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Measurement of Gastrointestinal Blood Flow by Means of Gas Absorption
Vol. 52, No.2, Part Z Printed in U.S.A.
GASTRO ENTEROLOGY
Copyright © 1967 by The Williams & Wilkins Co.
MEASUREMENT OF GASTROINTESTINAL BLOOD FLOW BY MEANS OF GAS ABSORPTION ROBERT
E.
FORSTER ,
M.D.
Department of Physiology, Division of Graduate Medicine, University of Pennsylvania, Phi ladelphia, Pennsylvania
Theoretically, the rate at which a biologically inert gas, such as N 2 0 or acetylene, is absorbed from a closed gas space in the body, such as a gas-filled portion of the gastrointestinal tract, depends at least in part upon the blood flow to the tissure enclosing the space. 1 This principle has been applied to the estimations of blood flow in subcutaneous pouches and in the gastrointestinal tract. 2 ,3 The mechanism of gas exchange from any closed pocket in the body is essentially the same in principle, and, owing to the paucity of data on the gastrointestinal tract, experimental results from measurements on subcutaneous gas pockets in rats 3 and in the bladder of the dog (R. Coburn, B. Luomanmaki, R. E. Forster, and S. Swerdlow, unpublished results) will be employed to predict results in the alimentary canal. The simplest arrangement for the bloodexchanging vessels in this system is diagramed in figure 1. There is no diffusion exchange in those vessels approaching the surface, but at the surface there is minimal resistance to diffusion between the blood and gas phases. A mathematical relationship between the blood flow in the tissue surface and the rate of disappearance of an inert gas from the gas space can be derived as follows. Assuming that the inert gas would reach diffusion equilibrium between the blood and gas phases and that there is a negligible concentration of this gas in arterial blood, then the rate at which the inert gas is carried away may be described, dP . V-=-QaP L dt
(1)
where V is the volume of the gas phase in milliliters; P is the partial pressure of the 381
inert gas in the lumen in fraction of an atmosphere; P L is that in the blood at the end of the capillary; t is the time in minutes; Q is the blood flow in milliliters per minute; and a is the solubility of the inert gas in the blood in milliliters per (milliliters X atmosphere). This can be integrated, giving (2)
By measuring the inert gas tension as a function of time, as by direct sampling, we can calculate the value of . the exponential constant in equation 2, and, if the solubility coefficient, a, and the volume of the phase are obtained, we can go on to calculate the blood flow, Q. This is analogous to the calculation of blood flow in the lungs from inert gas disappearance. 4 Radioactive xenon or, for that matter, any radioactive inert gas could be used for this purpose with the technical advantage that the amount of gas remaining in the intestine can be measured by external counting. The principle remains the same. Selkurt and Wathen, and Folkow (see p. 387 and p. 423 in this issue of Gastroenterology) discuss a related method, in which the radioactive xenon is introduced by injection into the arterial supply of the organ. However, it is not unfair to state that this theory does not fit the experimental findings very welJ.3 For example, in the case of subcutaneous gas bubbles, the rate of removal of different inert gases does not vary as predicted from their solubilities in blood. In other words, the value of the blood flow calculated from equation 2 varied with solubility, which it should not. This causes one to reexamine the validity of equation 1, in particular, the assumption that the exchange is blood flow-
382
FORSTER
LUMEN
LUMEN
INERT GAS
INERT GAS
. : . . : : : . : ; . : . . . . : . ' , I~tn~I ' ,-II
Vol. 52, No .2, Part 2
LUMEN INERT GAS
FIG. 1. A diagram of the gas-exchanging blood vessels in the surface tissues of a gas cavity. This is the simplest case with negligible resistance to diffusion at the surface and no exchange in the vessels conducting blood to the surface. FIG. 2. Adiagram of the surface tissues of a gas cavity similar to that in figure 1, but including a diffusion resistance between the gas and surface blood vessels. A more complicated case. FIG. 3. A diagram of the gas-exchanging vessels of the surface tissues of a gas-filled cavity in the body, including resistance to diffusion between the gas and superficial vessels, partial exchange of gas across the walls of the conducting vessels, and arteriovenous shunts.
