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J Appl Physiol 89: 1591-1600, 2000;
8750-7587/00 $5.00
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Vol. 89, Issue 4, 1591-1600, October 2000

Influence of lung volume on pulmonary microvascular pressure-volume characteristics

George P. Topulos1,2, Richard E. Brown1, and James P. Butler2

1 Department of Anesthesiology, Perioperative and Pain Medicine, Brigham and Women's Hospital, and 2 Physiology Program, Harvard School of Public Health, Boston, Massachusetts 02115


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

The pressure-volume (P-V) characteristics of the lung microcirculation are important determinants of the pattern of pulmonary perfusion and of red and white cell transit times. Using diffuse light scattering, we measured capillary P-V loops in seven excised perfused dog lobes at four lung volumes, from functional residual capacity (FRC) to total lung capacity (TLC), over a wide range of vascular transmural pressures (Ptm). At Ptm 5 cmH2O, specific compliance of the microvasculature was 8.6%/cmH2O near FRC, decreasing to 2.7%/cmH2O as lung volume increased to TLC. At low lung volumes, the vasculature showed signs of strain stiffening (specific compliance fell as Ptm rose), but stiffening decreased as lung volume increased and was essentially absent at TLC. The P-V loops were smooth without sharp transitions, consistent with vascular distension as the primary mode of changes in vascular volume with changes in Ptm. Hysteresis was small (0.013) at all lung volumes, suggesting that, although surface tension may set basal capillary shape, it does not strongly affect capillary compliance.

capillary; diffuse light scattering; transit time; dog; hysteresis; mechanics


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

THE PRESSURE-VOLUME (P-V) characteristics of the lung microcirculation are important determinants of the pattern of pulmonary perfusion both regionally as well as on the smaller acinar scale. In addition, the pressures, volumes, and flows within the capillaries interact to influence gas exchange through red cell transit times. Importantly, the fact that the capillaries are mechanically linked to the alveolar septa and their stress-bearing support structures implies that capillary mechanics are likely to be influenced by lung volume (VL) and lung recoil pressure, which are continuously changing during breathing.

The mechanical properties of capillaries affect the transit times of erythrocytes (RBC) and leukocytes (PMN) but in different ways. To the extent that RBCs simply follow the local perfusion, the local ratio of capillary volume to blood flow determines the transit times. By contrast, because the diameter of PMNs is larger than the diameter of the capillaries (7, 18, 22, 23, 33), their transit times and, hence, sequestration are in part determined by the interaction of PMN deformability and capillary diameters. Whether changes in capillary volume occur through recruitment and derecruitment of segments or through vessel distension remains an open question.

Previous studies of the P-V characteristics of the pulmonary vasculature have involved microscopic sectioning after either freezing (13) or perfusion with elastomers (11), or have been limited to vessels larger than capillaries (e.g., Refs. 1 and 17 and others as summarized by Al-Tinawi et al. in Ref. 1), or to subpleural capillaries (14). Apart from these studies, little is known from direct measurements about the compliance of the capillaries (vessels <20-µm diameter) over a wide range of vascular transmural pressures (Ptm) and VL. In a previous report (30), we measured the fractional changes in pulmonary vascular blood volume (delta Vc/Vc) during the cardiac cycle in rabbit lung parenchyma, where more than two-thirds of the blood has been shown to be in pulmonary capillaries (8, 18). In this study, we measured delta Vc/Vc in excised perfused dog lungs during slow oscillations of pulmonary vascular pressure and after step changes in vascular volume over a wide range of Ptms and over a range of VL. We determined how vascular compliance changes with VL and whether the vasculature showed evidence of strain stiffening (a decrease of compliance with increasing Ptm). Finally, we quantified the hysteresis in P-V loops and examined their shapes for evidence of capillary recruitment.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

Animal preparation. We studied seven female mongrel dogs (18.5-22 kg). Each animal was anesthetized with pentobarbital sodium, initial dose ~15 mg/kg iv, with additional doses as needed to maintain adequate anesthesia (total ~25 mg/kg). The animal was placed supine, a tracheotomy was performed below the larynx, and the trachea was cannulated with a cuffed endotracheal tube. Blood gases and pH were monitored (Ciba Corning model 248). In most cases, the dog breathed air spontaneously, but, if necessary to restore arterial partial pressure of CO2 to 38-40 Torr, the dog was ventilated (respiratory rate 4-6 breaths/min, tidal volume 200-400 ml, 100% O2). Heparin (40,000 units iv) was given, and at least 2 min later the dog was exsanguinated via a femoral artery catheter. The blood was collected, and sodium bicarbonate was added as needed to keep the pH near 7.4. The measured hemoglobin concentration ranged from 11.3 to 14.6 grams per 100 ml. After ~1,000 ml of blood had been collected, the animal was killed with an overdose of pentobarbital sodium iv. As rapidly as practical, a median sternotomy was performed, and the heart and lungs were excised en bloc. Except for momentary episodes during lung excision, lung inflation was maintained by use of positive pressure at the airway opening (Pao). The lung was kept moist by spraying it with 0.9% saline.

The left or right lower lobe was isolated, and its pulmonary artery (PA) and vein (PV) were isolated and cannulated with large-bore catheters (18- to 24-Fr). The lobar bronchus was cannulated with a 4-mm tube. To limit intravascular air as much as possible, the PV catheter was initially back-flushed with saline, and then both the PA and PV cannulas were connected to a perfusion circuit that was filled with autologous blood. The mean time from death until perfusion was reestablished was 45 min (range 41-50 min). The lobe was suspended by the cannulas. To keep the pleural surface moist and to prevent gas exchange through the pleural surface, a flaccid plastic bag, ventilated with the same gas used for ventilating the lobe, was placed around the lobe. Between measurements, the lobe was ventilated with 95% O2 and 5% CO2 [Siemens 900, pressure-controlled mode, respiratory rate 10 breaths/min, transpulmonary pressure (PL) at end expiration ~4 cmH2O, PL at end inspiration ~15 cmH2O].

