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J Appl Physiol 97: 2104-2111, 2004. First published August 6, 2004; doi:10.1152/japplphysiol.00072.2004
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Effect of posture on regional gas exchange in pigs

William A. Altemeier,1 Steve McKinney,1 Melissa Krueger,1 and Robb W. Glenny1,2

Departments of 1Medicine and 2Physiology and Biophysics, University of Washington, Seattle, Washington 98195

Submitted 21 January 2004 ; accepted in final form 31 July 2004


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Although recent high-resolution studies demonstrate the importance of nongravitational determinants for both pulmonary blood flow and ventilation distributions, posture has a clear impact on whole lung gas exchange. Deterioration in arterial oxygenation with repositioning from prone to supine posture is caused by increased heterogeneity in the distribution of ventilation-to-perfusion ratios. This can result from increased heterogeneity in regional blood flow distribution, increased heterogeneity in regional ventilation distribution, decreased correlation between regional blood flow and ventilation, or some combination of the above (Wilson TA and Beck KC, J Appl Physiol 72: 2298–2304, 1992). We hypothesize that, although repositioning from prone to supine has relatively small effects on overall blood flow and ventilation distributions, regional changes are poorly correlated, resulting in regional ventilation-perfusion mismatch and reduction in alveolar oxygen tension. We report ventilation and perfusion distributions in seven anesthetized, mechanically ventilated pigs measured with aerosolized and injected microspheres. Total contributions of pulmonary structure and posture on ventilation and perfusion heterogeneities were quantified by using analysis of variance. Regional gradients of posture-mediated change in ventilation, perfusion, and calculated alveolar oxygen tension were examined in the caudocranial and ventrodorsal directions. We found that pulmonary structure was responsible for 74.0 ± 4.7% of total ventilation heterogeneity and 63.3 ± 4.2% of total blood flow heterogeneity. Posture-mediated redistribution was primarily oriented along the caudocranial axis for ventilation and along the ventrodorsal axis for blood flow. These mismatched changes reduced alveolar oxygen tension primarily in the dorsocaudal lung region.

ventilation-perfusion; heterogeneity; gravitational influence; mechanical ventilation

EFFICIENT GAS EXCHANGE BY the lung requires close matching of regional ventilation (A) and perfusion (). Despite the high degree of spatial heterogeneity observed in the lung for both regional (4, 16, 17, 21) and A (18, 25, 26), efficient gas exchange is preserved through close regional correlation between A and (2, 12, 18, 33).

It is well established that posture affects both arterial oxygenation and heterogeneity of A/ distribution in normal and injured lungs (1, 5, 8, 9). Despite this, rotation between supine and prone postures appears to have a modest effect on determining regional blood flow in both dogs and baboons (13, 15). Studies in the microgravity environment of the space shuttle found A/ heterogeneity similar to that observed with normal gravity (23), implying that differential vertical redistribution of A and secondary to reversal of the gravitational vector is unlikely to be the principal explanation for increased A/ mismatch in the supine posture. One potential explanation is regionally reduced lung compliance in areas adjacent to the diaphragm, resulting in decreased caudal A and regionally reduced A: correlation. Engel reported increased peridiaphragmatic closing volume in supine humans, resulting in redistribution of A away from caudal lung regions (10).

We hypothesize that posture has a small effect on overall A and distributions but does result in regionally decreased A: correlation and alveolar oxygen tensions, primarily in the peridiaphragmatic region. To evaluate this hypothesis, we measured regional A and in seven anesthetized, mechanically ventilated pigs in both supine and prone postures and evaluated for gradients in change of A, , and alveolar oxygen partial pressure (PAO2) in regions adjacent to and distant from the diaphragm.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Animal preparation.   The Animal Care Committee at the University of Washington approved these experiments. Seven purpose-bred, specific-pathogen-free pigs (S&S Farms, San Jose, CA) of either sex, weighing 18.5–25 kg, were studied. Anesthesia was induced with ketamine and xylazine intramuscularly followed by intravenous thiopental sodium and was maintained at a level sufficient to suppress spontaneous respiration with a continuous infusion of thiopental sodium. Animals were mechanically ventilated via tracheotomy with a tidal volume of 15 ml/kg and a respiratory rate sufficient to maintain an arterial carbon dioxide (CO2) tension between 30 and 40 Torr. Tidal volumes and respiratory rates, once set, were maintained constant throughout the experiment. One carotid and one femoral artery were cannulated for continuous blood pressure monitoring and withdrawal of blood samples, both femoral veins were cannulated for infusion of drugs and injection of microspheres, and a pulmonary arterial catheter was inserted via the right external jugular vein. Before other measurements, exhaled volume and CO2 tension were collected over three consecutive breaths by using an inline spirometer (RSS100, Korr Medical Technologies, Salt Lake City, UT) and infrared CO2 detector (model 1260, Novametrix Medical Systems, Wallingford, CT) for anatomic dead space calculation (11).