limited, that is, that the partial pressure of inert gas in blood leaving the region of transfer is equal to that in the luminal gas. While this appears to be true for the lung, where the capillaries are exposed to the gas phase with minimal tissue interposed, this is not necessarily true for the intestinal wall, where at least some capillaries involved in gas exchange are separated from the lumen by a much greater thickness of tissue. If we extend the theoretical considerations to include the possibility of diffusion limitation of gas exchange with the blood, we can represent an idealized vessel as in figure 2. If we consider an incremental volume of blood moving along the capillary, inert gas will diffuse into it according to t he relation, a dPe
Ve
ax L
=
D (P - P e)
ax
L
dt
in the capillary blood at any point, x, in atmospheres; P is again the partial pressure of inert gas in the lumen; V c is the total volume of the capillaries in milliliters; and D is the transfer coefficient in milliliters of gas per (minute X atmospheres). Making the simplifying assumption that the capillary is uniform, then dxl L, the differential fraction of the total length, multiplied by the total capillary blood volume, V c , gives the differential volume, and dx D I L is its transfer coefficient. dxlL cancels out on both sides of the equation. If we make the further assumption that the partial pressure of inert gas in the lumen i s constant during the transit of one increment of blood through the capillary bed, equation 3 can be integrated to give,
(3)
where x is the distance along the capillary and L the total length, both in centimeters; Pc is the partial pressure of the inert gas
where tL is the time the blood spends in the capillaries. This assumption does not introduce a significant error andinakes the
February 1967
MEASURING BLOOD FLOW BY GAS ABSORPTION
integration much easier. Equation 4 states that the end capillary partial pressure of inert gas will be less than that in the lumen gas by the factor in the parentheses. Although it might appear that choosing an inert gas with a low value of a, that is, a more insoluble gas, would increase the degree of equilibration of the end capillary blood with the gas in the lumen, this is not the case. The diffusion constant, or transfer coefficient, D, for any gas varies directly with its solubility and inversely with the square root of its molecular weight. This last is not a large factor over the range of available molecular weights. Any change in solubility will produce the same proportional change in the numerator and denominator of the exponent, canceling out. If we substitute this "correction term" which is a constant with time into equation 1 and integrate it, we obtain p,
=
V
-D)]
Po e [ - Qat ( 1 - e aQ
(5)
Experimental results on the absorption of a number of different inert gases of varying molecular weight and solubility in subcutaneous pockets in rats can be fitted to an analogous equation within the limits of experimental error. 3 This indicates that the inert gas absorption is not entirely flowlimited, and that only a crude estimate of blood flow can be obtained using these gases. A still more sophisticated view of the gas exchange process is diagramed in figure 3. First, there is some diffusion through the tissues of the wall, however small, which occurs independent of blood flow. This is generally neglected in comparison with gas carried away by the blood, or it can be corrected for by measuring the gas exchange when blood flow is zero. Second, some exchange of the inert gas must take place between the blood and the immediately surrounding tissue below the mucosal surface in the vessels larger in caliber than capillaries. It is implied in the equations derived so far that the inert gas does not exchange between blood in the larger conducting vessels and the im-
383
mediately surrounding tissue to any SIgnificant extent. The requirement for this assumption becomes clear if we consider the extreme case in which there is rapid diffusion across all the vascular walls. Under such circumstances, the partial pressure of the inert gas will be the same inside and outside the vessel at each point, and the flowing blood will not aid the movement of inert gas at all. The total rate of gas diffusion will be the same as if there were no blood vessels present. In order for blood flow to facilitate the movement of inert gas to the greatest extent, the blood vessels should be impermeable to the gas, except in the region of capillary exchange. It is difficult to estimate the importance of the exchange of gas across the conducting vessel walls without direct experimental measurements, since this will depend on the dimensions of the vessels and the rapidity of the blood flow through them, the dimensions of the intestinal wall, and the diffusion coefficient of the various tissues. Significant gas diffusion occurs through the walls of the larger vessels in the lungs. 5 CO has advantages for the measurement of surface blood flow compared with inert gases. Hemoglobin has a very high affinity for the gas, so that in the vicinity of at. blood vessel it will become bound in the: red cell. Furthermore, once bound in the blood, it will not easily reexchange with the tissues around the vessel, so that the"hair pin" mechanism will not be operative. As an example, in figure 4 is shown a graph of CO absorption from a loop of rabbit intestine filled with CO in N2 (W. Powell, R. E. Forst.er, and R. Coburn, unpublished da'ta). As Peo increases, the CO absorption rate also increases proportionally, suggesting that the process is diffusion-limited. An "intestinal diffusing capacity" can be calculated from these data and in the example in figure 4 is 0.00042 ml per (min X mm Hg). At about 400 mm Hg of Peo in the lumen gas, the CO uptake rate levels off. It is presumed that this represents saturation of the blood hemoglobin with CO before the end of the capillary transit. Dividing this limiting
FORSTER
384 0 .16
CO UPTAKE IN
0.12
ML
MiN 0 .08
0.04
400
'CO IN
800
LUMEN
IN
1200
MM HG
FIG. 4. A graph of CO absorption from the gas-filled lumen of a segment of rabbit ileum as a function of the partial pressure of CO in the gas. From data of W. Powell, R. E. Forster, and R. Coburn (unpublished material). The measurements were made in a hyperbaric chamber.