Figure 1 shows a schematic of the perfusion circuit. An adjustable roller pump (Stockert Shiley model 10) pumped blood from a reservoir through a heat exchanger, which kept the blood at 37-38°C, into the PA; blood drained passively from the PV into the reservoir. The height of the reservoir could be adjusted to control the PV pressure (Ppv), or the PA pressure (Ppa) if the bypass around the pump was open. Vascular pressures were measured (Sorenson Abbott Transpac 2) at the PA and PV cannulas, with the transducer heights matched to the height on the lobe where the optical probe was placed (midlobe and far from any margin). Vascular pressures were measured relative to barometric pressure, which, in this case, was the same as pleural pressure. Between measurements, the height of the reservoir was set at midlobe level, and the pump was set to a flow that resulted in a Ppa of ~20 cmH2O (usually ~100-200 ml/min).


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  		Fig. 1.   Diagram of experimental setup. Slow oscillations of vascular pressure were achieved by raising and lowering the blood reservoir to control pressure in the pulmonary vein (Ppv) or pulmonary artery (Ppa). Step changes in vascular volume were achieved by rapid syringe injections. Between measurements, the lobe was perfused with a roller pump (RP) and ventilated. During measurements, RP was off, and the bronchus was connected to a continuous positive airway pressure (CPAP) source. X denotes clamp sites. Airway opening pressure (Pao) was continuously monitored. Optical fibers delivered light to the lung and returned backscattered light from three discrete locations to individual photodiodes.

Optical methods. Point illumination of the pleural surface of the lung results in a distinctive pattern of backscattered light from which the fractional change in blood volume can be derived (30). Optical fibers delivered laser light of two wavelengths (693 and 808 nm; output powers ~30 mW) to a point on the lobe surface and carried backscattered light from the lobe surface back to sensing photodiodes (Fig. 1). The two source fibers (each 0.008 mm2) were held together at the animal end, such that the center-to-center distance was ~0.135 mm. Each of the three receiving fibers had an area of 0.290 mm2. The animal end of the source and the receiving fibers were held securely in a plastic block (area 1.9 × 5 cm, height 2.9 cm), such that the fibers were in a fixed position relative to each other. The fibers and block were supported by a flexible gooseneck stand and placed gently against the lung, with the fibers approximately perpendicular to the lung surface. The lasers were cycled alternately on and off, with a duty cycle of 0.25 and a period of 8 ms. The signal from each photodiode was demultiplexed and provided wavelength-specific light intensity at each known radial distance from the source fibers.

Before each experiment, the offsets and gains of each receiving channel were determined. The electronic offsets (i.e., the dark signal level) were measured with the receiving fibers shielded from light. These offsets were subtracted from all measured intensities. The gains of channels 1 and 2 relative to channel 3 (picked as the reference channel) for each wavelength were measured as follows. The source and receiving fibers were placed in an array of holes in an opaque box filled with an open-cell foam that diffusely scattered the incoming light. The order of the receiving fibers was sequentially permuted. The ratios of the intensities in these permutations of distance from the source then gave the relative gains for each receiving channel (consisting of a fiber, photodiode, and signal processor).

Experimental protocol. Each experiment involved two different, quasi-static interventions at four different airway pressures: 1) slow oscillations of vascular pressure or 2) step changes in vascular volume. The perfusion pump was off while data were collected. Oscillations in vascular pressure were generated, 54 runs in seven dogs, by slowly raising and lowering the blood reservoir connected to either the PA or PV, while the cannula to the other vessel was clamped. Each pressure cycle took 10-60 s, and the rate was adjusted in an attempt to keep Ppa and Ppv as close to each other as practical. During each data collection period, the vascular pressure was cycled 3-5 times. Microcirculatory intravascular pressure (Pvas) was defined as the pressure in the vessel that was clamped during the maneuver, either Ppa or Ppv, because there was minimal flow (and therefore minimal flow-resistive pressure loss) between the capillaries and the clamped vessel. Ptm was defined as Pvas - Pao. Ppa and Ppv were varied such that Ptm during each cycle covered the range ~-1.4 to +16 cmH2O in the first three dogs and ~-6.5 to +40 cmH2O in the last four dogs.1

Step changes in pulmonary vascular volume were generated, 19 runs in three dogs, with rapid (~2 s/injection) injections of blood in 10-ml increments into the PA while the PV cannula was clamped. Each injection was followed by a pause of 5-10 s; this was repeated, until either 40 ml had been injected or Ptm >=  ~40 cmH2O. During injections, the reservoir was excluded from the circuit. Because the compliance of the entire perfusion circuit, excluding the reservoir, was negligible, essentially all of the injected blood entered the vasculature.

Measurements were made at PL of 4, 10, 20, and 30 cmH2O, chosen to cover the range from functional residual capacity (FRC) to total lung capacity (TLC). Before each data collection period, the lobe was exposed to a standard volume history; PL was cycled from 2 to 30 cmH2O three times and then deflated from 30 cmH2O to the target PL.

Data acquisition. Raw signals from each pressure transducer (Ppa, Ppv, Pao) and the wavelength-specific light intensities at the three known distances from the optical origin were sampled at 100 Hz per channel and stored on computer using a 12-bit analog-to-digital board and data acquisition software (both Dataq Instruments, Akron, OH). All raw data were averaged over 1-s intervals. These averages were used in all subsequent analyses.