Study protocol.   All animals received stacked breaths to twice the tidal volume at ~10-min intervals 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 immediately following a stacked breath. Each data collection included values for mean arterial pressure, pulmonary arterial pressure, end-inspiratory static or plateau airway pressure, temperature, hematocrit, and the average of three thermodilution cardiac output measurements. Arterial and mixed-venous blood samples were collected for blood-gas determination. Following each data collection, regional pulmonary blood flow and A distribution were marked by deposition of aerosolized and injected microspheres, as previously described (25). Briefly, for each measurement, a solution of 1-µm fluorescent microspheres (FluoSpheres, Molecular Probes, Eugene, OR) was aerosolized with a constant output atomizer (TSI model 3076, Thermo Systems, St. Paul, MN). The aerosol was passed through a silica gel diffusion dryer (TSI 3062) and Krypton-85 source-charge neutralizer (TSI 3012) before delivery to the animal via a bag-in-box system driven by a large-animal piston pump ventilator (Harvard Bioscience, Holliston, MA). Simultaneous with each aerosol delivery, a different colored suspension of 15-µm fluorescent microspheres (FluoSpheres) was intravenously injected in multiple, small, evenly spaced increments over 10 min to measure regional . One measurement each of regional A and regional was randomly chosen for simultaneous duplicate measurement in each experiment. A total of 10 different fluorescent colors were used (1-µm microspheres: yellow-green, yellow, orange, orange-red, red; 15-µm microspheres: blue, blue-green, green, crimson, scarlet). After the last data collection, 10,000 units of heparin and 1.5 ml of papavarine were intravenously injected, and the animal was killed by exsanguination under deep anesthesia.

Lung preparation and data collection.   Fluorescence from the injected and aerosolized microspheres was quantified as previously described (2). Briefly, the lungs were removed from the thorax and inflated to 25 cmH2O with a constant airflow heated to 40°C until dry. The dried lungs were fixed in a rapidly setting foam within a rectangular mold. The foam-embedded lungs were sliced into transverse sections and systematically diced into ~2-cm3 cubes by using a miter box with the rectilinear coordinates for each piece noted. Fluorescent dyes were extracted from the microspheres in each tissue piece by using 2-ethoxyethyl acetate. Fluorescent signals for the 10 colors were measured in each sample with a fluorimeter (LS-50B, Perkin-Elmer, Boston, MA). Between blocks of 50 samples, fluorescent intensity for each color excitation/emission wavelength pair was determined in a blank sample containing only 2-ethoxyetheyl acetate. Following spillover correction (27), the mean and SD for the blank samples were determined at each color. In each lung piece, any color fluorescence that was within the mean +2 x SD of the blank signal was considered to be indistinguishable from zero. Pieces with airway content ≥25% of total piece volume were excluded from further analysis. Fluorescent signals from each piece were normalized to that piece's weight to correct for heterogeneity in measured A and caused by variation in piece size. The fluorescent intensity of each color in each piece was also normalized to the mean intensity of that color across all pieces to allow an estimate of regional A and blood flow, independent of the absolute minute ventilation and cardiac output.

To calculate regional PAO2, raw fluorescent signals for each piece were converted to milliliters per minute by using measured cardiac output and alveolar minute ventilation calculated from the measured expired minute ventilation and Fowler dead space. Regional A and distributions for each condition were combined with measured hemoglobin concentration, body temperature, and mixed-venous blood composition to calculate regional gas tensions, as previously described (3).

