Flow-limited Tracer Oxygen Distribution in the Isolated Perfused Rat Liver: Effects of Temperature and Hematocrit IBRAHIM KASSISSIA,l'

COLIN P. ROSE,^, CARL A. GORESKY,'. 2, ANDREAS J. SCHWAB,'. SUZETTEGUIRGUIS~.

GLENG. BACH4 AND

lMcGil1 University Medical Clinic in the Montreal General Hospital and the Departments of 'Medicine, 3Physiology and 4Mechanical Engineering of McGill University, Montreal, Quebec H3G 1A4, Canada

We used the multiple-indicatordilution technique to have long been measured and have been used, with blood examine the kinetics of tracer oxygen distribution and flows, to document the rates of oxygen consumption in uptake in the rat liver perfused in a nonrecirculating this organ, tracer oxygen has not previously been fashion with blood. 6'Cr-labeled '80,-saturated eryth- utilized to explore the characteristics of the uptake rocytes, labeled albumin, sucrose and water (the process. The tracer approach, with analysis, is expected tracers for oxygen and vascular, interstitial and cellular references) were iqjected simultaneouslyinto the to provide evidence for the presence of any processes or portal vein. Timed anerobic samples were collected barriers limiting tracer distribution (these could include from the hepatic vein and analyzed by mass spec- release from hemoglobin in the RBC, the RBC memtrometry for relative le0, enrichment and radioac- brane and the liver cell membrane in the liver) and may tivity. In a set of experiments performed at 32" C, provide estimates of the space of distribution available to oxygen uptake was substantially diminished; tracer tracer oxygen. oxygen profiles approached those expected for a comTo gain this information, it is appropriate to use a set pletely recovered, flow-limited substance. At 37" C, of steady-state conditions under which a pulse tracer much larger tracer oxygen sequestration occurred. experiment can be carried out. The tracer experiment Erperimenta were carried out at each temperature at can be performed with the multiple-indicator dilution higher and lower hematocrit, and oxygen consumption approach (11, which can provide the contiguous refat each temperature was found to be independent of hematocrit. The tissue space of distribution for tracer erence space information needed for the interpretation oxygpn relative to the total sinusoidal vascular content of the data. Tracers for RBC, plasma and interstitial and was influenced by the hematocrit: it was smaller at cellular spaces can then be simultaneously introduced. higher hematocrit and larger at lower hematocrit, as Securing of the tracer oxygen information demands the expected. The derived partition coefficient of oxygen use of a tracer oxygen species for which it is possible, at for liver cells relative to plasma (expressedin terms of a practical level, to carry out the proposed experiments, the liver and plasma water spaces) was, on average, and model analysis for the interpretation of tracer 2.62 muml; it was independent of the hematocrit. oxygen outflow data. The radioactive species of oxygen Analwis of the indicator dilution experiments indi- have such short half-lives that they must be generated catesthat the tracer oxygen is distributed into tissue in a flow-limited rather than a barrier-limited fashion, locally; their short half-lives make their use difficult. We and that with this, an ongoing concomitant intracel- therefore chose, in this study, to use 1802, the stable lular sequestration of tracer cam be seen. (HEPATOLOGYoxygen species. We had previously developed and

utilized the mass spectrometry technique needed for in a study of tracer oxygen behavior in the use of 1802 The cell intake of and consumption of oxygen con- heart (2). Previous steady-state observations in the heart have stitute a prime metabolic function of the liver. Although demonstrated that in uzuo tissue oxygen tension values steady-state concentration differences across the liver in muscle fibers are far below those in coronary artery and vein. Analysis of tracer oxygen studies in the heart indicated unexpected barrier-limited transfer (3) of Received February 10, 1992; accepted April 28, 1992. tracer oxygen from cardiac capillaries to heart muscle; This study was supported by grants from the Medical Research Council of consumption of oxygen beyond this resistance accounted Canada,the Quebec Heart Foundation, and the Fast Foundation. C.P.R is a for the observed low tissue oxygen tension values (2,4). chercheur-boursier of the Fonds de Recherche en Sant4 of the Province of Quebec, C.A.G. is a career investigator of the M e d i d Research Council of The resistance at the interface appeared to arise mainly Canada and A.J.S.is an associate professor with research support !+om the from the microvascular structure, the continuous capNational Institutes of Health. illary endothelial lining in the heart. The effective Addreas reprint requests to: Carl A. Goresky, M.D., University Medical Clinic, transfer coefficient at the microvascular surface in this Room 1068,Montreal General Hospital, 1650 Cedar Ave., Montreal, QC, H3G situation is an oxygen permeability surface area product lA4, Canada. 91/1/39%48 (for the capillaries) divided by the volume of distribution 19@2;16:763-775.)