CO upt ake rate of 0.14 ml per min by the blood C O capacity of about 0.18 ml per ml gives the blood flow, in this case 0.070 ml per (min X g) of intestine. These data can be substituted into equation 4 to obtain a value for the relative equilibration of an inert gas such as N2 between the gas phase in the lumen and the end capillary blood. At 37 C, the exponent becomes about -25, so that end capillary PN2 equals luminal PN2 . Whatever fraction of the t otal blood flow is actually absorbing the CO from the intestinal lumen, it is sufficiently well exposed that an inert gas would be perfectly equilibrated. These measurements of CO uptake were started a matter of minutes after the gas was first introduced into the intestinal lumen, and they lasted generally for 20 min. The experiments were not carried out over extended periods, so that the gas had not rea ched a quasi steady state composition as in the chronic subcutaneous air pocket studies of Piiper and associates quoted above. I • 3 However, there is no obvious reason why the duration of the experiments per se should alter the mechanisms of gas absorption in the two cases. Figure 5 is a graph of CO and C2H 2 disappearance from the dog bladder (R. Coburn, R. E. Forster, B. Luomanmaki, and S. Swerdlow, unpublished data) . At the arrow, the circulation was stopped with an injection of KCl. Although the CO absorption dropped almost to zero, the acetylene up-
Vol . 52, N o. 2, Part 2
take was relatively unchanged. This suggest s t hat inert gas uptake from this hollow viscus is not sensitive to blood flow through the surface tissues, but that CO uptake is. This is what would be expected from the mechanism outlined in figure 3. rt is, at least theoretically, possible 6 to calculate the blood volume of the exchanging vessels (capillaries) by measuring CO uptake rates at different gas P0 2 tensions and at P eo t ensions which are low enough so that CO uptake is not flow-limited entirely-in ot her words, by measuring the "diffusing capacity" of the tissue surface at different P0 2 tensions. CO binds hemoglobin, preventing its effective use a s an oxygen carrier. However, in these experiments the blood P0 2 was kept high enough to prevent local tissue anoxia. CO also competes with O2 for cytochrome oxidase, but concentrations of CO must rise to about 10 times that of O2 before one-half the enzyme is inhibited.7 There were no discernible pathological changes in the intestine by microscopic study after exposure to CO. We therefore concluded that local toxic effects of CO
FRACTION OF 90 INITIAL AMOLtlT
IN %
8
CIRCULATORY ARREST
70
60
50
4·~---r--~--'---~--r-~ o 10 20 30 40 50 60 TIME
IN MINUTES
FIG. 5. A s m e ilogarithmic graph of disappearance of CO and C.H. from the gas in a dog's urinary bladder. The individual gas concentrations are plotted as a percentage of that present initially.