Data analysis.   A and data were analyzed in an identical manner; all further discussion of analysis methods also applies to data analysis. To quantify the relative influence of posture on the overall heterogeneity of the A distribution, we used a two-way crossed random effects model:

(1)
where yijk is the ventilation to piece i in posture j (prone or supine) during repetition k (1 or 2); µ is the grand mean ventilation across all pieces, conditions, and repetitions; {tau} is the effect on ventilation resulting from structural effects independent of postural influence; {beta} is the effect resulting from posture; {tau}{beta} is the interaction effect from structure and posture; and {epsilon} is the combined effect of temporal and methodological variability. As detailed in the APPENDIX, the term for posture effect ({beta}) drops out as a consequence of using data that have been normalized to the mean signal. Therefore, the term for structure x posture interaction is used to quantify the maximum possible effect of posture on A distribution. ANOVA was applied to this model to partition the relative contributions of structure, posture, and temporal/methodological variability on overall heterogeneity of A (see APPENDIX). In this analysis, the contribution of "structure" to overall heterogeneity was defined as the portion of overall heterogeneity that is unaffected by changes of posture and across repetitions.

Changes in A, , and PAO2 with posture were characterized by the base 10 logarithm (log) of the ratio of each variable in the supine posture to prone posture. For example, log ratio of A refers to the logarithm of the ratio of A in the supine posture to A in the prone posture of a given lung piece. A log ratio equal to zero meant that there was no difference between A (or blood flow or PAO2) between the supine and prone postures; a log ratio greater than zero meant that A was greater in the supine posture; and a log ratio less than zero meant that A was greater in the prone posture. For the small number of pieces with A or blood flow of zero in either the supine or prone posture, we assigned a log ratio of –3 or 3, respectively.

To examine regional changes with posture, mean log ratios of A, blood flow, and PAO2 were calculated for each transverse section of lung and regressed against the caudocranial axis of the lung. Regressions were weighted by the square root of the number of data points in each lung section. To test our hypothesis that the peridiaphragmatic region behaves differently following posture change with respect to A, blood flow, and PAO2, we compared the degree of fit for two different models by ANOVA. In the first, mean log ratios for all transverse sections were regressed against caudocranial axis. In the second, caudocranial regressions were calculated within each of two regions defined as to whether or not a transverse section of lung was adjacent to the diaphragm at any point. Mean log ratios were also calculated for coronal lung sections and regressed against the ventrodorsal axis of the lung. To assess the relative impact of the peridiaphragmatic or caudal lung region and the cranial lung region on gas exchange, we calculated means and SDs of the natural logarithm (ln) A/ distributions of each region.

All results are reported as mean values ± SD. One-sample t-tests were used to test the null hypothesis that a group of slopes were not different from zero. Paired t-tests were used to compare physiological results between postures and to compare slopes of linear regressions of A and log ratios against caudocranial or ventrodorsal location. Statistical significance was defined at a P value ≤ 0.05.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Mean values for physiological data in each posture are reported in Table 1. Alveolar-arterial oxygen difference (A-aDO2) was significantly greater in the supine posture. There was a trend toward lower cardiac outputs and lower mixed-venous oxygen tensions in the supine posture that did not reach statistical significance.


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  		Table 1. Average physiological measurements in supine and prone postures

 
Relative effects of structure and posture on A and distributions.   The majority of the regional variability for both A and (74.0 ± 4.7 and 63.3 ± 4.2%, respectively) was determined by structure independent of posture, temporal variability, or methodological noise (Fig. 1). Posture accounted for 23.9 ± 4.7% of the total variability of regional distribution, and 16.4 ± 5.0% of the total variability in regional A. The combination of temporal variability and methodological noise contributed 9.6 ± 1.3 and 12.8 ± 4.6%, respectively, to overall measured heterogeneity of A and .



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  		Fig. 1. Box plot of relative contributions of structure, posture, and temporal/methodological variability to the total heterogeneity of the ventilation and perfusion distributions. The boxes define the interquartile range of the data, and the bars define the full range of the data. One statistical outlier for the structural contribution to ventilation heterogeneity is identified as a single point.

 
Spatial distribution of posture-mediated changes.   The mean log ratios of ventilation in the supine posture to ventilation in the prone posture for transverse lung sections were spatially oriented with lower ratios in the caudal lung region (Fig. 2A). A similar, although less pronounced, spatial organization was present for log ratios of both regional blood flow and PAO2 (Fig. 2, B and C). Caudocranial linear regressions within each of two separate regions defined by proximity to the diaphragm provided a significantly better fit compared with regression over the entire lung for A (r2 = 0.907 vs. r2 = 0.583, P < 0.001), blood flow (r2 = 0.736 vs. r2 = 0.444, P < 0.001), and PAO2 (r2 = 0.859 vs. r2 = 0.616, P < 0.001). Figure 3 shows the regression lines for the two-compartment model for individual animals. Three animals demonstrated a smaller gradient of caudal ventilation and, to a lesser extent, blood flow and PAO2 in the supine posture. The posture randomization for these three animals resulted in one or two periods in the prone posture between measurements made in the supine posture. The four animals with a greater reduction of caudal ventilation were randomized to sequential periods in the supine posture.



