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Diffusion of oxygen from gas pockets to capillaries
257-265(1969)
MICROVASCULARRESEARCHl,
Diffusion
of Oxygen
HUGHD.VANLIEW,WARRENH.
from
Gas
Pockets
SCHOENFISCH,*AND
to Capillaries* MICHAEL
M. GOLDBERG~
Depar fment of Physiology, State University of New York at Buffalo, B&alo, New York 14214 Received July 16, 1968 Exit rate of 0, from subcutaneous gas pockets in unanesthetized rats was studied at 1 atm pressure, breathing air or pure 02, and in a hyperbaric environment, breathing 1 atm of 02, remainder N2. The findings were (a) rats had lower 0, exit rate( &)when breathingOz thanwhenbreathingair,and(b)atlowP,,,,curvesof vO:b, vs pocket PO, were concave downward but changed to linear or concave upward above 1 atm. These data are consistent with a model which assumes that 0, diffuses through tissueuntilit meets a capillary and that the means by which blood carries O2 changesaspocketPd,increases: Hbdoesnot becomesaturatedatlowP,,, butdoesat higher PO,, and physical solution becomes important at very high PO,. The success of the model implies that for diffusion of gases, the tissue-capillary milieu approximates a homogeneous medium in which both diffusion and clearance take place at the same time and at every location. INDEX DESCRIPTORS: Blood gases; Capillaries; Diffusion; Gas pockets; Hemoglobin; Oxygen; Tissue gases.
The rat subcutaneous gas pocket preparation introduced by Rahn and Canheld (1955) allows quantitative measurement of a depot of gas surrounded by tissue, and therefore can be used to study exchange across a gas-tissue interface. Oxygen exchanges are particularly challenging because of the complexities of O2 carriage in blood. Investigations with 0, in gas pockets have shown several intriguing features : (a) Blood flow seems to have only a minor effect, for 0, leaves pockets of freshly killed rats almost as rapidly as in live ones (Van Liew, 1962a, 1968a); (b) exit rate of O2 (ljoJ increases as pocket PO, increases, but not in a linear manner-the slope of the curve of Tioz vs. pocket PO, decreases at PO2between 100 and 600 mm Hg (Piiper, 1963; Van Liew, 1968a); and (c) behavior of oxygen in the pocket is markedly affected by the presence of carbon monoxide in the pocket (Wilks, 1959; Ryo, 1964; Van Liew, 1968b). These phenomena cannot be explained by two early models that were discussed and rejected
by Piiper,
Canfield,
a strictly di.ffusion-limited
and Rahn (1962) and Van Liew (1962a).
If the pocket were
system, with all resistance to diffusion concentrated in one
barrier and perfect stirring beyond, there should be no interaction between CO and 02, and vo, should be a straight line function of the difference between pocket and tissue PO,. If the pocket operated as a strictly perfusion-limited system similar to the
lung, in which a certain amount of blood per unit of time comes into equilibrium with the gas in the pocket, PO, should tend to level off when pocket PO, is above 100 mm Hg because Hb of blood
would
be saturated.
i This work was supported in part by the U.S. Air Force, Air Force Systems Command, Aerospace Medical Division, and by ONR contract Nonr 969W). * Graduate Fellow under the USPHS Physiology Training Program. 3 Medical Student supported by USPHS Summer Research Fellowship Program. 257
258
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
A third possibility is a partially perfusion-limited system (Piiper, Canfield and Rahn, 1962; Van Liew, 1962a). According to this model, blood in a certain number of capillaries picks up gas but does not reach equilibrium with the pocket gas because of a diffusion barrier between the pocket and the blood. In this case, vo2 should tend to level off also, but at pocket PO, well above 100 mm Hg, for PO2 in the blood would be less than in the pocket. Preliminary data with CO supported this model; in intestinal segments, CO exit rate was constant when PC0 was above 400 mm Hg (Forster, 1967). However, in the experiment of this paper, O2 exit rate was studied at pocket PO, up to 3000 mm Hg, and instead of leveling off, the curve became steeper at the highest PO, values. The present data will be discussed in connection with a fourth model which is based on the assumption that gas molecules diffuse varying distances into the tissue until they enter capillaries and are removed from the system as the blood leaves via the veins (Van Liew, 1968a, 1968b). The volume of tissue taking part in gas exchange varies from one situation to another, or with different gases, so the amount of blood that participates in gas carriage varies also. This is in marked contrast to the assumption that a given amount of blood becomes partly equilibrated, which is implicit in the “partial perfusion limitation” model mentioned above. METHODS Gas pockets were formed on the backs of young adult female Wistar rats by injection of 30 ml of air subcutaneously at least 1 week prior to the beginning of the experiments. The pockets were maintained at approximately 30 ml by addition of a few milliliters of air every few days. Total volume of these pockets can be measured by withdrawing all the gas into a calibrated syringe, noting the volume, and then reinjecting the gas. Composition of the gas can be measured with a small aliquot analyzed on the 0.5 ml apparatus of Scholander (1947). Exit rate of O2 was calculated from total pocket volume and pocket composition at the beginning and end of a carefully timed period of 2 or 3 hr. Before the beginning of the timed period, pocket composition was kept near the intended test composition for at least 20 min to minimize unsteady state effects, such as reversible solution of gas in the pocket wall. During the experimental periods, the unanesthetized rats breathed either (a) air at 1 atm (b) pure O2 at 1 atm, or (c) 1 atm of O2 at 2,4, or 4.5 atm (absolute) in a hyperbaric chamber, with N2 being the remainder of the inspired gas. When test gas in the pocket had high O2 concentration in the hyperbaric experiments, pocket O2 could be as much as 4.5 atm but tissue O2 would be approximately the same as that of rats breathing O2 at 1 atm. For the various environments, the rats were kept in 7-liter glass jars supplied with a flow of 1 or 2 liters/min of appropriate gas from a compressed-gas cylinder, except in the experiments at 4 and 4.5 atm, in which the rats were kept in their cages in the hyperbaric chamber breathing 24 % O2 (4 atm) or air (4.5 atm), both of which gave PIoz of approximately 700 mm Hg. In all situations, PIcoz was less than 4 mm Hg. Average PO1 in the pocket during a timed period was taken as the arithmetic mean of the initial and final values. Measured gas volumes were corrected to standard conditions with the assumptions that temperature of the measuring syringe was 30”, near the