763

764

KASSISSIA ET AL.

in the vessel. The distribution volume in the capillary is equal to the sum of the plasma and RBC oxygen pools; the latter is expressed in terms of an equivalent plasma volume. As an example, at normal hematocrit values the oxygen pool in the RBCs in arterial blood, when expressed in this fashion, is approximately 65 times that in plasma. The large RBC capacity then results in expansion of the oxygen pool accessible to plasma and, conversely, in a corresponding reduction in the effective transfer coefficient for the passage of oxygen tracer across the capillary. The derived capillary permeability to tracer oxygen in the heart is relatively high (slightly larger than that for labeled water). If the RBC capacity effect were not present, the resistance at the capillary barrier would be expected to lead to only small divergence between capillary and tissue oxygen tension values. However, in the presence of the normal, comparatively huge RBC oxygen pool and substantial consumption of oxygen (despite the quite large capillary permeability surface area pqoduct) the transfer coefficient becomes limiting and the observed low tissue oxygen tension values result. The effect of the barrier becomes, comparatively, much greater (2). We expect events in the liver to be different. The endothelial lining cells of the hepatic sinusoids are perforated by sieve plates (groups of fenestrae) allowing free communication between the plasma and Disse or interstitial space. The first, underlying barrier, the hepatocyte plasma membrane, is expanded by a mammillated network of microvilli. The permeability surface area for materials entering liver cells rapidly is so large that no resistance at the cell membrane is perceptible in tracer experiments for these in the in situ liver. Labeled water and the C,- to C,-labeled monohydric alcohols (the latter in the presence of steady-state saturating concentrations of ethanol) exhibit flow-limited distribution (they are distributed radially in the small space available to them in these directions as rapidly as they are presented [l, 5, 61; evidence for a contribution of longitudinal diffusion to the tracer outflow profiles for such materials [7]is very minor). What to expect of tracer oxygen behavior in the liver is not entirely clear. The RBC effect on tracer oxygen transfer across the first tissue barrier, the hepatocyte cell membrane, is present. If the hepatocyte permeability surface area product for oxygen is large enough, then despite this effect no limitation of tracer oxygen cell entry is found; if it is smaller, an effect is seen. Explorations with labeled xenon provide a set of expectations for the case in which there is no apparent limiting effect at the hepatocyte cell membrane but there is a RBC capacity effect much smaller than that expected for labeled oxygen (8).Labeled xenon partitions preferentially into RBCs with respect to plasma, in a 3: 1 concentration ratio, and into liver cells, with a ratio of 1.9 d m l . The labeled xenon is found to exhibit flow-limited distribution, with an outflow curve close to that for labeled water; its position in a set of curves from a simultaneously injected group of reference substances can be varied, however, by changing the hematocrit.