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  		Fig. 2. Mean and SD values for log ratios of ventilation (a; A), perfusion (; B), and alveolar oxygen partial pressure (PAO2; C) across transverse sections of lung from 1 animal. The dashed line indicates the ventrodorsal dividing line that is tangential to the most cranial portion of the diaphragm and used to separate the lung into a caudal compartment and a cranial compartment. Note the different scale for the log ratio of PAO2.

 


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  		Fig. 3. Individual caudocranial regression lines for a 2-compartment model defined by location relative to the diaphragm for a (A), (B), and PAO2 (C).

 
When the entire lung was considered, there was a small gradient of decreasing log ratios of ventilation along the ventral-to-dorsal axis (mean slope = –0.029 ± 0.030, P = 0.043). There were small gradients for both log ratios of blood flow (mean slope = 0.039 ± 0.038, P = 0.033) and of PAO2 (mean slope = –0.014 ± 0.004, P < 0.001) along the ventral-to-dorsal axis. Because the caudal lung region is predominantly dorsal, reduced ventilation and blood flow to the caudal lung region in the supine posture diminishes the observed vertical redistribution. Reanalyzing the data excluding all lung pieces within a transverse section adjacent to the diaphragm nearly doubled the ventrodorsal gradient of blood flow redistribution (mean slope = 0.077 ± 0.038, P value = 0.002) (Fig. 4B). Additionally, the vertical gradient of PAO2 redistribution reversed so that, with posture change, a small increase in PAO2 in ventral lung regions and a small decrease in dorsal lung regions were observed with rotation from the prone to supine posture (mean slope = –0.011 ± 0.003, P < 0.001) (Fig. 4C). With exclusion of lung pieces from the dorsocaudal lung region, the observed vertical gradient of ventilation redistribution was eliminated (Fig. 4A).



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  		Fig. 4. Individual ventrodorsal regression lines excluding lung regions adjacent to the diaphragm for log ratios of a (A), (B), and PAO2 (C).

 
When analyzing the entire lung, the SD of the ln A/ distribution was greater in the supine posture compared with the prone posture, consistent with the increased A-aDO2 in the supine posture (Fig. 5A). There was a trend toward a higher mean ln A/ distribution in the supine posture consistent with the slightly lower cardiac output in the supine posture (Fig. 5B). When the caudal and cranial lung regions are analyzed separately in the supine posture, there is a trend toward a greater SD ln A/ in the caudal lung (Fig. 5A). Additionally, the mean ln A/ distribution is significantly lower in the caudal lung. The combination of both lower mean regional A/ and greater A/ heterogeneity in the caudal lung results in lower regional alveolar (and end-capillary) oxygen tensions in the caudal lung (Figs. 6 and 7).



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  		Fig. 5. Effect of posture and of caudal-cranial location in the supine posture on ventilation-perfusion (A/) heterogeneity (SD of lnA/; A) and on the average A/ ratio (mean lnA/; B).

 


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  		Fig. 6. Three-dimensional reconstructions of regional PAO2 change in 1 animal following rotation from prone to supine posture. A: anterior view. B: left posterior oblique view, supine posture. Red regions increased calculated PAO2 by ≥20%, blue regions decreased calculated PAO2 by ≥20%, and gray regions changed by ≤20%.

 


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  		Fig. 7. Histogram of log ratio PAO2 (supine/prone) from a representative animal.

 

   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
This study examined the mechanisms by which gas exchange is altered with repositioning between prone and supine postures by measuring regional A and with aerosolized and injected fluorescent-labeled microspheres. The important findings of this study were that 1) the majority of regional ventilation and blood flow heterogeneity was determined by factors independent of posture; 2) although modest, ventilation and blood flow redistribution associated with repositioning from prone to supine was regionally variable: ventilation primarily shifted away from caudal lung regions and blood flow redistributed in a gravitationally oriented manner; and 3) impaired gas exchange in the supine posture was primarily due to reduced ventilation in the caudal lung region.