Data analysis and statistics. The rate of change of light intensity with distance from the source is a direct measure of the wavelength-specific diffuse absorption coefficients, from which the fractional change in blood volume can be derived (see APPENDIX A). We reduced all delta Vc/Vc vs. Ptm data at each VL to three outcome variables: 1) the specific compliance at Ptm = 5 cmH2O, 2) the rate of change of specific compliance with vascular pressure, and 3) the hysteresis of the delta Vc/Vc vs. Ptm loops. This was accomplished as follows.

During slow oscillations of vascular pressure, data were recorded continuously. To provide a standard vascular volume history, data collected during the first cycle in each set were discarded. The calculation of hysteresis requires the beginning and end points of an oscillatory run to be the same. This was accomplished by 1) selecting beginning and end points in the midrange of Ptm, both being either on the ascending or descending limb, and 2) subtracting, from each of the delta Vc/Vc vs. time and Ptm vs. time curves, straight lines that both preserved the means and connected the beginning and end points. During step changes in vascular volume, data were also recorded continuously, but data collected during the sharp transients (~2 s) seen during each injection were discarded.

Fractional changes in blood volume are measured relative to a reference volume, that is, the capillary volume at a reference Ptm. delta Vc/Vc was regressed quadratically against Ptm, constrained such that delta Vc/Vc was zero at the reference Ptm of 5 cmH2O. We defined the derivative and second derivative of each regression, at Ptm = 5 cmH2O, as the microvascular specific compliance (Cc) and rate of change of specific compliance (dCc/dPtm), respectively. Note that, at each VL, changes in blood volume density are normalized to the blood volume density at Ptm = 5 cmH2O. A negative value of dCc/dPtm denotes strain stiffening, i.e., a decrease in compliance as vascular Ptm increases. Finally, the hysteresis was computed as the ratio of the average area bounded by the loops to the average size of the delta Vc/Vc vs. Pvas circumscribing rectangle (16). The average loop area was computed by dividing the total area of all loops by the number of loops. The average circumscribing rectangle area was computed as the product of the average peak-to-peak delta Vc/Vc and the average peak-to-peak Ptm.

We found a curvilinear relationship of both Cc and dCc/dPtm vs. PL but a linear relationship of both Cc and dCc/dPtm vs. VL. VL was estimated to be 40 (FRC), 75, 90, and 100% TLC at PL of 4, 10, 20, and 30 cmH2O, respectively (12, 21). This allowed us to simplify statistical modeling by grouping data from all dogs by the estimated VL at which they were collected. Values are reported as means ± SE of all points from all dogs at each VL. We used a general linear model and performed an ANOVA to determine which experimental parameters and control variables resulted in changes in an outcome variable (Cc, dCc/dPtm, or hysteresis). The experimental parameters and control variables were: VL, perfusate pH and PCO2, maximum and minimum Ptm, and length of time from when the animal was killed until data collection. Indicator variables were used for individual animals, intervention (slow oscillations of vascular pressure or step change in vascular volume), and site of pressure oscillation (PA or PV). A parameter was defined as significant if its regression coefficient was significantly different from zero, P < 0.05.

The slopes and intercepts of the regression lines for both Cc and dCc/dPtm vs. VL for the two interventions (slow oscillations in Pvas and between step changes in vascular volume) were not significantly different from each other, and so the data obtained using both methods were pooled for further analysis.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

Figure 2 shows examples of delta Vc/Vc vs. Ptm data from four separate data collection periods at constant PL of 10 and 30 cmH2O. The loops are composed of data collected during slow oscillations of vascular pressure. The points are data collected during the pauses between four step changes in vascular volume.


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  		Fig. 2.   Fractional change in capillary blood volume (delta Vc/Vc) from the reference state, where vascular transmural pressure (Ptm) = 5 cmH2O, vs. Ptm. Continuous loops are from slow oscillation of vascular pressure; discrete points are from step changes in vascular volume. A: transpulmonary pressure (PL) = 10 cmH2O. B: PL = 30 cmH2O. delta Vc/Vc vs. Ptm loops were highly consistent except at PL = 4 cmH2O, where they were more variable. Data from slow oscillations and step changes were strikingly similar. The vasculature was more compliant and showed more stiffening with increasing Ptm at lower PL (A) compared with high PL (B). Loops exhibited little hysteresis; their shapes were smooth, without sharp transitions in vascular volumes.

Cc decreased significantly as VL increased. Figure 3 shows the pooled mean Cc at each VL for all animals and the linear regression. In one animal, Cc was significantly lower than for the other six. Cc also varied significantly with the length of time from death until data collection. Despite its statistical significance, the magnitude of the time effect was not physiologically important (<0.22%/cmH2O). The other experimental parameters and control variables had no statistically significant effects on Cc.


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  		Fig. 3.   Microvascular specific compliance (Cc) (mean ± SE) at Ptm = 5 cmH2O for all animals at each VL. Note that Cc falls as lung volume increases. VL, lung volume as a fraction of total lung capacity (TLC). Regression equation Cc = 10.6 - 0.080 VL, where Cc is expressed in %/cmH2O and VL in %TLC.

At PL = 4 cmH2O, the scatter of the data was large (Fig. 3), and P-V loops were more variable. There are both physiological and technical factors that may have contributed to this finding. First, at low VL, the lung is very compliant, and small variations in PL result in large variations in VL and acinar dimensions, which could have resulted in large variations in the actual Cc. VL errors would also have resulted in variation in the diffuse absorption coefficient used in calculations of delta Vc/Vc. Second, at low VL, the lung was less physically stable and tended to move relative to the optical sensors as blood volume changed during oscillations or step maneuvers. Third, the slight amount of pressure exerted by the optical probe may have caused more variable deformation of the lung at low VL.

