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Am J Respir Crit Care Med. 2008 February 1; 177(3): 292–300.
Published online 2007 October 11. doi:  10.1164/rccm.200703-484OC
PMCID: PMC2218852

Relation between Shunt, Aeration, and Perfusion in Experimental Acute Lung Injury


Rationale: In a pulmonary process characterized by spatially heterogeneous loss of aeration, the impairment of gas exchange is expected to depend on the regional distribution of perfusion relative to that of aeration.

Objectives: To investigate how regional aeration, shunt, and perfusion are interrelated at different levels of end-expiratory pressure and how their interplay relates to global shunt fraction in acute lung injury.

Methods: Regional shunt and perfusion were assessed by imaging with positron emission tomography the pulmonary kinetics of [13N]nitrogen infused in saline solution in five sheep after lung lavage. The lung field was divided in six horizontal regions.

Measurements and Main Results: Each animal showed an inverse relation between regional shunt (Fs) and gas (Fg) fractions: Fs = −m · Fg + Fs0. This relation was similar among animals (m = 1.25 ± 0.14, Fs0 = 0.75 ± 0.15) and invariant with end-expiratory pressure, despite lack of correlation between global shunt and gas fractions and large interanimal variability in global shunt fraction. When this relation was used to estimate global shunt fraction as a perfusion-weighted average of the estimates of regional shunt fraction derived from regional gas fraction, 72% of the interanimal variability in global shunt fraction could be explained.

Conclusions: Despite large interanimal variability in global shunt fraction, there was a consistent inverse relation between regional shunt and gas fractions, independent of end-expiratory pressure. Most of the interanimal variability in global shunt fraction could be explained by the combined effect of this relation and the distribution of perfusion on regional shunt, rather than by differences in global aeration.

Keywords: artificial respiration, adult respiratory distress syndrome, positron emission tomography, mechanical ventilators, X-ray computed tomography


Scientific knowledge on the subject

Previous studies have reported conflicting results when attempting to relate global loss of aeration to shunt fraction, or PaO2, in acute lung injury.

What This Study Adds to the Field

In lavage-induced acute lung injury, we found an inverse relation between regional shunt and gas fractions, which was independent of positive end-expiratory pressure and consistent between animals despite lack of correlation between global shunt and gas fractions and large variability in global shunt.

A decrease in lung aeration and the ensuing impairment of oxygenation are defining features of acute lung injury (ALI) and the acute respiratory distress syndrome (1). Because in ALI the loss of aeration is spatially heterogeneous, with poorly aerated lung tissue being predominantly in dependent regions (24), the relation between reduction in aeration and impairment of gas exchange may not be straightforward. Indeed, computed tomographic (CT) studies reported conflicting data on this relation. Although some studies found that shunt fraction, or venous admixture, correlated positively with average lung density (5) and lung mass (6), and negatively with functional residual capacity (6), another study did not find a correlation with the extent of lung opacification (3). When the contribution of density-defined tissue “compartments” to gas exchange impairment was probed, results have been inconsistent. PaO2, shunt fraction, or venous admixture, and their changes with positive end-expiratory pressure (PEEP), have been variably reported as strongly (7), moderately (5), or not correlated (6, 8) with the fraction of “nonaerated” lung, defined by CT attenuation greater than −100 Hounsfield units (HU). The fraction of poorly aerated lung tissue, defined by CT attenuation between −500 and −100 HU, was not correlated with PaO2 or shunt fraction in two studies (5, 7). In contrast, Crotti and coworkers (9) reported a stronger correlation of PaO2 with the fraction of poorly aerated tissue than with that of nonaerated tissue, and Malbouisson and colleagues (6) found a correlation between PEEP-induced alveolar recruitment and improvement of oxygenation only by accounting for the increase in aeration of both poorly aerated and nonaerated tissue.

