Impact of axial diffusion on nitric oxide exchange in the lungs.

Nitric oxide (NO) appears in the exhaled breath and is a potentially important clinical marker. The accepted model of NO gas exchange includes two compartments, representing the airway and alveolar region of the lungs, but neglects axial diffusion. We incorporated axial diffusion into a one-dimensional trumpet model of the lungs to assess the impact on NO exchange dynamics, particularly the impact on the estimation of flow-independent NO exchange parameters such as the airway diffusing capacity and the maximum flux of NO in the airways. Axial diffusion reduces exhaled NO concentrations because of diffusion of NO from the airways to the alveolar region of the lungs. The magnitude is inversely related to exhalation flow rate. To simulate experimental data from two different breathing maneuvers, NO airway diffusing capacity and maximum flux of NO in the airways needed to be increased approximately fourfold. These results depend strongly on the assumption of a significant production of NO in the small airways. We conclude that axial diffusion may decrease exhaled NO levels; however, more advanced knowledge of the longitudinal distribution of NO production and diffusion is needed to develop a complete understanding of the impact of axial diffusion.     

A new and more accurate technique to characterize airway nitric oxide using different breath-hold times.

Exhaled nitric oxide (NO) arises from both airway and alveolar regions of the lungs, which provides an opportunity to characterize region-specific inflammation. Current methodologies rely on vital capacity breathing maneuvers and controlled exhalation flow rates, which can be difficult to perform, especially for young children and individuals with compromised lung function. In addition, recent theoretical and experimental studies demonstrate that gas-phase axial diffusion of NO has a significant impact on the exhaled NO signal. We have developed a new technique to characterize airway NO, which requires a series of progressively increasing breath-hold times followed by exhalation of only the airway compartment. Using our new technique, we determined values (means +/- SE) in healthy adults (20-38 yr, n = 8) for the airway diffusing capacity [4.5 +/- 1.6 pl.s(-1).parts per billion (ppb)(-1)], the airway wall concentration (1,340 +/- 213 ppb), and the maximum airway wall flux (4,350 +/- 811 pl/s). The new technique is simple to perform, and application of this data to simpler models with cylindrical airways and no axial diffusion yields parameters consistent with previous methods. Inclusion of axial diffusion as well as an anatomically correct trumpet-shaped airway geometry results in significant loss of NO from the airways to the alveolar region, profoundly impacting airway NO characterization. In particular, the airway wall concentration is more than an order of magnitude larger than previous estimates in healthy adults and may approach concentrations (approximately 5 nM) that can influence physiological processes such as smooth muscle tone in disease states such as asthma.     

Airway contribution to alveolar nitric oxide in healthy subjects and stable asthma patients

Alveolar nitric oxide (NO) concentration (Fa(NO)), increasingly considered in asthma, is currently interpreted as a reflection of NO production in the alveoli. Recent modeling studies showed that axial molecular diffusion brings NO molecules from the airways back into the alveolar compartment during exhalation (backdiffusion) and contributes to Fa(NO). Our objectives in this study were 1) to simulate the impact of backdiffusion on Fa(NO) and to estimate the alveolar concentration actually due to in situ production (Fa(NO,prod)); and 2) to determine actual alveolar production in stable asthma patients with a broad range of NO bronchial productions. A model incorporating convection and diffusion transport and NO sources was used to simulate Fa(NO) and exhaled NO concentration at 50 ml/s expired flow (Fe(NO)) for a range of alveolar and bronchial NO productions. Fa(NO) and Fe(NO) were measured in 10 healthy subjects (8 men; age 38 +/- 14 yr) and in 21 asthma patients with stable asthma [16 men; age 33 +/- 13 yr; forced expiratory volume during 1 s (FEV(1)) = 98.0 +/- 11.9%predicted]. The Asthma Control Questionnaire (Juniper EF, Buist AS, Cox FM, Ferrie PJ, King DR. Chest 115: 1265-1270, 1999) assessed asthma control. Simulations predict that, because of backdiffusion, Fa(NO) and Fe(NO) are linearly related. Experimental results confirm this relationship. Fa(NO,prod) may be derived by Fa(NO,prod) = (Fa(NO) - 0.08.Fe(NO))/0.92 (Eq. 1). Based on Eq. 1, Fa(NO,prod) is similar in asthma patients and in healthy subjects. In conclusion, the backdiffusion mechanism is an important determinant of NO alveolar concentration. In stable and unobstructed asthma patients, even with increased bronchial NO production, alveolar production is normal when appropriately corrected for backdiffusion.     

