Intrapleural fluid movements described by a porous flow model GIUSEPPE MISEROCCHI, MARIA CARLA GILARDI,
DANIELE VENTUROLI, DANIELA AND RICCARDO BELLINA
NEGRINI,
Instituto di Fisiologia Umanu, Universitd degli Studi and Servizio di Medicina Ospedale San Raffaele, 20133 Milan, Italy MISERWCHI, GIUSEPPE,DANIELE VENTUROLI, DANIELA NEGRINI,MARIA CARLAGILARDI,ANDRKCARDOBELLINA.Intrapleurul fluid movements described by a porous fh model. J. Appl. Physiol. 73(6): 2511-2516, 1992.-We injected technetium-labeled albumin (at a concentration similar to that of the pleural fluid) in the costal region of anesthetized dogs(n = 13) either breathing spontaneously or apneic. The decay rate of labeledactivity at the injection site was studied with a gamma camera placed either in the anteroposterior (AP) or laterolateral (LL) projection. In breathing animals (respiratory frequency 40 cycles/min), 10 min after the injection the activity decreasedby -50% on AP and -2% on LL imaging;in apneic animalsthe correspondingdecreasein activity was reducedto m15 and -3%, respectively. We consideredlabel translocation from AP and LL imaging as a result of bulk flows of liquid alongthe costomediastinaland gravity-dependent direction, respectively. We related intrapleural flows to the hydraulic pressure gradients existing along these two directions and to the geometry of the pleural space.The pleural spacewas considered as a porous medium partially occupied by the mesh of microvilli protruding from mesothelial cells. Solution of the Kozeny-Carman equation for the observedflow velocities and pressuregradientsyielded a meanhydraulic radius of the pathways followed by the liquid ranging from 2 to 4 pm. The hydraulic resistivity of the pleural spacewas estimated at 4.5 X 105dyn s .crnm4,five orders of magnitude lower than that of interstitial tissue. l
pleural liquid pressure;apnea;pleural spacemechanics;pleural liquid turnover; microvilli geometry; fluid dynamics; tissueflow resistance TRANSPORT across the pleural membranes and within the pleural space reflects a highly dynamic situaLIQUID
tion. In fact, hydraulic pressure gradients develop among the various pleural regions (12, 18), resulting from both the mechanical interaction between chest wall and lung and the dynamics of pleural fluid turnover, the two mechanisms being geared to guarantee a steady-state condition of pleural liquid pressure (Pliq), volume, and composition (10, 14, 16). The manner in which pleural liquid flows is, however, still largely unknown. This investigation intended to bridge this gap, providing data to model intrapleural flows. In practice, we followed with a gamma camera the intrapleural distribution of a radiolabeled tracer injected in the pleural cavity of eupneic and apneic animals. The results indicate that apnea hinders the intrapleural liquid movements physiologically observed in the spontane0161-7567/92
$2.00 Copyright
Nuclear-e,
ously breathing an .imals (15, 17, 18). An attempt made to relate the label movements to the liquid
was bulk framing
flows down the intrapleural pressure gradients, the data into a flow-resistive model coherent with the geometry of the pleural space. METHODS
Experiments with the use of the gamma camera were done in dogs [n = 13, bodywt = 13.8 t 7 (SD) kg] anesthetized with pentobarbital sodium (initial dose 30-40 kg body wt), injected via a venous catheter that was also used for supplemental anesthesia, delivered on the base of the cornea1 reflexes. Labeling of the albumin required reduction of ggmTcO with SnCl under 100% N,. We assessed by gel filtration chromatography (Sephadex Gl50, Pharmacia Fine Chemicals, Uppsala, Sweden) that -85% of radioactivity was related to a monomeric frac-
mg/
tion of labeled albumin (20). The remaining activity was
due to dimeric fraction and, by no more than 2%, to free pertechnetate; these fractions remained stable up to 24 h. The surgical procedure was performed with the animal lying in either the prone or the supine posture. To prepare the site for intrapleural injection, a small incision was made in the third, fourth, or sixth intercostal space at 60% lung height, the skin cut, and the superficial muscles resected. The label Was injected in the pleural space through a stainless steel cannula (0.9 mm OD, 0.5 mm ID) connected to a short catheter and a three-way stopcock. Intrapleural insertion of the cannula was done by holding it tangenti al to the pleural surface to avoid lung puncture. The cannula was kept horizontal and entered the pleural space for a length of ~1.0-1.5 cm. The injection sites were chosen so that the estimated intrapleural position of the cannula tip was far from the lobar margins. We injected 0.3-0.5 ml of saline solution containing ~5 mg/ml of ““Tc-albumin at a concentration similar to that physiologically existing in the pleural liquid (16). Labeling was done with TCK kit (Sorin Biomedica, Saluggia, Italy). The total activity in a single injection bolus was in the range of 850 PCi. Injection lasted 4-5 s and was done by exerting a minimum of pressure to minimize the increase in Pliq at the injection site. In previous research (18) we found that the
pressure transient caused by injection is essentially over within 1 min from the end of the injection; after this time, Pliq returned to the preinjection value.
0 1992 the American
Physiological
Society
2511
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2512
INTRAPLEURAL
apneic
0 CY 40
I
t
0123456789
’
t
1
I
f
t
t
I
I
10
1,
11
12
time, min 1. Anteroposterior (AP) imaging. Shown is decrease in activity at injection site, as percentage of initial value, in eupneic breathing and in apnea. Data are means t SD from injections in 3rd and 6th intercostal spaces in prone and supine posture. ROI, region of interest. FIG.