DIFFUSION OF o2 INTO TISSUE CAPILLARIES
259
temperature of the operator’s hand, that temperature in the gas pocket was 3’7, the average rectal temperature of the rats, and that total pressure inside the pocket was the same as the prevailing atmosphere, since the pocket walls are loose and flaccid. In the hyperbaric experiments, to compensate for the decrease of gas volume due to compression, additional test gas was injected into the pockets after reaching pressure. Measurement of volume and taking of samples were done at pressure inside the chamber. In all, 60 rats were used and each rat was used 2-4 times. To minimize bias due to individual differences between rats, to age of the pockets, or to effects of previous treatments, no rat was given the same test gas in the pocket more than once, and the different breathing gases were administered in random order. Data on N2 exit rates, obtained simultaneously with the O2 data, will be presented separately (Van Liew, Schoenfisch, and Olszowka, 1968). RESULTS Figure 1 shows that when the rats breathe pure oxygen at 1 atm (lower curve and open circles), the vO, from subcutaneous pockets is less at every pocket PO2than when the rats breathe air (upper curve and closed circles). Each point on the figure is mean and .05T
FIG. 1. Exit rate of O2 vs. pocket Po, in rats breathing air (closed circles) or breathing 100’~ O2 (open circles) at 1 atmosphere. Derived from 90 data points on 24 rats.
standard error of lo-12 measurements, grouped according to the original composition of the test gas (zero, 20, 50, or 100 % 02, with N2 the remainder). The intercepts of the data curves of Fig. 1 with the PO, axis, where PO2in the pocket is presumably near equilibrium with PO,of the tissue, are approximately 35 mm Hg in air-breathing and 65 mm Hg in O,-breathing. Figure2 shows the data obtainedwith very high pocket PO2in the hyperbaric chamber. Each point is a mean with SE of 11-16 experimental values grouped according to pocket Pol. Variability increases in proportion to environmental pressure because inherent error of measurement with the syringe is the same at any pressure, but in hyperbaric experiments it represents a greater volume of gas when reduced to standard conditions.
260
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
P I
7
nP
. 0 a2 A n 0
P
,
1000
2OQct
atm t land2
2 and4 4 4.5
3000
mm Hg
6
2. Exit rate of O2 with high PO, in the pocket, I& determinations with 36 rats. The symbols indicate the environmental pressure; the rats breathed 1 atm of O2 at all pressures. FIG.
The curve at the lower left is the O,-breathing data of Fig. 1, and it is seen that the two different experiments fit together well, although the data were obtained with different rats and by different operators. The overall trend of the data of Fig. 2 shows Ti,, to be more or less a linear function of pocket PO,. However, three investigations have shown that below 1 atm, voio2is a
70 ’ mmHg i
_.-*
. ...‘.
mm PO 2 ’
Hg
FIG. 3. Pocket PcoB vs. pocket Pof, both at the end of the experimental periods. The PCOpr which reflects local tissue Pco,, rises with increasing P op. at least partly due to the CDH effect (see Discussion). Open circles, rats breathe one atmosphere of O2 at normal and hyperbaric pressure; closed circles, rats breathe air at normal pressure.
DIFFUSION
OF o2 INTO
TISSUE
CAPILLARIES
261
concave-downward, curvilinear function of P02: (a) the work of Piiper (1963) ; (b) one of our papers (1968a); and (c) the data of Fig. 1. Therefore it must be concluded that ljof as a function of PO, changes at about 1500 mm Hg from concave-downward to linear or concave-upward. Since CO2 exchanges of gas pockets are relatively rapid (Van Liew, 1962b), CO2 had time to come near to tissue P ,-03 by the end of the experimental period even though O2 and N2 were far from equilibrium. Figure 3 shows the PcOz at the end of the experimental periods, plotted against the PO, at the end of the periods. Each point is mean with SE of points grouped according to PO,. Open circles are for rats breathing the equivalent of 1 atm of 02, both at normal pressure and in a hyperbaric environment (obtained with the data shown in Figs. 1 and 2), and closed circles are for air-breathing rats (obtained with data shown in Fig. 1). It is seen that Pc02 rises with increasing PO, in the pocket and that at a given PO2 the Pcoz in O,-breathing rats is higher than in air-breathing rats. The curves are drawn by eye. DISCUSSION An important implication of our model (Van Liew, 1968a, 1968b) concerns the tissuecapillary milieu. The model assumes that each infinitesimally small region of tissue operates in two ways: Gas diffuses through it, and it acts as a capillary in that gas disappears within it. The only allowance that is made for the channeling of blood through discrete vessels is the introduction of a coefficient of end-capillary equilibration (see Van Liew, 1968a). Warburg (1923) and Greven (1959) used the same type of equations with oxygen uptake of excised, metabolizing tissue. It is well known that oxygen utilization is mainly limited to mitochondria, but the success of the equations shows that mitochondria are small enough and well enough dispersed that the tissue operates as though it were homogeneous. The implication of the present work is that the assumption of functional homogeneity is feasible on an even larger scale in the case of removal of gases from tissue by capillary blood flow; apparently in the context of the diffusivity of gases, capillaries are also small and well dispersed so that the tissue approximates a homogeneous medium. Below are the details of the application of the model to the data of this paper. Blood Carriage of O2 vs. P,,. The mathematical basis of the model is that disappearance or removal of gas from tissue is proportional to the second derivative of P, the pressure of the gas, with respect to x, the distance from the gas-tissue interface. The value of this second derivative depends on the means by which the gas disappears. For example, LIZP/dx2 equals a constant when O2 disappears only by means of metabolism, because metabolic rate per volume of the tissue is constant. This is also the case where the amount of gas removed by each unit of blood is constant, as when hemoglobin of blood picks up a given quantity of CO or 02. According to the derivation (Van Liew, 1968a), O2 exit rate from the pocket, vo,, is a function of the square root of pocket PO, if Hb becomes saturated before blood leaves the capillaries. Between pocket PO, of 350 and 650 mm Hg, exit rate results were a good fit of a square root curve (Van Liew, 1968a). Apparently blood hemoglobin became saturated in a large region so that this means of carriage of 02 dominated the exit rate.
