Acinar flow irreversibility caused by perturbations in reversible alveolar wall motion.

Mixing associated with "stretch-and-fold" convective flow patterns has recently been demonstrated to play a potentially important role in aerosol transport and deposition deep in the lung (J. P. Butler and A. Tsuda. J. Appl. Physiol. 83: 800-809, 1997), but the origin of this potent mechanism is not well characterized. In this study we hypothesized that even a small degree of asynchrony in otherwise reversible alveolar wall motion is sufficient to cause flow irreversibility and stretch-and-fold convective mixing. We tested this hypothesis using a large-scale acinar model consisting of a T-shaped junction of three short, straight, square ducts. The model was filled with silicone oil, and alveolar wall motion was simulated by pistons in two of the ducts. The pistons were driven to generate a low-Reynolds-number cyclic flow with a small amount of asynchrony in boundary motion adjusted to match the degree of geometric (as distinguished from pressure-volume) hysteresis found in rabbit lungs (H. Miki, J. P. Butler, R. A. Rogers, and J. Lehr. J. Appl. Physiol. 75: 1630-1636, 1993). Tracer dye was introduced into the system, and its motion was monitored. The results showed that even a slight asynchrony in boundary motion leads to flow irreversibility with complicated swirling tracer patterns. Importantly, the kinematic irreversibility resulted in stretching of the tracer with narrowing of the separation between adjacent tracer lines, and when the cycle-by-cycle narrowing of lateral distance reached the slowly growing diffusion distance of the tracer, mixing abruptly took place. This coupling of evolving convective flow patterns with diffusion is the essence of the stretch-and-fold mechanism. We conclude that even a small degree of boundary asynchrony can give rise to stretch-and-fold convective mixing, thereby leading to transport and deposition of fine and ultrafine aerosol particles deep in the lung.     

Contribution of upper airway geometry to convective mixing

We investigated the axial dispersive effect of the upper airway structure (comprising mouth cavity, oropharynx, and trachea) on a traversing aerosol bolus. This was done by means of aerosol bolus experiments on a hollow cast of a realistic upper airway model (UAM) and three-dimensional computational fluid dynamics (CFD) simulations in the same UAM geometry. The experiments showed that 50-ml boluses injected into the UAM dispersed to boluses with a half-width ranging from 80 to 90 ml at the UAM exit, across both flow rates (250, 500 ml/s) and both flow directions (inspiration, expiration). These experimental results imply that the net half-width induced by the UAM typically was 69 ml. Comparison of experimental bolus traces with a one-dimensional Gaussian-derived analytical solution resulted in an axial dispersion coefficient of 200-250 cm(2)/s, depending on whether the bolus peak and its half-width or the bolus tail needed to be fully accounted for. CFD simulations agreed well with experimental results for inspiratory boluses and were compatible with an axial dispersion of 200 cm(2)/s. However, for expiratory boluses the CFD simulations showed a very tight bolus peak followed by an elongated tail, in sharp contrast to the expiratory bolus experiments. This indicates that CFD methods that are widely used to predict the fate of aerosols in the human upper airway, where flow is transitional, need to be critically assessed, possibly via aerosol bolus simulations. We conclude that, with all its geometric complexity, the upper airway introduces a relatively mild dispersion on a traversing aerosol bolus for normal breathing flow rates in inspiratory and expiratory flow directions.     

Pulmonary blood flow remains fractal down to the level of gas exchange.

The spatial distribution of pulmonary blood flow is increasingly heterogeneous as progressively smaller lung regions are examined. To determine the extent of perfusion heterogeneity at the level of gas exchange, we studied blood flow distributions in rat lungs by using an imaging cryomicrotome. Approximately 150,000 fluorescent 15-microm-diameter microspheres were injected into tail veins of five awake rats. The rats were heavily anesthetized; the lungs were removed, filled with an optimal cutting tissue compound, and frozen; and the spatial location of every microsphere was determined. The data were mathematically dissected with the use of an unbiased random sampling method. The coefficients of variation of microsphere distributions were determined at varying sampling volumes. Perfusion heterogeneity increased linearly on a log-log plot of coefficient of variation vs. volume, down to the smallest sampling size of 0.53 mm(3). The average fractal dimension, a scale-independent measure of perfusion distribution, was 1.2. This value is similar to that of other larger species such as dogs, pigs, and horses. Pulmonary perfusion heterogeneity increases continuously and remains fractal down to the acinar level. Despite the large degree of perfusion heterogeneity at the acinar level, gases are efficiently exchanged.     

Aerosol bolus dispersion and convective mixing in human and dog lungs and physical models.