In some instances, and only in apneic conditions, several injections were performed in the same animal. Gamma camera acquisition. The intrapleural movements of the label from the injection time up to -10-E min were followed by a large-field gamma camera (Selo, Milan, Italy) equipped with a collimator with a spatial resolution of 7.5 mm at a distance of 10 cm from the collimator. The gamma camera was interfaced with a computer (Medusa 12B, Turin, Italy) that had a processor with 64 MB of core memory. Images corresponding to the acquisition were displayed on a 256 X 256 display terminal. The counting error, as estimated by standard methods, did not exceed 1%. All activities were automatically corrected for the radioactive decay rate of ““TcO (6.04 h). The attenuation of the counting with increasing distance from the gamma camera averaged 3.8%/cm depth, with the assumption of a lung density of 0.3 g/cm3. The activity at the injection site, identified as the region of interest (ROI), was estimated either on a frontal anteroposterior (AP) or on a laterolateral (LL) projection. These two projections proved useful to follow the intrapleural spreading of the-label after costal injection. In fact, we found that with the animal in the horizontal posture, the injected label moves in accordance with the hydraulic pressure gradients down two major directions: 1) horizontally from the costal to the mediastinal and diaphragmatic regions and 2) vertically in the gravitydependent direction. The former and- the latter label trans locations are detectable from an AP and LL projection, respectively. By using markers at known distance on the chest of the animal, we estimated that the surface area of a ROI projected on a plane parallel to the collimator of the gamma camera was 25 cm? The minimum duration of the acquisition frame was 10 s. However, the time course of activity over the ROI was adequately described by averaging data over much longer periods of time. AP imaging was obtained for injections done in the third OF sixth intercostal space (corresponding respectively to the costaf surface of either the upper or lower lobe) with the animal either supine or prone. For LL imaging the label was injected in the fourth intercostal space at -80% lung height with
FLUID
FLUXES
the animal either prone or supine. When successive label injections were performed, the intrapleural translocation of the label was evaluated by subtracting the background activity. Four separate groups of gamma camera acquisition data were considered: AP eupneic (n = 4), LL eupneic (n = 4), AP apneic (n = 7)) and LL apneic (n = 7). Five of the animals were studied in both the eupneic and apneic conditions. Apnea was induced with an intravenous injection of pancuronium chloride (Pavulon, 0.2 ml/kg); supplemental 50% humidified 0, was delivered intratracheally at an alveolar pressure 4 cmH,O. Pleural liquid pressure measurements. In five more dogs (body wt = 15.5 t 1 kg) not used for gamma camera acquisition, we measured Pliq in supine posture using intrapleural saline-filled cannulas connected to pressure transducers. To record from the costal surface, cannulas were inserted horizontally for -1.5 cm, and care was taken to place their tip far from lobar fissures. To measure mediastinal Pliq the cannulas were advanced into a lobar fissure for -6-7 cm. The Pliq data gathered in the present study were implemented with the data base from previous experiments (12, 14, 16, 18). RESULTS
Figure 1 summarizes data from AP imaging. Data from supine and prone experiments and from injections performed in the third and sixth intercostal space were grouped as substantially similar. The decrease in activity of the ROI at 10 min amounted to -50% (P < 0.05) in eupneic animals and to -15% (P < 0.05) in apneic animals. The respiratory frequency of the eupneic animals averaged 10 breaths/min. Figure 2 summarizes data from LL imaging, pooling again results from prone and supine animals. At 10 min, the activity decreased by -20 and 3% in eupneic breathing (10 breaths/min) and in apnea, respectively, with both changes being significant (P < 0.05). For apneic data the significance is also validated by the linear regression fitted through the data (y = -0.23x + 99.7, ? = 0.85, P < 0.05).
A pooled analysis of variance (ANOVA)
on the lumped
T T T T ---@-a,@-.
-aT--!-i-i eupneic
T -*
8
time, min Laterolateral (LL) imaging. Shown is decrease in activity at injection site, as percent of initial value, in eupneic breathing and in apnea. Data are means t SD from injections in 4th intercostal space in prone and supine posture. Lines were drawn by eye. FIG.
2.
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INTRAPLEURAL
data from apneic conditions indicates that the time course of activity in AP and LL are significantly different (F = 50, df = 1, 23, P < 0.001). End-expiratory Pliq in supine animals did not differ in eupneic and apneic conditions (Table 1). From the absolute Pliq values one can derive the driving pressure gradients on costal side along the vertical and the costomediastinal directions. The vertical pressure gradient (VPG) is given by VPG (cmH,O/cm) = (Pt - P,)/H, HJ, where P and H indicate the hydraulic pressure and recording height, respectively, and subscripts t and b identify a top and a bottom recording point within the cavity, respectively. As the pleural fluid density was equal to that of water, the driving pressure gradient in the gravity-dependent direction (DPG) is given by -1 VPG, where -1 cmH,O/cm is the hydrostatic pressure gradient. A negative DPG value sustains a top-to-bottom fluid flow. Table 2 shows that on the costal side DPG in apnea (-0.29 t 0.1 cmH,O/cm) was not significantly different from that occurring during spontaneous breathing at end expiration (-0.21 t 0.1 cmH,O/cm) and end inspiration (-0.2 1 t 0.1 cmH,O /cm), respectively. The end-expiratory Pliq on the mediastinal side and thus the end-expiratory costomediastinal gradient were similar in eupneic and apneic animals (Tables 1 and 2); the end-inspiratory costomediastinal gradient, as taken from Ref. 18, was threefold higher in eupneic compared with apneic animals. DISCUSSION
The intrapleural translocation of the label may occur by three mechanisms: diffusion, bulk flow of fluid, and finally sedimentation. The latter could only occur in the gravity-dependent direction; because sedimentation of labeled albumin dispersed in saline solution (17) is negligible, it can be neglected in our experiments. Diffusion of the label within the pleural fluid might be aided by a mixing process due to the sliding of pleural membranes. However, the following conclusions can be made: 1) the. pattern of intrapleural distribution of a label injected with saline reveals a highly specific localization (15, 17, 18); 2) the label moves intrapleurally down pressure gradients; and 3) the specific activity in the areas where the label collects is about an order of magnitude higher than over the rest of the pleural cavity, as documented by following the tracer activity up to 3 h (21). Furthermore, the average velocity of progression of the label within the pleural space in eupneic breathing was at least one order of magnitude higher (15, 17, 18) than that expected on 1. Pliq at end expiration during eupneic breathing and in apnea in supine dogs TABLE
Pliq Costal, cmH,U Recording height, cm
9 12 16
Control end expiration -5.2zk1.5 -6.lk1.6 -11.2k1.5
Apnea 20 min -5.5t2.1 -6.6k2.4 -11.2t2.1
Pliq Mediastinal, Control end expiration
-1O.lk4.1
Values are means k SD. Pliq, pleural liquid pressure.