262
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
The square root function is not expected to apply at low PO, (for then Hb would not reach saturation), nor at very high PO, (where in addition to carriage by Hb, appreciable amounts of O2 are carried in physical solution). When the pocket contains O2 at 4 atm, blood nearest the pocket might pick up 5 or 10 vol % of O2 on hemoglobin, plus like quantities in physical solution (solubility of O2 is 2.3 vol % per atm). Because the means by which blood carries O2 changes as PO, changes, the IjoZ vs. PO, curve can be arbitrarily divided into three regions: (a) where hemoglobin picks up O2 but does not become saturated (below 350 mm Hg, at the left of Fig. 1); (b) where hemoglobin becomes saturated but PO, is not high enough to allow appreciable amounts of O2 to be carried in physical solution in blood (perhaps from PO, = 350 to 800 mm (Fig. 2)), and (c) where in addition to carriage by Hb, appreciable amounts of O2 are carried in physical solution (at the right of Fig. 2). Where Hb is Saturated. Equation (1) gives O2 exit rate when Hb is saturated but dissolved O2 is not important (Van Liew, 1968a) : Ijo = A%‘& D(C, - Cv) &P, - P,).
(1)
In Eq. (l), p,,, is exit rate of 02, ml sTPDper min; A is total surface area of the pocket wall, cm2; at is solubility of O2 in tissue, ml of O2 per ml of tissue per mm Hg; D is ditfusivity of O2 in tissue, cm* per min; C’sis O2 content of blood when Hb is saturated, ml of O2 per ml of blood (C, x 100 = O2 capacity in vol %); C, is O2 content the venous blood would have had if it had not picked up O2 from the pocket, or O2 content of venous blood beyond the influence of the pocket, ml of O2 per ml of blood; Q is perfusion to the tissue of the pocket wall, ml of blood per ml of tissue per min; and (P, -P,) is PO2 difference between the inside of the pocket and the tissue beyond the influence of the pocket, mm Hg. Equation (1) explains why ro, is lower with 02-breathing than with air-breathing (Fig. 1). Blood hemoglobin can only carry as much O2 away from the pocket site as it would ordinarily lose to metabolism. In air-breathers, the tissue’s metabolism is equal to blood flow times arteriovenous O2 difference, &C, - C,.), where C, is arterial O2 content. This is approximately equal to the content difference term in Eq. (1). With 02-breathing animals, C, is higher, and if e and metabolism do not change, C, must be higher, so the difference (C, - C,) of Eq. (1) must decrease, which causes ljof to be less. Similar reasoning explains the earlier finding that O2 exit rate from pockets in freshly killed rats is practically the same as in live rats (Van Liew, 1962a; 1968a). Assume that metabolism and O2 diffusion are equal in the surviving, metabolizing tissue of a freshly killed rat and in the perfused tissue of a live rat. The amount of O2 which disappears due to metabolism in a freshly killed rat is equal to the amount of O2 that can be added to Hb of blood flowing through the unit of volume in a live rat. Where Physical Solution is Important. When PO, is very high, as in the hyperbaric experiments, the amount of O2 carried on Hb equals &C, - C,) and the amount carried by physical solution is (kP - PJ 0 a,,, where ab is solubility in blood. The k is a coefficient of end-capillary equilibration and can have a value between zero and 1 (Van Liew, 1968a).
263
DIFFUSION OF o2 INTO TISSUE CAPILLARIES
The initial differential equation is: d2 P/dx2 = & t
[&cs - c,) + d,, ek(P - P,/k)].
The solution of Eq. 2 is:
1 .
As with a gas which is carried only in physical solution (Van Liew, Schoenfisch, and Olszowka, 1968), the solution shows Fi to be a straight line function of P. To put Eq. (3) to a quantitative test, the hatched area of Fig. 4 shows the data of Fig. 2 as a confidence interval (mean 5 2 SE). Three theoretical lines are included also:
FIG. 4. Theoretical lines and data for 0, exit rate vs. PO,. The solid line is predicted from text Eq. (3) and values from Table 1, and the dotted line shows the effect of a 30% change of solubility. The dashed line shows the result expected in a “partially perfusion-limited” system.