A possible explanation for these discrepancies is that, whereas measurements of CT attenuation are usually performed at a fixed airway pressure, commonly at end inspiration or expiration, blood gases are sampled throughout the respiratory cycle. Because PaO2 varies during the respiratory cycle in the acutely injured lung (10, 11), lack of synchrony between the phases of the cycle at which lung density and blood gases are measured is expected to introduce spurious variability in the relation between shunt fraction and lung aeration. Another possible explanation is that measurements of regional density do not take into account the effect of the regional distribution of perfusion on gas exchange. This effect may be important, as suggested by the fact that impairment of hypoxic pulmonary vasoconstriction with shift of perfusion toward edematous, atelectatic, or consolidated regions worsened oxygenation (1214), whereas perfusion redistribution away from edematous regions ameliorated hypoxemia (13, 15). When the loss of aeration is spatially heterogeneous, dissecting the relation between tissue density and global shunt requires determination of both regional shunt fraction and perfusion. Indeed, previous studies that evaluated regional aeration by CT and shunt by inert gas elimination, which does not enable a spatial analysis of the distribution of shunt or perfusion, could neither ascertain the topographical relation between shunt and density nor isolate the mechanism responsible for the dissociation between PEEP-induced lung recruitment and PEEP's effect on global shunt fraction (16). Accordingly, the need to combine measurements of regional perfusion, shunt, \lung structure relationship' in ALI (4) was recently stated.

In this study, we assessed the relation between aeration and shunt fraction in a lung lavage model of ALI. Each animal was studied at two levels of end-expiratory pressure to increase the spectrum of values of aeration and shunt fraction over which this relation was explored. Our aim was to investigate how regional aeration, shunt, and perfusion are interrelated in ALI and how the interplay among these variables is reflected in the global shunt fraction. To pursue this aim, we used positron emission tomography (PET) imaging of the pulmonary kinetics of [13N]nitrogen (13N2) infused intravenously in saline solution to measure regional perfusion and shunt fraction.

Some of the results of this study were previously reported in the form of an abstract (17).


Methods used are further described in the online supplement.

Experimental Protocol

In five ventilated sheep (tidal volume, 13.7 ± 2.7 ml/kg; respiratory rate, 18 breaths/min; inspiratory-to-expiratory ratio, 1:1.5; FiO2, 1), lung injury was induced by lavage (18) with 500 ml (24 ± 2 ml/kg) of 0.2% polysorbate 80 in saline (19, 20). If PaO2 was higher than 300 mm Hg (21) at 30 minutes after the first lavage, a second lavage (500 ml) was performed. If PaO2 was lower than 50 mm Hg, PEEP was set at 5 cm H2O, and increased further to 10 cm H2O if PaO2 remained lower than 50 mm Hg. According to this algorithm, animals 1 and 2 underwent two lavages and did not require PEEP, animal 3 underwent a single lavage without PEEP, whereas animals 4 and 5 required PEEP of 10 and 5 cm H2O, respectively, after a single lavage (Figure 1). After injury, the animals were placed in supine position in the PET scanner and ventilated at previous settings (Table E1 of the online supplement). Five minutes after a “recruitment maneuver” to 50 cm H2O, physiologic data were collected and PET scans acquired to measure regional aeration, shunt, and perfusion at the baseline PEEP level (lower PEEP). PEEP was then increased to 15 cm H2O in all animals (higher PEEP) and, 20 minutes later, physiologic data and PET scans were collected. At least 2 hours passed between the last lung lavage and measurements at lower PEEP.

Figure 1.
Protocol schema. a = animal number; PEEP = positive end-expiratory pressure, cm H2O; PET = positron emission tomography. 13N2 = [13N]nitrogen.

PET Imaging

The PET scanner imaged 15 slices of thorax, corresponding to approximately 70% of the lung (22).

Transmission (density) scan.

This scan was used to demarcate the lung field and to calculate gas fraction (2326) of the lung (FgL) and of six horizontal regions of interest (ROIs) of equal height (Fgi, i = 1–6, in the ventral-to-dorsal direction). Relative lung volume was calculated as the ratio of the number of voxels within an ROI (ni) to that in the lung field (nL). Ventral-to-dorsal and cranial-to-caudal gas fraction gradients were calculated by linear regression (25).

13N2–saline bolus infusion (perfusion) scan.