cmH,O Apnea 20 min
-9.9k3.7
FLUID TABLE
2513
FLUXES
2. Intrapleural pressure gradients End Expiration Control
DPG costal CMG
-0.Zlt0.1 -0.56t0.37
Apnea 20 min -029~0.1 -0.46+0.25
End Inspiration -0.21~0.1* -1.5*
are means k SD in cmH,O/cm. Negative signs of driving gradient in gravity-dependent direction on costal side (DPG costal) and along costomediastinal direction (CMG) indicate a top-tobottom and a costomediastinal pressure head, respectively. * Data from Miserocchi et al. (12, 18). Values pressure
the basis of a simple diffusion process. Accordingly, the observed label movements ought to reflect intrapleural bulk flows of liquid rather than diffusional processes. Lai-Fook et al. (5) have suggested modeling the gravity-dependent pleural flow through an equation describing flow between concentric stationary cylinders separated by a thin layer of fluid. This model assumes that pleural membranes are completely flat, an assumption that appears poorly substantiated on anatomic grounds. In fact, pleural surfaces are quite irregular, as they deploy a dense mesh of microvilli (2, 23). We therefore attempted to model intrapleural flows by a different approach and considered the Kozeny-Carman equation that describes liquid flows in a porous material (9) and has been previously applied to describe flows in various organic tissues (8). The use of the Kozeny-Carman equation to describe the flow-resistive properties of the pleural space is pertinent if one thinks of its complex geometry; indeed the space between opposing pleurae is partly occupied by microvilli (2, 23) protruding into the pleural space and constituting at some places a dense mesh through which reciprocal touching between opposing pleurae may occur. A tight fitting of opposing pleurae is also expected considering that pleural liquid volume is kept minimal by lymphatic removal (14). Thus, on the basis of anatomic evidence, one may conceive of the paths followed by liquid flowing in the pleural space as tortuous channels in the complex mesh of microvilli. The model assumes laminar flows because velocities are very small and the flow passages are very narrow. Furthermore the Kozeny-Carman equation is based on Darcy’s law that specifically implies that the pressure gradient in the direction of flow (change in pressure as a function of distance) is not constant but may change according to the geometry; this implies corresponding changes in average velocity. In fact, according to Darcy’s law, which was experimentally derived, each particle moves along a continuously curvilinear path at a continuously varying speed and with a varying acceleration. Therefore, our approach adequately describes a nonsteady situation of flow in a complex geometry. This is at variance with the model proposed by Lai-Fook et al. based on Poiseuille flow and a constant geometry with each particle moving along a straight path with no acceleration so that inertial forces are nil unless turbulence occurs. Equation 1 (Kozeny-Carman equation) describes the mean flow velocity in the direction of flow (~6)as a function of the pressure (AP), the viscosity of fluid (q), and the mean hydraulic radius of the channels (r’)
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INTRAPLEURAL
2514 U= AP
FLUID FLUXES
t3
TABLE
for AP
(1 - E)2
3. Average AA, V, and corresponding Festimated and LL projections AP
Two parameters appearing in Eq. I define the “porosity” of the mesh, Eand K (Kozeny factor). The parameter K describes the tortuosity of the path as the ratio between the straight and the effective path and could be quantitated, as described in the APPENDIX, by assuming a fixed geometry for the fibers constituting the mesh and their spatial orientation [as suggested by Happel and Brenner (4)]. Eis a value expressing the ratio between the volume of voids and the total volume through which liquid may flow (namely volume of voids plus volume of solids); thus E ranges from 0 (no voids) to 1 (no solids). We chose E = 0.6, a value commonly assumed for porous material and also for interstitial tissue devoid of the matrix fibers (8). For a given geometry of the mesh, the dependence of K on Emay be calculated (see APPENDIX). The curves in Fig. 3, A and B, show the velocity vs. hydraulic radius relationships representing the solution of 0.02
-A eupneic
I;
0.00
’
1
I
I
I
I
1
2
3
4
5
6
2
3
4
5
6
El
eupnelc
1
7, pm FIG. 3. A: velocity (6) vs. mean hydraulic radius (3 from KozenyCarman equation for data from AP imaging. Two curves shown represent solutions of Eq. 1 for change in pressure (AP) corresponding to eupneic breathing and apnea, respectively. IIorizontal lines are 0 estimated from AP imaging in eupneic breathing and in apnea; decrease in 6 in apnea is consistent with a decrease in AP for same F (- 3 pm). B: V vs. F from Kozeny-Carman equation for data from LL imaging. Horizontal lines are fi corresponding to eupneic breathing and apnea from LL imaging. Only 1 curve is shown here because AP is unchanged from apnea to eupneic breathing. Intersection of curve with 2 horizontal lines indicates F of 4.7 and -2 pm for eupneic breathing and apnea, respectively.
Eupneic
’
LL Apneic
Eupneic
Apneic
-1.4 -0.2 AA, %/min -4.8 -1.6 0.01 6, mm/s 0.17 0.06 0.07 3.2 3.2 4.7 1.8 6 pm AP, anteroposterior; LL, laterolateral; AA, rate of changeof regional activity; 6, average flow velocity; F, mean hydraulic radius.
Eq. 1 for the AP occurring in the gravity-dependent direction and along the costomediastinal direction (as from Table 2). Although the use of intrapleural cannulas inevitably causes pleural distortion, the extent to which this artifact affects intrapleural pressure is still a matter of debate. Yet, at least for costal side, end-expiratory Pliq’ measurements obtained with cannulas were confirmed by using a least invasive micropuncture technique (11). Furthermore, despite the variability in Pliq values, depending on the author or the technique, there is general agreement on the existence of a pressure gradient to sustain flow in the gravity-dependent direction. The horizontal lines in Fig. 3, A and B, refer to the average velocity of label progression away from the ROI, as determined from AP and LL imaging. The average intrapleural flow velocity has been directly measured from the time interval covered by the label to travel along the interlobar fissures from the injection point at the costal side to the mediastinal region (15): the tracer velocity from an AP projection was found to average 0.017 cm/s. In a subsequent study (17), an LL projection was used to evaluate a gravity-dependent pleural liquid flow. The flow velocity was found proportional to the rate of change of activity in a given region; accordingly, one can derive the intrapleural flow velocity from the decay rate of the label. In fact, the activity (A) under the gamma camera is proportional to the quantity (Q) of label so that A K Q, where Q = CV (where C is the concentration of the label dispersed in the volume V). Thus the decrease in local activity is proportional to dQ/ dt = CdVldt, where dV/dt is the pleural liquid outflow from the scanned area toward other compartments. Because dV/dt = ES, where 6 is the average flow velocity occurring through a surface area S, one has dA/dt cc iS and U cc USdAldt. Table 3 summarizes the 6 values corresponding to the observed average rate of change in activities over the time considered (as determined from Figs. 1 and 2). In Fig. 3A the horizontal lines refer to fiestimated from AP imaging in eupneic breathing and in apnea; the two curves shown represent the solutions of Eq. 1 for AP corresponding to eupneic breathing and apnea, respectively. q was assumed equal to that of water (0.007 dyns se cme2). As it can be seen, a decrease in Gin apnea is consistent with a decrease in AP for the same mean hydraulic radius (--3 pm). In Fig. 3B the horizontal lines refer to korresponding to eupneic breathing and apnea as determined from LL imaging. Only one curve is shown here for AP, which is l
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INTRAPLEURAL TABLE
and
4. Hydraulic resistivity of pleural interstitial tissues
space
of variuus
Hydraulic
Pleural space Subcutaneous tissue Wharton’s jelly Cornea1 stroma Cartilage
Resistivity,
8.5 t 7.8 11.6 4.7 80-180 500--1,000
x x x x x
dyn s crnm4 l
l
lo5 10” * NY0 * lU1’ * lu10 *
Value for pleural space is mean t SD, * Data from Levi& (8).