(a) The dashed line, lowest on the graph, shows what would be expected if the gas pocket were the type of perfusion-limited system in which a given amount of blood becomes partially equilibrated with gas in the pocket. The line shows the linear rise as O2 is added to the blood in physical solution, assuming that Hb saturates when pocket PO, is 500 mm Hg, that the blood flow involved in gas exchange is 0.5 ml/min (from vo, at 500 mm Hg divided by a (C, - C,) of 6 vol %), and that solutility of O2 is 2.3 vol %/ atm. (b) The solid line was drawn from Eq. (3), the parameters of Table 1, and the intercept of O2 breathing data of Fig. 1 for the value of P,/k. It is apparent that this solid line is more nearly consistent with the data than the dashed lower line. (c) The dotted line, highest on the figure, was drawn from Eq. (3), but for a 30% increase of TVover the value given in Table 1. It is seen that this change brings the theory and
264
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
data closer together at the extreme right side of the diagram. It is important to remember that the data should not fit the theoretical curves at the extreme left side of the diagram, for there the theory does not cover the actual means by which blood carries Oz. The discrepancy between the theoretical solid line on Fig. 4 and the data could have several explanations: (a) The very simple basic assumptions concerning the functional geometry of the tissues and capillaries may be inadequate, so although the theoretical solid line is better than the dashed line, the premises still are not sophisticated enough to give a perfect fit. (b) The values of parameters used in the calculations may not be correct. For example, the solubility factor of Table 1 is for a lean tissue; if there were much fat in the wall of the gas pockets, physical solubility might easily be higher, and the dotted line shows that the 30% increase of CLgave a considerable change. (c) It is possible that one of the parameters is a function of PO,. High PO, may affect local blood flow, or perhaps the effective k changes with PO, as physical solution becomes more TABLE
I
ASSUMPTIONSEORPHYSICALCONSTANTSANDPHYSIOLOGICALPARAMETERS
Reference
A aoaa DO, 0
60cm* 3.0x 10msmm Hg-’ 5.7 x 10m4cm* min-’ 0.37 min-’
>
Van Liew, 1962a Bartels and Opitz, 1958 and Krogh, 1936 Van Liew, 1968a
’ Assume Q = a,,.
important. (d) Finally, it is possible that physiological state of the animal changes at high pressure due to such factors as nitrogen narcosis, or altered respiration due to increased work of breathing the dense gas. The high pocket Pco2 at high pocket PO2(data of Fig. 3) suggests decrease of blood flow at high Paz. However, it is not readily put into quantitative terms, for the Christiansen, Douglas, Haldane effect can be expected to increase PC,, under this condition also. As Hb becomes saturated with O2 which diffuses from the pocket to the blood, the increased acidity of Hb liberates CO2 from bound forms. The liberated CO2 tends to diffuse away, but as the tissue region in which Hb becomes saturated with O2 becomes larger and larger, the Pcoz of the region will become nearer and nearer a maximal Pco,. The maximum can be estimated from the maximal amount of CO2 which can be liberated from blood when Hb goes from reduced to oxygenated form. An analogous phenomenon, liberation of O2 from Hb by carbon monoxide, has been discussed in detail elsewhere (Van Liew, 1968b). The CDH effect will increase Pco, a maximum of IO-15 mm Hg, depending on the CO2 content (Sherwood Jones et al., 1950). During air-breathing, the normal venous blood of the tissue around the rat pocket is 30% saturated (Pco, = 45 from Fig. 3, PO, = 35 from Fig. l), and the rat nomogram (Sherwood Jones et al., 1950) predicts that addition of O2 saturation would change Pco, to 55 mm Hg. This is consistent with the data for air-breathing rats in Fig. 3; there is a suggestion at the right that Pco, will
DIFFUSION
OF o2 INTO
TISSUE
265
CAPILLARIES
level off at 55 mm Hg. This explanation can be interpreted to mean that the entire PC,, elevation for air-breathing rats seen on Fig. 3 may be a consequence of the CDH effect. The Pco, data of the O,-breathing rats, Fig. 3, can at least partly be explained by the same reasoning. The blood-gas nomogram predicts increase of Pco, from 55 to 60 when hemoglobin goes from 70% saturated (PO, = 65; PC,, = 55) to complete saturation, about half the observed rise of Fig. 3. These estimates of the CDH effect are necessarily crude because the nomogram may be inadequate or because of high-pressure effects on pulmonary ventilation, but the general conclusion must be that if there is a blood flow change at all, it is in the direction of a decreased flow at pocket PO,above 1500 mm Hg. Decrease of blood flow would cause the theoretical solid line of Fig. 4 to have a higher intercept because of a larger (Cs - C,) term in Eq. 3, with the result that the new line could be made to go through the data at the right side of the figure. ACKNOWLEDGMENT
We are very much indebted to Dr. Edward H. Lanphier, Mr. Richard A. Morin and Mr. Michael P. Hlastala for help with the hyperbaric experiments. REFERENCES BARTELS, H., AND OPITZ, E. (1958). In “Handbook of Respiration” (D. S. Dittmer and R. M. Grebe, eds.), Tables 12, 13 and 14. Saunders, Philadelphia. FORSTER,R. E. (1967). Gustroenterology 52,381. GREVEN, K. (1959). Pfltigers Arch. 269, 38. KROGH, A. (1936). “Anatomy and Physiology of Capillaries.” Yale Univ. Press, New Haven. PIIPER,J., CANRELD, R. E., AND RAHN, H. (1962). J. Appi. Physiol. 17,268. PILPER,J. (1963). Am. J. Physiol. 205,1005. RAHN, H., AND CANFIELD, R. E. (1955). Wright Air Development Center Technical Report 55357,395. RYO, U. Y. (1964). J. Korean Med. Assoc. 7, 1. SCHOLANDER,P. F. (1947). J. Biol. Chem. 167,235. SHERWOODJONES,E., MAEGRAITH, B. G., AND SCULTHORPE,H. H. (1950). Ann. Trop. Med. Parusitol. 44,168.
VAN LIEW, K-I. D. (1962a). Am. J. Physiol. 202,53. VAN LIEW, H. D. (1962b). J. Appl. Physioi. 17,851. VAN LIEW, H. D. (1968a). Am. J. Physiol. 214, 1176. VAN LIEW, H. D. (1968b). Respir. Physiol. 5,202. VAN LIEW, H. D., SCHOENFISCH,W. H., AND OLSZOWSKA, A. J. (1968). Respir. WARBURG, 0.(1923). Biochem.Z. 142,317. WILKS, S. S. (1959). J. Appl. Physiol. 14, 311.
Physiol.
In press.
