measured at two flow rates in a 3:1 scale model of the human central airways in the presence of five modes of endotracheal intubation. The presence of an orifice or a short endotracheal tube had no significant effect on the velocity profiles distal to the carina. Long endotracheal tubes change the profiles in both main bronchi. A significant peak occurred in the frontal plane near the walls, and the maximum velocity in the airway was almost identical to the endotracheal tube center-line velocity. The flow impinging on the medial wall of the main bronchus was redirected up around the anterior and posterior walls yielding bipeak velocity profiles in the sagittal plane. A tube placed eccentrically in the trachea over the right main bronchus did not alter the velocity profiles in the left main bronchus, suggesting a redirection of flow over the carina into the left lung. An endobronchial tube at the mouth of the right main bronchus did change the shape of the velocity profiles in the left main bronchus. In the left upper lobar bronchus the presence of trachea intubation had no effect on the velocity profiles. However, in the right upper lobar bronchus, the long endotracheal tube flattened the velocity profiles from the strongly skewed ones seen in the absence of the endotracheal inserts. These results not only are relevant to distribution of ventilation and aerosol particle deposition, but also have strong implications in intrapulmonary gas mixing, especially when high-frequency low tidal-volume ventilation is involved.     

Effect of the larynx on oscillatory flow in the central airways: a model study

Measurements were made of the effect of the larynx on the oscillatory flow profiles in a 3:1 scale model of the human central airways. A fixed glottic aperture corresponding to the shape and size at midinspiration was used. Oscillatory airflows at peak Reynolds numbers, similar to those obtained during spontaneous breathing and panting, were studied. The flow distribution to the five lobar bronchi was maintained by distally placed linear resistors. A hot-wire anemometer probe was used to measure the local velocity along two perpendicular diameters at six stations distributed through the model. Near the proximal end of the trachea, the flat velocity profiles at the beginning of the flow cycle peaked at maximum flow because of the jet created by the glottic aperture. This peaked structure was conserved during the latter half of the inspiratory cycle. Close to the carina, the jet had almost dissipated and the entry conditions into the main bronchi corresponded to those in the absence of the laryngeal model. The effect of the glottic aperture on the mean velocity was not felt beyond the carina, and the characteristic skewed profiles seen in oscillatory flows, in the absence of the larynx, were present in the main and lobar bronchi.     

Model simulations of gas mixing and ventilation distribution in the human lung

A new lung model that incorporates intra-acinar diffusion- and convection-dependent inhomogeneities (DCDI) and interregional and intraregional convection-dependent inhomogeneities (CDI) is described. The model is divided into two regions, each containing two subunits. Each of the four subunits in the model consists of a multi-branch-point structure, based on the anatomic data from Haefeli-Bleuer and Weibel (Anat. Record 220: 401-414, 1988). The subunit turnover (TO), i.e., the ratio of subunit tidal to resting volume, and the flow sequences (FS) between the subunits are used as model parameters. The model simulates the normalized alveolar slope (Sn), Fowler and Bohr dead space (VDF and VDB), and alveolar mixing efficiency (AME) as a function of breath number (n) during a multiple-breath N2 washout (MBNW). For the first breath of the MBNW, these indexes are poorly sensitive to the TO distribution or FS between the subunits. However, as the washout proceeds, the n dependence of both Sn and VDB becomes markedly distinct for simulations with different TO and FS. VDF increases only slightly with n during the MBNW for a large range of TO and FS combinations, and AME is independent of FS. Comparison of published experimental observations with model simulations gave a consistent picture of ventilation maldistribution in the human lung. MBNW simulations in conditions of weightlessness, which will be performed shortly in Spacelab, suggest that it will be possible to evaluate quantitatively the intraregional elastic inhomogeneities in the human lung.     

An axisymmetric single-path model for gas transport in the conducting airways

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel's symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%-30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.     

Computational simulations of airflow in an in vitro model of the pediatric upper airways

In order to understand mechanisms of gas and aerosol transport in the human respiratory system airflow in the upper airways of a pediatric subject (male aged 5) was calculated using Computational Fluid Dynamic techniques. An in vitro reconstruction of the subject's anatomy was produced from MRI images. Flow fields were solved for steady inhalation at 6.4 and 8 LPM. For validation of the numerical solution, airflow in an adult cadaver based trachea was solved using identical numerical methods. Comparisons were made between experimental results and computational data of the adult model to determine solution validity. It was found that numerical simulations can provide an accurate representation of axial velocities and turbulence intensity. Data on flow resistance, axial velocities, secondary velocity vectors, and turbulent kinetic energy are presented for the pediatric case. Turbulent kinetic energy and axial velocities were heavily dependant on flow rate, whereas turbulence intensity varied less over the flow rates studied. The laryngeal jet from an adult model was compared to the laryngeal jet in the pediatric model based on Tracheal Reynolds number. The pediatric case indicated that children show axial velocities in the laryngeal jet comparable to adults, who have much higher tracheal Reynolds numbers than children due to larger characteristic dimensions. The intensity of turbulence follows a similar trend, with higher turbulent kinetic energy levels in the pediatric model than would be expected from measurements in adults at similar tracheal Reynolds numbers. There was reasonable agreement between the location of flow structures between adults and children, suggesting that an unknown length scale correlation factor could exist that would produce acceptable predictions of pediatric velocimetry based off of adult data sets. A combined scale for turbulent intensity as well may not exist due to the complex nature of turbulence production and dissipation.     

Effect of breathing pattern on gas mixing in a model with asymmetrical alveolar ducts

A model of the pulmonary airways was used to study three single-breath indices of gas mixing, dead space (VD), slope of the alveolar plateau, and alveolar mixing inefficiency (AMI). In the model, discrete elements of airway volume were represented by nodes. Using a finite difference technique the differential equation for simultaneous convection and diffusion was solved for the nodal network. Conducting airways and respiratory bronchioles were modeled symmetrically, but alveolar ducts asymmetrically, permitting interaction between convection and diffusion. VD, alveolar slope, and AMI increased with increasing flow. Similar trends were seen with inspired volume, although slope decreased at high inspired volumes with constant flow. VD was affected most by inspiratory flow and AMI and alveolar slope by expiratory time. VD fell approximately exponentially with time of breath holding. Eight different breathing patterns were compared. They had a small effect on alveolar slope and AMI and a greater effect on VD. The model shows how series and parallel inhomogeneity occur together and interact in asymmetrical systems: the old argument as to which is the more important should be abandoned.     

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.     

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.     

Clearance of surfactant phosphatidylcholine via the upper airways in rabbits

A possible route of clearance of surfactant phosphatidylcholine from the lungs is via the airways. To quantify surfactant loss via this pathway, latex bags were surgically placed into the abdomens of adult rabbits such that secretions cleared via the esophagus could be collected. The rabbits then were given treatment or trace doses of radiolabeled phosphatidylcholine-surfactant by tracheal injection and/or intravascular radiolabeled precursors of phosphatidylcholine. Labeled saturated phosphatidylcholine was measured in all fluids that were collected from the bags at 2-h intervals for 24 h and in alveolar washes and lung tissues at 24 h. No more than 7% of either treatment or trace doses of intratracheal surfactant-saturated phosphatidylcholine was lost via clearance up the airways over 24 h. Clearances of endogenously synthesized and secreted saturated phosphatidylcholine were estimated to be no more than 3% of the flux of labeled saturated phosphatidylcholine through the alveolar pool. These experiments demonstrate that surfactant phosphatidylcholine clearance via movement up the airways is not a major pathway leading to surfactant catabolism.