HEPATOLOGY

When the hematocrit (the RBC capacity for label) is high, the labeled xenon outflow curve is found earlier in the reference set (before that for labeled water); when the hematocrit is low, it is later (after that for labeled water). A similar but much magnified (in view of the larger capacity of hemoglobin for oxygen) hematocrit effect might be expected for oxygen if no barrier is present at the liver cell membrane. In addition to these effects, the tracer oxygen undergoes irreversible sequestration, catalyzed by cytochrome oxidase, to form its oxidation end-product, water. The consumption leads to a set of longitudinal gradients in oxygen concentration in the sinusoids and in the adjacent liver cells. We therefore set out to experimentally examine the behavior of tracer oxygen in the liver. Multiple-indicator dilution studies were carried out with stable lSO2 in the perfused rat liver. To provide for variation in the RBC capacity and in the rates of oxygen consumption, experiments were carried out with lower and higher hematocrits and with normal and reduced temperatures. Decrease in temperature, with its predicted reduction in oxygen consumption, was expected to be particularly helpful in defining the relative space of distribution accessible to tracer oxygen in tissue. MATERIALS AND MJ3THODS Experimental &sign. The behavior of tracer oxygen was studied in a group of portally perfused normal rat livers in situ by means of the multiple-indicator dilution technique. This is the only feasible nondestructive experimental method of obtaining information on transcapillary exchange in live, functioning organs over short times. An injection mixture (0.1 ml) consisting of blood containing SICr-labeled RBCs saturated with lSO2, 1261-labeledalbumin, 14C-sucrose and 3H-enriched water, with a hematocrit equal to that of the perfusion fluid and at the temperature selected for the study, was injected into the portal vein of an isolated perfused rat liver. Timed anaerobic samples (9) were collected continuously from the hepatic venous effluent. From the outflow concentrations of each indicator, transport functions were constructed; these are expressed as a fraction of the activity injected per second. The reference substances chosen for the study were a set of flow-limited materials completely recovered at the outflow, each with its own volume of distribution (1). The labeled RBCs are confined to the vascular space, labeled sucrose diffuses freely into the Disse space, labeled albumin enters a restricted volume in the Disse space because of the excluded volume effect imposed by its contained polymers and labeled water freely penetrates all of the accessible vascular and tissue water spaces. These references provide a framework in which to view the potential behavior of the tracer oxygen molecules; we expected them to provide useful insights, particularly when metabolic sequestration was suppressed. To carry the process further, appropriate data sets defining tracer oxygen behavior are necessary, and the various possibilities underlying the distribution of tracer oxygen must be explored at a modeling level. From this the best approach must be formulated for the description of the tracer oxygen tissue penetration and uptake processes, and the usefulness of approach for describing the data sets must be appraised. We expect the analysis of the tracer oxygen data to provide new information on the behaviour of labeled oxygen in the liver. It

Vol. 16,No.3, 1992

TRACER OXYGEN BEHAVIOR IN RAT LIVER

would also be of interest if it were possible to simultaneously derive information concerning the expected tracer product, water containing the l80, species. The background "0, enrichment and the overall bulk water concentration in the organ are such, however, that the effiw of stable tracer into the product water species should not be accurately discernible; to examine this phenomenon, a radioactive tracer oxygen experiment would be needed. Animuls. Twenty male Sprague-Dawley rats weighing between 300 and 400 gm (Charles River Canada Ltd., St-Constant, Quebec) were kept on a 12-hr light-dark cycle. Liver weights varied from 13 to 20 gm. The animals were fed a regular rat chow diet ad libitum, (Purina rat chow; Ralston Purina Inc., Mississauga,Ontario, Canada) and had free access to tap water. Experimental Protocol. Rats were anesthetized with pentobarbital (50 m&, intraperitoneally), and the abdomen was opened through a midline incision. The portal vein was exposed near the Mum of the liver and then cannulated with a 14-gaugeblunt needle. The inferior vena cava was exposed and cannulated with a 14-gauge blunt needle between the hepatic veins and the heart. The hepatic artery was ligated. During the first minute, each liver was washed with a heparinized Krebs-Henseleit solution, oxygenated with a mixture of 95% 0, and 5% CO, and adjusted to a pH of 7.4. Lines were then connected to a fixed flow, pressure-independent perfusion apparatus (WAmbec perfusion system twolten; M x International, Inc., Aurora, CO). The perfusate consisted of KrebsHenseleit solution containing a lower (15%) or higher (30%) (voVvo1)proportion of prewashed canine erythrocytes, 2 gmldl BSA and 100 mgldl dextrose. The details of the surgical exposure and catheter installation were as outlined by Varin and Huet (10). All experiments were carried out in exactly the same way except for the variables imposed, the change in hematocrit and change in temperature. Thus 10 rats were perfused with a perfusate containing 15% RBCs, and 10 rats were perfused with a perfusate containing 30% RBCs. Again, half of each group was perfused with the perfusate at 37" C and half were perfused at 32" C. The major experimental modification needed was an outflow pump, which was used to overcome the pressure head of the mercury in the anaerobic collection bath. An overflow tube was attached to the outflow tube to keep the outflow pressure atmospheric. The sequence of selected temperatures and hematocrits was varied randomly for each experiment. I*ection Mixture Preparation and Analysee. The mixture containing the radioactive tracers was deoxygenated in a tonometer flushed with a gas consisting of 95%N, and 5%CO,. The deoxygenated mixture was aspirated into a syringe and reoxygenated with "0, added stepwise to the syringe from a 0.1-L reservoir of lSO, (containing 96.5 atom % lSO; Merck Frosst Canada, Montreal, Canada). After a 20-min equilibration period, 0.1 ml of the injection mixture was removed anaerobically and injected as a pulse into the portal vein. Thirty timed anaerobic samples were collected from the inferior vena cava catheter over approximately 30 sec by use of a multiple-syringe mercury-trough fraction collector (9); all of the outflow was collected. Flow was measured by collecting the outflow from an anaerobic sample well in a syringe over a timed interval. Flow values calculated from the areas under the completely recovered reference substances corresponded almost precisely to those determined by collection. Each sample contained about 0.4 ml blood. From this, 0.1 ml was diluted with 1.5 ml of saline, pipetted into a counting tube and assayed for radioactivity in a Nuclear Chicago gamma ray