essentially unchanged from apnea to eupneic breathing (-0.25 cmH,O/cm). The intersection of the curve with the two horizontal lines indicates F = 4.7 and ~2 pm for eupneic breathing and apnea, respectively. It is at present difficult to explain why, in face of a similar AP, U and Fdecrease going from eupneic breathing to apnea; in general this indicates an increase, although small, of the hydraulic resistivity (see also below). The values of r (reported also in Table 3) cannot be promptly related to the thickness of the pleural space, although one may assume Fis proportional to it. Therefore, rshould be taken as a functional indication. In general terms, the range of F values for the observed flow velocities and pressure gradients is compatible with the observed range of pleural liquid thickness over the costal side [Z-20 ,um (1, 2, 6)]. One may note that assuming zlifferent Evalues would of course change the corresponding fi however, changing Efrom 0.3 to 0.8 would change Pby do%, namely about five times less than the observed variability in pleural liquid thickness. Thus we believe that the Kozeny-Carman equation is a useful tool to model intrapleural flows. It is worth noting here that the intrapleural flows of liquid, estimated at 0.006 and 0.012 ml kg-l. h-l (17) for top-to-bottom and costal-to-extracostal directions, respectively, are consistent with the measured regional Pliq gradients and with the geometry of the pleural space. Equation 1 can also be used to quantitate the hydraulic resistivity to intrapleural flow given by R = [K(c) /( cr2)] q. The hydraulic resistivity is influenced by the value of Darameter i?Z, reflecting the spatial orientation of the Fibers of the mesh. However, for K ranging from its minimum to its maximum value, the change in hydraulic resis;ance does not exceed 30%. Table 4 reports the mean hydraulic resistivity for intrapleural flows compared with values obtained for other tissues (8). As it can be seen, the hydraulic resistivity of pleural space is about five orders of magnitude lower than that of interstitial tissues. We framed intrapleural flows into a more general design of liquid turnover, implying areas of preferential filtration and others of preferential absorption (10, 14, 19, 20). The present data indicate that lung motion can substantially contribute to redistribute fluid within the pleural cavity, a concept also addressed by other investigators (3). More recent data also suggest that pleural liquid flows may differ between pleural surfaces and interlobar margins (7, 24). l
FLUID
FLUXES
2515
A final comment is due on pleural fluid turnover, considering that end-expiratory Pliq remained essentially unchanged up to 20 min of apnea. In fact, we have shown that most of pleural liquid drainage is provided by lymphatic action, and the latter seems enhanced by breathing movements and heart rate (14) so that one would expect apnea to reduce lymphatic drainage. In fact, recent data indicate that myogenic activity of initial lymphatic action is more important than tissue movement to cause lymphatic drainage (22). Furthermore, apnea implies less negative overall Pliq values compared with eupneic breathing and thus smaller filtration pressure gradients. To the extent that lymphatic drainage and pleural fluid filtration are both reduced, one would expect, at least within a limited period of time, no change in end-expiratory Pliq. APPENDIX
The Kozeny-Carman equation was developed to describe flow in porousmaterials (9). A rigorous analysisis very difficult becauseof the complex variability of the individual flow passages,although velocities are solow that a laminar flow can be assumed.The porosity is expressedby parameter Ethat is an important factor in determining the flow velocity. Eis fairly constant for similar particles occupying the spacerandomly. Most materials of granular type have an Eranging from 0.3 to 0.6. For particles having a higher surface-to-volume ratio, E tends to increase.Ehas been assumedequal to 0.6 for interstitial tissue, neglectingthe contribution to flow resistancedue to intercellular fibers asglycosaminoglycansor proteoglycans (8). Parameter IY, also named Kozeny’s parameter or Kozeny’s function, describing the “tortuosity” of path, dependson geometrical characteristics and disposition of obstaclesconstituting the meshand may be expressedas a function of E.Happel and Brenner (4) developedthe theoretical dependenceof K on c considering a bed of cylindrical fibers variously oriented relative to the flow direction. They calculated the dependenceof K on c in the caseof fibers oriented either parallel (I$,) or at right angle (IQ relative to the direction of flow, obtaining the following equations
K,(4 =
For a random orientation of the fibers, the following relationship holds
K remainsfairly stable for Eranging from 0.3 to 0.8, whereasit increasessharply for c approaching 1 (namely a high fractional void volume). This research was supported by the Italian Ministry of the University and Scientific Research, by National Research Council Grant CT89.03944, and partly by Grant PSN-87-042.
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2516
INTRAPLEURAL
Address for reprint Umana, Via Mangiagalli
requests: G. Miserocchi, Istituto di Fisiologia 32, 20133 Milan, Italy. Received 8 August 1991; accepted in final form 9 July 1992. REFERENCES
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tures of Starling-lymphatic interaction at pleural level in mammals. J. Appl. Physiol. 56: 1151-1156, 1984. 17. MISEROCCHI, G., D. NEGRINI, M. PISTOLESI, C. R. BELLINA, M. C. GILARDI, V. BETTINARDI, AND F. ROSSITTO. Intrapleural flow down a gravity-dependent hydraulic pressure gradient. J. Appl. Physiol. 64: 577-584, 1988. 18. MISEROCCHI, G., M. PISTOLESI, M. MINIATI, C. R. BELLINA, D. NEGRINI, AND C. GIUNTINI. Pleural liquid pressure gradients and intrapleural distribution of injected bolus. J. Appl. Physiol. 56: 526532, 1984. 19. NEGRINI, D., C. CAPELLI, M. MORINI, AND G. MISEROCCHI. Gravity
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7. LAI-FOOK, S. J., AND P. M. WANG. Movements of fluorescent microspheres along lobar margin in the pleural space due to cardiogenic motion (Abstract). FASEB J. 5: A747, 1991. 8. LEVICK, J. R. Flow through interstitium and other fibrous matri-
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M. PISTOLESI, M. MINIATI, R. C. BELLINA, C. GIUNG. MISEROCCHI. Regional protein absorption rates from the pleural cavity in dogs. J. Appl. Physiol. 58: 2062-2067, 1985. 22. RODDIE, I. C. Lymph transport mechanisms in peripheral lymphatics. News Physiol. Sci. 5: 85-89, 1990. 23. WANG, N. S. The regional difference of pleural mesothelial cells in rabbits. Am. Reu. Respir. Dis. 110: 623-633, 1974. 24. WANG, P. M., AND S. J. LAI-FOOK. Upward movement of pleural liquid along lobar margins due to cardiogenic motion (Abstract).
1987.