The dispersion of aerosol boluses in the lung is a probe for convective mixing and has been proposed as a marker for abnormal lung function. To better understand the factors underlying this phenomenon, aerosol dispersion was compared in human subjects, dogs, and various physical models. In all systems, dispersion increased with the volumetric penetration of the aerosol bolus. The rate of this increase was 83% greater in humans compared with dogs. Dispersion in dogs was close to that in a packed bed with beads of 2.5 mm. Aerosol dispersion decreased with increasing flow rate in human subjects. An artificial larynx inserted into the straight tube caused a 33% increase in dispersion. In humans, aerosol dispersion was significantly correlated with forced expired flow between 25 and 75% of vital capacity. A 2-s pause between inspiration and expiration increased dispersion 23-58% in three isolated dog lungs but did not affect dispersion in the packed bed. The data suggest that lung geometry, flow rate, particle mobility, and the larynx all significantly affect aerosol dispersion by influencing the reversibility of aerosol transport between inspiration and expiration.     

A class of flow bifurcation models with lognormal distribution and fractal dispersion

We report a quantitative analysis of a simple dichotomous branching tree model for blood flow in vascular networks. Using the method of moment-generating function and geometric Brownian motion from stochastic mathematics, our analysis shows that a vascular network with asymmetric branching and random variation at each bifurcating point gives rise to an asymptotic lognormal flow distribution with a positive skewness. The model exhibits a fractal scaling in the dispersion of the regional flow in the branches. Experimentally measurable fractal dimension of the relative dispersion in regional flow is analytically calculated in terms of the asymmetry and the variance at local bifurcation; hence the model suggests a powerful method to obtain the physiological information on local flow bifurcation in terms of flow dispersion analysis. Both the fractal behavior and the lognormal distribution are intimately related to the fact that it is the logarithm of flow, rather than flow itself, which is the natural variable in the tree models. The kinetics of tracer washout is also discussed in terms of the lognormal distribution.     

Effect of ventilation distribution on aerosol bolus dispersion and recovery

It has beenspeculated that convective ventilatory inhomogeneities are an importantfactor influencing aerosol bolus behavior in the compromisedlung. Multiple-breath¹³³Xe washout(MBW_Xe) is a commonly acceptedtest of ventilation distribution. By comparing aerosol bolus parametersto MBW_Xe in 9 healthy subjects and14 cystic fibrosis patients with mild-to-moderate airway obstruction,we have attempted to discern the effect of altered ventilationdistribution on aerosol bolus dispersion and recovery. Aerosol boluses(150-ml width) were delivered to the volumetric penetrations of 250 and500 ml. Similar tidal volumes (~1.25 liters) and flow rates (0.4 l/s)were used for aerosol bolus andMBW_Xe maneuvers. Associationsbetween bolus parameters and ventilation distribution were onlyobserved in the cystic fibrosis patients. We conclude that aerosolbolus dispersion and recovery are both influenced by convectiveventilatory inhomogeneities induced by airway obstruction in these patients.

     

Aerosol-derived lung morphometry: comparisons with a lung model and lung function indexes.

This study evaluated the ability of aerosol-derived lung morphometry to noninvasively probe airway and acinar dimensions. Effective air-space diameters (EAD) were calculated from the time-dependent gravitational losses of 1-microns particles from inhaled aerosol boluses during breath holding. In 17 males [33 +/- 7 (SD) yr] the relationship between EAD and volumetric penetration of the bolus into the lungs (Vp) could be expressed by the linear power-law function, log (EAD) alpha beta log (Vp). Our EAD values were consistent with Weibel's symmetric lung model A for small airways and more distal air spaces. As lung volume increased from 57 to 87% of total lung capacity (TLC), EAD at Vp of 160 and 550 cm3 increased 70 and 41%, respectively. At 57% TLC, log (EAD) at 160 cm3 was significantly correlated with airway resistance (r = -0.57, P less than 0.0204) but not with forced expired flow between 25 and 75% of vital capacity. Log (EAD) at 400 cm3 was correlated with deposition of 1-micron particles (r = -0.73, P less than 0.0009). We conclude that aerosol-derived lung morphometry is a responsive noninvasive probe of peripheral air-space diameters.     

Microsphere maps of regional blood flow and regional ventilation.