13N2 dissolved in saline was infused intravenously over the initial 3 seconds of a 60-second apnea performed at mean airway pressure (20, 27, 28). Because of the low solubility of nitrogen, the pulmonary kinetics of 13N2 during apnea, measured with sequential PET frames, differ between regions that are perfused and aerated, in which virtually all 13N2 accumulates in the alveolar airspace in proportion to regional perfusion (25, 29), and regions with shunting alveolar units. In the latter, the concentration of 13N2 reaches a peak in early apnea, related to regional perfusion, followed by a decrease during the remainder of apnea. This decrease is related to regional shunt, because flooded, atelectatic, or consolidated units do not retain 13N2 (20, 22, 28). By fitting the time–activity curve of 13N2 with a tracer kinetic model (30, 31), regional perfusion (equation M1), expressed as a fraction of perfusion to the imaged lung, and shunt fraction (Fsi) were estimated for each ROI in which the coefficient of determination of the model fit was higher than 0.975. To determine the contribution of an ROI to global shunt fraction, relative regional shunted perfusion was calculated as follows: equation M2, where equation M3 represents the fraction of imaged perfusion shunted within an ROI.

Statistical Analysis

Comparisons between lower and higher PEEP were performed with the Sign test (32), comparisons between ROIs with the Friedman test (33).


Global Physiologic Variables

At lower PEEP, there was large interanimal variability in PaO2 and shunt fraction (FsO2), whereas the range of variation of gas fraction was narrow (Figure 2). Consequently, the coefficient of variation of FsO2 was fivefold greater than that of FgL (0.54 vs. 0.11). As expected, in all animals the increment in PEEP improved PaO2 (Table 1), reduced shunt fraction, and increased gas fraction (Figure 2). The coefficient of variation of FsO2 remained fivefold greater than that of FgL at higher PEEP (0.45 vs. 0.09). FsO2 was not correlated with FgL (r = −0.11, P = 0.8). Shunt fraction of the imaged lung measured by PET (FsL) was correlated with FsO2 (FsO2 = 0.97 · FsL + 0.05; r = 0.93, P < 0.001).

Figure 2.
Shunt fraction measured from blood gases (FsO2) versus gas fraction of the imaged lung field (FgL) at lower (solid circles) and higher (open circles) positive end-expiratory pressure (PEEP). The increment in PEEP reduced FsO2 and increased FgL in all ...

Relation between Regional Aeration, Shunt, and Perfusion

All animals had a vertical gradient of gas fraction favoring nondependent (ventral) regions (Table E2). The gradient was steeper at lower PEEP than at higher PEEP (0.039 ± 0.013 vs. 0.029 ± 0.017 cm−1, respectively; P < 0.05). This ventral-to-dorsal gradient was significantly greater than the absolute value of the cranial-to-caudal gradient (0.034 ± 0.015 vs. 0.008 ± 0.003 cm−1, respectively; P < 0.01). Regional 13N2 time–activity curves (Figure 3) revealed a vertical dependency of gas exchange impairment: From ROI 4 to ROI 6, there was a progressively greater drop of tracer activity during the latter part of apnea, consistent with worsening shunt.

Figure 3.
[13N]nitrogen (13N2) pulmonary kinetics and positron emission tomography images from animal 5 at lower (upper panel) and higher (lower panel) positive end-expiratory pressure (PEEP). For the tracer kinetics, the imaged lung field was divided in six horizontal ...

For each animal, there was an inverse relation between regional shunt (Fs) and gas (Fg) fractions (Figure 4):

equation M8

From less dependent (ventral) to more dependent (dorsal), the ROIs showed progressively higher shunt and lower gas fraction. The interanimal variability in the regression parameters was low, as coefficients of variation for m and Fs0 were, respectively, 0.11 and 0.19. Consequently, a single relation could fit all data points (Fs = −1.27 · Fg + 0.77; r = −0.90, P < 0.0001). This relation remained essentially unchanged when only the data at lower PEEP were fitted (Fs = −1.37 · Fg + 0.79; r = −0.90, P < 0.0001). Thus, the effect of increasing PEEP was to shift data points corresponding to dependent ROIs (i.e., ROIs 4–6) down and to the right along the Fs versus Fg relation (Figure 4). The improvement of regional shunt due to the PEEP increment could be visualized from the PET images (Figure 3): Compared with those at lower PEEP, images at higher PEEP showed increased 13N2 retention at the end of apnea in the dorsal lung, indicating restored aeration and gas exchange.

Figure 4.
Regional shunt (Fs) and gas (Fg) fractions in horizontal regions of interest (ROIs) at lower (solid symbols) and higher (open symbols) positive end-expiratory pressure (PEEP). The ROI symbol shape succession in the dependent (dorsal) to nondependent (ventral) ...

