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University of Washington, Departments of 1 Medicine and 2 Physiology and Biophysics, Seattle, Washington, 98195-6522
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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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.
gas exchange; lung airway; lung mechanics
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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THE PRINCIPAL FUNCTION OF the lung is to exchange
oxygen and carbon dioxide between blood and inspired air and is
dependent on local matching of regional ventilation-to-perfusion ratio
(
A/
). Traditional
theory, developed from measurements using radioactive gases and chest
wall scintillation counters, proposed that
A/ matching
is accomplished by gravity-mediated gradients of both ventilation and
perfusion (19, 34, 35).
Experiments using higher resolution techniques in nonprimate species have demonstrated significantly greater heterogeneity of pulmonary perfusion than can be explained by gravitational mechanism alone (10, 14, 20, 25). Glenny et al. (10) estimated the maximal contribution of gravity to overall perfusion heterogeneity at ~7% in dogs. Recently, high-resolution measurements of regional perfusion in baboons (9) and indirect measurements of perfusion in humans under sustained microgravity conditions (24) suggested that nongravitational mechanisms of pulmonary perfusion distribution are also important in humans.
If gases are efficiently exchanged, regional perfusion heterogeneity
has significant implications for regional ventilation. Wilson and Beck
(36) mathematically demonstrated that, for a given heterogeneity of
regional perfusion, as regional ventilation heterogeneity increases,
the correlation between ventilation and perfusion must improve to
preserve a narrow distribution of
A/ values.
Recent high-resolution measurements using either aerosolized 0.005-µm
99mTc-labeled carbon particles (18) or aerosolized 1-µm
fluorescent microspheres (1, 26) demonstrated that regional ventilation is heterogeneous and highly correlated with local perfusion. Although mechanisms of ventilation heterogeneity have not been well studied, nitrogen washout experiments during space shuttle flights demonstrated persistent ventilation heterogeneity during microgravity, confirming the importance of nongravitational mechanisms on regional ventilation distribution (13, 23).
Close correlation between regional ventilation and perfusion suggests
that regional ventilation has spatial characteristics similar to
regional perfusion. One method used to characterize regional
ventilation and perfusion distributions is fractal analysis. The
incentive for applying fractal analysis in the study of perfusion or
ventilation heterogeneity is that the observed heterogeneity of either
measure is complicated by dependence on the scale of resolution. With
the use of fractal analysis, this problem is resolved because the
scale-dependent variability is described by a scale-independent fractal
dimension. Fractal analysis is useful for several other reasons. A
fractal pattern in ventilation heterogeneity implies the presence of
spatial clustering in which ventilation to a given region is correlated
with that of neighboring regions (12); this, in turn, can give insight
into the mechanisms of regional ventilation distribution. Glenny (8)
suggested that spatial clustering of regional blood flow supports the
hypothesis that regional perfusion is determined by resistive
differences in the branching pulmonary vascular tree (3). Fractal
analysis may also be useful for identifying the anatomic level at which gas exchange is determined. Ventilation heterogeneity is unlikely to
continue increasing as resolution improves because of forces that
promote mixing, such as gas diffusion, reinspiration of common dead
space gas, and cardiogenic oscillations. At some regional volume,
alveolar gas tensions will become uniform, despite any perfusion
heterogeneity. The volume of this region, termed the unit of gas
exchange, would be identified by a change in the slope of the fractal
ventilation plot (Fig. 1). Finally, the
scale-independent fractal dimension (D) provides a way to
compare measurements of regional ventilation by using different
techniques with varying resolutions.
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To determine whether regional ventilation has fractal properties similar to regional perfusion, we measured ventilation and perfusion with aerosolized and injected microspheres in six juvenile pigs. To determine if posture had similar effects on regional ventilation and perfusion, measurements were taken in supine and prone postures.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Animal preparation. The Animal Care Committee at the University of Washington approved these experiments. Six pigs, of either gender, weighing 18.5-25 kg, were studied. Anesthesia was introduced intramuscularly with ketamine and xylazine and followed by continuous intravenous thiopental sodium, at a rate sufficient to suppress spontaneous respiration. The animals were mechanically ventilated via tracheostomy with a tidal volume of ~15 ml/kg and a respiratory rate sufficient to maintain an arterial carbon dioxide tension between 30 and 40 Torr. One carotid and one femoral artery were cannulated for continuous blood pressure monitoring and withdrawal of blood samples. Two femoral veins were cannulated for administration of anesthesia and injection of microspheres. A pulmonary artery catheter was inserted through an external jugular vein. A standard solution of six inert gases was infused, but resultant data were not used for this analysis.
