INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

FRACTAL ANALYSIS HAS BEEN used extensively to analyze the distribution of perfusion throughout the lung (3). The method is to infuse 15-µm-diameter fluorescent latex particles into the pulmonary circulation and then count the number of trapped particles in blocks of frozen or air-dried lungs (15). The blocks, which range in size from 0.5 mm³ to 2 cm³, are grouped mathematically to allow particle counts to be obtained in successive volumes of tissue that range from single tissue blocks up to groups of blocks on the scale of the whole lung (4). For groups of each volume, the mean and SD of the particle counts are calculated for the blocks that compose the group. A fractal plot is assembled by plotting the log of the coefficient of variation (CV; SD/mean) of the group count against the log of the group tissue volume. When this is done for groups of all volumes, it produces a linear plot that shows that the CV of the particle count increases as the group tissue volume decreases. The linearity of such plots is considered to be evidence of a fractal system, which means that perfusion distribution within the lung follows a fractal pattern. Fractals are complex geometric shapes that exhibit a scale-independent property of self-similarity such that the smallest part, no matter how highly magnified, resembles the whole (11). Using this approach, Glenny and colleagues (4) showed that pulmonary perfusion distribution remained fractal down to a tissue volume of 0.5 cm³ (5E11 µm³).

It is interesting to speculate whether or not this pattern continues down to the level of the alveolus. An alveolus with a diameter of 75 µm has a volume of 2.2E5 µm³, but present methods do not allow fractal analysis to be conducted at that level of resolution.

To address this, we developed a method utilizing confocal microscopy in which fractal analysis could be conducted to a level of resolution of 1.7E2 µm³. Our approach was to infuse 4-µm-diameter fluorescent latex particles into anesthetized, spontaneously breathing rats. We removed and air dried the lungs and then used confocal microscopy to obtain digital images of the particles within lung slices. We divided these images into tissue volume increments that ranged from 1.7E2 to 2.8E8 µm³ and counted the number of particles within each increment. The variation in the particle counts among the increments allowed us to establish fractal dimensions for the particle distribution throughout the range of tissue volumes. We found that the distribution was fractal (fractal dimension = 1.29 ± 0.04) within the volume range 7E5 to 2.8E8 µm³. However, in the volume range from 2E2 to 7E5 µm³ we measured a fractal dimension of 1.50 ± 0.03, which is the value associated with a random or Poisson distribution. The tissue volume at which the inflection point occurred (7E5 µm³) is approximately equal to that of one alveolus. Our results suggest that flow distribution is nonrandom at tissue volumes greater than that of one alveolus but at subalveolar volumes flow distribution appears to be random.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The experimental protocols employed in these studies were approved by the institutional animal care committee of the University of Wisconsin-Madison.

Animal Preparation

Using a specimen knife (Pathco), we collected slices (2-3 mm) from eight specific lung regions of each dried lung (Fig. 1). Our goal was to determine whether particle distribution differed among regions. We analyzed particle distribution in each slice using the methods described below (Analysis of Particle Distribution).

View larger version (36K): [in this window] [in a new window]   Fig. 1.   Confocal latex particle mapping scheme. Lungs were air dried, and 4 slices each were cut from the left and right lungs, as shown. A set of confocal particle maps was obtained in each of the 8 slices. Each set consisted of a pair of contiguous maps that each measured 3,360 × 3,360 × 100 µm (×4 objective), as well as a map that measured 672 × 672 × 100 µm (×20 objective). An example is shown in Fig. 3.

Particle Infusion

Microvascular Trapping

We measured particle trapping in intact, spontaneously breathing rats (n = 2) by collecting simultaneous lung inflow and outflow blood samples (5 pairs, 1 ml) during particle infusion into a femoral vein. The outflow sample was collected from the abdominal aorta, and the inflow sample was collected from the inferior vena cava (IVC). The IVC sample did not represent all blood entering the pulmonary artery. However, we assumed that IVC flow represented 75% of pulmonary artery flow; we, therefore, reduced the IVC particle counts to 75% of those measured to estimate particle concentrations in the pulmonary artery (9). Particle concentrations in blood samples were measured by using the FACScan.