Probing the impact of axial diffusion on nitric oxide exchange dynamics with heliox.

Exhaled nitric oxide (NO) is a potential noninvasive index of lung inflammation and is thought to arise from the alveolar and airway regions of the lungs. A two-compartment model has been used to describe NO exchange; however, the model neglects axial diffusion of NO in the gas phase, and recent theoretical studies suggest that this may introduce significant error. We used heliox (80% helium, 20% oxygen) as the insufflating gas to probe the impact of axial diffusion (molecular diffusivity of NO is increased 2.3-fold relative to air) in healthy adults (21-38 yr old, n = 9). Heliox decreased the plateau concentration of exhaled NO by 45% (exhalation flow rate of 50 ml/s). In addition, the total mass of NO exhaled in phase I and II after a 20-s breath hold was reduced by 36%. A single-path trumpet model that considers axial diffusion predicts a 50% increase in the maximum airway flux of NO and a near-zero alveolar concentration (Ca(NO)) and source. Furthermore, when NO elimination is plotted vs. constant exhalation flow rate (range 50-500 ml/s), the slope has been previously interpreted as a nonzero Ca(NO) (range 1-5 ppb); however, the trumpet model predicts a positive slope of 0.4-2.1 ppb despite a zero Ca(NO) because of a diminishing impact of axial diffusion as flow rate increases. We conclude that axial diffusion leads to a significant backdiffusion of NO from the airways to the alveolar region that significantly impacts the partitioning of airway and alveolar contributions to exhaled NO.     

Microscopic modeling of NO and S-nitrosoglutathione kinetics and transport in human airways.

Nitric oxide (NO) appears in the exhaled breath and is elevated in inflammatory diseases. We developed a steady-state mathematical model of the bronchial mucosa for normal small and large airways to understand NO and S-nitrosoglutathione (GSNO) kinetics and transport using data from the existing literature. Our model predicts that mean steady-state NO and GSNO concentrations for large airways (generation 1) are 2.68 nM and 113 pM, respectively, in the epithelial cells and 0.11 nM (approximately 66 ppb) and 507 nM in the mucus. For small airways (generation 15), the mean concentrations of NO and GSNO, respectively, are 0.26 nM and 21 pM in the epithelial cells and 0.02 nM (approximately 12 ppb) and 132 nM in the mucus. The concentrations in the mucus compare favorably to experimentally measured values. We conclude that 1) the majority of free NO in the mucus, and thus exhaled NO, is due to diffusion of free NO from the epithelial cell and 2) the heterogeneous airway contribution to exhaled NO is due to heterogeneous airway geometries, such as epithelium and mucus thickness.     

Examining axial diffusion of nitric oxide in the lungs using heliox and breath hold.

Exhaled nitric oxide (NO) is highly dependent on exhalation flow; thus exchange dynamics of NO have been described by multicompartment models and a series of flow-independent parameters that describe airway and alveolar exchange. Because the flow-independent NO airway parameters characterize features of the airway tissue (e.g., wall concentration), they should also be independent of the physical properties of the insufflating gas. We measured the total mass of NO exhaled (A(I,II)) from the airways after five different breath-hold times (5-30 s) in healthy adults (21-38 yr, n = 9) using air and heliox as the insufflating gas, and then modeled A(I,II) as a function of breath-hold time to determine airway NO exchange parameters. Increasing breath-hold time results in an increase in A(I,II) for both air and heliox, but A(I,II) is reduced by a mean (SD) of 31% (SD 6) (P < 0.04) in the presence of heliox, independent of breath-hold time. However, mean (SD) values (air, heliox) for the airway wall diffusing capacity [3.70 (SD 4.18), 3.56 pl.s(-1).ppb(-1) (SD 3.20)], the airway wall concentration [1,439 (SD 487), 1,503 ppb (SD 644>)], and the maximum airway wall flux [4,156 (SD 2,502), 4,412 pl/s (SD 2,906)] using a single-path trumpet-shaped airway model that considers axial diffusion were independent of the insufflating gas (P > 0.55). We conclude that a single-path trumpet model that considers axial diffusion captures the essential features of airway wall NO exchange and confirm earlier reports that the airway wall concentration in healthy adults exceeds 1 ppm and thus approaches physiological concentrations capable of modulating smooth muscle tone.     