Study protocol. All animals were hyperinflated to twice the tidal volume every 10 min and before all measurements to minimize atelectasis. Data were collected twice in the prone posture and twice in the supine posture for each animal. Posture order was randomized for each experiment. Data collections were carried out at 30-min intervals, with posture change occurring at the beginning of the interval. Each data collection included measurement of mean arterial pressure, pulmonary artery pressure, peak airway pressure, temperature, hematocrit, the average of three thermodilution cardiac output measurements, and blood gas determined from arterial and mixed venous samples. After each data collection, aerosolized 1-µm fluorescent microspheres (FluoSpheres, Molecular Probes, Eugene, OR) were delivered over 10 min to measure regional ventilation as previously described (26). Simultaneously, 15-µm fluorescent microspheres (FluoSpheres, Molecular Probes) were injected intravenously in multiple, small, evenly spaced increments to measure regional perfusion. One regional ventilation measurement and one regional perfusion measurement were randomly chosen for simultaneous duplicate measurement in each experiment. A total of 10 different fluorescent labels were used (1-µm microspheres: yellow-green, yellow, orange, orange-red, red; 15-µm microspheres: blue, blue-green, green, crimson, scarlet). The fluorescent-label orders for both ventilation and perfusion markers were independently randomized before each experiment. After the last data collection, 10,000 units of heparin and 1.5 ml of papaverine were intravenously injected, and the animal was killed by exsanguination under deep anesthesia.
Lung preparation and data collection. A sternotomy was performed, the main pulmonary artery and left atrium were cannulated, and the aorta was ligated. The pulmonary vasculature was flushed with a dextran solution, and the lungs and trachea were dissected from the chest cavity and dried, inflated at 25-cmH2O pressure.
The dried lungs were fixed in a rapid-setting foam, sliced, mapped, and diced into cubes of 1.5- to 2.0-cm3 volume. Each piece was weighed, visually scored for airway and blood content, and soaked for 4 days in 2-ethoxyethyl acetate to extract the fluorescent dyes. Fluorescent signals for the 10 colors were measured in each piece with a fluorometer (LS50B, Perkin-Elmer, Beaconsfield, Buckinghamshire, UK). Spillover signals from colors adjacent in the spectrum were corrected by using matrix inversion of fixed wavelength intensities (28). Fluorescent signals were converted to number of microspheres by using the fluorescent intensity of reference samples containing a known number of microspheres. Pieces with airway content
25% of total piece volume were excluded from further analysis. Signals for each
piece were normalized to that piece's weight, correcting for
heterogeneity in ventilation and perfusion due to variation in piece
size. The number of microspheres of each color in each piece was
normalized to the mean number of microspheres of that color in all
pieces, correcting for variations in the total number of microspheres
of each given color.
Noise estimation.
Observed heterogeneity of injected or aerosolized microsphere
deposition consists of both true heterogeneity of regional ventilation or perfusion and heterogeneity introduced by methodological error. Methodological error for measurement of regional blood flow by injected
microspheres approximates a Poisson distribution; therefore, the
standard deviation of multiple simultaneous measurements will equal the
square root of the mean measurement 
(2, 4, 38). Therefore, the coefficient of variation (CV,
where CV = SD/
) for simultaneous
measurements will equal
1/
. To evaluate
the significance of methodological noise for measurement of regional
ventilation by using aerosolized microspheres, four colors were
simultaneously given to two animals over a 15-min period.
In each animal, Pearson correlation coefficients (r) were calculated between each color and the mean of the other three colors.