765

spectrometer (Nuclear Chicago Corp., Des Plaines, IL) set for the photopeaks characteristic of lZ5Iand 51Cr.Trichloroacetic acid (25%, 0.2 ml) was then added to lyse the RBCs and precipitate the RBC and plasma proteins. After centrifugation, 0.4 ml of the supernatant fluid was pipetted into a scintillation vial containing 7 ml of scintillation fluid for assay of 14C and 3H activities. The samples were then counted in a Beckman LS-250B scintillation counter (Beckman Instruments, Palo Alto, CA). Crossover standards (consisting of each of the radioactive tracers alone) and standards from the injection mixture were treated identically. From the activity of the crossover standards in their primary channel and their spillover into the various other channels, the activity in the outflow samples due to each tracer in its primary channel was determined. The details of the manner in which the characteristics of the radiation and the chemical treatment of the samples provide for the resolution of the activities due to each of the four radioisotopes are as follows. 51Cr and lZ5I are gamma emitters, and no contribution is made by the 14Cor 3H during the assay of the gamma radiation. The low-energy lZsI does not contribute to the radiation observed in the region of the 51Cr photopeak; the contribution of the 51Cr activity to the lZ5I photopeak was, on average, 0.16 of the activity recorded in the W r photopeak region. The protein precipitation brings down all of the lZ5Iactivity and almost all of the 51Cr activity. The 14C and 3H activities contained in the supernatant are then assayed in the liquid scintillation counter. Ten times as much 3H activity as 14C activity was added to the injection mixture. A higher-energy channel was used to record the predominantly 14C activity, and a lower one was used for the 3H region. On average, with the settings used, 0.02 of the 3H activity recorded in the lower channel was seen in the upper channel, 0.32 of the 14C activity recorded in the upper channel was seen in the lower channel and 0.06 of the W r counts per minute recorded in the upper channel of the gamma well was seen as counts per minute in the lower liquid scintillation channel. The resolution of the two gamma activities thus is a two-channel problem and, after subtraction of the W r crossover, resolution of the 14C and 3H activity is also a two-channel problem. Ordinarily, lo4 cpm were recorded from the dominant channel in either counter. The amounts of activities used were approximately: 20 pCi for 51Cr-labeled RBCs, 20 p,Ci for 1251-labeledalbumin, 15 pCi for sucrose and 150 pCi for 3H-enriched water. Of the remaining blood in each sample, 0.3 ml was injected anaerobically into individual helium-filled, sealed-glass chromatographic vials that contained crystalline potassium ferricyanide and trichloroacetic acid to induce the release of the oxygen bound to the hemoglobin into the overlying gas phase in the vial (2). A 28-gauge helium-filled needle, connected through a switching valve to a direct-interface quadrupole Hewlett-Packard 5970 series gas mass spectrometer (HewlettPackard Corp., Mountain View, CA), was introduced through the cork of the chromatographic vial. When the valve was turned, the head-space gas phase was aspirated into the h g h vacuum of the mass spectrometer. The gas samples were analyzed for their relative contents of the followingmasses: 32, 34 and 36 for oxygen isotopes; 40 for argon; and 44 for carbon dioxide. The system was set up in such a way that the mass spectrometer was flushed with helium after each measurement. The lSOzenrichment above background in each sample and in an aliquot of the injection mixture was determined in either of two ways. From ordinary definitions, the lSO2 enrichment

766

HEPATOLOGY

KASSISSIA ET AL.