MICROVASCULARRESEARCHl,
Diffusion
of Oxygen
HUGHD.VANLIEW,WARRENH.
from
Gas
Pockets
SCHOENFISCH,*AND
to Capillaries* MICHAEL
M. GOLDBERG~
Depar fment of Physiology, State University of New York at Buffalo, B&alo, New York 14214 Received July 16, 1968 Exit rate of 0, from subcutaneous gas pockets in unanesthetized rats was studied at 1 atm pressure, breathing air or pure 02, and in a hyperbaric environment, breathing 1 atm of 02, remainder N2. The findings were (a) rats had lower 0, exit rate( &)when breathingOz thanwhenbreathingair,and(b)atlowP,,,,curvesof vO:b, vs pocket PO, were concave downward but changed to linear or concave upward above 1 atm. These data are consistent with a model which assumes that 0, diffuses through tissueuntilit meets a capillary and that the means by which blood carries O2 changesaspocketPd,increases: Hbdoesnot becomesaturatedatlowP,,, butdoesat higher PO,, and physical solution becomes important at very high PO,. The success of the model implies that for diffusion of gases, the tissue-capillary milieu approximates a homogeneous medium in which both diffusion and clearance take place at the same time and at every location. INDEX DESCRIPTORS: Blood gases; Capillaries; Diffusion; Gas pockets; Hemoglobin; Oxygen; Tissue gases.
The rat subcutaneous gas pocket preparation introduced by Rahn and Canheld (1955) allows quantitative measurement of a depot of gas surrounded by tissue, and therefore can be used to study exchange across a gas-tissue interface. Oxygen exchanges are particularly challenging because of the complexities of O2 carriage in blood. Investigations with 0, in gas pockets have shown several intriguing features : (a) Blood flow seems to have only a minor effect, for 0, leaves pockets of freshly killed rats almost as rapidly as in live ones (Van Liew, 1962a, 1968a); (b) exit rate of O2 (ljoJ increases as pocket PO, increases, but not in a linear manner-the slope of the curve of Tioz vs. pocket PO, decreases at PO2between 100 and 600 mm Hg (Piiper, 1963; Van Liew, 1968a); and (c) behavior of oxygen in the pocket is markedly affected by the presence of carbon monoxide in the pocket (Wilks, 1959; Ryo, 1964; Van Liew, 1968b). These phenomena cannot be explained by two early models that were discussed and rejected
by Piiper,
Canfield,
a strictly di.ffusion-limited
and Rahn (1962) and Van Liew (1962a).
If the pocket were
system, with all resistance to diffusion concentrated in one
barrier and perfect stirring beyond, there should be no interaction between CO and 02, and vo, should be a straight line function of the difference between pocket and tissue PO,. If the pocket operated as a strictly perfusion-limited system similar to the
lung, in which a certain amount of blood per unit of time comes into equilibrium with the gas in the pocket, PO, should tend to level off when pocket PO, is above 100 mm Hg because Hb of blood
would
be saturated.
i This work was supported in part by the U.S. Air Force, Air Force Systems Command, Aerospace Medical Division, and by ONR contract Nonr 969W). * Graduate Fellow under the USPHS Physiology Training Program. 3 Medical Student supported by USPHS Summer Research Fellowship Program. 257
258
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
A third possibility is a partially perfusion-limited system (Piiper, Canfield and Rahn, 1962; Van Liew, 1962a). According to this model, blood in a certain number of capillaries picks up gas but does not reach equilibrium with the pocket gas because of a diffusion barrier between the pocket and the blood. In this case, vo2 should tend to level off also, but at pocket PO, well above 100 mm Hg, for PO2 in the blood would be less than in the pocket. Preliminary data with CO supported this model; in intestinal segments, CO exit rate was constant when PC0 was above 400 mm Hg (Forster, 1967). However, in the experiment of this paper, O2 exit rate was studied at pocket PO, up to 3000 mm Hg, and instead of leveling off, the curve became steeper at the highest PO, values. The present data will be discussed in connection with a fourth model which is based on the assumption that gas molecules diffuse varying distances into the tissue until they enter capillaries and are removed from the system as the blood leaves via the veins (Van Liew, 1968a, 1968b). The volume of tissue taking part in gas exchange varies from one situation to another, or with different gases, so the amount of blood that participates in gas carriage varies also. This is in marked contrast to the assumption that a given amount of blood becomes partly equilibrated, which is implicit in the “partial perfusion limitation” model mentioned above. METHODS Gas pockets were formed on the backs of young adult female Wistar rats by injection of 30 ml of air subcutaneously at least 1 week prior to the beginning of the experiments. The pockets were maintained at approximately 30 ml by addition of a few milliliters of air every few days. Total volume of these pockets can be measured by withdrawing all the gas into a calibrated syringe, noting the volume, and then reinjecting the gas. Composition of the gas can be measured with a small aliquot analyzed on the 0.5 ml apparatus of Scholander (1947). Exit rate of O2 was calculated from total pocket volume and pocket composition at the beginning and end of a carefully timed period of 2 or 3 hr. Before the beginning of the timed period, pocket composition was kept near the intended test composition for at least 20 min to minimize unsteady state effects, such as reversible solution of gas in the pocket wall. During the experimental periods, the unanesthetized rats breathed either (a) air at 1 atm (b) pure O2 at 1 atm, or (c) 1 atm of O2 at 2,4, or 4.5 atm (absolute) in a hyperbaric chamber, with N2 being the remainder of the inspired gas. When test gas in the pocket had high O2 concentration in the hyperbaric experiments, pocket O2 could be as much as 4.5 atm but tissue O2 would be approximately the same as that of rats breathing O2 at 1 atm. For the various environments, the rats were kept in 7-liter glass jars supplied with a flow of 1 or 2 liters/min of appropriate gas from a compressed-gas cylinder, except in the experiments at 4 and 4.5 atm, in which the rats were kept in their cages in the hyperbaric chamber breathing 24 % O2 (4 atm) or air (4.5 atm), both of which gave PIoz of approximately 700 mm Hg. In all situations, PIcoz was less than 4 mm Hg. Average PO1 in the pocket during a timed period was taken as the arithmetic mean of the initial and final values. Measured gas volumes were corrected to standard conditions with the assumptions that temperature of the measuring syringe was 30”, near the
DIFFUSION OF o2 INTO TISSUE CAPILLARIES