London: Van Nostrand Rein-
hold, 1989. 10. MISEROCCHI, G. Pleural pressure and fluid transport. In: The Lung: Scientific Foundation, edited by R. G. Crystal and J. B. West. New York: Raven, 1991, p. 885-893. 11. MISEROCCHI, G., S. KELLY, AND D. NEGRINI. Pleural and extrapleural interstitial liquid pressure measured by cannulas and micropipettes. J. Appl. Physiol. 65: 555-562, 1988. 12. MISEROCCHI, G., E. MARIANI, AND D. NEGRINI. Role of the dia-
eta1 extrapleural
differences in pariand pleural liquid pressure. J. Appl. Physiol. 67:
1967-1972,1989. 21. NEGRINI, D., TINI,
AND
Physiologist
33: A81,
1990,
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DANIELE VENTUROLI, DANIELA AND RICCARDO BELLINA
NEGRINI,
Instituto di Fisiologia Umanu, Universitd degli Studi and Servizio di Medicina Ospedale San Raffaele, 20133 Milan, Italy MISERWCHI, GIUSEPPE,DANIELE VENTUROLI, DANIELA NEGRINI,MARIA CARLAGILARDI,ANDRKCARDOBELLINA.Intrapleurul fluid movements described by a porous fh model. J. Appl. Physiol. 73(6): 2511-2516, 1992.-We injected technetium-labeled albumin (at a concentration similar to that of the pleural fluid) in the costal region of anesthetized dogs(n = 13) either breathing spontaneously or apneic. The decay rate of labeledactivity at the injection site was studied with a gamma camera placed either in the anteroposterior (AP) or laterolateral (LL) projection. In breathing animals (respiratory frequency 40 cycles/min), 10 min after the injection the activity decreasedby -50% on AP and -2% on LL imaging;in apneic animalsthe correspondingdecreasein activity was reducedto m15 and -3%, respectively. We consideredlabel translocation from AP and LL imaging as a result of bulk flows of liquid alongthe costomediastinaland gravity-dependent direction, respectively. We related intrapleural flows to the hydraulic pressure gradients existing along these two directions and to the geometry of the pleural space.The pleural spacewas considered as a porous medium partially occupied by the mesh of microvilli protruding from mesothelial cells. Solution of the Kozeny-Carman equation for the observedflow velocities and pressuregradientsyielded a meanhydraulic radius of the pathways followed by the liquid ranging from 2 to 4 pm. The hydraulic resistivity of the pleural spacewas estimated at 4.5 X 105dyn s .crnm4,five orders of magnitude lower than that of interstitial tissue. l
pleural liquid pressure;apnea;pleural spacemechanics;pleural liquid turnover; microvilli geometry; fluid dynamics; tissueflow resistance TRANSPORT across the pleural membranes and within the pleural space reflects a highly dynamic situaLIQUID
tion. In fact, hydraulic pressure gradients develop among the various pleural regions (12, 18), resulting from both the mechanical interaction between chest wall and lung and the dynamics of pleural fluid turnover, the two mechanisms being geared to guarantee a steady-state condition of pleural liquid pressure (Pliq), volume, and composition (10, 14, 16). The manner in which pleural liquid flows is, however, still largely unknown. This investigation intended to bridge this gap, providing data to model intrapleural flows. In practice, we followed with a gamma camera the intrapleural distribution of a radiolabeled tracer injected in the pleural cavity of eupneic and apneic animals. The results indicate that apnea hinders the intrapleural liquid movements physiologically observed in the spontane0161-7567/92
$2.00 Copyright
Nuclear-e,
ously breathing an .imals (15, 17, 18). An attempt made to relate the label movements to the liquid
was bulk framing
flows down the intrapleural pressure gradients, the data into a flow-resistive model coherent with the geometry of the pleural space. METHODS
Experiments with the use of the gamma camera were done in dogs [n = 13, bodywt = 13.8 t 7 (SD) kg] anesthetized with pentobarbital sodium (initial dose 30-40 kg body wt), injected via a venous catheter that was also used for supplemental anesthesia, delivered on the base of the cornea1 reflexes. Labeling of the albumin required reduction of ggmTcO with SnCl under 100% N,. We assessed by gel filtration chromatography (Sephadex Gl50, Pharmacia Fine Chemicals, Uppsala, Sweden) that -85% of radioactivity was related to a monomeric frac-
mg/
tion of labeled albumin (20). The remaining activity was
due to dimeric fraction and, by no more than 2%, to free pertechnetate; these fractions remained stable up to 24 h. The surgical procedure was performed with the animal lying in either the prone or the supine posture. To prepare the site for intrapleural injection, a small incision was made in the third, fourth, or sixth intercostal space at 60% lung height, the skin cut, and the superficial muscles resected. The label Was injected in the pleural space through a stainless steel cannula (0.9 mm OD, 0.5 mm ID) connected to a short catheter and a three-way stopcock. Intrapleural insertion of the cannula was done by holding it tangenti al to the pleural surface to avoid lung puncture. The cannula was kept horizontal and entered the pleural space for a length of ~1.0-1.5 cm. The injection sites were chosen so that the estimated intrapleural position of the cannula tip was far from the lobar margins. We injected 0.3-0.5 ml of saline solution containing ~5 mg/ml of ““Tc-albumin at a concentration similar to that physiologically existing in the pleural liquid (16). Labeling was done with TCK kit (Sorin Biomedica, Saluggia, Italy). The total activity in a single injection bolus was in the range of 850 PCi. Injection lasted 4-5 s and was done by exerting a minimum of pressure to minimize the increase in Pliq at the injection site. In previous research (18) we found that the
pressure transient caused by injection is essentially over within 1 min from the end of the injection; after this time, Pliq returned to the preinjection value.
0 1992 the American
Physiological
Society
2511
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2512
INTRAPLEURAL
apneic
0 CY 40
I
t
0123456789
’
t
1
I
f
t
t
I
I
10
1,
11
12
time, min 1. Anteroposterior (AP) imaging. Shown is decrease in activity at injection site, as percentage of initial value, in eupneic breathing and in apnea. Data are means t SD from injections in 3rd and 6th intercostal spaces in prone and supine posture. ROI, region of interest. FIG.