Analysis of Particle Distribution

Particle maps. The maps were made by using a laser-scanning confocal fluorescence microscope (BioRad MRC 1024ES). Maps were made in each of the eight regions per lung (Fig. 1). The areas mapped were randomly chosen from fields that lacked major vessels or airways (>0.5 mm). Maps of each lung region consisted of two adjacent low-power maps encompassing an area of 6,732 × 3,366 × 100 µm, plus a high-power map that encompassed an area of 672 × 672 × 100 µm. Each of the two low-power maps was a composite of 20 sequential confocal images (3,366 × 3,366 µm) that were acquired stepwise into the tissue through a depth of 100 µm by use of the ×4 objective of the microscope. The 20 images were digitally stacked to form a single image that encompassed a thickness of 100 µm. Thus the overall tissue volumes were those encompassed by this stack. The high-power map was prepared similarly by use of the ×20 objective of the microscope. An example confocal image acquired via the ×4 objective is shown in Fig. 2.

View larger version (232K): [in this window] [in a new window]   Fig. 2.   Low-power confocal image of a lung infused with 2E3 4-µm-diameter latex particles (red). The image is a composite of 20 consecutive confocal images (optical sections) that were obtained into the plane of the tissue (5-µm thickness per image). The image encompasses a tissue area of 3,360 × 3,360 × 100 µm, which is one-half of the area of a low-power map (Fig. 1). The particle map of this area is shown in Fig. 3.

View larger version (56K): [in this window] [in a new window]   Fig. 3.   One-half of a low-power latex particle map (Fig. 1), representing the tissue in Fig. 2. The map has been subdivided 2 × 2 into 4 cells, each of which encompasses 1,680 × 1,680 × 100 µm (2.8E8 µm3). To conduct fractal analysis, particle counts were determined in these 4 cells as well as in the 4 cells of the other half-map, and the mean, SD, and coefficient of variation (SD/mean) were determined for all 8 cells. We then subdivided the map again (8 × 4) and repeated the counting. This process was repeated through 9 generations, as well as through 3 additional generations in images obtained using the ×20 objective of the microscope (Fig. 1; Table 1). A fractal plot was constructed by plotting the coefficient of variation of each generation (vertical axis) against its subdivision volume (Fig. 6).

Particle distribution analysis. We used multiscale statistical analysis to evaluate particle dispersion within the maps. The foundations of this method are described in the DISCUSSION. To conduct this analysis, each pair of low-power maps was subdivided stepwise. An example is shown in Fig. 3, which is one-half of a low-power map that has been subdivided into a 2 × 2 array that consists of four subdivisions, each of which measures 1,680 × 1,680 × 100 µm (2.8E3 µm³). We counted the number of particles in each of the four subdivisions, as well as in the four subdivisions of the other half of the map, and determined the mean and SD for the counts in all eight subdivisions. We then plotted the CV of this count (SD/mean) against the subdivision tissue volume (2.8E3 µm³). We next subdivided the two images into an 8 × 4 array, counted the number of particles in each of the 32 subdivisions, and again plotted the log of the CV of the particle count against the log of the subdivision tissue volume (step 2). We repeated this process through a total of nine steps, as well as through an additional three steps using the high-power maps. The number of subdivisions and the volume of each are shown in Table 1. To assemble a fractal plot, we plotted the CV of the particle count (vertical axis, log scale) vs. the subdivision tissue volume (horizontal axis, log scale) for all 12 steps and fit a regression line through the data. We assembled separate plots for animals that received 1E7 particles and for those that received 2E8 particles.

Statistics

We found that the fractal plots consisted of two slopes: one that corresponded to tissue volumes less than 7.4E5 µm³ and one that corresponded to tissue volumes greater than this value. We used a repeated-measures analysis of variance to determine whether these two slopes differed among lung regions and between lungs that received 1E7 or 2E8 particles. Pairwise comparisons of factor interactions were made by use of Fisher's protected least significant difference test. Differences were considered to be significant at P  0.05. All analyses were performed by using SAS statistical software (SAS Institute, Cary, NC).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Particle Trapping

Particle Counts Per Map

View larger version (17K): [in this window] [in a new window]   Fig. 4.   Average number of latex particles in maps made from each lung region (mean ± SD) in rats infused with 1E7 particles (n = 3). The regions include left (L) and right (R) dorsal (D), middle (M), ventral (V), and upright (U) (Fig. 1). Values are shown for both low-power and high-power maps. Counts were not significantly different among regions.