The CV of the four measurements of regional ventilation was plotted
against in that piece to determine if
methodological variation approximated a Poisson distribution.
Fractal analysis and statistics.
The same method of fractal analysis is applied to characterize both
regional ventilation and perfusion; therefore, for simplicity, all
further discussion of the method will implicitly apply to perfusion as
well as ventilation. Heterogeneity of regional ventilation can be
characterized by the CV. Given a Poisson distribution of methodological
noise, the true CV (CVtrue) is estimated from the observed
CV (CVobs) by
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(1) |
is the mean number of microspheres
per region (22). When n is large, this equation simplifies to
the more familiar equation
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(2) |
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(3) |
) is the CV of ventilation at a regional volume and
CV(ref) is the CV of ventilation at the smallest
regional volume examined in this study (~2 cm3). The
logarithm of both sides of Eq. 2 describes a linear
relationship with a slope of 1 
D
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(4) |
/ref.
We initially calculated the CV for a distribution of regional
ventilation measured at a resolution of ~2 cm3. Estimates
of CV for ventilation distributions measured at larger regional volumes
were calculated by randomly choosing a starting piece and then
combining its ventilation with the ventilation of adjacent
2-cm3 pieces. The software performing these calculations
was constrained as follows: 1) for each cluster size, the
software formed as many clusters as possible without including any
2-cm3 piece from more than one cluster, and 2)
clusters cannot contain pieces from more than one lobe. These
constraints resulted in fewer ventilation measurements at larger
cluster sizes. Therefore, the software repeated the calculations,
starting with a new 2-cm3 piece for cluster sizes greater
than three pieces. This allowed calculation of a mean CV and standard
error. A weighted linear regression algorithm was used to calculate the
slope of the fractal plot. The total number of measurements used to
calculate a CV at a given cluster size was used as a weighting factor
for the linear regression calculation. For example, at the highest
resolution, the CV of ventilation may be calculated from 1,000 measurements and is therefore weighted by 1,000. At a cluster size of
eight pieces, the CV may be calculated from three repetitions of the clustering algorithm, each using an average of 109 ventilation measurements; therefore, 3 × 109 or 327 would weight that CV. Because of the constraints of the clustering software, increasing numbers of 2-cm3 pieces were excluded from the CV
calculation of larger cluster sizes, resulting in decreased confidence
in the accuracy of the CV and a corresponding decreased weighting in
the linear regression calculation.
Measurements of regional ventilation and perfusion were taken twice in
both the supine and prone postures. To look at the interanimal
variability of ventilation and perfusion heterogeneity, a mean value
for each posture was calculated for CV and D of both ventilation and perfusion in each animal. All values are presented as
mean ± SD. Paired t-tests were used for statistical
comparisons, with P < 0.05 considered a significant difference.
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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Physiological response. Tidal volumes and respiratory rates, once set, remained constant throughout the experiment, except for the second animal, in which respiratory rate was decreased after the second set of measurements to correct for respiratory alkalosis. There was no significant difference between prone and supine postures for airway, mean arterial, and mean pulmonary artery pressures. There was a trend toward a lower cardiac output in the supine posture, by a mean of 215 ml/min, but this did not reach statistical significance (P = 0.063). The average alveolar-arterial oxygen tension was significantly greater in the supine posture compared with the prone posture (mean difference = 7.38 Torr, P = 0.028).
Methodological noise estimate.
Two animals were studied to estimate the contribution of methodological
noise to the observed heterogeneity of ventilation. In the second
animal studied, the last 100 samples had significant degradation of
yellow-green intensity, likely attributable to exposure to a heat
source. These 100 samples were excluded from the analysis, leaving 715 pieces. All 954 pieces of the first animal's lung were included in
analysis. In both animals, the total number of microspheres
administered varied from color to color due to imprecision in the
administration of the quantities of aerosols. We compensated for this
difference by averaging the total number of microspheres deposited
between colors and normalizing the number of microspheres in each piece
to this value. Correlations between a specific color and the mean of
the other three colors are given in Table 1
and averaged 0.995 ± 0.002. In both animals, the CV of regional
deposition of four simultaneously administered aerosols decreased as a
power function of the mean number of regional microspheres (Fig.