To assess whether global shunt fraction could be recovered from regional aeration if the distribution of perfusion (Figure 5) and the relation between regional shunt and gas fractions (Equation 1) were taken into account, we calculated for each animal at each PEEP level:

equation M9

where the summation was performed over the ROIs for which, in a given animal at a given PEEP, equation M10 could be estimated from the tracer kinetic model (Figure 5). FsEST thus represents the perfusion-weighted average of the estimates of regional shunt fraction derived from measurements of regional gas fraction through the relation expressed by Equation 1. FsEST was correlated with FsO2 (FsO2 = 0.87 · FsEST + 0.07; r = 0.85, P < 0.01), and most of the interanimal variance in FsO2 (r2 = 0.72) was explained by this relation (Figure 6).

Figure 5.
Perfusion fraction in ventral-to-dorsal regions of interest (ROIs 1–6) for each animal and their average (bottom right panel). For each ROI, the solid bars represent measurements at lower positive end-expiratory pressure (PEEP) and the open bars ...
Figure 6.
(A) Shunt fraction measured from blood gases (FsO2) versus that estimated (FsEST) from regional gas fraction (Fgi; Figure 4), perfusion fraction (equation M15; Figure 5), and the regional relation between shunt and gas fractions (Fs = −m · ...

In contrast to the vertical distribution of perfusion, which depended on the size of the ROIs and reflected the shape of the lung (Figure 5), perfusion relative to lung volume [equation M17] increased from nondependent (ventral) to dependent (dorsal) ROIs (Figure 7).

Figure 7.
Perfusion fraction (equation M18) normalized by relative lung volume (ni/nL) in ventral-to-dorsal regions of interest (ROIs 1–6) at lower (solid bars) and higher (open bars) positive end-expiratory pressure (PEEP). equation M19 is expected to be unity when perfusion ...

Regional Shunted Perfusion

Relative shunted perfusion varied significantly between ROIs both at lower (P < 0.01) and higher (P < 0.05) PEEP (Figure 5). Although gas fraction was systematically lower in ROI 6 compared with ROI 5 both at lower (P < 0.05) and higher (P < 0.05) PEEP (Figure 4), shunted perfusion was highest, on average, in ROI 5.

The net effect of the PEEP increment on shunted perfusion of the most dependent (dorsal) ROI (i.e., equation M21) was the result of two processes with competing effects: a systematic increase in aeration with an ensuing reduction in regional shunt fraction (Figure 4), which tended to decrease shunted perfusion, and a shift of perfusion toward the most dependent ROI (Figure 5), which tended to increase shunted perfusion. When the shift of perfusion outweighed the beneficial effect of the increase in aeration, as in ROI 6 of animal 1, the net effect was an increase, rather than a decrease, of regional shunted perfusion at the higher PEEP.


The main result of this study was the finding of an inverse relation between regional shunt and gas fractions that was systematic and consistent both within and between animals, and unaffected by PEEP, despite lack of relation between global shunt and gas fractions and large interanimal variability in global shunt fraction. A secondary result was the experimental demonstration that a shift of perfusion can act as a mechanism of dissociation between the PEEP-induced gain in aeration of a nonaerated region (i.e., “anatomical” recruitment) and the ensuing contribution of that region to global shunt fraction (i.e., “functional” recruitment).

Rationale and Critique of the Experiment

We chose the lung lavage model because it presents the vertical distribution of lung density characteristic of ALI (34, 35) and maintains significant recruitment with sufficient PEEP (3639). Therefore, this model appeared likely to allow investigation of the relation between shunt and gas fractions over a wide spectrum of lung inflation, especially with varying levels of PEEP. Because lower PEEP was set according to oxygenation and could hence be expected to differ between animals, we chose a single higher PEEP to assess whether any interanimal variability present at lower PEEP was maintained at a uniform PEEP. Although the lavage model does not encompass the pathophysiologic complexity of human ALI, it is likely to reflect several of its features, such as surfactant dysfunction (40, 41), atelectasis (18), and edema (36, 38). Addition of a detergent (19, 21, 39) allows the target hypoxemia to be reached with a lower volume of fluid than pure saline (34, 35, 41). More important, the detergent inactivates any surfactant produced after injury, affording the model to remain stable over time (19). Although the percentage of lavage fluid recovered (60.1 ± 0.3%) was lower than in other studies (34, 41), the amount of fluid retained (289 ± 104 ml) was similar.