View larger version (17K): [in this window] [in a new window]   Fig. 5.   Average number of latex particles in maps made from each lung region (means ± SD) (Fig. 1) in rats infused with 2E8 particles (n = 3). Values are shown for both low-power and high-power maps. Counts did not differ significantly among regions.

Fractal Dimensions

View larger version (23K): [in this window] [in a new window]   Fig. 6.   Fractal plot showing the distribution of 4-µm-diameter particles in lungs infused with 1E7 or 2E8 particles. Each set consists of data pooled from all 8 lung regions (Fig. 1). Both sets showed a change in slope between steps 5 and 6, corresponding to a subdivision volume of 7.4E5 µm3 (2E8, P = 0.0001; 1E7, P = 0.0003). The sampled lung volume at which this change occurs is equal to that of a sphere with a diameter of 112 µm, which is approximately the diameter of 1 alveolus (see Fig. 7).

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Our main finding is the noticeable inflection in the fractal plot, especially in the 2E8 data, at a tissue volume of 7.4E5 µm³. To the left of this inflection the data have a fractal dimension of 1.50, which is a value that corresponds to CSR (see Particle Distribution Analysis, below). To the right of the inflection, the fractal dimension is 1.29, which is a value that corresponds to a clustered particle distribution. The tissue volume at the inflection point (7.4E5 µm³) corresponds to a sphere with a diameter of 112 µm, which is approximately that of an alveolus. Thus this change in the fractal dimension occurs at tissue volumes approximately equal to that of one alveolus (Fig. 6).

The interpretation suggested by this is that pulmonary microvascular perfusion is distributed randomly at tissue volumes smaller than the alveolus, and at larger tissue volumes perfusion distribution is clustered. The cause of this clustering is unknown but may be the result of vasoactive control. We consider below (Effect of Parenchyma on Particle Distribution) the possibility that parenchymal distribution may be responsible for this particle clustering.

Particle Distribution Analysis

If an HPPP was used to generate a figure like that of one of our particle maps (Fig. 3), and if that figure was partitioned into a grid of subdivisions, as we did to conduct fractal analysis, then an HPPP has the important property that the mean number of particles per subdivision (µ) would equal the variance of the particles per subdivision (²). Thus, regardless of the subdivision size, the variance-to-mean ratio, ²/µ, would be unity for an HPPP. This ratio is known as the dispersion index (DI) and is widely used as a measure of spatial pattern. Under CSR, DI = 1, which means that it is impossible to improve predictions of the location of a point by knowing the location of any other point. However, if DI > 1, it means that the points are clustered more than would be expected under CSR. The points are no longer independent, and knowing that a point is located at x,y increases the probability that another point is in the near neighborhood of x,y. In contrast, if DI < 1, the points are more regularly spaced than expected under CSR. In the extreme case of DI = 0, all subdivisions would have exactly the same number of particles, as in the distribution of squares on a checker board. If D < 1, and if we know that a point is located at x,y, such knowledge now decreases the probability that another point is in the neighborhood of x,y and increases the probability that an adjacent point is at some greater distance from x,y.

These values are incorporated in the Grieg-Smith method, which is one of the oldest and most widely used methods of analyzing the scale of spatial patterns and which is based on the fact that DI equals unity if the spatial pattern of points was generated by an HPPP (8). This is so regardless of the fineness or coarseness of the grid of subdivisions. In this method, a surface is successively partitioned into finer and finer grids, and at each level the DI or log(DI) is plotted against the subdivision size. Conspicuous kinks in the resulting plot are interpreted as indicating the scale at which important changes in pattern occur. Fractal analysis is an example of this method.

It is rare to find CSR patterns in biological systems. Clustering or aggregation is the norm. In fact, it is quite common for there to be a hierarchy of clustering, or clustering of clusters. As the spatial scale changes, this clustering of clusters often leads to a smooth change in the DI for various spatial biological phenomena. It is well known that this smooth change obeys power laws of the form ² = µ = (v), where  is the mean count per grid at the smallest grid unit; for any subdivision consisting of v units, µ = v. In ecology, this model is known as Taylor's power law, and various stochastic models can generate spatial patterns with such structure (10). The power law includes CSR as a special case, for which  = 1 and  = 2.