At low VL, Cc decreased significantly as Ptm increased, i.e., the vessels exhibited strain stiffening. This effect decreased significantly as VL increased and was essentially absent at TLC. Figure 4 illustrates, at each VL, how Cc would change as a function of Ptm. The other experimental parameters and control variables had no statistically significant effects on dCc/dPtm.


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  		Fig. 4.   Predicted Cc normalized to Ptm = 5 cmH2O as a function of Ptm at each of four VL. The four Cc points at Ptm = 5 cmH2O are the measured specific compliances. The slopes of the lines extending from these points are the measured rate of change of specific compliance (dCc/dPtm). At functional residual capacity, the compliance decreased sharply with increasing Ptm (dCc/dPtm = -0.002 ± 0.001%/cmH2O2). This stiffening effect decreased at higher VL and was virtually absent at TLC (dCc/dPtm = -0.00014 ± 0.00006%/cmH2O2).

The mean hysteresis of delta Vc/Vc vs. Ptm loops during slow oscillations of Ptm was 0.013 ± 0.0054. Hysteresis did not vary significantly with VL or other experimental parameters and control variables, except indicator variables for individual animals and maximum Ptm during the data collection run.

The shapes of delta Vc/Vc vs. Ptm loops during slow oscillations of Ptm were smooth. We observed no sharp transitions that would have suggested recruitment over a narrow range of opening pressures (see DISCUSSION).

If all of the 10 ml injected during each bolus injection had distended the capillaries, then delta Vc/Vc could be used to estimate upper limits of the baseline capillary blood volume. Calculated values of capillary blood volume (Vc) based on these estimates were unrealistically high, suggesting that, as expected, a substantial fraction of the bolus injection distended parts of the vasculature outside our sampled volume (p. 99, Fig. 4 in Ref. 10, and Ref. 29).

Between bolus injections, the Ppa-Ppv differences were small (root mean square ~1 cmH2O). However, even though Ppa - Ppv oscillated around 0 cmH2O during slow-pressure oscillations, the Ppa and Ppv did not track each other as well as expected (root mean square ~4 cmH2O). The pressure difference often persisted even when the pressure was held constant (the height of the reservoir bag was unchanged) for several seconds. The Ppa-Ppv differences were most likely due to persistent blood flow either into or out of the reservoir or via redistribution within the vasculature.

Just after each set of data was obtained, blood draining from the lobe was collected and analyzed for pH and PCO2. The mean pH was 7.45 (range 7.40-7.57). The mean PCO2 was 33 (range 21-40) Torr. The interval from an animal's death until an individual data set was collected ranged from 70 to 280 min.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

We measured the P-V characteristics of the pulmonary microvasculature over a wide range of Ptm and VL. The major findings were: 1) the compliance of the microvasculature was ~8%/cmH2O at FRC, decreasing with increasing VL to ~2.7%/cmH2O at TLC, 2) vessels exhibited strain stiffening at low VL but much less at higher VL, 3) loops of delta Vc/Vc vs. Ptm had little hysteresis, and 4) shapes of the P-V loops support vascular distension rather than recruitment as the primary mode of volume change. In the following paragraphs, we quantitatively compare our measures of Cc with those of others, then discuss the key physiological implications of these findings.

Capillary compliance. Figure 5 shows our estimates of Cc and estimates based on the data of others. There are no other data available on Cc near FRC. At PL 10 cmH2O, our value is close to those of previous studies. However, at higher PL there is a striking difference. Unlike Glazier et al. (13), we found a lower, not a higher, compliance at increased PL. This result is consistent with our earlier work in rabbits (30), which showed that Vc fluctuated during the cardiac cycle at low, but not at high, VL, which suggested that compliance falls as VL rises. We believe our data are most appropriately compared with Glazier's data for change in RBCs per length of capillary segment, not to their data for change in capillary width (all are shown in Fig. 5). Because, at fixed VL, capillary segment lengths are fixed and all volume changes occur through proportional changes in area (28), we believe the change in number of RBCs per length of capillary segment is analogous to our optical measure of blood (hemoglobin) volume per unit volume.


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  		Fig. 5.   Comparison of microvascular specific compliance at Ptm of 5 cmH2O vs. lung volume (estimated as described in METHODS). See DISCUSSION for details. Fung and Sobin (as summarized by Fung in Ref. 11), our estimates from their data in cats at PL of 10 cmH2O. Glazier et al. (13), our estimates from their Fig. 4, erythrocytes (RBCs) per length capillary segment and their Fig. 8, capillary width, both in dogs at PL of 10 and 25 cmH2O. Note that, for comparison, we estimated specific compliances from the data of others.

These comparisons raise the issue of the different primary measurements and how they are best compared. Glazier et al. (13) reported changes in capillary "width," assumed to be the diameter of a tube, and changes in the number of RBCs per length of capillary segment. Fung and Sobin (as summarized by Fung pp. 306-309 in Ref. 11) reported changes in "thickness," assumed to be that of a sheet. Our primary measures are changes in blood volume density. For a tube model of the capillaries (13), the fractional change in vessel diameter will be approximately one-half the fractional change in Vc (segment lengths are fixed at constant VL), whereas the fractional change in the number of RBCs per length of capillary segment (13) is equal to the fractional change in Vc. In the sheet model (11), the sheet area is constant at fixed VL, and the fractional change in sheet thickness is equal to the fractional change in Vc. Note that our primary data are volume based and so are not dependent on either the tube or the sheet model for their fundamental interpretation. On the other hand, as discussed below, our results do not support a model of the pulmonary capillary bed consisting of a collection of cylindrical tubes.