In some instances, and only in apneic conditions, several injections were performed in the same animal. Gamma camera acquisition. The intrapleural movements of the label from the injection time up to -10-E min were followed by a large-field gamma camera (Selo, Milan, Italy) equipped with a collimator with a spatial resolution of 7.5 mm at a distance of 10 cm from the collimator. The gamma camera was interfaced with a computer (Medusa 12B, Turin, Italy) that had a processor with 64 MB of core memory. Images corresponding to the acquisition were displayed on a 256 X 256 display terminal. The counting error, as estimated by standard methods, did not exceed 1%. All activities were automatically corrected for the radioactive decay rate of ““TcO (6.04 h). The attenuation of the counting with increasing distance from the gamma camera averaged 3.8%/cm depth, with the assumption of a lung density of 0.3 g/cm3. The activity at the injection site, identified as the region of interest (ROI), was estimated either on a frontal anteroposterior (AP) or on a laterolateral (LL) projection. These two projections proved useful to follow the intrapleural spreading of the-label after costal injection. In fact, we found that with the animal in the horizontal posture, the injected label moves in accordance with the hydraulic pressure gradients down two major directions: 1) horizontally from the costal to the mediastinal and diaphragmatic regions and 2) vertically in the gravitydependent direction. The former and- the latter label trans locations are detectable from an AP and LL projection, respectively. By using markers at known distance on the chest of the animal, we estimated that the surface area of a ROI projected on a plane parallel to the collimator of the gamma camera was 25 cm? The minimum duration of the acquisition frame was 10 s. However, the time course of activity over the ROI was adequately described by averaging data over much longer periods of time. AP imaging was obtained for injections done in the third OF sixth intercostal space (corresponding respectively to the costaf surface of either the upper or lower lobe) with the animal either supine or prone. For LL imaging the label was injected in the fourth intercostal space at -80% lung height with
FLUID
FLUXES
the animal either prone or supine. When successive label injections were performed, the intrapleural translocation of the label was evaluated by subtracting the background activity. Four separate groups of gamma camera acquisition data were considered: AP eupneic (n = 4), LL eupneic (n = 4), AP apneic (n = 7)) and LL apneic (n = 7). Five of the animals were studied in both the eupneic and apneic conditions. Apnea was induced with an intravenous injection of pancuronium chloride (Pavulon, 0.2 ml/kg); supplemental 50% humidified 0, was delivered intratracheally at an alveolar pressure 4 cmH,O. Pleural liquid pressure measurements. In five more dogs (body wt = 15.5 t 1 kg) not used for gamma camera acquisition, we measured Pliq in supine posture using intrapleural saline-filled cannulas connected to pressure transducers. To record from the costal surface, cannulas were inserted horizontally for -1.5 cm, and care was taken to place their tip far from lobar fissures. To measure mediastinal Pliq the cannulas were advanced into a lobar fissure for -6-7 cm. The Pliq data gathered in the present study were implemented with the data base from previous experiments (12, 14, 16, 18). RESULTS
Figure 1 summarizes data from AP imaging. Data from supine and prone experiments and from injections performed in the third and sixth intercostal space were grouped as substantially similar. The decrease in activity of the ROI at 10 min amounted to -50% (P < 0.05) in eupneic animals and to -15% (P < 0.05) in apneic animals. The respiratory frequency of the eupneic animals averaged 10 breaths/min. Figure 2 summarizes data from LL imaging, pooling again results from prone and supine animals. At 10 min, the activity decreased by -20 and 3% in eupneic breathing (10 breaths/min) and in apnea, respectively, with both changes being significant (P < 0.05). For apneic data the significance is also validated by the linear regression fitted through the data (y = -0.23x + 99.7, ? = 0.85, P < 0.05).
A pooled analysis of variance (ANOVA)
on the lumped
T T T T ---@-a,@-.
-aT--!-i-i eupneic
T -*
8
time, min Laterolateral (LL) imaging. Shown is decrease in activity at injection site, as percent of initial value, in eupneic breathing and in apnea. Data are means t SD from injections in 4th intercostal space in prone and supine posture. Lines were drawn by eye. FIG.
2.
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INTRAPLEURAL
data from apneic conditions indicates that the time course of activity in AP and LL are significantly different (F = 50, df = 1, 23, P < 0.001). End-expiratory Pliq in supine animals did not differ in eupneic and apneic conditions (Table 1). From the absolute Pliq values one can derive the driving pressure gradients on costal side along the vertical and the costomediastinal directions. The vertical pressure gradient (VPG) is given by VPG (cmH,O/cm) = (Pt - P,)/H, HJ, where P and H indicate the hydraulic pressure and recording height, respectively, and subscripts t and b identify a top and a bottom recording point within the cavity, respectively. As the pleural fluid density was equal to that of water, the driving pressure gradient in the gravity-dependent direction (DPG) is given by -1 VPG, where -1 cmH,O/cm is the hydrostatic pressure gradient. A negative DPG value sustains a top-to-bottom fluid flow. Table 2 shows that on the costal side DPG in apnea (-0.29 t 0.1 cmH,O/cm) was not significantly different from that occurring during spontaneous breathing at end expiration (-0.21 t 0.1 cmH,O/cm) and end inspiration (-0.2 1 t 0.1 cmH,O /cm), respectively. The end-expiratory Pliq on the mediastinal side and thus the end-expiratory costomediastinal gradient were similar in eupneic and apneic animals (Tables 1 and 2); the end-inspiratory costomediastinal gradient, as taken from Ref. 18, was threefold higher in eupneic compared with apneic animals. DISCUSSION
The intrapleural translocation of the label may occur by three mechanisms: diffusion, bulk flow of fluid, and finally sedimentation. The latter could only occur in the gravity-dependent direction; because sedimentation of labeled albumin dispersed in saline solution (17) is negligible, it can be neglected in our experiments. Diffusion of the label within the pleural fluid might be aided by a mixing process due to the sliding of pleural membranes. However, the following conclusions can be made: 1) the. pattern of intrapleural distribution of a label injected with saline reveals a highly specific localization (15, 17, 18); 2) the label moves intrapleurally down pressure gradients; and 3) the specific activity in the areas where the label collects is about an order of magnitude higher than over the rest of the pleural cavity, as documented by following the tracer activity up to 3 h (21). Furthermore, the average velocity of progression of the label within the pleural space in eupneic breathing was at least one order of magnitude higher (15, 17, 18) than that expected on 1. Pliq at end expiration during eupneic breathing and in apnea in supine dogs TABLE
Pliq Costal, cmH,U Recording height, cm
9 12 16
Control end expiration -5.2zk1.5 -6.lk1.6 -11.2k1.5
Apnea 20 min -5.5t2.1 -6.6k2.4 -11.2t2.1
Pliq Mediastinal, Control end expiration
-1O.lk4.1
Values are means k SD. Pliq, pleural liquid pressure.