A fractal plot is a log-log plot of Taylor's power law. In fractal analysis, a nonlinear log-log plot, such as that we found (Fig. 6), is said to be indicative of a nonfractal pattern (5). Describing a relationship between CV and subdivision volume as fractal is equivalent to saying that the mean and variance obey a power law relationship. Such power law relationships are to be expected in random branching processes such as that of the pulmonary circulation.

Although we expressed our data in terms of fractal analysis, it would be more accurate to say that we were interested in knowing whether Taylor's power law held at lung volumes less than 0.5 mm³. Glenny and Robertson considered this question and predicted how the CV of blood flow should behave as the tissue subdivision volume approached what they described as "the anatomic limit of the capillary" (5). At such a volume, they predicted that blood flow would become uniform among lung units, producing a fractal plot that was horizontal (fractal dimension 1.0) as it extended leftward through smaller and smaller tissue subdivision volumes. At larger subdivisions, the plot would be fractal, producing a linear plot with a fractal dimension of 1.16.

Glenny and Robertson's requirement for a conspicuous flattening of the fractal plot might be too strong a condition for observance of uniformity of flow (5). By definition, latex particle distribution is more uniform than CSR whenever DI < 1, which, in terms of a log CV plot (fractal plot), translates into the condition log CV < 1/2log v  1/2log. That is, particle distribution is uniform whenever the fractal plot falls below the line described by 1/2log v  1/2log. The distance from this line measures the departure from CSR. Specifically, the distance  below the line is measured as  = log_v 1/2log(v). The more negative the value of , the more uniform the distribution. Interestingly,  = 1/2log(DI), which means that the distance of interest is 1/2 the log of the DI. A substantial departure from CSR toward uniformity would not necessarily result in a conspicuous departure from the CSR reference line. For example, a DI of 0.5 (²/µ = 0.5µ), which suggests a substantial trend toward uniformity, would only depart from the CSR reference line by 1/2log (0.5) = 0.15. Thus uniformity of flow need not result in curvature as extreme as that proposed by Glenny and Robertson and may include plots that are concave upward. This is what we found in the fractal plot of our data (Fig. 6).

Because of these relationships, plots of log(DI) are easier to interpret than plots of log(CV). If a process is fractal, i.e., linear with respect to log(CV), it is also linear with respect to log(DI). Furthermore, if a process consists of CSR at all scales, the plot of log(DI) has a slope and intercept of zero. We replotted our data as a DI plot to illustrate this point (Fig. 7). Visually, it is easier to detect departures from this pattern than from the reference line of 1/2log v  1/2log as in log(CV) plots (fractal plots). The fractal dimension (D_s) can be obtained from the regression line of log(DI) as D_s = 3/2  /2, where  is the regression slope of log(DI).

View larger version (18K): [in this window] [in a new window]   Fig. 7.   Dispersion index (DI) analysis (variance-to-mean ratio 2/µ, where 2 is variance of the particles per subdivision and µ is mean number of particles per subdivision) of data in Fig. 6. In this plot, complete spatial randomness (CSR; 2/µ = 1.0; log 1.0 = 0) is signified by a horizontal line, unlike the fractal plot in which CSR is signified by a line with a slope of 1 (fractal dimension 1.5). Thus deviations from CSR are more obvious in the DI plot. A horizontal axis in units of alveolar volumes (alveolar diameter 75 µm) is included to emphasize that deviation of the data from CSR occurs at a volume approximately equal to that of 1 alveolus. This suggests that particle dispersion is nonrandom (clustered) at tissue volumes 1 alveolus.

Effect of Parenchyma on Particle Distribution

We show in the APPENDIX how we can correct for this by using only that portion of each particle map that includes tissue. We used this approach to examine the distribution of particles in tissue alone, without the confounding influence of air space. Our method was to collect separate but coincident confocal images of parenchyma and latex particles. This was possible because parenchyma exhibited autofluorescence in the green while the particles fluoresced in the red. Thus images of each could be collected simultaneously from the same tissue area by using two of the confocal microscope's photodetectors. This allowed us to use the pixel coordinates of the tissue as the space in which the particle distribution analysis was conducted. We used five pairs of parenchyma-particle images for this analysis. These images were made using only the ×4 objective of the microscope. Thus they represent subdivision volumes ranging from 3.5E3 to 2.8E8 µm³.