Systematically mapped samples cut from lungs previously labeled with intravascular and aerosol microspheres can be used to create high-resolution maps of regional perfusion and regional ventilation. With multiple radioactive or fluorescent microsphere labels available, this methodology can compare regional flow responses to different interventions without partial volume effects or registration errors that complicate interpretation of in vivo imaging measurements. Microsphere blood flow maps examined at different levels of spatial resolution have revealed that regional flow heterogeneity increases progressively down to an acinar level of scale. This pattern of scale-dependent heterogeneity is characteristic of a fractal distribution network, and it suggests that the anatomic configuration of the pulmonary vascular tree is the primary determinant of high-resolution regional flow heterogeneity. At approximately 2-cm(3) resolution, the large-scale gravitational gradients of blood flow per unit weight of alveolar tissue account for <5% of the overall flow heterogeneity. Furthermore, regional blood flow per gram of alveolar tissue remains relatively constant with different body positions, gravitational stresses, and exercise. Regional alveolar ventilation is accurately represented by the deposition of inhaled 1.0-microm fluorescent microsphere aerosols, at least down to the approximately 2-cm(3) level of scale. Analysis of these ventilation maps has revealed the same scale-dependent property of regional alveolar ventilation heterogeneity, with a strong correlation between ventilation and blood flow maintained at all levels of scale. The ventilation-perfusion (VA/Q) distributions obtained from microsphere flow maps of normal animals agree with simultaneously acquired multiple inert-gas elimination technique VA/Q distributions, but they underestimate gas-exchange impairment in diffuse lung injury.     

Exercise alters fractal dimension and spatial correlation of pulmonary blood flow in the horse.

We determined the changes in fractal dimensions and spatial correlations of regional pulmonary blood flow with increasing exercise in race horses (n = 4) by using 15-microm fluorescent microspheres. Fluorescence was measured to quantitate regional blood to 1.3-cm(3) samples (n = 1,621-2,503). Perfusion distributions were characterized with fractal dimensions (a measure of spatial variability) and spatial correlations. On average, the fractal dimension decreased with exercise (trot 1.216 to gallop 1.173; P < 0. 05) despite a variable fractal dimension at rest. Spatial correlation of flow to neighboring pieces increased with exercise (trot 0.57 +/- 0.074 to gallop 0.73 +/- 0.051) and was inversely correlated with fractal dimension, indicating better spatial correlation as blood flow distribution becomes more uniform. This is the first study to document a change in fractal dimension as a result of increasing pulmonary blood flow. Spatial differences in response to vasoregulatory mediators may play a role in this phenomenon.     

Exhaled Aerosol Pattern Discloses Lung Structural Abnormality: A Sensitivity Study Using Computational Modeling and Fractal Analysis

Background

Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases.

Objective and Methods

In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns.

Findings

Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma.

Conclusion

Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities.     

Fractal nature of regional ventilation distribution.

High-resolution measurements of pulmonary perfusion reveal substantial spatial heterogeneity that is fractally distributed. This observation led to the hypothesis that the vascular tree is the principal determinant of regional blood flow. Recent studies using aerosol deposition show similar ventilation heterogeneity that is closely correlated with perfusion. We hypothesize that ventilation has fractal characteristics similar to blood flow. We measured regional ventilation and perfusion with aerosolized and injected fluorescent microspheres in six anesthetized, mechanically ventilated pigs in both prone and supine postures. Adjacent regions were clustered into progressively larger groups. Coefficients of variation were calculated for each cluster size to determine fractal dimensions. At the smallest size lung piece, local ventilation and perfusion are highly correlated, with no significant difference between ventilation and perfusion heterogeneity. On average, the fractal dimension of ventilation is 1.16 in the prone posture and 1. 09 in the supine posture. Ventilation has fractal properties similar to perfusion. Efficient gas exchange is preserved, despite ventilation and perfusion heterogeneity, through close correlation. One potential explanation is the similar geometry of bronchial and vascular structures.     

Convective mixing in human respiratory tract: estimates with aerosol boli

Convective gas mixing in the respiratory tract of 17 healthy male subjects was studied by an aerosol bolus technique. The monodisperse 1 micron di(2-ethylhexyl)sebacate droplets we used behaved as a nondiffusing gas. As the bolus was inspired to different depths and then expired, we measured the extent to which the bolus spread. We found that the deeper the bolus penetrated into the lungs, the more it became dispersed. The half-width of the expired bolus was a linear function of the volume to which the bolus penetrated at volumetric penetrations of 100-800 cm3. This suggests that convective mixing is not confined to central airways but can also occur in the lung periphery.     

A fractal analysis of the radial distribution of bronchial capillaries around large airways.