2), with an average exponent of 0.51 ± 0.11.
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Fractal analysis.
The CV for both ventilation and perfusion at the smallest region size
are shown in Table 2. There is no
significant difference between CV for ventilation and perfusion in
either posture, despite the wide range of CV observed between animals.
CV is significantly greater in the supine posture compared with the
prone posture for both ventilation (mean difference = 0.065; P = 0.04) and perfusion (mean difference = 0.105; P = 0.02).
Despite the high degree of observed heterogeneity in regional
ventilation and perfusion, a narrow distribution of
A/ is preserved through
close correlation between regional ventilation and perfusion (Table
3).
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32 × ref, the standard deviation of the CV measurement
increases significantly, and the data are not as well described by
Eq. 4. Because of the constraint that all pieces in a cluster
be within the same lobe, it is difficult to form more than a few
clusters at sizes 32 × ref. Given the finite
ventilation or perfusion to a given lung, flow will be negatively
correlated between large clusters, resulting in a poor fit to the
linear model at the largest cluster sizes (clusters >32 × n in animals of this size). This poor fit of the largest
clusters to the fractal model has minimal effect on the calculation of
D because the linear regression is weighted by the number of
measurements used to calculate CV at each resolution.
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DISCUSSION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
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This study uses aerosolized deposition of fluorescently labeled microspheres to measure regional ventilation with resolution similar to that of regional perfusion measurements. With the use of a clustering algorithm, the fractal characteristics of ventilation are examined in a fashion analogous to that applied to regional perfusion. The important findings from this study are that 1) regional ventilation and perfusion are similarly heterogeneous, but closely correlated, permitting efficient gas exchange; 2) regional ventilation and perfusion have similar fractal characteristics; 3) the D of both ventilation and perfusion is lower in the supine posture than in the prone posture; and 4) the error of measuring regional ventilation is small and partially explained by a Poisson distribution.
Implications for gas exchange.
Wilson and Beck (36) have mathematically shown that
A/ heterogeneity and
gas exchange are determined by the heterogeneity of regional perfusion,
regional ventilation, and the correlation between ventilation and
perfusion. This study demonstrates that, as the resolution of regional
ventilation and perfusion measurement improves, the observed
heterogeneity of both ventilation and perfusion increases. Despite this
heterogeneity, a narrow distribution of A/ is preserved through
close correlation of regional ventilation and perfusion (Fig.
4). Because both observed perfusion
heterogeneity (11) and variability of parenchymal expansion (27)
increase at resolutions greater than those obtained in this study, gas exchange efficiency is likely determined by the degree of regional correlation between ventilation and perfusion at volumes <2
cm3. At some level, mixing of alveolar gas by diffusion and
reinspiration of common dead space will result in a homogeneous gas
composition and uniform end-capillary oxygen contents within the volume
of ventilation. Experiments measuring the change in physiological dead
space after graded embolization suggest that homogeneous gas exchange
occurs at the level of the acinus (37). However, modeling of nitrogen
washouts within an acinus suggests that heterogeneity of regional gas
composition is present at a subacinar level (7).
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Implications for ventilation distribution.
A fractal pattern of ventilation heterogeneity implies that regional
ventilation has spatial clustering characteristics similar to those of
regional perfusion (Fig. 5) (12). This
spatial pattern of regional ventilation promotes speculation regarding
mechanisms that determine regional ventilation. Recent theoretical work
by West et al. (32, 33) shows that fractal distribution of a substrate
explains the 1/4 allometric scaling law observed
throughout nature. Their model, based, in part, on the assumption that
the energy required to distribute a substrate throughout a region must
be minimized for maximal efficiency, predicts observed allometric exponents relating lung structure and function to body mass. Fractal regional ventilation must be determined by regional heterogeneity of
lung structure. Given the fractal structure of the bronchial tree (17,
31), it is tempting to attribute regional ventilation heterogeneity
primarily to differences in regional airway impedance. Studies using
both modeling and measurement of alveolar pressure demonstrate that
tissue impedance comprises a significant component of total lung
impedance at normal ventilation frequencies and is responsible for
almost all of the frequency dependence of lung impedance (15, 16, 21).