To the extent that some of the blood in the volume sampled is in vessels larger than capillaries, and to the extent that larger vessels are stiffer than capillaries, our measure of Cc (an average for all the vessels in the sampled volume) will underestimate true capillary specific compliance. More than two-thirds of the blood in lung parenchyma is in pulmonary capillaries (8, 18), and the contribution of capillary blood to our measurements is likely to be larger because we are sampling far from the hilum, in a region where large and moderately sized vessels are scarce. Nonetheless, some of the blood in our sampled volume is in larger vessels. Average value for compliance of the canine noncapillary microvasculature near FRC (Ref. 17 and others as summarized by Al-Tinawi et al., Ref. 1), expressed in terms of vessel diameters, is <2%/mmHg, corresponding to a fractional change in volume <4%/mmHg or <3%/cmH2O. If we assume that 70% of the blood in our sampled volume is in the capillaries and that the remaining 30% is in larger vessels with a compliance of 3%/cmH2O, then our results would imply a true capillary specific compliance of 11%/cmH2O.

Mechanism of changes in compliance with VL. We found that Cc decreased as VL increased, but this need not have been the case; in fact, Glazier et al. (13) found the opposite relationship between Cc and VL (Fig. 5). On the one hand, as VL increases, so do vessel lengths and tissue forces (Pt) (e.g., p. 327 in Ref. 32, and Ref. 14), as well as surface tension (gamma ). All of these contribute to decreased Cc. On the other hand, as VL increases, the alveolar capillaries become flatter in cross section (p. 327 in Ref. 32). Such a change in geometry can substantially increase compliance by providing a pathway for volume displacement with little or no change in circumference and therefore tissue strain. In addition, if vessels had a smaller baseline volume at high VL, as suggested by the data of Glazier et al. (13), then the same absolute change in volume would result in a greater specific compliance. We conclude from the increased stiffness we found at higher VL that either increased Pt or gamma , rather than change in vessel shape or baseline volume, dominates the change in Cc as VL changes. The complex effects of gamma  are discussed below.

Changes in compliance with Ptm. At low VL, the compliance of the pulmonary microcirculation decreased as Ptm increased; that is, vessels exhibited the strain stiffening typical of most tissue. At high VL, the capillaries were stiffer at all Ptm, but, surprisingly, strain stiffening decreased, and it was virtually absent above 90% TLC (Fig. 4). This suggests that, at high VL, changes in tissue geometry may result in more linear capillary P-V characteristics. Alternatively, supporting tissues with more linear stress-strain behavior, which were unimportant at lower VL, may come to dominate the capillary P-V characteristics.

Hysteresis. We saw little hysteresis in loops of delta Vc/Vc vs. Ptm. Our value (0.013) is about one-fourth the steady-state value that Beck and Hildebrandt (4) found for the entire pulmonary circulation. In addition, they summarize other reports, all of which find either no or low values of lung vascular P-V hysteresis. In contrast, hysteresis of lung P-V loops, which are dominated by gamma , are more than 10 times greater (2, 6). The low value that we found for microvascular hysteresis implies that, even though pulmonary capillaries are exposed to an air-tissue interface, gamma  has little influence on Cc (see below) and that vascular mechanics have little dependence on their volume history. This second finding is further supported by our experimental observation that Cc and dCc/dPtm values were not significantly different when measured during slow pressure oscillations (10-60 s) or after step changes in volume. The low value of hysteresis also indicates that the pulmonary capillaries behave in an almost purely elastic fashion in the sense that there is little dissipative energy loss.

What does the low value of hysteresis imply about lung architecture? Imagine a pulmonary capillary, exposed to a surfactant-lined gas-liquid interface. The changes in Ptm of such a vessel are the sum of the changes in surface forces (Pgamma ) and Pt. Vc doubled in our experiments, which would result in fractional changes of vessel surface area ~0.4 if the vessels were circular tubes. The delta Vc/Vc vs. Ptm loops for these volume excursions had hysteresis values of 0.013. Yet, in vitro loops of gamma  vs. surfactant area, associated with fractional changes in area of 0.4, result in hysteresis values >0.3 (20). This 20-fold difference in hysteresis values suggests that either Pgamma  < Pt or the vessels are noncircular and their surface area changed much less than the anticipated 40%. Pgamma in the lung is known to be greater than, not substantially less than, Pt (p. 96 in Ref. 19). Our data are inconsistent with any model of the pulmonary capillary bed that, at fixed VL, involves substantial change in area of an air liquid interface with changes in Ptm.

Another line of reasoning suggests that vessels exposed to a surfactant-lined gas-liquid interface cannot be small tubes with circular cross sections. If a vessel had a baseline radius = 3 µm and was coated with surfactant with an average gamma  of 10 dyn/cm, then vessel Pgamma  = gamma /radius (LaPlace's law) would be 34 cmH2O. This would make the capillary intravascular pressure (Pgamma  + Pt) > 30 cmH2O, which is much higher than known values.

In summary, the very low value of hysteresis suggests that gamma  does not, in a direct way, strongly affect Cc. Nonetheless, it may play an important role in setting basal capillary shape, by keeping capillary walls flat. The effects of changes in gamma  on capillary mechanics need further investigation.