cmH,O Apnea 20 min
-9.9k3.7
FLUID TABLE
2513
FLUXES
2. Intrapleural pressure gradients End Expiration Control
DPG costal CMG
-0.Zlt0.1 -0.56t0.37
Apnea 20 min -029~0.1 -0.46+0.25
End Inspiration -0.21~0.1* -1.5*
are means k SD in cmH,O/cm. Negative signs of driving gradient in gravity-dependent direction on costal side (DPG costal) and along costomediastinal direction (CMG) indicate a top-tobottom and a costomediastinal pressure head, respectively. * Data from Miserocchi et al. (12, 18). Values pressure
the basis of a simple diffusion process. Accordingly, the observed label movements ought to reflect intrapleural bulk flows of liquid rather than diffusional processes. Lai-Fook et al. (5) have suggested modeling the gravity-dependent pleural flow through an equation describing flow between concentric stationary cylinders separated by a thin layer of fluid. This model assumes that pleural membranes are completely flat, an assumption that appears poorly substantiated on anatomic grounds. In fact, pleural surfaces are quite irregular, as they deploy a dense mesh of microvilli (2, 23). We therefore attempted to model intrapleural flows by a different approach and considered the Kozeny-Carman equation that describes liquid flows in a porous material (9) and has been previously applied to describe flows in various organic tissues (8). The use of the Kozeny-Carman equation to describe the flow-resistive properties of the pleural space is pertinent if one thinks of its complex geometry; indeed the space between opposing pleurae is partly occupied by microvilli (2, 23) protruding into the pleural space and constituting at some places a dense mesh through which reciprocal touching between opposing pleurae may occur. A tight fitting of opposing pleurae is also expected considering that pleural liquid volume is kept minimal by lymphatic removal (14). Thus, on the basis of anatomic evidence, one may conceive of the paths followed by liquid flowing in the pleural space as tortuous channels in the complex mesh of microvilli. The model assumes laminar flows because velocities are very small and the flow passages are very narrow. Furthermore the Kozeny-Carman equation is based on Darcy’s law that specifically implies that the pressure gradient in the direction of flow (change in pressure as a function of distance) is not constant but may change according to the geometry; this implies corresponding changes in average velocity. In fact, according to Darcy’s law, which was experimentally derived, each particle moves along a continuously curvilinear path at a continuously varying speed and with a varying acceleration. Therefore, our approach adequately describes a nonsteady situation of flow in a complex geometry. This is at variance with the model proposed by Lai-Fook et al. based on Poiseuille flow and a constant geometry with each particle moving along a straight path with no acceleration so that inertial forces are nil unless turbulence occurs. Equation 1 (Kozeny-Carman equation) describes the mean flow velocity in the direction of flow (~6)as a function of the pressure (AP), the viscosity of fluid (q), and the mean hydraulic radius of the channels (r’)
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INTRAPLEURAL
2514 U= AP
FLUID FLUXES
t3
TABLE
for AP
(1 - E)2
3. Average AA, V, and corresponding Festimated and LL projections AP
Two parameters appearing in Eq. I define the “porosity” of the mesh, Eand K (Kozeny factor). The parameter K describes the tortuosity of the path as the ratio between the straight and the effective path and could be quantitated, as described in the APPENDIX, by assuming a fixed geometry for the fibers constituting the mesh and their spatial orientation [as suggested by Happel and Brenner (4)]. Eis a value expressing the ratio between the volume of voids and the total volume through which liquid may flow (namely volume of voids plus volume of solids); thus E ranges from 0 (no voids) to 1 (no solids). We chose E = 0.6, a value commonly assumed for porous material and also for interstitial tissue devoid of the matrix fibers (8). For a given geometry of the mesh, the dependence of K on Emay be calculated (see APPENDIX). The curves in Fig. 3, A and B, show the velocity vs. hydraulic radius relationships representing the solution of 0.02
-A eupneic
I;
0.00
’
1
I
I
I
I
1
2
3
4
5
6
2
3
4
5
6
El
eupnelc
1
7, pm FIG. 3. A: velocity (6) vs. mean hydraulic radius (3 from KozenyCarman equation for data from AP imaging. Two curves shown represent solutions of Eq. 1 for change in pressure (AP) corresponding to eupneic breathing and apnea, respectively. IIorizontal lines are 0 estimated from AP imaging in eupneic breathing and in apnea; decrease in 6 in apnea is consistent with a decrease in AP for same F (- 3 pm). B: V vs. F from Kozeny-Carman equation for data from LL imaging. Horizontal lines are fi corresponding to eupneic breathing and apnea from LL imaging. Only 1 curve is shown here because AP is unchanged from apnea to eupneic breathing. Intersection of curve with 2 horizontal lines indicates F of 4.7 and -2 pm for eupneic breathing and apnea, respectively.
Eupneic
’
LL Apneic
Eupneic
Apneic
-1.4 -0.2 AA, %/min -4.8 -1.6 0.01 6, mm/s 0.17 0.06 0.07 3.2 3.2 4.7 1.8 6 pm AP, anteroposterior; LL, laterolateral; AA, rate of changeof regional activity; 6, average flow velocity; F, mean hydraulic radius.
Eq. 1 for the AP occurring in the gravity-dependent direction and along the costomediastinal direction (as from Table 2). Although the use of intrapleural cannulas inevitably causes pleural distortion, the extent to which this artifact affects intrapleural pressure is still a matter of debate. Yet, at least for costal side, end-expiratory Pliq’ measurements obtained with cannulas were confirmed by using a least invasive micropuncture technique (11). Furthermore, despite the variability in Pliq values, depending on the author or the technique, there is general agreement on the existence of a pressure gradient to sustain flow in the gravity-dependent direction. The horizontal lines in Fig. 3, A and B, refer to the average velocity of label progression away from the ROI, as determined from AP and LL imaging. The average intrapleural flow velocity has been directly measured from the time interval covered by the label to travel along the interlobar fissures from the injection point at the costal side to the mediastinal region (15): the tracer velocity from an AP projection was found to average 0.017 cm/s. In a subsequent study (17), an LL projection was used to evaluate a gravity-dependent pleural liquid flow. The flow velocity was found proportional to the rate of change of activity in a given region; accordingly, one can derive the intrapleural flow velocity from the decay rate of the label. In fact, the activity (A) under the gamma camera is proportional to the quantity (Q) of label so that A K Q, where Q = CV (where C is the concentration of the label dispersed in the volume V). Thus the decrease in local activity is proportional to dQ/ dt = CdVldt, where dV/dt is the pleural liquid outflow from the scanned area toward other compartments. Because dV/dt = ES, where 6 is the average flow velocity occurring through a surface area S, one has dA/dt cc iS and U cc USdAldt. Table 3 summarizes the 6 values corresponding to the observed average rate of change in activities over the time considered (as determined from Figs. 1 and 2). In Fig. 3A the horizontal lines refer to fiestimated from AP imaging in eupneic breathing and in apnea; the two curves shown represent the solutions of Eq. 1 for AP corresponding to eupneic breathing and apnea, respectively. q was assumed equal to that of water (0.007 dyns se cme2). As it can be seen, a decrease in Gin apnea is consistent with a decrease in AP for the same mean hydraulic radius (--3 pm). In Fig. 3B the horizontal lines refer to korresponding to eupneic breathing and apnea as determined from LL imaging. Only one curve is shown here for AP, which is l
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INTRAPLEURAL TABLE
and
4. Hydraulic resistivity of pleural interstitial tissues
space
of variuus
Hydraulic
Pleural space Subcutaneous tissue Wharton’s jelly Cornea1 stroma Cartilage
Resistivity,
8.5 t 7.8 11.6 4.7 80-180 500--1,000
x x x x x
dyn s crnm4 l
l
lo5 10” * NY0 * lU1’ * lu10 *
Value for pleural space is mean t SD, * Data from Levi& (8).