A confounding aspect of this approach was to determine the appropriate gray-scale value for the parenchymal pixels. Parenchymal fluorescence spanned the 8-bit gray-scale range of the photodetectors, which meant that fluorescence could range from values of 1 to 256. For analysis, we selected threshold values of >20, >50, and >100. We expressed the results as DI plots, which are shown in Fig. 8.

View larger version (80K): [in this window] [in a new window]   Fig. 8.   Effect of lung parenchyma on latex particle distribution. Particle DI (Fig. 7) may be a result of parenchymal distribution because particles are confined to parenchyma. To test effect of parenchyma on DI, we conducted DI analysis using 5 pairs of maps obtained from lungs infused with 2E8 particles. Each map pair consisted of a particle map and a parenchymal map. (Parenchymal maps above are of 1 of the 5 areas analyzed.) Pixel x,y addresses in the parenchymal maps determined allowable space in which particle DI analysis was conducted. Thus particle analysis was confined to areas that included parenchyma; regions occupied by air space were excluded. (See APPENDIX for rationale of this approach.) Note that tissue pixel gray-scale value affects the volume of the parenchymal space. To account for this, we repeated the analysis by using tissue gray-scale values of >20 (A), >50 (B), and >100 (C) [pixel gray-scale range: 1 (white) to 255 (black)]. Tissue volumes at which deviations from CSR occurred (top, 1E5-1E6 µm3) were affected little by these variations and were similar to the volumes at which deviations from CSR occurred in the uncorrected analysis (Fig. 7). However, the magnitude of the deviation from CSR was reduced at threshold values >100 (note change in vertical axis values). These results suggest that particle clustering is affected by factors independent of the parenchyma and may be evidence for control of pulmonary microvascular perfusion down to the alveolar level.

DI plots resulting from this approach (Fig. 8) show deviations from CSR at tissue volumes of between 1E5 and 1E6 µm³ at all three gray-scale threshold values. The magnitude of the deviation from CSR is less at threshold value >100 than it is at >20, demonstrating that the magnitude of the particle clustering is inversely proportional to the space in which the pattern analysis is conducted. However, the most important finding of this analysis is that the particle distribution deviation from CSR occurs at the same subdivision volume as that seen in Fig. 7, where parenchymal effects were not accounted for. This suggests that the deviation of the perfusion distribution from CSR at tissue volumes equivalent to that of an alveolus is not due exclusively to the distribution of the lung tissue itself, but is due to other factors. This further suggests that perfusion distribution may be controlled down to the alveolar level.

Perfusion distribution throughout the lung is assumed to be controlled by arterioles, which may have diameters as small as 30 µm (12). This is based on the observation that these are the smallest vessels around which a partial circumferential smooth muscle layer may occasionally be seen. If variations in the tone of these vessels were responsible for the particle clustering patterns we observed, we would expect deviations from CSR to first appear among tissue volumes equal to that supplied by individual 30-µm-diameter arterioles. We can estimate the number of alveoli supplied by each vessel of this size by dividing the total number of alveoli in the lung by the total number of 30-µm arterioles. Data for this calculation are available for dog lungs, for which we calculate a ratio of 750 alveoli per 30-µm arteriole (13, 14). We assume a similar ratio for rat lungs. Thus, if perfusion distribution were controlled by 30-µm-diameter arterioles, we would expect deviations from CSR to begin among tissue volumes consisting of 750 alveoli each. However, our data show that deviations from CSR begin in tissue volumes equal approximately to that of one alveolus (Fig. 7). Thus we found deviations from CSR in far fewer alveoli than those that would be expected to be supplied by individual arterioles. This again suggests that control of pulmonary microvascular perfusion may exist within much smaller vessels than those previously thought, through some mechanism not yet recognized.