February 1967
MEASURING BLOOD FLOW BY GAS ABSORPTION
on the intestine were not important under the conditions of our experiments. Thermal diffusion is analogous to diffusion of gases, with the exception that the constant of proportionality, corresponding to D in equation 3, becomes the thermal conductivity which has a greater value than the diffusion coefficient. Therefore, it is reasonable to conclude that, if gaseous diffusion exchange across the conducting vessels leading to the surface is sufficient to nullify or at least attenuate the expected transport capabilities of the flowing blood, thermal exchange across these same conducting vessels would reduce the expected facilitation of heat transport by the flowing blood to an even greater extent. This raises a question as to the meaning of the calculations of blood flow made from thermal exchanges. Blood flow would facilitate thermal transport when the blood in the conducting vessels does not have an opportunity to become thermally equilibrated with the tissues surrounding it, as would presumably be the case when the vessels are large in diameter and the velocity of blood within them is rapid. Thus, while blood flow in the mucosa might not facilitate heat transfer, blood flow through a limb or from the deeper tissues through the subcutaneous fat to the skin should. These hypothetical considerations were given some tenuous support by T. B. Ferguson and myself (unpublished observations) in Dr. Landis' laboratory 20 years ago, by studies on the thermal conductivity across the wall of an isolated, perfused segment of dog colon. There was no striking change in the conductivity, whether blood was flowing or not. In all of these considerations, it has been assumed that the dimensions and exchange properties of the blood vessels are the same throughout the tissue surface. In other words, the entire diffusion-exchanging surface can be represented by a single idealized blood vessel, as in the several figures. If the gas exchange is f1owlimited, as in figure 1, and the blood at the end of the capillary is in diffusion equilibrium with the gas in the lumen
385
(which is considered completely mixed at all times), inhomogeneity is unimportant, since regardless of the rate of the blood flow through the vessels it will leave the surface in equilibrium with the gas. However, for the more complicated and more realistic cases, variations in capillary blood volume and flow and in the diffusion characteristics of the tissues interposed between the gas and the blood would tend to make the gas transport function of the blood less efficient. This is, fortunately, too complicated a subject to consider here. It is always possible to measure blood flow to the gastrointestinal tract by combining measurements of the rate of disappearance of a gas from the lumen with simultaneous measurements of the arteriovenous concentration difference of this gas. However, the critical datum here is the arteriovenous concentration difference and not the rate of disappearance of the gas. The use of gas is not specific; any material that moves into the blood in sufficient quantities to cause an arteriovenous difference and is not produced or metabolized locally will suffice. Therefore, this method will be considered an application of the Fick technique and will not be discussed here. The exchange of CO 2 and O2 could be used to measure blood flow to the intestine, instead of inert gas. However, these two gases have several disadvantages which will be shown by the two examples that follow. They are normally present in blood, and, therefore, arterial and venous tensions must be known to calculate blood flow. They are metabolized in the intestinal wall and, therefore, equation 1 cannot be used. I conclude that the usefulness of gas exchange between the lumen and surrounding gastrointestinal wall as a measure of blood flow depends on the basic mechanisms involved, as outlined above. There are theoretical and experimental considerations suggesting that an inert gas, which has about the same effective solubility in blood and in the interposing tissues, is not flow-limited in its exchange. At the other extreme, CO, which has a much greater
386
FORSTER
effective solubility in the blood than in the tissues, for both theoretical and experimental reasons appears to be blood flow-limited in its uptake, once the partial pressure of CO has been raised high enough to saturate the hemoglobin at the end of the capillary. Therefore, the use of CO to measure blood flow in the gastrointestinal tract or in other closed spaces should be explored further.
3.
4.
5.
REFERENCES 1. Piiper, J. 1965. Physiological equilibria of gas cavities in the body. In Handbook of physiology, Section 3, Vol. II, Ch. 48, p. 12051218. American Physiological Society, Washington, D. C. 2. Henning, N., L. Demling, and H. Kinzlmeier. 1950. Die enterale Acetylenresorptionsprobe, eine neue Methode zur Funktionspriifung
6.
7.
Vol. 52, No.2, Part 2
des Pfortaderkreislaufs und des Diinndarmepithels. Klin. W schr. 28: 134-135. Piiper, J., R. E. Canfield, and H. Rahn. 1962. Absorption of various inert gases from subcutaneous gas pockets in rats. J. Appl. Physiol. 17: 268-274. Cander, L., and R. E. Forster. 1959. Determination of pulmonary parenchymal tissue volume and pulmonary capillary blood flow in man. J. Appl. Physiol. 14: 541-551. Sackner, M. A., K. A. Feisal, and D. N. Karsch. 1964. Size of gas exchange vessels in the lung. J. Clin. Invest. 43: 1847-1855. Forster, R. E. 1964. Diffusion of gases. In Handbook of physiology, Section 3, Vol. I, Ch. 33, p. 839-872. American Physiological Society, Washington, D. C. Ball, E. G., C. F. Strittmatter, and O. Cooper. 1951. The reaction of cytochrome oxidase with carbon monoxide. J. BioI. Chern. 193: 635-647.