essentially unchanged from apnea to eupneic breathing (-0.25 cmH,O/cm). The intersection of the curve with the two horizontal lines indicates F = 4.7 and ~2 pm for eupneic breathing and apnea, respectively. It is at present difficult to explain why, in face of a similar AP, U and Fdecrease going from eupneic breathing to apnea; in general this indicates an increase, although small, of the hydraulic resistivity (see also below). The values of r (reported also in Table 3) cannot be promptly related to the thickness of the pleural space, although one may assume Fis proportional to it. Therefore, rshould be taken as a functional indication. In general terms, the range of F values for the observed flow velocities and pressure gradients is compatible with the observed range of pleural liquid thickness over the costal side [Z-20 ,um (1, 2, 6)]. One may note that assuming zlifferent Evalues would of course change the corresponding fi however, changing Efrom 0.3 to 0.8 would change Pby do%, namely about five times less than the observed variability in pleural liquid thickness. Thus we believe that the Kozeny-Carman equation is a useful tool to model intrapleural flows. It is worth noting here that the intrapleural flows of liquid, estimated at 0.006 and 0.012 ml kg-l. h-l (17) for top-to-bottom and costal-to-extracostal directions, respectively, are consistent with the measured regional Pliq gradients and with the geometry of the pleural space. Equation 1 can also be used to quantitate the hydraulic resistivity to intrapleural flow given by R = [K(c) /( cr2)] q. The hydraulic resistivity is influenced by the value of Darameter i?Z, reflecting the spatial orientation of the Fibers of the mesh. However, for K ranging from its minimum to its maximum value, the change in hydraulic resis;ance does not exceed 30%. Table 4 reports the mean hydraulic resistivity for intrapleural flows compared with values obtained for other tissues (8). As it can be seen, the hydraulic resistivity of pleural space is about five orders of magnitude lower than that of interstitial tissues. We framed intrapleural flows into a more general design of liquid turnover, implying areas of preferential filtration and others of preferential absorption (10, 14, 19, 20). The present data indicate that lung motion can substantially contribute to redistribute fluid within the pleural cavity, a concept also addressed by other investigators (3). More recent data also suggest that pleural liquid flows may differ between pleural surfaces and interlobar margins (7, 24). l
FLUID
FLUXES
2515
A final comment is due on pleural fluid turnover, considering that end-expiratory Pliq remained essentially unchanged up to 20 min of apnea. In fact, we have shown that most of pleural liquid drainage is provided by lymphatic action, and the latter seems enhanced by breathing movements and heart rate (14) so that one would expect apnea to reduce lymphatic drainage. In fact, recent data indicate that myogenic activity of initial lymphatic action is more important than tissue movement to cause lymphatic drainage (22). Furthermore, apnea implies less negative overall Pliq values compared with eupneic breathing and thus smaller filtration pressure gradients. To the extent that lymphatic drainage and pleural fluid filtration are both reduced, one would expect, at least within a limited period of time, no change in end-expiratory Pliq. APPENDIX
The Kozeny-Carman equation was developed to describe flow in porousmaterials (9). A rigorous analysisis very difficult becauseof the complex variability of the individual flow passages,although velocities are solow that a laminar flow can be assumed.The porosity is expressedby parameter Ethat is an important factor in determining the flow velocity. Eis fairly constant for similar particles occupying the spacerandomly. Most materials of granular type have an Eranging from 0.3 to 0.6. For particles having a higher surface-to-volume ratio, E tends to increase.Ehas been assumedequal to 0.6 for interstitial tissue, neglectingthe contribution to flow resistancedue to intercellular fibers asglycosaminoglycansor proteoglycans (8). Parameter IY, also named Kozeny’s parameter or Kozeny’s function, describing the “tortuosity” of path, dependson geometrical characteristics and disposition of obstaclesconstituting the meshand may be expressedas a function of E.Happel and Brenner (4) developedthe theoretical dependenceof K on c considering a bed of cylindrical fibers variously oriented relative to the flow direction. They calculated the dependenceof K on c in the caseof fibers oriented either parallel (I$,) or at right angle (IQ relative to the direction of flow, obtaining the following equations
K,(4 =
For a random orientation of the fibers, the following relationship holds
K remainsfairly stable for Eranging from 0.3 to 0.8, whereasit increasessharply for c approaching 1 (namely a high fractional void volume). This research was supported by the Italian Ministry of the University and Scientific Research, by National Research Council Grant CT89.03944, and partly by Grant PSN-87-042.
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2516
INTRAPLEURAL
Address for reprint Umana, Via Mangiagalli
requests: G. Miserocchi, Istituto di Fisiologia 32, 20133 Milan, Italy. Received 8 August 1991; accepted in final form 9 July 1992. REFERENCES
E., G. MI~ER~CCHI AND M. V. BONANNI. Thickness and pressure of the pleural liquid in some mammals. R&r. Physiol. 6:
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245-256,1969. 2. ALBERTINE,
K. H., J. P. WIENER-KRONISH, J. BASTACKY, AND N. C. STAUB. No evidence for mesothelial cell contact across the costal pleural space of sheep. j. Appl. Physiol. 70: 123-134, 1991. 3. BUTLER, J. P., T. A. WILSON, AND S. H. LORING. Lung motion can contribute to regulation of pleural fluid thickness (Abstract). FA-
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LOW Reynolds
Number
Hydrodynam-
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FLUID
FLUXES
phragm in setting liquid pressure in the serous cavities. Respir. Physiol. 50: 381-392, 1982. 13, MISEROCCHI, G., AND D. NEGRINI.
Contribution of Starling and lymphatic flows to pleural liquid exchange in anesthetized rabbits.
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tures of Starling-lymphatic interaction at pleural level in mammals. J. Appl. Physiol. 56: 1151-1156, 1984. 17. MISEROCCHI, G., D. NEGRINI, M. PISTOLESI, C. R. BELLINA, M. C. GILARDI, V. BETTINARDI, AND F. ROSSITTO. Intrapleural flow down a gravity-dependent hydraulic pressure gradient. J. Appl. Physiol. 64: 577-584, 1988. 18. MISEROCCHI, G., M. PISTOLESI, M. MINIATI, C. R. BELLINA, D. NEGRINI, AND C. GIUNTINI. Pleural liquid pressure gradients and intrapleural distribution of injected bolus. J. Appl. Physiol. 56: 526532, 1984. 19. NEGRINI, D., C. CAPELLI, M. MORINI, AND G. MISEROCCHI. Gravity
dependent distribution
of parietal subpleural interstitial
pressure.
7. LAI-FOOK, S. J., AND P. M. WANG. Movements of fluorescent microspheres along lobar margin in the pleural space due to cardiogenic motion (Abstract). FASEB J. 5: A747, 1991. 8. LEVICK, J. R. Flow through interstitium and other fibrous matri-
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