Recruitment vs. distension. The delta Vc/Vc vs. Ptm curves were smooth and showed little hysteresis. These features are consistent either with distension or with recruitment of vessels with widely distributed, but equal, opening and closing pressures. In other words, our data are not consistent with recruitment whether there is a narrow range of opening pressures or whether there are significant differences between opening and closing pressures (independent of how distributed the pressures may be). In particular, recruitment over a narrow range of opening pressures would have resulted in loops with nearly vertical slopes at the opening pressure, such as those found by Fung and Sobin (e.g., Ref. 11, Fig. 6.5:1, p. 307, at PL = 10-15 cmH2O) and by Godbey et al. (Fig. 1A in Ref. 14 at PL = 2.7 cmH2O). Godbey et al. (14) suggest abrupt opening at low VL but more distributed opening pressures at higher VL. However, even at low VL and at Ptm near zero, our loops of delta Vc/Vc vs. Ptm were smooth and showed no segments with nearly vertical slopes. Moreover, independent of the distribution of opening pressures, significant differences between opening and closing pressures would be reflected in significant hysteresis in the overall P-V loops; we did not observe this at any VL.

Even though the primary measurement varies greatly among these studies, we have no clear explanation for the different findings. The data of Fung and Sobin (reported in Ref. 11) are from microscopic morphometry of cat lungs that had been perfused with a silicone elastomer. The data of Godbey and colleagues (14) are from videomicroscopy of subpleural vessels in dog lungs perfused with blood, and the presence or absence of blood flow (indicated by RBC transit visualized in capillary segments) is the primary measurement. Because blood flow is designated as either present or absent, there is both a threshold and a maximum value. In contrast, our quantification of delta Vc/Vc is continuous. Our data demonstrate that blood persists in the capillaries even at low Ptm, but this does not mean blood flow must be present. A segment of the vessel downstream of the capillaries could be closed at negative Ptm, trapping blood in capillaries. Albeit under very different circumstances, an unperfused but ventilated lung remains distinctly pink, as opposed to a lung perfused with a clear solution, which has a starkly white appearance; this also suggests persistence of blood in the pulmonary microvasculature.

What do these data imply about the distribution of pulmonary vascular resistance and compliance? During slow oscillation of vascular pressure, Cc, dCc/dPtm, and hysteresis values were all independent of the side of the pulmonary circulation to which we applied pressure. The symmetry of hysteresis values implies that there was no significant vascular compliance outside the sampled volume, or that any compliance outside the volume of view had a short time constant compared with the time course of the pressure oscillations. This is most consistent with a simple model of the pulmonary vasculature: upstream and downstream resistances, with an intervening capillary capacitance. By contrast, the falling Vc that we sometimes saw between step changes in vascular volume implies a redistribution of blood to regions with significant compliance outside the sampled volume. We attribute these differences to the different time courses of the pressure oscillations (10-60 s per cycle) vs. the step changes in volume (~2 s per injection).

Pressure swings in the pulmonary capillaries with changes in Q and during the cardiac cycle. Our results for microvascular compliance, which relate changes in Vc to changes in Ptm, allow a semiquantitative estimate of the fractional change in microvascular pressure, in zone III, with changes in cardiac output (Q). As has been pointed out (3, 24), there are two effects. The first is direct: there is a simple increase in Pvas due to the increased flow-resistive pressure loss. But the increase in Pvas results in a decrease in resistance secondary to an increase in vessel diameter, and this second, indirect, effect attenuates the increase in Pvas. An expression describing these effects (Eq. B4) is derived in APPENDIX B. Suppose we started at FRC with Pvas = 5 cmH2O, left atrial pressure (Pla) = 0 cmH2O, and Cc = 8%/cmH2O. Equation B4 predicts that if Q doubled or quadrupled, then capillary pressure would increase 2 or 5 cmH2O, respectively, similar to values in the literature (e.g., Table 3 in Ref. 25 and p. 593 in Ref. 26). The point here is that because the indirect effect of Cc on increases in Pvas with Q is of the same order of magnitude as the direct effect, increases in Q would result in only about half of the increase in capillary pressures that would occur if Cc were zero. A more rigorous examination of this issue can be found in Linehan et al. (24).

Turning to pressure swings during the cardiac cycle, if Cc were 8%/cmH2O at FRC in humans, as we have found in dogs, and if the entire stroke volume of 70 ml were to distend a microvascular bed of 200 ml, then the pressure oscillations in the microvasculature would be ~4.4 cmH2O. However, the actual pressure change would be significantly less because one-third to one-half of the stroke volume distends larger upstream vessels (10, 29) and there is continuous runoff into the PV. If the delta Vc/Vc during the cardiac cycle at FRC is ~13%, as we previously found in rabbits (30), the pressure swings in the capillaries would be ~1.6 cmH2O.

Changes in RBC transit time. This same line of argument can be used to estimate the change in transit times of RBCs with increasing Q (the transit times of PMNs are discussed below). If transit time falls to too low a value, blood may pass through the lung without equilibrating with alveolar gas. Here again there are two effects. The direct effect of increased Q is simply to reduce transit time by moving blood more quickly through the vascular bed, because transit time = Vc/Q. The indirect effect blunts the reduction in transit time by increasing Vc secondary to the increased Pvas as Q goes up. A quantitative expression for these effects (Eq. B6) is also derived in APPENDIX B. Suppose we again began at FRC with Pvas = 5 cmH2O, Pla = 0 cmH2O, and Cc = 8%/cmH2O. Equation B6 predicts that transit time would fall to 59 and 35% of its initial value if Q doubled and quadrupled, respectively, rather than to 50 and 25% if Cc were 0. These figures are surprisingly close to the experimental results of Presson et al. (25), who measured the distribution of RBC transit times with sequential doublings of pulmonary blood flow and found reductions in transit time of 60 and 36% when Q doubled and quadrupled, respectively.2

Changes in PMN transit time. PMNs are larger in diameter than many pulmonary capillaries (7, 18), and, compared with RBCs, they have a wider range of transit times in the pulmonary vasculature and move through at an unsteady rate, stopping for various times in pulmonary capillaries (22). These transit times are determined by a combination of the deformability of PMNs and the baseline diameter and distensibility of the capillaries. Under normal circumstances, the deformability of PMNs is thought to be much greater than that of capillaries (7, 22, 27). However, this does not imply that Cc is not important, because capillary pressures and compliance set the baseline capillary diameters. This interaction between PMNs and capillaries may change greatly in disease in which PMNs exhibit increased stiffness (9) and pulmonary vascular pressures often change considerably. However, the effects of disease on Cc are unknown.