GASTRO ENTEROLOGY
Copyright © 1967 by The Williams & Wilkins Co.
MEASUREMENT OF GASTROINTESTINAL BLOOD FLOW BY MEANS OF GAS ABSORPTION ROBERT
E.
FORSTER ,
M.D.
Department of Physiology, Division of Graduate Medicine, University of Pennsylvania, Phi ladelphia, Pennsylvania
Theoretically, the rate at which a biologically inert gas, such as N 2 0 or acetylene, is absorbed from a closed gas space in the body, such as a gas-filled portion of the gastrointestinal tract, depends at least in part upon the blood flow to the tissure enclosing the space. 1 This principle has been applied to the estimations of blood flow in subcutaneous pouches and in the gastrointestinal tract. 2 ,3 The mechanism of gas exchange from any closed pocket in the body is essentially the same in principle, and, owing to the paucity of data on the gastrointestinal tract, experimental results from measurements on subcutaneous gas pockets in rats 3 and in the bladder of the dog (R. Coburn, B. Luomanmaki, R. E. Forster, and S. Swerdlow, unpublished results) will be employed to predict results in the alimentary canal. The simplest arrangement for the bloodexchanging vessels in this system is diagramed in figure 1. There is no diffusion exchange in those vessels approaching the surface, but at the surface there is minimal resistance to diffusion between the blood and gas phases. A mathematical relationship between the blood flow in the tissue surface and the rate of disappearance of an inert gas from the gas space can be derived as follows. Assuming that the inert gas would reach diffusion equilibrium between the blood and gas phases and that there is a negligible concentration of this gas in arterial blood, then the rate at which the inert gas is carried away may be described, dP . V-=-QaP L dt
(1)
where V is the volume of the gas phase in milliliters; P is the partial pressure of the 381
inert gas in the lumen in fraction of an atmosphere; P L is that in the blood at the end of the capillary; t is the time in minutes; Q is the blood flow in milliliters per minute; and a is the solubility of the inert gas in the blood in milliliters per (milliliters X atmosphere). This can be integrated, giving (2)
By measuring the inert gas tension as a function of time, as by direct sampling, we can calculate the value of . the exponential constant in equation 2, and, if the solubility coefficient, a, and the volume of the phase are obtained, we can go on to calculate the blood flow, Q. This is analogous to the calculation of blood flow in the lungs from inert gas disappearance. 4 Radioactive xenon or, for that matter, any radioactive inert gas could be used for this purpose with the technical advantage that the amount of gas remaining in the intestine can be measured by external counting. The principle remains the same. Selkurt and Wathen, and Folkow (see p. 387 and p. 423 in this issue of Gastroenterology) discuss a related method, in which the radioactive xenon is introduced by injection into the arterial supply of the organ. However, it is not unfair to state that this theory does not fit the experimental findings very welJ.3 For example, in the case of subcutaneous gas bubbles, the rate of removal of different inert gases does not vary as predicted from their solubilities in blood. In other words, the value of the blood flow calculated from equation 2 varied with solubility, which it should not. This causes one to reexamine the validity of equation 1, in particular, the assumption that the exchange is blood flow-
382
FORSTER
LUMEN
LUMEN
INERT GAS
INERT GAS
. : . . : : : . : ; . : . . . . : . ' , I~tn~I ' ,-II
Vol. 52, No .2, Part 2
LUMEN INERT GAS
FIG. 1. A diagram of the gas-exchanging blood vessels in the surface tissues of a gas cavity. This is the simplest case with negligible resistance to diffusion at the surface and no exchange in the vessels conducting blood to the surface. FIG. 2. Adiagram of the surface tissues of a gas cavity similar to that in figure 1, but including a diffusion resistance between the gas and surface blood vessels. A more complicated case. FIG. 3. A diagram of the gas-exchanging vessels of the surface tissues of a gas-filled cavity in the body, including resistance to diffusion between the gas and superficial vessels, partial exchange of gas across the walls of the conducting vessels, and arteriovenous shunts.