259
temperature of the operator’s hand, that temperature in the gas pocket was 3’7, the average rectal temperature of the rats, and that total pressure inside the pocket was the same as the prevailing atmosphere, since the pocket walls are loose and flaccid. In the hyperbaric experiments, to compensate for the decrease of gas volume due to compression, additional test gas was injected into the pockets after reaching pressure. Measurement of volume and taking of samples were done at pressure inside the chamber. In all, 60 rats were used and each rat was used 2-4 times. To minimize bias due to individual differences between rats, to age of the pockets, or to effects of previous treatments, no rat was given the same test gas in the pocket more than once, and the different breathing gases were administered in random order. Data on N2 exit rates, obtained simultaneously with the O2 data, will be presented separately (Van Liew, Schoenfisch, and Olszowka, 1968). RESULTS Figure 1 shows that when the rats breathe pure oxygen at 1 atm (lower curve and open circles), the vO, from subcutaneous pockets is less at every pocket PO2than when the rats breathe air (upper curve and closed circles). Each point on the figure is mean and .05T
FIG. 1. Exit rate of O2 vs. pocket Po, in rats breathing air (closed circles) or breathing 100’~ O2 (open circles) at 1 atmosphere. Derived from 90 data points on 24 rats.
standard error of lo-12 measurements, grouped according to the original composition of the test gas (zero, 20, 50, or 100 % 02, with N2 the remainder). The intercepts of the data curves of Fig. 1 with the PO, axis, where PO2in the pocket is presumably near equilibrium with PO,of the tissue, are approximately 35 mm Hg in air-breathing and 65 mm Hg in O,-breathing. Figure2 shows the data obtainedwith very high pocket PO2in the hyperbaric chamber. Each point is a mean with SE of 11-16 experimental values grouped according to pocket Pol. Variability increases in proportion to environmental pressure because inherent error of measurement with the syringe is the same at any pressure, but in hyperbaric experiments it represents a greater volume of gas when reduced to standard conditions.
260
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
P I
7
nP
. 0 a2 A n 0
P
,
1000
2OQct
atm t land2
2 and4 4 4.5
3000
mm Hg
6
2. Exit rate of O2 with high PO, in the pocket, I& determinations with 36 rats. The symbols indicate the environmental pressure; the rats breathed 1 atm of O2 at all pressures. FIG.
The curve at the lower left is the O,-breathing data of Fig. 1, and it is seen that the two different experiments fit together well, although the data were obtained with different rats and by different operators. The overall trend of the data of Fig. 2 shows Ti,, to be more or less a linear function of pocket PO,. However, three investigations have shown that below 1 atm, voio2is a
70 ’ mmHg i
_.-*
. ...‘.
mm PO 2 ’
Hg
FIG. 3. Pocket PcoB vs. pocket Pof, both at the end of the experimental periods. The PCOpr which reflects local tissue Pco,, rises with increasing P op. at least partly due to the CDH effect (see Discussion). Open circles, rats breathe one atmosphere of O2 at normal and hyperbaric pressure; closed circles, rats breathe air at normal pressure.
DIFFUSION
OF o2 INTO
TISSUE
CAPILLARIES
261
concave-downward, curvilinear function of P02: (a) the work of Piiper (1963) ; (b) one of our papers (1968a); and (c) the data of Fig. 1. Therefore it must be concluded that ljof as a function of PO, changes at about 1500 mm Hg from concave-downward to linear or concave-upward. Since CO2 exchanges of gas pockets are relatively rapid (Van Liew, 1962b), CO2 had time to come near to tissue P ,-03 by the end of the experimental period even though O2 and N2 were far from equilibrium. Figure 3 shows the PcOz at the end of the experimental periods, plotted against the PO, at the end of the periods. Each point is mean with SE of points grouped according to PO,. Open circles are for rats breathing the equivalent of 1 atm of 02, both at normal pressure and in a hyperbaric environment (obtained with the data shown in Figs. 1 and 2), and closed circles are for air-breathing rats (obtained with data shown in Fig. 1). It is seen that Pc02 rises with increasing PO, in the pocket and that at a given PO2 the Pcoz in O,-breathing rats is higher than in air-breathing rats. The curves are drawn by eye. DISCUSSION An important implication of our model (Van Liew, 1968a, 1968b) concerns the tissuecapillary milieu. The model assumes that each infinitesimally small region of tissue operates in two ways: Gas diffuses through it, and it acts as a capillary in that gas disappears within it. The only allowance that is made for the channeling of blood through discrete vessels is the introduction of a coefficient of end-capillary equilibration (see Van Liew, 1968a). Warburg (1923) and Greven (1959) used the same type of equations with oxygen uptake of excised, metabolizing tissue. It is well known that oxygen utilization is mainly limited to mitochondria, but the success of the equations shows that mitochondria are small enough and well enough dispersed that the tissue operates as though it were homogeneous. The implication of the present work is that the assumption of functional homogeneity is feasible on an even larger scale in the case of removal of gases from tissue by capillary blood flow; apparently in the context of the diffusivity of gases, capillaries are also small and well dispersed so that the tissue approximates a homogeneous medium. Below are the details of the application of the model to the data of this paper. Blood Carriage of O2 vs. P,,. The mathematical basis of the model is that disappearance or removal of gas from tissue is proportional to the second derivative of P, the pressure of the gas, with respect to x, the distance from the gas-tissue interface. The value of this second derivative depends on the means by which the gas disappears. For example, LIZP/dx2 equals a constant when O2 disappears only by means of metabolism, because metabolic rate per volume of the tissue is constant. This is also the case where the amount of gas removed by each unit of blood is constant, as when hemoglobin of blood picks up a given quantity of CO or 02. According to the derivation (Van Liew, 1968a), O2 exit rate from the pocket, vo,, is a function of the square root of pocket PO, if Hb becomes saturated before blood leaves the capillaries. Between pocket PO, of 350 and 650 mm Hg, exit rate results were a good fit of a square root curve (Van Liew, 1968a). Apparently blood hemoglobin became saturated in a large region so that this means of carriage of 02 dominated the exit rate.