TABLE 1. Experimentally determined, observed and fitted parameters

Group 1: low temperature, low hematocrit 1 13.0 1.69 2 17.0 1.41 3 15.0 1.31 4 14.2 1.50 5 13.1 1.53 Mean f S.D. 14.5 f 1.6 1.49 t 1.07 Group 2: low temperature, high hematocrit 1 14.2 2.11 2 13.0 2.00 3 17.0 1.47 4 15.8 1.33 5 15.1 1.46 Mean t S.D. 15.0 ? 1.5 1.67 f 0.36 Group 3: high temperature, low hematocrit 1 15.0 1.31 2 14.2 1.50 3 15.5 1.45 4 15.4 1.43 5 19.0 1.11 Mean f S.D. 15.8 f 1.8 1.36 t 0.16 Group 4: high temperature, high hematocrit 1 15.4 1.43 1.11 2 19.0 3 21.4 1.12 4 24.6 1.18 Mean f S.D. 20.1 f 3.9 1.21 f 0.15 AN'OVA' Temperature Hematocrit -

15 12 15 15 13 14.0 2 1.4

13 8 15 17 15 14 f 3

0.43 0.21 0.34 0.12 0.42 0.30 k 0.14

0.54 t 0.04 0.43 t 0.03 0.30 t 0.02 0.44 f 0.04 0.66 f 0.03 0.47 t 0.15

0.49 & 0.05 0.0109 0.55 f 0.04 0.0088 0.54 f 0.03 0.0210 0.71 k 0.05 0.0054 0.0268 0.82 f 0.05 0.62 f 0.14 0.0146 2 0.0090

30 33 25 34 37 31.8 f 4.5

4 8 5 8 9

0.36 0.47 0.28 0.48 0.43 0.40 f 0.08

0.33 t 0.02 0.69 t 0.07 0.20 t 0.02 0.34 f 0.02 0.37 t 0.01 0.38 f 0.18

0.28 f 0.03 0.0072 0.23 '. 0.05 0.0085 0.20 +. 0.02 0.0053 0.28 f 0.03 0.0125 0.38 f 0.02 0.0167 0.27 f 0.07 0.0100 f 0.0046

0.33 t 0.03 0.73 f 0.06 0.91 t 0.06 0.60 f 0.04 0.43 t 0.03 0.60 & 0.23

0.57 & 0.04 0.0401 0.73 f 0.08 0.0403 0.1017 0.74 f 0.06 0.59 f 0.05 0.0292 0.46 f 0.05 0.0843 0.62 f 0.12 0.0591 f 0.0318 0.20 f 0.04 0.0217 0.45 f 0.04 0.0187 0.49 f 0.07 0.0185 0.16 f 0.07 0.0423 0.33 f 0.17 0.0253 t 0.0114

7

f

2

15 15 15 15 14 14.8 k 0.4

32 22 46 21 46 33 f 12

0.73 0.69 1.70 0.63 0.91 0.93 f 0.44

36 30 29 29 31.0 t 3.4

17 20 21 33 23 f 7

1.15 0.88 1.03 1.54 1.15 t 0.28

0.57 f 0.04 0.52 t 0.04 0.59 t 0.08 0.49 t 0.09 0.54 f 0.04

p < 0.01 NS

NS NS

NS p < 0.01

p < 0.01 p < 0.05

"S.D.6 for the parameters calculated from the information matrix for each experiment are listed in this column. bTwo-factoranalysis, 95% confidence limits.