limited, that is, that the partial pressure of inert gas in blood leaving the region of transfer is equal to that in the luminal gas. While this appears to be true for the lung, where the capillaries are exposed to the gas phase with minimal tissue interposed, this is not necessarily true for the intestinal wall, where at least some capillaries involved in gas exchange are separated from the lumen by a much greater thickness of tissue. If we extend the theoretical considerations to include the possibility of diffusion limitation of gas exchange with the blood, we can represent an idealized vessel as in figure 2. If we consider an incremental volume of blood moving along the capillary, inert gas will diffuse into it according to t he relation, a dPe
Ve
ax L
=
D (P - P e)
ax
L
dt
in the capillary blood at any point, x, in atmospheres; P is again the partial pressure of inert gas in the lumen; V c is the total volume of the capillaries in milliliters; and D is the transfer coefficient in milliliters of gas per (minute X atmospheres). Making the simplifying assumption that the capillary is uniform, then dxl L, the differential fraction of the total length, multiplied by the total capillary blood volume, V c , gives the differential volume, and dx D I L is its transfer coefficient. dxlL cancels out on both sides of the equation. If we make the further assumption that the partial pressure of inert gas in the lumen i s constant during the transit of one increment of blood through the capillary bed, equation 3 can be integrated to give,
(3)
where x is the distance along the capillary and L the total length, both in centimeters; Pc is the partial pressure of the inert gas
where tL is the time the blood spends in the capillaries. This assumption does not introduce a significant error andinakes the
February 1967
MEASURING BLOOD FLOW BY GAS ABSORPTION
integration much easier. Equation 4 states that the end capillary partial pressure of inert gas will be less than that in the lumen gas by the factor in the parentheses. Although it might appear that choosing an inert gas with a low value of a, that is, a more insoluble gas, would increase the degree of equilibration of the end capillary blood with the gas in the lumen, this is not the case. The diffusion constant, or transfer coefficient, D, for any gas varies directly with its solubility and inversely with the square root of its molecular weight. This last is not a large factor over the range of available molecular weights. Any change in solubility will produce the same proportional change in the numerator and denominator of the exponent, canceling out. If we substitute this "correction term" which is a constant with time into equation 1 and integrate it, we obtain p,
=
V
-D)]
Po e [ - Qat ( 1 - e aQ
(5)
Experimental results on the absorption of a number of different inert gases of varying molecular weight and solubility in subcutaneous pockets in rats can be fitted to an analogous equation within the limits of experimental error. 3 This indicates that the inert gas absorption is not entirely flowlimited, and that only a crude estimate of blood flow can be obtained using these gases. A still more sophisticated view of the gas exchange process is diagramed in figure 3. First, there is some diffusion through the tissues of the wall, however small, which occurs independent of blood flow. This is generally neglected in comparison with gas carried away by the blood, or it can be corrected for by measuring the gas exchange when blood flow is zero. Second, some exchange of the inert gas must take place between the blood and the immediately surrounding tissue below the mucosal surface in the vessels larger in caliber than capillaries. It is implied in the equations derived so far that the inert gas does not exchange between blood in the larger conducting vessels and the im-
383
mediately surrounding tissue to any SIgnificant extent. The requirement for this assumption becomes clear if we consider the extreme case in which there is rapid diffusion across all the vascular walls. Under such circumstances, the partial pressure of the inert gas will be the same inside and outside the vessel at each point, and the flowing blood will not aid the movement of inert gas at all. The total rate of gas diffusion will be the same as if there were no blood vessels present. In order for blood flow to facilitate the movement of inert gas to the greatest extent, the blood vessels should be impermeable to the gas, except in the region of capillary exchange. It is difficult to estimate the importance of the exchange of gas across the conducting vessel walls without direct experimental measurements, since this will depend on the dimensions of the vessels and the rapidity of the blood flow through them, the dimensions of the intestinal wall, and the diffusion coefficient of the various tissues. Significant gas diffusion occurs through the walls of the larger vessels in the lungs. 5 CO has advantages for the measurement of surface blood flow compared with inert gases. Hemoglobin has a very high affinity for the gas, so that in the vicinity of at. blood vessel it will become bound in the: red cell. Furthermore, once bound in the blood, it will not easily reexchange with the tissues around the vessel, so that the"hair pin" mechanism will not be operative. As an example, in figure 4 is shown a graph of CO absorption from a loop of rabbit intestine filled with CO in N2 (W. Powell, R. E. Forst.er, and R. Coburn, unpublished da'ta). As Peo increases, the CO absorption rate also increases proportionally, suggesting that the process is diffusion-limited. An "intestinal diffusing capacity" can be calculated from these data and in the example in figure 4 is 0.00042 ml per (min X mm Hg). At about 400 mm Hg of Peo in the lumen gas, the CO uptake rate levels off. It is presumed that this represents saturation of the blood hemoglobin with CO before the end of the capillary transit. Dividing this limiting
FORSTER
384 0 .16
CO UPTAKE IN
0.12
ML
MiN 0 .08
0.04
400
'CO IN
800
LUMEN
IN
1200
MM HG
FIG. 4. A graph of CO absorption from the gas-filled lumen of a segment of rabbit ileum as a function of the partial pressure of CO in the gas. From data of W. Powell, R. E. Forster, and R. Coburn (unpublished material). The measurements were made in a hyperbaric chamber.