To prevent alveolar derecruitment throughout the apnea (10, 35) and to match lung volume during the 13N2 scan, at which regional shunt was measured, with mean lung volume during the transmission scan, at which aeration was measured, apnea was performed at an airway pressure equal to mean airway pressure during breathing. Blood gas samples were drawn over two respiratory cycles to minimize variability due to sample timing (11). Accordingly, measurements of shunt and aeration should reflect the physiologic condition of the lung at approximately mean lung volume and be comparable to measurements of lung density obtained by averaging dynamic CT frames over consecutive respiratory cycles (42, 43). This approach should minimize the spurious variability that could be introduced in the relation between shunt and aeration by lack of temporal registration between gas exchange and lung density measurements.

We used an FiO2 of 1 to be consistent with the majority of previous studies that probed the relation between shunt fraction, or PaO2, and lung density (6, 7, 34, 38, 42, 43). At high FiO2, the contribution of alveolar units with low ventilation-to-perfusion ratio to shunt fraction measured with the Berggren equation is expected to decrease. If poorly aerated regions represented low ventilation-to-perfusion units, it could be argued that high FiO2 would lead to underestimating their contribution to hypoxemia. Although discrepancies in the literature could be partly related to differences in FiO2, inconsistencies regarding the effect of poorly aerated tissue, as defined by CT, on shunt or PaO2 persist among studies performed at similar FiO2, whether it is 1 (6, 7, 42, 43) or less (5, 9), indicating that differences in FiO2 alone can not explain those discrepancies. It is possible that, had we used lower FiO2, shunt would have been less, because an FiO2 of 1 is expected to promote resorption atelectasis (44) and blunt hypoxic pulmonary vasoconstriction in shunting regions through its effect on mixed venous Po2 (45).

The rationale for the analysis by horizontal ROIs was the large and systematic variation of gas fraction in the ventral-to-dorsal direction (Table E2). Despite the fact that the ROIs were large, the variation of aeration and perfusion across these ROIs was sufficient to capture the major source of interanimal variability in shunt fraction. However, variation of aeration in the cranial-to-caudal direction, which occurs in ALI (2), may also be important, as suggested by the fact that animals 4 and 5, with the most severe hypoxemia, had lower gas fraction in caudal compared with cranial lung, whereas the other animals had higher gas fraction in caudal lung (Table E2).

Relation between Shunt Fraction, Aeration, and Perfusion

Despite absence of any significant relation between global shunt and gas fractions, the inverse relation between regional shunt and gas fractions was consistent among animals, as shown by the low coefficient of variation of the regression parameters. Furthermore, this relation was not affected by the level of PEEP, because a single equation could fit all data at lower PEEP, even though lower PEEP varied from 0 to 10 cm H2O, and this equation remained essentially unchanged when data obtained at PEEP of 15 cm H2O were added. These results differ from previous ones in several respects. Tokics and coworkers (16) reported a linear relation between fraction of atelectatic lung and global shunt fraction in anesthetized healthy subjects. In contrast, we could not confirm a similar relation in this model of ALI. Although the marked variability in global shunt fraction was unrelated to global gas fraction, most of this variability could be recovered from an estimate of global shunt fraction that accounted for the effects of the inverse relation between regional shunt and gas fractions and of regional perfusion on regional shunted perfusion (Figure 6). The disconnect between regional and global behavior is potentially clinically relevant because it suggests that, whereas regional shunt fraction is tightly linked to regional aeration, global indices of hypoxemia may not reflect the severity of loss of aeration in ALI. Accordingly, a high shunt fraction or low PaO2/FiO2 may not be sensitive indicators of loss of aeration and hence may not be suited, for example, to assess lung derecruitment or stratify patients for their risk of ventilator-associated lung injury. Mechanisms such as hypoxic pulmonary vasoconstriction (1215) or vascular compression and obstruction (46) may alter the distribution of perfusion and thus be responsible for the global to regional disconnect in ALI.