Monte Carlo simulation of simultaneous gas flow and diffusion in an asymmetric distal pulmonary airway model

In order to evaluate the effect of anatomic asymmetries on the gas concentration distribution in the pulmonary airways, a Monte Carlo simulation of combined bulk flow and molecular diffusion was carried out in a realistic distal airway model (Parkeret al., 1971). This airway model, composed of branches distal to the 0.5-ram diameter airways, contained an upper symmetric segment consisting of four generations of conducting airways and a lower asymmetric segment of alveolar ducts and sacs arranged in five transport paths of varying lengths. In accounting for the volume increases of these ducts and sacs occurring during normal respiration, uniform alveolar filling rates and a fixed length-to-diameter ratio of all airways were assumed. For a pulse injection of inert tracer gas, the simulation was employed to determine the longitudinal concentration profiles in the conducting airways. In the alveolated airways, not only were the longitudinal profiles determined along each path, but radial transport from the core to the periphery of the airways was considered. The results of the simulations indicate that geometric asymmetries alone contribute substantially to regional concentration variations in the distal airways. For example, when a gas bolus is injected at mid*inspiration, there are concentration differences as great as 40% between two points along different transport paths located equi-distant from the proximal end of the model. As viewed from the terminal end of the model (acinus), average concentration differences as large as 6-to-1 exist between the longest and shortest transport paths respectively for gas boli introduced near the end of inspiration. The results further indicate because of large radial diffusion rates, no significant concentration differences exist between the periphery a-ld the central core of alveolated airways. Simulation of the expired concentration profiles indicate that boll injected very late during inspiration exhibit a sloping tail, unlike the earlier injected boll whose tails are virtually horizontal. Through the use of superposition teehniqnes, it was found that these sloping tails correspond to an alveolar slope of 1.5 vol% between 750 and 1250 ml expired for a continuous washing of tracer. This result is in disagreement with other transport analyses which did not directly account for the effect of geometric asymmetries.     

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.     

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.     

Simultaneous measurement of nitric oxide production by conducting and alveolar airways of humans.

Human airways produce nitric oxide (NO), and exhaled NO increases as expiratory flow rates fall. We show that mixing during exhalation between the NO produced by the lower, alveolar airways (VL(NO)) and the upper conducting airways (VU(NO)) explains this phenomenon and permits measurement of VL(NO), VU(NO), and the NO diffusing capacity of the conducting airways (DU(NO)). After breath holding for 10-15 s the partial pressure of alveolar NO (PA) becomes constant, and during a subsequent exhalation at a constant expiratory flow rate the alveoli will deliver a stable amount of NO to the conducting airways. The conducting airways secrete NO into the lumen (VU(NO)), which mixes with PA during exhalation, resulting in the observed expiratory concentration of NO (PE). At fast exhalations, PA makes a large contribution to PE, and, at slow exhalations, NO from the conducting airways predominates. Simple equations describing this mixing, combined with measurements of PE at several different expiratory flow rates, permit calculation of PA, VU(NO), and DU(NO). VL(NO) is the product of PA and the alveolar airway diffusion capacity for NO. In seven normal subjects, PA = 1.6 +/- 0.7 x 10(-6) (SD) Torr, VL(NO) = 0.19 +/- 0.07 microl/min, VU(NO) = 0.08 +/- 0.05 microl/min, and DU(NO) = 0.4 +/- 0.4 ml. min(-1). Torr(-1). These quantitative measurements of VL(NO) and VU(NO) are suitable for exploring alterations in NO production at these sites by diseases and physiological stresses.     

A simple technique to characterize proximal and peripheral nitric oxide exchange using constant flow exhalations and an axial diffusion model.