    APPENDIX A
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

The extraction of delta Vc/Vc from optical measurements was accomplished in two steps. We first determined the diffuse extinction coefficients at two wavelengths, 693 nm and 808 nm. From this pair, we then determined the fractional changes in blood volume.

To the extent that the typical distances over which we measure optical intensities (<1.5 cm) are small compared with the radius of curvature of the pleural surface, and to the extent that there is sufficient absorption such that the remote boundaries of the lung do not contribute to scattering amplitudes, the lung can be viewed as a semi-infinite half space bounded by a plane tangent to the pleural surface. The theory of diffuse scattering when such a medium is illuminated with a point source of light has been treated elsewhere (5, 15). The intensity I falls off sharply with radial distance r from the optical origin. A rigorous treatment of this phenomenon shows that I(r) is well approximated by
I(r) ∝ L(1+kr)e<SUP>−kr</SUP>/r<SUP>3</SUP> (A1)
where L is the optical mean free path, k is the diffuse extinction coefficient, and the constant of proportionality is the incident power. For large r, this says that I(r) is proportional to e-kr/r2, or, equivalently, ln I(r)r2 = const - kr. It follows that the linear term in a regression of ln I(r)r2 vs. r yields -k. [Note that, in our previous work, we took kr to be much less than unity, resulting in the use of a regression of ln I(r)r3 against r to find k. We no longer make this assumption. Because the exponential function decreases faster than any power of r, this turns out to make a negligible difference in the results.] The diffuse extinction coefficients for both wavelengths were determined by the above method, with intensities measured at three different locations relative to the optical origin, namely at 0.396, 0.792, and 1.189 cm.

As argued in Topulos et al. (30), the square of the diffuse extinction coefficient is an additive function of all absorbing species. From that work, we have
k<SUP>2</SUP>=<FR><NU>&agr;</NU><DE>L</DE></FR> <FENCE>A+[Hb] <FR><NU>Vc</NU><DE>V</DE></FR> [<IT>&egr;</IT><SUB>HbO<SUB><IT>2</IT></SUB></SUB>S<IT>+&egr;</IT><SUB>Hb</SUB>(<IT>1−</IT>S)]</FENCE> (A2)
where alpha  is the ratio of L to the geometric mean linear intercept, A is absorption due to nonblood components of lung tissue, [Hb] is total hemoglobin concentration in millimoles per liter, Vc/V is capillary blood volume density (volume blood per volume lung), epsilon HbO2 and epsilon Hb are the extinction coefficients for oxygenated and deoxygenated Hb, respectively (31), and S is mean oxygen saturation. Use of Eq. A2 requires elimination of the unknown constant alpha /L, and this can be accomplished in two ways: if S of blood in the sampled volume is known, one can measure the differential absorption at two different wavelengths; if S is unknown, one can add another absorbing species, such as indocyanine green dye, in known concentrations (30). In the intact animal, it is not possible to know the saturation of the pulmonary blood. However, in the excised perfused lung (with essentially no metabolism), the saturation of all blood can be controlled and measured, and so the simpler two wavelength calibration method is possible. In all experiments, lobes were ventilated with 95% O2, with saturation of all blood in the system effectively 100% at all times. This was confirmed by explicit measurements of both pulmonary arterial and venous blood. In this case
k<SUP>2</SUP>=<FR><NU>&agr;</NU><DE>L</DE></FR> <FENCE>A+[Hb] <FR><NU>Vc</NU><DE>V</DE></FR><IT> &egr;</IT><SUB>HbO<SUB><IT>2</IT></SUB></SUB></FENCE> (A3)
The difference in k2 between the two wavelengths is therefore given by
&Dgr;k<SUP>2</SUP>=<FR><NU>&agr;</NU><DE>L</DE></FR> [Hb] <FR><NU>Vc</NU><DE>V</DE></FR><IT> &Dgr;&egr;</IT> (A4)
where Delta epsilon  = epsilon 808 -epsilon 693. Now consider the change in k2 associated with changes in Vc from a reference state, at the isobestic wavelength of 808 nm. From Eq. A3, we have
&dgr;k<SUP>2</SUP>=<FR><NU>&agr;</NU><DE>L</DE></FR> [Hb] <FR><NU><IT>&dgr;</IT>Vc</NU><DE>V</DE></FR><IT> &egr;<SUB>808</SUB></IT> (A5)
Here we explicitly assume that, if VL is fixed, L and alpha  are also fixed. But the unknown factors in this expression are precisely those related to the change of k2 with wavelength through differences in epsilon . Combining Eqs. A4 and A5, we get
&dgr;k<SUP>2</SUP>=<FR><NU>&Dgr;k<SUP>2</SUP></NU><DE>&Dgr;&egr;</DE></FR> <FR><NU>&dgr;Vc</NU><DE>Vc</DE></FR><IT> &egr;<SUB>808</SUB></IT> (A6)
or equivalently
<FR><NU>&dgr;Vc</NU><DE>Vc</DE></FR><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>&egr;<SUB>808</SUB></IT></DE></FR> <FR><NU><IT>&Dgr;&egr;</IT></NU><DE><IT>&Dgr;k<SUP>2</SUP></IT></DE></FR><IT> &dgr;k<SUP>2</SUP></IT> (A7)
This is the formula used for the estimation of delta Vc/Vc . Note that this equation only applies at fixed VL.