Another difference with the findings of Tokics and colleagues (16) is that, whereas they showed that the slope of the relation between fraction of atelectatic lung and global shunt fraction changed with PEEP, we found that the regional relation between shunt and gas fractions was invariant with PEEP. In the absence of regional measurements of perfusion and shunt, Tokics and coworkers (16) were admittedly unable to isolate the mechanism responsible for that change of slope. Combination of topographical measurements of perfusion and shunt allowed us to demonstrate that PEEP-induced shift of perfusion toward dependent regions, consistent with previous results (4749), can dampen or even outweigh the beneficial effect of improved aeration on regional shunt. This observation could offer one explanation for the dissociation that can occur between PEEP-induced lung recruitment and variation in gas exchange in ALI (50). It also lends experimental evidence to the speculation that a shift of perfusion toward atelectatic areas was the most likely mechanism for the PEEP-induced change in slope of the relation between fraction of atelectatic lung and global shunt fraction observed in healthy anesthetized subjects (16).

In line with previous results (27), ROIs showed a progressive increase in shunt fraction as gas fraction decreased below approximately 0.5. This observation, combined with the notion that “true” shunt is the main mechanism of gas exchange impairment in ALI at high FiO2 (51, 52), suggests that the inverse relation between regional shunt and gas fractions is due to a “quantal” loss of gas-exchanging units, so that the decrease in aeration of a region is not apportioned uniformly among its units, but is absorbed only by some of them, which become atelectatic, while the remaining units preserve their aeration and gas exchange. The progressive increase in regional shunt fraction could thus be the effect of an increase in the ratio of shunting to normally aerated alveoli. This could provide an explanation, in addition to the lack of temporal registration between gas exchange and CT measurements, for variable findings on the relation between global shunt fraction, or PaO2, and CT–defined lung compartments (3, 5, 79, 42, 43). Indeed, what is defined as poorly aerated lung over the resolution element, be it a voxel or an ROI, could comprise nonaerated shunting units and units with normal ventilation-to-perfusion ratio. The contribution to global shunt fraction, however, will be a function of the partitioning of perfusion between these two types of units and of total perfusion, both of which may vary depending on several factors (1215, 46). The systematic relation between regional shunt and gas fractions (Figure 4) is also compatible with the strong correlation reported between fraction of lung with CT attenuation greater than −300 HU and global shunt fraction (42, 43). Because the increase in regional shunt fraction is progressive as gas fraction decreases below 0.5, a CT threshold close to −500 HU will tend to overestimate global shunt fraction, whereas a threshold close to −100 HU will underestimate it. An intermediate threshold, around −300 HU, would be expected to yield the best correlation. As Figure 4 shows, however, this should not be interpreted as indicating that a single threshold can separate the shunting and nonshunting compartments, at least as long as spatial resolution remains lower than the alveolar scale.

The observation that nondependent ROIs were hypoperfused relative to their lung volume (Figure 7), but had normal gas fraction (Figure 4), likely represents the regional basis of our previous finding that the aerated alveolar volume of distribution of infused 13N2 is lower than intrapulmonary gas volume in supine sheep that underwent lung lavage (31). Thus, in ALI, not only functional residual capacity is reduced but the volume of gas participating in gas exchange may be further decreased because of the disparity in the distribution of gas content relative to that of perfusion.

In summary, in an experimental model of ALI with spatially heterogeneous loss of aeration, we found a systematic inverse relation between regional, but not global, shunt and gas fractions. This relation was not affected by PEEP. This relation appears to be relevant to understand the gas exchange effects of changes in regional aeration because most of the interanimal variability in global shunt fraction could be explained by the combined effect of this relation and of the distribution of perfusion on regional shunted perfusion, rather than by differences in global aeration.

Supplementary Material

[Online Supplement]


The authors thank Kevin R. O'Neill, M.D., for tracer kinetic modeling; Steven B. Weise for technical assistance with image acquisition; John A. Correia, Ph.D., William M. Buceliewicz, and David F. Lee, B.S., for preparation of the radioisotope; O. Syrkina, M.D., for assistance with animal preparation; and Warren M. Zapol, M.D., for continued support of this project.


Supported by National Institutes of Health grants HL076464 and HL086827, and by a research grant from the Foundation for Anesthesia Education and Research and the American Society of Critical Care Anesthesiologists.

This article has an online supplement, which is accessible from this issue's table of contents at

Originally Published in Press as DOI: 10.1164/rccm.200703-484OC on October 11, 2007

Conflict of Interest Statement: None of the authors has a financial relationship with a commercial entity that has an interest in the subject of this manuscript.


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