Determinants of regional A and heterogeneity and gas exchange.   The relative importance of gravitational and nongravitational influences on pulmonary blood flow has been extensively debated in the literature (4, 13, 14, 19, 21, 28, 29, 31). High-resolution measurements using intravascularly deposited markers of blood flow distribution suggest that structural properties of the lung that are independent of gravitational influence have a prominent role in determining regional blood flow distribution (4, 15, 16, 21). Although ventilation has similar overall heterogeneity as blood flow (2, 18, 25), studies quantifying the relative influence of gravitational and nongravitational determinants on ventilation distribution have not been reported. We found that gravitationally oriented forces have a modest influence on regional ventilation distribution that is similar to what has been observed for blood flow. These data support indirect measurements of ventilation heterogeneity made in humans in the microgravity environment of the space shuttle (24).

Despite the lesser contribution of posture to overall A and heterogeneity, A-aDO2 values were consistently greater in the supine posture. A-aDO2 is a clinical measure of how well regional A and are matched. Wilson and Beck (33) mathematically demonstrated that A/ heterogeneity is determined by a combination of the overall heterogeneity of ventilation distribution, blood flow distribution, and the correlation between regional ventilation and blood flow. If posture has a relatively small effect on the overall heterogeneity of ventilation and blood flow distribution, then it must decrease the correlation between regional ventilation and blood flow. Because posture change should affect ventilation and blood flow distribution over relatively macroscopic regions secondary to changes in hydrostatic force and/or thoracic compliance, we examined posture-mediated change in ventilation and blood flow distributions as a function of caudocranial and ventrodorsal distribution. In the supine posture, A redistribution was primarily directed away from caudal lung regions, whereas redistributed primarily along the ventrodorsal axis, consistent with a hydrostatic effect. Combined, this resulted in reduced A/ and alveolar oxygen tensions primarily in the dorsocaudal lung region (Figs. 6 and 7).

Redistribution along the caudocranial axis.   In the supine posture, there was reduction of ventilation in lung adjacent to and beneath the diaphragm. This was most likely the result of decreased regional compliance secondary to an alteration in diaphragmatic conformation and increased transdiaphragmatic pressure. These results are consistent with prior low-resolution measurements in humans (10). The response to supine posture was mixed, with three animals having relatively modest reduction in caudal ventilation and four animals having a more substantial reduction (Fig. 4A). The only identified difference between these two groups was the duration of time in the supine posture. The animals with a greater reduction in regional ventilation had two sequential periods in the supine posture as opposed to the remaining animals that had at least one period prone between supine periods. However, when the individual measurements for the caudal lung region were examined, there was no evidence of significant progressive ventilation loss or increasing A-aDO2 in these animals in the supine posture.

Caudal blood flow was also reduced in the supine posture, although to a lesser extent than regional ventilation. Because the most caudal lung was dependent in the supine posture, this reduction in blood flow was in the opposite direction expected from a hydrostatic pressure gradient. Because blood flow was not reduced to the same extent as ventilation, the mean A/ was reduced, resulting in lower regional end-capillary oxygen content decrease, contributing to the increased whole lung A-aDO2 in the supine posture.

Redistribution along the ventrodorsal axis.   When the whole lung was considered, there was a small ventral-to-dorsal redistribution of blood flow in the supine posture and a small redistribution of ventilation in the opposite direction. However, when the caudal lung region was excluded from analysis, there was a greater ventral-dorsal redistribution of blood flow and no significant gradient of ventilation redistribution. This suggests that previous estimates of the relative contribution of a hydrostatic gradient to total pulmonary blood flow heterogeneity in anesthetized, supine animals were confounded by reduced blood flow in caudal regions. Glenny et al. (13) estimate a much greater gravitational effect on regional perfusion distribution in baboons based on measurements made in the upright and head-down position. They attribute this to possible species differences as well as a greater hydrostatic gradient. A contributing factor may have been that, as opposed to supine and prone postures, any peridiaphragmatic atelectasis will occur in the head-down posture, thereby augmenting rather than opposing effects from the hydrostatic gradient.

Limitations of the present study.   The present study has two main limitations related to the methodology used to measure regional ventilation and blood flow distribution. Regional ventilation was measured by deposition of an aerosol of 1-µm fluorescent microspheres. One-micrometer particles will deposit in the alveoli primarily by gravitational settling and inertial impaction (6); therefore, this method will not accurately reflect alveolar ventilation distribution. However, ventilation distribution at the scale used in this study will primarily be via convection and should be accurately represented by aerosol distribution. Our laboratory (3) has previously shown that regional ventilation and blood flow distributions, as measured by the fluorescent microsphere method, provide a good estimate of overall gas exchange in the lung.