This would suggest that regional ventilation distribution is primarily
determined by regional tissue impedance; however, these methods do not
give adequate spatial information to draw this conclusion. Despite
tissue impedance being greater than airway impedance, if tissue
impedance is uniformly distributed, then airway structure may still be
the principal determinant of regional ventilation
heterogeneity.
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Implications of posture effect on D.
The D of both perfusion and ventilation is lower in the supine
posture compared with the prone posture. The significance of this is
that spatial correlation must be greater for both ventilation and
perfusion in the supine posture. This likely represents the superimposition of an organizing influence on the innate heterogeneity caused by pulmonary structure. Likely candidates for this effect are a
hydrostatic gradient for pulmonary perfusion (35) and a topographically
distributed change in compliance for ventilation (19). These mechanisms
resulted in only a small increase in heterogeneity of both ventilation
and perfusion (Table 1); however, the effects on ventilation and
perfusion are apparently not spatially matched, resulting in increased
A/ mismatch and,
therefore, the increased alveolar-arterial oxygen difference observed
in the supine posture.
Contribution of method error to regional heterogeneity measurement.
The aerosolized microsphere method has minimal noise and good
reproducibility, as demonstrated by the high correlations between simultaneously aerosolized microspheres. The CV of
si- multaneously aerosolized microspheres decreases in
proportion to the inverse square root of 
suggesting that a Poisson distribution describes a portion of the
method error. The aerosol concentration of individual colors was two to
four times greater in the fractal experiments than in the experiments
estimating method error. Hence, the contribution of method error to our
measurements is small at measurement resolution. Method error decreases
as regional volume increases (resolution decreases) because of
increasing regional microsphere deposition.
A/ matching in uninjured lungs (5, 6, 29, 30). In pigs, there is minimal ventilation
redistribution after regional perfusion changes from microembolism,
suggesting that active regulation of ventilation distribution is
minimal (1). Passive matching of ventilation and perfusion by pulmonary
structure is appealing because it requires the least amount of energy.
An optimally engineered system requires no active feedback mechanisms
during normal function. Pathological conditions, however, may require
feedback mechanisms to correct instabilities. Regional ventilation and
blood flow are both distributed through fractal structures that share
similar geometry. It is tempting to assign responsibility for the
fractal distribution patterns of ventilation and blood flow to the
bronchial and pulmonary arterial trees, respectively. The high
correlation between regional ventilation and perfusion that permits
efficient gas exchange, despite high spatial heterogeneity, may be
explained by the close correlation of the developing bronchial tree and
pulmonary arterial tree during organogenesis, as first suggested by
Weibel (31). Fractal distribution networks for ventilation and
perfusion provide several inherent advantages. Fractal structures are
the most efficient way to fill a three-dimensional structure and
provide the most energy efficient substrate transport (33). A
fundamental characteristic of a fractal structure is that its basic
form is replicated over a range of scales. This repetition would permit
efficient genetic coding. The fractal nature of heterogeneity, as
measured by our analysis, does not prove that regional ventilation and
pulmonary perfusion distribution are determined by fractal pulmonary
structure, but it is supportive of this idea. Further
investigation into the determinants of regional ventilation and the
matching between ventilation and perfusion is necessary to fully
understand the gas exchange function of the lung.
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ACKNOWLEDGEMENTS |
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We thank Dowon An and Shen-Sheng Wang for technical assistance and Dave Frazer for assistance with figure preparation.
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FOOTNOTES |
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This work was supported by National Heart, Lung, and Blood Institute Grant HL-10003 and by an American Lung Association Washington State Affiliate Research Grant.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Address for reprint requests and other correspondence: W. A. Altemeier, Div. of Pulmonary and Critical Care Medicine, BB-1253 Health Sciences Building, Box 356522, Seattle, Washington 98195-6522 (E-mail: billa{at}u.washington.edu).
Received 23 September 1999; accepted in final form 14 December 1999.
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TOP
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METHODS
RESULTS
DISCUSSION
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