The most common technique employed to describe pulmonary gas exchange of nitric oxide (NO) combines multiple constant flow exhalations with a two-compartment model (2CM) that neglects 1) the trumpet shape (increasing surface area per unit volume) of the airway tree and 2) gas phase axial diffusion of NO. However, recent evidence suggests that these features of the lungs are important determinants of NO exchange. The goal of this study is to present an algorithm that characterizes NO exchange using multiple constant flow exhalations and a model that considers the trumpet shape of the airway tree and axial diffusion (model TMAD). Solution of the diffusion equation for the TMAD for exhalation flows >100 ml/s can be reduced to the same linear relationship between the NO elimination rate and the flow; however, the interpretation of the slope and the intercept depend on the model. We tested the TMAD in healthy subjects (n = 8) using commonly used and easily performed exhalation flows (100, 150, 200, and 250 ml/s). Compared with the 2CM, estimates (mean +/- SD) from the TMAD for the maximum airway flux are statistically higher (J'aw(NO) = 770 +/- 470 compared with 440 +/- 270 pl/s), whereas estimates for the steady-state alveolar concentration are statistically lower (CA(NO) = 0.66 +/- 0.98 compared with 1.2 +/- 0.80 parts/billion). Furthermore, CA(NO) from the TMAD is not different from zero. We conclude that proximal (airways) NO production is larger than previously predicted with the 2CM and that peripheral (respiratory bronchioles and alveoli) NO is near zero in healthy subjects.     

Convective gas transport in the pulmonary acinus: Comparing roles of convective and diffusive lengths

To investigate the relative importance of convection and diffusion in the transport of oxygen in the pulmonary acinus, it is often useful to locate the transition from convection-dominated to diffusion-dominated transport. Traditionally, this is done by estimating the values of a Peclet number. This dimensionless number compares the bulk ductal flow velocity at an acinar generation with a diffusion velocity over a characteristic length scale. Here, we revisit the convection–diffusion transition by comparing the relative importance of convective and diffusive lengths. We introduce the ratio of such lengths (L_conv/L_diff) to quantify the extent of convective transport in the acinus over an inhalation phase. We distinguish between convection along the acinar airways and within alveoli, respectively. Results for L_conv/L_diff suggest that convection in acinar ducts may play a potential role in more peripheral airways compared with values obtained for a Peclet number. Within alveoli, however, independent of acinar depth, oxygen transport is governed by diffusion as soon as molecules enter within alveolar cavities.     

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.     

Nitric oxide paradox in asthma

Asthma results from allergen-driven intrapulmonary Th2 response, and is characterized by intermittent airway obstruction, airway hyperreactivity (AHR), and airway inflammation. Accumulating evidence indicates that inflammatory diseases of the respiratory tract are commonly associated with elevated production of nitric oxide (NO). It has been shown that exhaled NO may be derived from constitutive NO synthase (NOS) such as endothelial (NOS 3) and neural (NOS 1) in normal airways, while increased levels of NO in asthma appear to be derived from inducible NOS2 expressed in the inflamed airways. Nevertheless, the functional role of NO and NOS isoforms in the regulation of AHR and airway inflammation in human or experimental models of asthma is still highly controversial. In the present commentary we will discuss the role of lipopolysaccharides contamination of allergens as key element in the controversy related to the regulation of NOS2 activity in experimental asthma.     

Simultaneous diffusion and convection in single breath lung washout

Two mathematical models of pulmonary single breath gas washout (one analytic, one numerical) are developed and their predictions compared with experimental data on human subjects. Weibel's 23 generation symmetric anatomical model is used as a guide to bronchial tree geometry. Experimental plots of nitrogen concentration versus volume expired, dead space versus breath holding time, and dead space versus tidal volume are compared with plots predicted by the models. Agreement is good. A plot of nitrogen concentration in the airways as predicted by the numerical model at different times during inhalation and exhalation of a single breath of oxygen is shown. Model predictions for changes in dead space with changes in washout gas and expiratory flow rate are discussed. Use of the analytic model for obtaining average values of the path length from mouth to alveoli in a given subject is discussed. To the extent of their agreement with experiment, the models provide a sound physical basis for the correlation of airway structure and function.     

Lung gas mixing during expiration following an inspiration of air

The airway system of the lung from the mouth to the pulmonary membrane is modelled by matching a cylindrical model of a pathway through the respiratory region of the lung onto a one-dimensional trumpet model for the conducting airways. The concentration of O₂ in gas expired from this model airway system is investigated following an inspiration of air at two different flow rates (10 litres/min and 85 litres/min). In each case, expiration occurs at the same constant flow rate as that during the previous inspiration. The inspirations, which are studied in an earlier paper, are each of 2 sec duration and begin at a lung volume of 2300 ml and a lung oxygen tension of 98 mm Hg. The equations are solved numerically and plots of expired O₂ concentration against time and against expired volume are shown. It is found that at 85 litres/min, gas mixing in the lung is complete after about 0.7 sec of expiration whereas at 10 litres/min, about 2.6 sec of expiration is required for complete equilibration. It is suggested that the experimental alveolar plateau slope is not in general caused by a slow approach to equilibrium of gas concentrations; except at very low flow rates in the early part of the concentration/time plateau.     