262
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
The square root function is not expected to apply at low PO, (for then Hb would not reach saturation), nor at very high PO, (where in addition to carriage by Hb, appreciable amounts of O2 are carried in physical solution). When the pocket contains O2 at 4 atm, blood nearest the pocket might pick up 5 or 10 vol % of O2 on hemoglobin, plus like quantities in physical solution (solubility of O2 is 2.3 vol % per atm). Because the means by which blood carries O2 changes as PO, changes, the IjoZ vs. PO, curve can be arbitrarily divided into three regions: (a) where hemoglobin picks up O2 but does not become saturated (below 350 mm Hg, at the left of Fig. 1); (b) where hemoglobin becomes saturated but PO, is not high enough to allow appreciable amounts of O2 to be carried in physical solution in blood (perhaps from PO, = 350 to 800 mm (Fig. 2)), and (c) where in addition to carriage by Hb, appreciable amounts of O2 are carried in physical solution (at the right of Fig. 2). Where Hb is Saturated. Equation (1) gives O2 exit rate when Hb is saturated but dissolved O2 is not important (Van Liew, 1968a) : Ijo = A%‘& D(C, - Cv) &P, - P,).
(1)
In Eq. (l), p,,, is exit rate of 02, ml sTPDper min; A is total surface area of the pocket wall, cm2; at is solubility of O2 in tissue, ml of O2 per ml of tissue per mm Hg; D is ditfusivity of O2 in tissue, cm* per min; C’sis O2 content of blood when Hb is saturated, ml of O2 per ml of blood (C, x 100 = O2 capacity in vol %); C, is O2 content the venous blood would have had if it had not picked up O2 from the pocket, or O2 content of venous blood beyond the influence of the pocket, ml of O2 per ml of blood; Q is perfusion to the tissue of the pocket wall, ml of blood per ml of tissue per min; and (P, -P,) is PO2 difference between the inside of the pocket and the tissue beyond the influence of the pocket, mm Hg. Equation (1) explains why ro, is lower with 02-breathing than with air-breathing (Fig. 1). Blood hemoglobin can only carry as much O2 away from the pocket site as it would ordinarily lose to metabolism. In air-breathers, the tissue’s metabolism is equal to blood flow times arteriovenous O2 difference, &C, - C,.), where C, is arterial O2 content. This is approximately equal to the content difference term in Eq. (1). With 02-breathing animals, C, is higher, and if e and metabolism do not change, C, must be higher, so the difference (C, - C,) of Eq. (1) must decrease, which causes ljof to be less. Similar reasoning explains the earlier finding that O2 exit rate from pockets in freshly killed rats is practically the same as in live rats (Van Liew, 1962a; 1968a). Assume that metabolism and O2 diffusion are equal in the surviving, metabolizing tissue of a freshly killed rat and in the perfused tissue of a live rat. The amount of O2 which disappears due to metabolism in a freshly killed rat is equal to the amount of O2 that can be added to Hb of blood flowing through the unit of volume in a live rat. Where Physical Solution is Important. When PO, is very high, as in the hyperbaric experiments, the amount of O2 carried on Hb equals &C, - C,) and the amount carried by physical solution is (kP - PJ 0 a,,, where ab is solubility in blood. The k is a coefficient of end-capillary equilibration and can have a value between zero and 1 (Van Liew, 1968a).
263
DIFFUSION OF o2 INTO TISSUE CAPILLARIES
The initial differential equation is: d2 P/dx2 = & t
[&cs - c,) + d,, ek(P - P,/k)].
The solution of Eq. 2 is:
1 .
As with a gas which is carried only in physical solution (Van Liew, Schoenfisch, and Olszowka, 1968), the solution shows Fi to be a straight line function of P. To put Eq. (3) to a quantitative test, the hatched area of Fig. 4 shows the data of Fig. 2 as a confidence interval (mean 5 2 SE). Three theoretical lines are included also:
FIG. 4. Theoretical lines and data for 0, exit rate vs. PO,. The solid line is predicted from text Eq. (3) and values from Table 1, and the dotted line shows the effect of a 30% change of solubility. The dashed line shows the result expected in a “partially perfusion-limited” system.