We analyzed published measurements of the bronchial circulation and airway wall (Anderson JC, Bernard SL, Luchtel DL, Babb AL, and Hlastala MP. Respir Physiol Neurobiol 132: 329-339, 2002) and determined that the radial distribution of bronchial capillary cross-sectional area was fractal. We limited our analysis to bronchial capillaries, diameter < or =10 mum, that resided between the epithelial basement membrane and adventitia-alveolar boundary, the airway wall tissue. Thirteen different radial distributions of capillary-to-tissue area were constructed simply by changing the number of annuli (i.e., the annular size) used to form each distribution. For the 13 distributions created, these annuli ranged in size from to of the size of the airway wall area. Radial distributions were excluded from the fractal analysis if the sectioning procedure resulted in an annulus with a radial thickness less than the diameter of a capillary. To determine the fractal dimension for a given airway, the coefficient of variation (CV) for each distribution was calculated, and ln(CV) was plotted against the logarithm of the relative piece area. For airways with diameter >2.4 mm, this relationship was linear, which indicated the radial distribution of bronchial capillary cross-sectional area was fractal with an average fractal dimension of 1.27. The radial distribution of bronchial capillary cross-sectional area was not fractal around airways with diameter <1.5 mm. We speculated on how the fractal nature of this circulation impacts the distribution of bronchial blood flow and the efficiency of mass transport during health and disease. A fractal analysis can be used as a tool to quantify and summarize investigations of the bronchial circulation.     

Vasomotor tone does not affect perfusion heterogeneity and gas exchange in normal primate lungs during normoxia.

To determine whether vasoregulation is an important cause of pulmonary perfusion heterogeneity, we measured regional blood flow and gas exchange before and after giving prostacyclin (PGI(2)) to baboons. Four animals were anesthetized with ketamine and mechanically ventilated. Fluorescent microspheres were used to mark regional perfusion before and after PGI(2) infusion. The lungs were subsequently excised, dried inflated, and diced into approximately 2-cm(3) pieces (n = 1,208-1,629 per animal) with the spatial coordinates recorded for each piece. Blood flow to each piece was determined for each condition from the fluorescent signals. Blood flow heterogeneity did not change with PGI(2) infusion. Two other measures of spatial blood flow distribution, the fractal dimension and the spatial correlation, did not change with PGI(2) infusion. Alveolar-arterial O(2) differences did not change with PGI(2) infusion. We conclude that, in normal primate lungs during normoxia, vasomotor tone is not a significant cause of perfusion heterogeneity. Despite the heterogeneous distribution of blood flow, active regulation of regional perfusion is not required for efficient gas exchange.     

Saline aerosol bolus dispersion. I. The effect of acinar airway alteration.

We explored the possibility of using a saline aerosol for bolus dispersion measurements to detect peripheral airway alterations in smokers. Indexes of ventilation inhomogeneity in conductive (S(cond)) and acinar (S(acin)) lung zones, as derived from the multiple-breath N(2) washout (Verbanck S, Schuermans D, Van Muylem A, Noppen M, Paiva M, and Vincken W, J Appl Physiol 83: 1807-1816, 1997), were also measured. The saline bolus test consisted of inhaling 60-ml saline aerosol boluses to different volumetric lung depths (VLD) in the 1.1 liter volume above functional residual capacity. In the never-smoker group (n = 12), saline boluses showed bolus dispersion values consistent with normal values reported in the literature for 0.5- to 1-microm aerosols. In the smoker group (n = 12; 28 +/- 9 pack years, mean +/- SD), significant increases were seen on dispersion and skew of the most peripherally inhaled saline boluses (VLD = 800 ml; P < 0.05) as well as on S(acin) (P = 0.007) with respect to never-smokers. Shallow inhaled boluses (VLD = 200 ml) and S(cond) did not reveal any significant differences between smokers and never-smokers. This study shows the consistent response of two conceptually independent tests, in which both saline aerosol and gas-derived indexes point to a heterogeneous distribution of smoking-induced structural alterations in the lung periphery.     

Respiratory deposition model of an inhaled aerosol bolus

The bolus delivery method is designed to deliver a dose to the desired location in the lung, and it has the advantage of fewer side effects and a more efficient way of delivery. Based upon the lung deposition model developed for continuously inhaling aerosols of constant concentration, a mathematical model of aerosol bolus deposition is proposed. The calculated results show that the recovery depends on the bolus penetration depth, flow rate, particle size, breath holding time and bolus volume. Three sets of published experimental data with different controlling factors (particle size, flow rate and breath holding time) are adopted to make the quantitative comparisons with the calculated results. The predictions and data for the low intrinsic motion particles (～1 μm) have good agreement, as do the coarse particles in the shallow airways region. For females, the recovery was found to be consistently lower than that for males.     