Finally, we remark on the choice of the reference state from which changes in k8082, and hence changes in Vc, are measured. We chose a vascular pressure of 5 cmH2O relative to airway pressure as the reference Ptm for all measurements. That is, by definition, delta Vc/Vc = 0 at Ptm = 5 cmH2O. The reference value of k8082 was estimated by <k8082>, defined to be the average value of k8082 over all measurements where 3 < Ptm < 7 cmH2O. This reference value was then used to compute the change in the diffuse extinction coefficient needed in Eq. A7 by defining
&dgr;k<SUP>2</SUP>=k<SUP>2</SUP><SUB>808</SUB>−⟨k<SUP>2</SUP><SUB>808</SUB>⟩ (A8)
Similarly, Eq. A4 above, relating Delta k2 to Delta epsilon for calibration purposes, also applies at the reference state, for which we used
&Dgr;k<SUP>2</SUP>=⟨k<SUP>2</SUP><SUB>808</SUB>⟩−⟨k<SUP>2</SUP><SUB>693</SUB>⟩ (A9)
Note that this implies that the quantity delta Vc/Vc is not the discrete logarithmic differential of the capillary volume, as would be required for a strict interpretation of this as a volume-specific increment. Rather, it is explicitly the change in volume normalized by the fixed reference volume delta Vc/Vc = (Vc - Vcref)/Vcref. Of course, the compliance normalized to a reference volume and the specific compliance differ negligibly near the reference volume; it is only for large departures therefrom that these are different. Our normalization to a reference volume has the advantage that, apart from this scaling factor, our measurements of delta Vc/Vc vs. Ptm are the actual P-V curves of the microvasculature.


    APPENDIX B
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

Changes in Q are associated with changes in microvascular pressure, and a quantitative expression for this relationship can be derived as follows. The difference (Delta P) Pvas - Pla, resistance (R) between those sites, and Q are related by Delta P = QR. Nondimensionalize this expression with respect to a reference state (designated by subscript 0) by defining p = Delta P/Delta P0, q =Q/Q0, and r = R/R0, in terms of which
p=qr (B1)
(Note that here the symbol r is the nondimensional resistance and has no relation to the radial distances referred to in APPENDIX A and in the text.)

As Q increases, there are two contributions to the increase in vascular pressure. First, there is the direct effect of q itself for any given r, through the increased flow-resistive pressure loss. Second, there is the indirect effect associated with a decrease in r as p increases, secondary to the increase in capillary volume (and therefore vessel diameter). In pulmonary capillaries, where the Reynolds and Womersley numbers are much smaller than 1 (p. 361 in Ref. 11), resistance R is proportional to the inverse fourth power of the capillary radii (Poiseuille flow), or, equivalently, to the inverse square of the capillary cross-sectional areas A. As argued in the text, at fixed VL, capillary segment lengths are fixed, and all volume changes occur through proportional changes in area (28); this model assumes pure distension and no vascular recruitment. It follows, then, that because R proportional to  A-2 and A proportional to  Vc, we have
r=v<SUP>−2</SUP> (B2)
where v = Vc/Vc0 is the nondimensional microvascular volume. This volume is related to the microvascular pressure through the compliance, Vc = Vc0[1 + Cc(Delta P -Delta P0)], or
v=1+c(p−1) (B3)
where c = CcDelta P0. Combining Eqs. B1, B2, and B3 then yields the relationship between the nondimensional microvascular pressure and Q
q=p[1+c(p−1)]<SUP>2</SUP> (B4)
This is an implicit expression for pressure as a function of Q; it can be evaluated either numerically or by noting that it is a simple cubic in p.

This same line of reasoning can be used to estimate the change in transit times (T) of RBCs with changes in Q. We begin with the elementary relationship T = Vc/Q; its nondimensional equivalent is
&tgr;=v/q (B5)
where tau  = T/T0. From Eqs. B3 and B4, we find
&tgr;=<FR><NU>1</NU><DE>p[1+c(p−1)]</DE></FR> (B6)
This expresses the nondimensional transit time in terms of pressure; for any given Q, the pressure is found from Eq. B4.


    ACKNOWLEDGEMENTS

We thank Sameer Bhalotra, Danielle Boudreau, Ben Fabry, Dan Fitzgerald, Noah Helman, and Kazuko Ryu for technical assistance; Henry Feldman for advice on statistical analysis, and Claire Doerschuk, Stephen Loring, and Wiltz Wagner for helpful discussions.


    FOOTNOTES

This research was supported by National Heart, Lung, and Blood Institute Grant 55569.

Address for reprint requests and other correspondence: G. P. Topulos, Dept. of Anesthesia, Brigham and Women's Hospital, 75 Francis St., Boston, MA 02115 (E-mail: topulos{at}zeus.bwh.harvard.edu).

1 The design of our experiments kept Ppa ~ Ppv, so the vasculature was in zone I when Ptm < 0 and in zone III when Ptm > 0. The microvasculature may have transiently gone through zone II conditions as Ptm went through zero.

2 Presson et al. (25) reported transit time ratios of 62, 60, and 59% respectively from the distribution modes, the input/output moments, and damped least squares methods in their Table 1 and Fig. 11.

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.

Received 28 December 1999; accepted in final form 21 June 2000.


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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX A
APPENDIX B
REFERENCES

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