CO upt ake rate of 0.14 ml per min by the blood C O capacity of about 0.18 ml per ml gives the blood flow, in this case 0.070 ml per (min X g) of intestine. These data can be substituted into equation 4 to obtain a value for the relative equilibration of an inert gas such as N2 between the gas phase in the lumen and the end capillary blood. At 37 C, the exponent becomes about -25, so that end capillary PN2 equals luminal PN2 . Whatever fraction of the t otal blood flow is actually absorbing the CO from the intestinal lumen, it is sufficiently well exposed that an inert gas would be perfectly equilibrated. These measurements of CO uptake were started a matter of minutes after the gas was first introduced into the intestinal lumen, and they lasted generally for 20 min. The experiments were not carried out over extended periods, so that the gas had not rea ched a quasi steady state composition as in the chronic subcutaneous air pocket studies of Piiper and associates quoted above. I • 3 However, there is no obvious reason why the duration of the experiments per se should alter the mechanisms of gas absorption in the two cases. Figure 5 is a graph of CO and C2H 2 disappearance from the dog bladder (R. Coburn, R. E. Forster, B. Luomanmaki, and S. Swerdlow, unpublished data) . At the arrow, the circulation was stopped with an injection of KCl. Although the CO absorption dropped almost to zero, the acetylene up-
Vol . 52, N o. 2, Part 2
take was relatively unchanged. This suggest s t hat inert gas uptake from this hollow viscus is not sensitive to blood flow through the surface tissues, but that CO uptake is. This is what would be expected from the mechanism outlined in figure 3. rt is, at least theoretically, possible 6 to calculate the blood volume of the exchanging vessels (capillaries) by measuring CO uptake rates at different gas P0 2 tensions and at P eo t ensions which are low enough so that CO uptake is not flow-limited entirely-in ot her words, by measuring the "diffusing capacity" of the tissue surface at different P0 2 tensions. CO binds hemoglobin, preventing its effective use a s an oxygen carrier. However, in these experiments the blood P0 2 was kept high enough to prevent local tissue anoxia. CO also competes with O2 for cytochrome oxidase, but concentrations of CO must rise to about 10 times that of O2 before one-half the enzyme is inhibited.7 There were no discernible pathological changes in the intestine by microscopic study after exposure to CO. We therefore concluded that local toxic effects of CO
FRACTION OF 90 INITIAL AMOLtlT
IN %
8
CIRCULATORY ARREST
70
60
50
4·~---r--~--'---~--r-~ o 10 20 30 40 50 60 TIME
IN MINUTES
FIG. 5. A s m e ilogarithmic graph of disappearance of CO and C.H. from the gas in a dog's urinary bladder. The individual gas concentrations are plotted as a percentage of that present initially.