Modeling pulmonary nitric oxide exchange.

Nitric oxide (NO) was first detected in the exhaled breath more than a decade ago and has since been investigated as a noninvasive means of assessing lung inflammation. Exhaled NO arises from the airway and alveolar compartments, and new analytical methods have been developed to characterize these sources. A simple two-compartment model can adequately represent many of the observed experimental observations of exhaled concentration, including the marked dependence on exhalation flow rate. The model characterizes NO exchange by using three flow-independent exchange parameters. Two of the parameters describe the airway compartment (airway NO diffusing capacity and either the maximum airway wall NO flux or the airway wall NO concentration), and the third parameter describes the alveolar region (steady-state alveolar NO concentration). A potential advantage of the two-compartment model is the ability to partition exhaled NO into an airway and alveolar source and thus improve the specificity of detecting altered NO exchange dynamics that differentially impact these regions of the lungs. Several analytical techniques have been developed to estimate the flow-independent parameters in both health and disease. Future studies will focus on improving our fundamental understanding of NO exchange dynamics, the analytical techniques used to characterize NO exchange dynamics, as well as the physiological interpretation and the clinical relevance of the flow-independent parameters.     

Diffusivity dependence of multiple-breath washouts of lung periphery

Subpleural concentrations of He and SF6 were measured during multiple-breath washouts from isolated dog lungs. Tidal volume, inspiratory flow, and frequency were in the normal range of canine ventilation. For each gas, there was a local minimum in concentration during inspiration (Cinsp) and a local maximum in concentration during exhalation (Cexp). SF6 exhibited a deeper inspiratory trough than He for each breath of every washout. For large tidal volumes (10-20 ml/kg), Cexp approximated a single exponential decay and He was cleared more rapidly than SF6. For small tidal volumes (2.5 ml/kg), Cexp was multiexponential and SF6 was cleared more rapidly than He. Cinsp/Cexp (a measure of the depth of the inspiratory trough) and the kinetics of Cexp decay were determined for washouts using a tidal volume of 10 and 20 ml/kg and different inspiratory flows. Under all conditions, an increase of inspiratory flow resulted in a deeper inspiratory trough for both He and SF6. For washouts using 10 ml/kg and 60 breaths/min, an increase of inspiratory flow increased the clearance of both gases. In washouts using lower ventilatory frequencies, gas clearance was independent of inspiratory flow. These findings are contrary to predictions of contemporary models of convection and diffusion in the lung. This study suggests that convective axial mixing and radial diffusion in the airways are important determinants of pulmonary gas transport.     

A two-component theory of aerosol deposition in lung airways

The deposition of aerosol particles in the human lung airways is due to two distinct mechanisms. One is by direct deposition resulting from diffusion, sedimentation and impaction as the aerosol moves in and out of the lung. The other is an indirect mechanism by which particles are transported mechanically from the tidal air to the residential air and eventually captured by the airways due to intrinsic particle motion. This last mechanism is not well understood at present. Using a trumpet airway model constructed from Weibel's data, a two-component theory is developed. In this theory, the particle concentrations in the airways and the alveoli at a given airway depth are considered to be quantitatively different. This difference in concentrations will cause a net mixing between the tidal and residential aerosol as the aerosol is breathed in and out. A distribution parameter is then introduced to account for the distribution of ventilation. The effect of intrinsic particle motion on the aerosol mixing is also included. From this theory, total and regional deposition in the lung at the steady mouth breathing without pause is calculated for several different respiratory cycles. The results agree reasonably well with the experimental data.     

The process of gas exchange in the pulmonary circulation incorporating the contribution of axial diffusion

A mathematical model is made to describe the process of gas exchange in the pulmonary circulation incorporating the contribution of axial diffusion. The model takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion due to the presence of haemoglobin as a carrier of the gases. The mathematical formulation leads to a coupled system of non-linear elliptic partial differential equations. A numerical scheme is described to solve such a system. It is found that the axial diffusion does not have an appreciable effect on the transport of the species in the blood.