Saline aerosol bolus dispersion. II. The effect of conductive airway alteration.

In a companion study (Verbanck S, Schuermans D, Vincken W, and Paiva M, J Appl Physiol 90: 1754-1762, 2001), we investigated whether saline aerosol bolus tests could also be used to detect proximal, as opposed to peripheral, airway alterations. We studied 10 never-smokers before and after histamine challenge, obtaining, for various volumetric lung depths (VLD), saline bolus-derived indexes computed by discarding aerosol concentrations below either 50% of the exhaled bolus maximum (half-width, H) or below cutoffs ranging from 5 to 25% (standard deviation, sigma(5%)-sigma(25%)) and skew (sk(5)-sk(25%)). Multiple-breath N(2) washout-derived indexes of conductive (S(cond)) and acinar (S(acin)) ventilation inhomogeneity were also determined. After histamine, S(cond) significantly increased (P = 0.008) whereas S(acin) remained unaffected, indicating purely conductive airway alteration. Consistent with this observation, sk(5%) (or sk(25%)) was increased to the same extent at all VLD, and sigma(5%) was increased preferentially at low VLD. By contrast, H and sigma(25%) displayed preferential increases at high VLD, a pattern similar to that induced by peripheral alterations. The present work shows that proximal airway alteration can be reliably identified by saline bolus tests only if these include measurements at low and high VLD and if bolus dispersion is quantified as a standard deviation with a low cutoff.     

A source of experimental underestimation of aerosol bolus deposition.

We examined the measurement error in inhaled and exhaled aerosol concentration resulting from the bolus delivery system when small volumes of monodisperse aerosols are inspired to different lung depths. A laser photometer that illuminated approximately 75% of the breathing path cross section recorded low inhaled bolus half-widths (42 ml) and negative deposition values for shallow bolus inhalation when the inhalation path of a 60-ml aerosol was straight and unobstructed. We attributed these results to incomplete mixing of the inhaled aerosol bolus over the breathing path cross section, on the basis of simultaneous recordings of the photometer with a particle-counter sampling from either the center or the edge of the breathing path. Inserting a 90 degrees bend into the inhaled bolus path increased the photometer measurement of inhaled bolus half-width to 57 ml and yielded positive deposition values. Dispersion, which is predominantly affected by exhaled bolus half-width, was not significantly altered by the 90 degrees bend. We conclude that aerosol bolus-delivery systems should ensure adequate mixing of the inhaled bolus to avoid error in measurement of bolus deposition.     

Respiratory deposition model of an inhaled aerosol bolus

The bolus delivery method is designed to deliver a dose to the desired location in the lung, and it has the advantage of fewer side effects and a more efficient way of delivery. Based upon the lung deposition model developed for continuously inhaling aerosols of constant concentration, a mathematical model of aerosol bolus deposition is proposed. The calculated results show that the recovery depends on the bolus penetration depth, flow rate, particle size, breath holding time and bolus volume. Three sets of published experimental data with different controlling factors (particle size, flow rate and breath holding time) are adopted to make the quantitative comparisons with the calculated results. The predictions and data for the low intrinsic motion particles (～1 μm) have good agreement, as do the coarse particles in the shallow airways region. For females, the recovery was found to be consistently lower than that for males.     

Lung structure parameters estimated from modeling aerosol deposition in isolated dog lungs

A three-compartment model predicting the recovery of aerosol boli (i.e., the ratio of the number of particles expired to the number inspired) as a function of breath-holding time and bolus penetration was fitted to experimental data measured in nine isolated dog lungs. For each lung, the diameters of alveoli and alveolar ducts, as well as the volume fractions of alveoli, alveolar ducts, and airways, were determined as parameters providing the best fit. Parameter values were alveolar diameter = 0.116 +/- 0.007 (SE) mm, alveolar duct diameter = 0.284 +/- 0.015 mm, total alveolar volume/total lung capacity (TLC) = 0.68 +/- 0.02, total alveolar duct volume/TLC = 0.24 +/- 0.02, and total airway volume/TLC = 0.09 +/- 0.01. These values agreed with published values for linear dimensions and volumetric fractions in the canine lung. The mean alveolar diameter determined by the model in the nine lungs agreed closely with a mean value of 0.115 +/- 0.002 mm determined by morphometric analysis of photographs of the subpleural alveoli in the same lungs. The procedure of fitting the model to experimental data appears to have promise as a noninvasive probe of the lung periphery. However, aerosol-derived dimensions were more variable than morphometric ones, possibly because of interlung differences in aerosol distribution not accounted for in the model.