Our results support those of Wagner and colleagues (16), who examined perfusion patterns in individual capillaries of adjacent alveoli. They measured patterns of red cell movement within capillaries of individual alveoli and found that these patterns were repetitive over time and, therefore, fractal. However, they also found that the patterns recorded in one alveolus bore virtually no relationship to those recorded in an adjacent alveolus. Thus temporal patterns of perfusion differed between adjacent alveoli. Our results suggest that clustering of perfusion, based on latex particle distribution, can be seen in tissue volumes equal to that of only one or perhaps a few alveoli. Thus our data and those of Wagner and colleagues demonstrate variations in perfusion patterns among individual or small groups of adjacent alveoli. Our data further suggest that these variations increase with the number of alveoli in the adjacent groups.

Glenny and colleagues (4) recently reported data on the fractal distribution of perfusion in rat lungs down to subdivision volumes of 0.53 mm³ (5.3E8 µm³). They utilized an imaging cryomicrotome to analyze the distribution of 15-µm-diameter latex particles throughout rat lungs fixed by freezing. A fractal plot through their data had an average value of 1.12. Their results suggest somewhat more clustering of perfusion [greater deviation from CSR (fractal dimension 1.5)] than we found in our 2E8 data, which have a fractal value of 1.26 (Fig. 6). The smallest unit of tissue volume they examined (5.3E8 µm³) is approximately twofold larger than our largest subdivision volume (2.8E8 µm³). Thus our studies extend those of Glenny and colleagues down to subalveolar tissue volumes. Differences in the fractal dimensions between our studies and theirs may be due to differences in the size of the particles used (4 vs. 15 µm) and differences in the methods used to measure particle positions (confocal microscopy vs. cryomicrotomy).

We did not utilize the vertical (z) axis resolution of the confocal microscope to determine the location of each particle within the vertical plane (100-µm thickness). Our interest was in determining the distribution of the particles among alveoli. Assuming that a rat alveolus has an average diameter of 75 µm, the low-power map dimensions (Fig. 1) measured ~90 × 45 × 1.3 alveoli (14). This is appropriate for evaluating interalveolar perfusion distribution. It is unlikely that distribution in the z-axis differed from that in the x- and y-axes.

We used 4-µm-diameter particles for our studies because we were interested in perfusion distribution among alveoli, not in flow per gram of tissue. We showed previously that these particles are trapped mainly in interalveolar corner vessels (1). Furthermore, our trapping data suggest that more than 91% of the infused particles were trapped within the pulmonary microcirculation. Thus these particles appear to be well suited for evaluating the distribution of perfusion among alveoli.

One goal of our studies was to determine the optimum number of particles to infuse. The optimum provides the greatest number of particles per map, while minimizing particle clustering. Greater numbers of particles increase pattern analysis resolution. The data (Figs. 6 and 7) show that deviations from CSR were greater for 2E8 particles than for 1E7, which demonstrates the effect of particle numbers on resolution. To determine the fraction of clustered particles in particle maps, we counted the number of pixels occupied by every particle in five randomly selected 2E8 maps. We assumed that single particles consisted of 10 pixels. We determined this value from particle maps in lungs infused with 1E7 particles where we assumed that the particles were widely dispersed enough so that only singlets were present; 10 was the largest number of pixels per particle in those images. In the 2E8 maps, 96.5% of the particles consisted of 10 pixels. The remaining 3.5% of particle images consisted of 19-33 pixels. We found no particle images that consisted of 11-18 pixels. This supports our belief that single particles consisted of 10 pixels and suggests that larger groups of pixels consisted of clusters of three or possibly four particles. However, the fact that these pixel groups accounted for only 3.5% of the total number of particles present suggests that particle clusters had an insignificant effect on the pattern analysis. Thus 2E8 appears to be an ideal number of particles for these studies.

Our goal was to evaluate flow distribution among alveoli, and we used statistical analysis of the particle distribution patterns as a way to accomplish that. We believe that this method provides a way to quantify the distribution of pulmonary microvascular perfusion at the scale of one to a few hundred alveoli. We hope this approach will provide new insights into mechanisms by which the distribution of pulmonary microvascular perfusion is controlled.

In conclusion, our results suggest that flow distribution among alveoli becomes nonfractal at the alveolar level and corresponds to a statistical state of CSR. However, at tissue volumes larger than that of one alveolus, we found that the flow distribution is clustered in a way that can be expressed quantitatively. The cause of this clustering is unknown, but it may be evidence that perfusion is controlled down to the alveolar level.