(a) The dashed line, lowest on the graph, shows what would be expected if the gas pocket were the type of perfusion-limited system in which a given amount of blood becomes partially equilibrated with gas in the pocket. The line shows the linear rise as O2 is added to the blood in physical solution, assuming that Hb saturates when pocket PO, is 500 mm Hg, that the blood flow involved in gas exchange is 0.5 ml/min (from vo, at 500 mm Hg divided by a (C, - C,) of 6 vol %), and that solutility of O2 is 2.3 vol %/ atm. (b) The solid line was drawn from Eq. (3), the parameters of Table 1, and the intercept of O2 breathing data of Fig. 1 for the value of P,/k. It is apparent that this solid line is more nearly consistent with the data than the dashed lower line. (c) The dotted line, highest on the figure, was drawn from Eq. (3), but for a 30% increase of TVover the value given in Table 1. It is seen that this change brings the theory and
264
VAN
LIEW,
SCHOENFISCH,
AND
GOLDBERG
data closer together at the extreme right side of the diagram. It is important to remember that the data should not fit the theoretical curves at the extreme left side of the diagram, for there the theory does not cover the actual means by which blood carries Oz. The discrepancy between the theoretical solid line on Fig. 4 and the data could have several explanations: (a) The very simple basic assumptions concerning the functional geometry of the tissues and capillaries may be inadequate, so although the theoretical solid line is better than the dashed line, the premises still are not sophisticated enough to give a perfect fit. (b) The values of parameters used in the calculations may not be correct. For example, the solubility factor of Table 1 is for a lean tissue; if there were much fat in the wall of the gas pockets, physical solubility might easily be higher, and the dotted line shows that the 30% increase of CLgave a considerable change. (c) It is possible that one of the parameters is a function of PO,. High PO, may affect local blood flow, or perhaps the effective k changes with PO, as physical solution becomes more TABLE
I
ASSUMPTIONSEORPHYSICALCONSTANTSANDPHYSIOLOGICALPARAMETERS
Reference
A aoaa DO, 0
60cm* 3.0x 10msmm Hg-’ 5.7 x 10m4cm* min-’ 0.37 min-’
>
Van Liew, 1962a Bartels and Opitz, 1958 and Krogh, 1936 Van Liew, 1968a
’ Assume Q = a,,.
important. (d) Finally, it is possible that physiological state of the animal changes at high pressure due to such factors as nitrogen narcosis, or altered respiration due to increased work of breathing the dense gas. The high pocket Pco2 at high pocket PO2(data of Fig. 3) suggests decrease of blood flow at high Paz. However, it is not readily put into quantitative terms, for the Christiansen, Douglas, Haldane effect can be expected to increase PC,, under this condition also. As Hb becomes saturated with O2 which diffuses from the pocket to the blood, the increased acidity of Hb liberates CO2 from bound forms. The liberated CO2 tends to diffuse away, but as the tissue region in which Hb becomes saturated with O2 becomes larger and larger, the Pcoz of the region will become nearer and nearer a maximal Pco,. The maximum can be estimated from the maximal amount of CO2 which can be liberated from blood when Hb goes from reduced to oxygenated form. An analogous phenomenon, liberation of O2 from Hb by carbon monoxide, has been discussed in detail elsewhere (Van Liew, 1968b). The CDH effect will increase Pco, a maximum of IO-15 mm Hg, depending on the CO2 content (Sherwood Jones et al., 1950). During air-breathing, the normal venous blood of the tissue around the rat pocket is 30% saturated (Pco, = 45 from Fig. 3, PO, = 35 from Fig. l), and the rat nomogram (Sherwood Jones et al., 1950) predicts that addition of O2 saturation would change Pco, to 55 mm Hg. This is consistent with the data for air-breathing rats in Fig. 3; there is a suggestion at the right that Pco, will
DIFFUSION
OF o2 INTO
TISSUE
265
CAPILLARIES
level off at 55 mm Hg. This explanation can be interpreted to mean that the entire PC,, elevation for air-breathing rats seen on Fig. 3 may be a consequence of the CDH effect. The Pco, data of the O,-breathing rats, Fig. 3, can at least partly be explained by the same reasoning. The blood-gas nomogram predicts increase of Pco, from 55 to 60 when hemoglobin goes from 70% saturated (PO, = 65; PC,, = 55) to complete saturation, about half the observed rise of Fig. 3. These estimates of the CDH effect are necessarily crude because the nomogram may be inadequate or because of high-pressure effects on pulmonary ventilation, but the general conclusion must be that if there is a blood flow change at all, it is in the direction of a decreased flow at pocket PO,above 1500 mm Hg. Decrease of blood flow would cause the theoretical solid line of Fig. 4 to have a higher intercept because of a larger (Cs - C,) term in Eq. 3, with the result that the new line could be made to go through the data at the right side of the figure. ACKNOWLEDGMENT
We are very much indebted to Dr. Edward H. Lanphier, Mr. Richard A. Morin and Mr. Michael P. Hlastala for help with the hyperbaric experiments. REFERENCES BARTELS, H., AND OPITZ, E. (1958). In “Handbook of Respiration” (D. S. Dittmer and R. M. Grebe, eds.), Tables 12, 13 and 14. Saunders, Philadelphia. FORSTER,R. E. (1967). Gustroenterology 52,381. GREVEN, K. (1959). Pfltigers Arch. 269, 38. KROGH, A. (1936). “Anatomy and Physiology of Capillaries.” Yale Univ. Press, New Haven. PIIPER,J., CANRELD, R. E., AND RAHN, H. (1962). J. Appi. Physiol. 17,268. PILPER,J. (1963). Am. J. Physiol. 205,1005. RAHN, H., AND CANFIELD, R. E. (1955). Wright Air Development Center Technical Report 55357,395. RYO, U. Y. (1964). J. Korean Med. Assoc. 7, 1. SCHOLANDER,P. F. (1947). J. Biol. Chem. 167,235. SHERWOODJONES,E., MAEGRAITH, B. G., AND SCULTHORPE,H. H. (1950). Ann. Trop. Med. Parusitol. 44,168.
VAN LIEW, K-I. D. (1962a). Am. J. Physiol. 202,53. VAN LIEW, H. D. (1962b). J. Appl. Physioi. 17,851. VAN LIEW, H. D. (1968a). Am. J. Physiol. 214, 1176. VAN LIEW, H. D. (1968b). Respir. Physiol. 5,202. VAN LIEW, H. D., SCHOENFISCH,W. H., AND OLSZOWSKA, A. J. (1968). Respir. WARBURG, 0.(1923). Biochem.Z. 142,317. WILKS, S. S. (1959). J. Appl. Physiol. 14, 311.
Physiol.
In press.