A second limitation of this study is that regional distributions of aerosolized and injected microspheres were measured in lungs dried at total lung capacity (TLC). Because alveolar density is relatively uniform at TLC, this method will give ventilation and blood flow per alveolus scaled to the volume of lung tissue studied. In contrast, noninvasive measures of ventilation and blood flow distribution have been typically made at functional residual capacity, resulting in a measure of ventilation and blood flow per unit lung volume with alveolar densities that vary in a gravitationally oriented pattern. As previously discussed (32), this results in measurements that are not directly comparable. Measurements made at TLC can be mathematically modified to approximate functional residual capacity measurements, resulting in a modest increase in gravitationally oriented distribution pattern (7, 32). Of note, however, when measurements of both A and are simultaneously made, they should be equally affected by homogeneity of alveolar density. Therefore, conclusions drawn in this study regarding the spatial pattern of gas exchange impairment should not be altered by the lung volume at which they are measured.

Conclusions.   In conclusion, this study confirmed that a major source of both regional blood flow and regional ventilation heterogeneity is innate pulmonary structure independent of posture. Although regional correlation between A and was not directly measured, the relatively small A-aDO2 values observed suggest that close spatial correlation between regional A and was present.

Despite minimal effect on global measures of A and heterogeneity, posture did impact gas exchange. This resulted from poorly correlated macroscopic redistribution of both and A. Regional perfusion redistributed primarily in a nondependent-to-dependent fashion following posture change, consistent with a hydrostatic pressure gradient effect as first postulated by West et al. (30). In contrast, ventilation redistributed primarily away from caudal lung regions in the supine posture presumably secondary to reduced regional compliance. The effect of uncorrelated redistribution of blood flow and ventilation on gas exchange will be magnified in clinical acute respiratory distress syndrome given the dependent predominance of air space consolidation (22). Intravenously distributed medications that modulate hypoxic vasoconstriction such as nitrates would also be expected to enhance posture-mediated decrements in gas exchange efficiency.


   APPENDIX
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The variance ({sigma}2) of A or blood flow may be described by the sum of the variances of the individual components of the two-way crossed random effects model:

(2)
Therefore, the relative contribution to the overall heterogeneity of either A or blood flow from each component of the model may be calculated by the ratio of that component's variance to the overall variance.

The variance for each component is estimated from the mean squares of the model components. The mean square for each component (MSx) is calculated from the sum of squares (SSx) as follows.

Structure component.  


where i is the average flow to piece i across all conditions and repetitions, µ is the average flow to all pieces across all conditions and repetitions, and n is the number of pieces.

Posture component.  


where j is the average flow across all pieces and repetitions for posture j.

Structure x posture interaction.  


where ij is the average flow across repetitions for piece i in posture j.

Temporal/method error component.  


The expected values of the individual mean squares, E(MSx), can be equated to the component variances as follows (20):




Combining the two sets of equations above, estimated variances for the individual components may be calculated:




Because the data used in these calculations are normalized to the mean value, the average flow across all pieces is 1.0 for all postures. This causes the SS{beta} and hence the MS{beta} to equal zero, resulting in an undefined value for {sigma}2({beta}). In this case, all of the effects of posture will be reflected in the interaction sum of SS{tau}{beta}, and {sigma}2({tau}{beta}) gives the upper limit for the posture effect.


   GRANTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
ACKNOWLEDGMENTS
 REFERENCES
 
This work was supported by the Francis Family Foundation, the American Lung Association Washington State Affiliate, and National Heart, Lung, and Blood Institute Grants HL-71020 and HL-24163.


   ACKNOWLEDGMENTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
REFERENCES
 
We thank Dowon An and Shen-Sheng Wang for technical assistance and Carmel Schimmel for assistance in correcting fluorescent signals for spillover and background noise.

S. McKinney is currently affiliated with Insightful Corporation, Seattle, WA.


   FOOTNOTES
 

Address for reprint requests and other correspondence: W. A. Altemeier, Division of Pulmonary & Critical Care Medicine, Univ. of Washington, Box 356522, Seattle, WA 98195–6522 (E-mail: billa{at}u.washington.edu)

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. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 

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