February 1967
MEASURING BLOOD FLOW BY GAS ABSORPTION
on the intestine were not important under the conditions of our experiments. Thermal diffusion is analogous to diffusion of gases, with the exception that the constant of proportionality, corresponding to D in equation 3, becomes the thermal conductivity which has a greater value than the diffusion coefficient. Therefore, it is reasonable to conclude that, if gaseous diffusion exchange across the conducting vessels leading to the surface is sufficient to nullify or at least attenuate the expected transport capabilities of the flowing blood, thermal exchange across these same conducting vessels would reduce the expected facilitation of heat transport by the flowing blood to an even greater extent. This raises a question as to the meaning of the calculations of blood flow made from thermal exchanges. Blood flow would facilitate thermal transport when the blood in the conducting vessels does not have an opportunity to become thermally equilibrated with the tissues surrounding it, as would presumably be the case when the vessels are large in diameter and the velocity of blood within them is rapid. Thus, while blood flow in the mucosa might not facilitate heat transfer, blood flow through a limb or from the deeper tissues through the subcutaneous fat to the skin should. These hypothetical considerations were given some tenuous support by T. B. Ferguson and myself (unpublished observations) in Dr. Landis' laboratory 20 years ago, by studies on the thermal conductivity across the wall of an isolated, perfused segment of dog colon. There was no striking change in the conductivity, whether blood was flowing or not. In all of these considerations, it has been assumed that the dimensions and exchange properties of the blood vessels are the same throughout the tissue surface. In other words, the entire diffusion-exchanging surface can be represented by a single idealized blood vessel, as in the several figures. If the gas exchange is f1owlimited, as in figure 1, and the blood at the end of the capillary is in diffusion equilibrium with the gas in the lumen
385
(which is considered completely mixed at all times), inhomogeneity is unimportant, since regardless of the rate of the blood flow through the vessels it will leave the surface in equilibrium with the gas. However, for the more complicated and more realistic cases, variations in capillary blood volume and flow and in the diffusion characteristics of the tissues interposed between the gas and the blood would tend to make the gas transport function of the blood less efficient. This is, fortunately, too complicated a subject to consider here. It is always possible to measure blood flow to the gastrointestinal tract by combining measurements of the rate of disappearance of a gas from the lumen with simultaneous measurements of the arteriovenous concentration difference of this gas. However, the critical datum here is the arteriovenous concentration difference and not the rate of disappearance of the gas. The use of gas is not specific; any material that moves into the blood in sufficient quantities to cause an arteriovenous difference and is not produced or metabolized locally will suffice. Therefore, this method will be considered an application of the Fick technique and will not be discussed here. The exchange of CO 2 and O2 could be used to measure blood flow to the intestine, instead of inert gas. However, these two gases have several disadvantages which will be shown by the two examples that follow. They are normally present in blood, and, therefore, arterial and venous tensions must be known to calculate blood flow. They are metabolized in the intestinal wall and, therefore, equation 1 cannot be used. I conclude that the usefulness of gas exchange between the lumen and surrounding gastrointestinal wall as a measure of blood flow depends on the basic mechanisms involved, as outlined above. There are theoretical and experimental considerations suggesting that an inert gas, which has about the same effective solubility in blood and in the interposing tissues, is not flow-limited in its exchange. At the other extreme, CO, which has a much greater
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effective solubility in the blood than in the tissues, for both theoretical and experimental reasons appears to be blood flow-limited in its uptake, once the partial pressure of CO has been raised high enough to saturate the hemoglobin at the end of the capillary. Therefore, the use of CO to measure blood flow in the gastrointestinal tract or in other closed spaces should be explored further.
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REFERENCES 1. Piiper, J. 1965. Physiological equilibria of gas cavities in the body. In Handbook of physiology, Section 3, Vol. II, Ch. 48, p. 12051218. American Physiological Society, Washington, D. C. 2. Henning, N., L. Demling, and H. Kinzlmeier. 1950. Die enterale Acetylenresorptionsprobe, eine neue Methode zur Funktionspriifung
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des Pfortaderkreislaufs und des Diinndarmepithels. Klin. W schr. 28: 134-135. Piiper, J., R. E. Canfield, and H. Rahn. 1962. Absorption of various inert gases from subcutaneous gas pockets in rats. J. Appl. Physiol. 17: 268-274. Cander, L., and R. E. Forster. 1959. Determination of pulmonary parenchymal tissue volume and pulmonary capillary blood flow in man. J. Appl. Physiol. 14: 541-551. Sackner, M. A., K. A. Feisal, and D. N. Karsch. 1964. Size of gas exchange vessels in the lung. J. Clin. Invest. 43: 1847-1855. Forster, R. E. 1964. Diffusion of gases. In Handbook of physiology, Section 3, Vol. I, Ch. 33, p. 839-872. American Physiological Society, Washington, D. C. Ball, E. G., C. F. Strittmatter, and O. Cooper. 1951. The reaction of cytochrome oxidase with carbon monoxide. J. BioI. Chern. 193: 635-647.