was determined from the mass peak area ratio of mass 36 t o the sum of (32 + 34 + 36) after subtracting from the 36 peak area the appropriate proportion of the mass 40 peak, which represents the mass 36 isotope of argon. Alternatively, the mass peak area ratio of mass 36, after subtraction of the content of the mass 36 isotope of argon, to that of a reference gas is determined; carbon dioxide (mass 44) was used as a reference gas because its concentration in the blood in each of the samples was the same. Either approach gives essentially the same result; the second is less sensitive to air leaks, which occasionally contaminate the samples. Data Analysis. Outflow profiles for each radioactive tracer were expressed as the normalized transport function Mt): the product of blood flow and the concentration of each indicator (the latter expressed as a fraction of the total activity injected per milliliter of the collected venous blood [ 111).In this format, the data are displayed as the outflow fractional recovery of each indicator per second vs. time. To obtain an analogous expression for the oxygen data, a different procedure had to be devised. Before each run, samples of the hepatic venous blood and of the perfusate and the injection mixture were analyzed for their oxygen content. These data were used to convert the lSO, enrichment in each outflow sample to a fractional recovery per milliliter as follows. The relative lSOZcontent in each hepatic venous sample (the product of its ISO, en-

richment and 0, content) was divided by the amount of "0, injected (the product of the injectate enrichment with the oxygen content of the injection mixture and the injection volume). That is,

where FR36hu is the normalized hepatic vein outflow fraction recovery per milliliter blood (ml-I); F36hu is the enrichment of l80, in the hepatic vein samples (dimensionless); F36injis the enrichment of I S 0 , in the injection mixture (dimensionless); C,, and Ci, are the oxygen contents of the hepatic venous blood and the injection mixture, respectively; and Vinjis the injection volume. The oxygen contents of the perfusate and the injection mixture were equivalent; the oxygen content of the perfusate could therefore be used in place of the concentration in the injection mixture. The normalized transport function for tracer oxygen, h(t)O,, is then the product of blood flow rate and FR36hv. Oxygen consumption is calculated as the product of blood flow and the difference in the oxygen contents of inflowing and outflowing blood. Because the calculation of the fractional recovery of tracer oxygen uses the values for the oxygen

TRACER OXYGEN BEHAVIOR IN RAT LIVER

Vol. 16, No. 3, 1992

~~~

0, curve fits

sucrose cucve fits

Coef%ient of variation

COefGeIent of determination

Coef6cient of variation

Coefflcient of determination

0.091 0.075 0.064 0.109 0.069 -

0.993 0.996 0.997 0.994 0.996

0.107 0.096 0.066 0.080 0.099

0.971 0.982 0.976 0.965 0.946

-

-

-

0.030 0.094 0.025 0.124 0.048 -

0.999 0.994 0.999 0.993 0.999 -

0.080 0.079 0.055 0.089 0.093 -

0.992 0.990 0.996 0.996 0.995 -

0.089 0.137 0.121 0.103 0.089

0.078 0.146 0.099 0.092 0.166

0.981 0.960 0.982 0.990 0.946

-

0.994 0.990 0.994 0.995 0.997 -

-

-

0.057 0.065 0.057 0.105 -

0.997 0.996 0.990 0.987 -

0.089 0.037 0.013 0.118

0.990 0.997 0.999 0.972

-

-

-

-

-

-

-

-

-

contents in the inflow and outflow, bulk and tracer recovery cannot be appraised separately. The interdependence arises because the mass spectrometric assay, as we utilized it, provides a ratio of mass values rather than an absolute concentration value. Statintical Anulytiis. Results are presented as mean 2 S.D. A two-factor unbalanced ANOVA with unrepeated measures was used to determine the significance of temperature and hematocrit in explaining the differences in any parameter between the groups. A multicomparison significance level of 95% was accepted.

RESULTS Ouylow profiles. The background data for each of the groups of tracer oxygen studies are given in Table 1. One representative set of outflow tracer transport functions from each group of animals is shown in semilogarithmic format in Figure 1 and in rectilinear format in Figure 2. The two kinds of representation convey different kinds of visual information. The semilogarithmic plot is particularly adapted to portraying curve shapes (it has proved particularly useful for discerning late second components of curves 1611, whereas the rectilinear plot provides direct visual information concerning areas under the curves (that is, recoveries), in each data set.

767

The reference labeled RBC, albumin and sucrose and water transport functions are found to exhibit similar patterns in each panel. Within each group, the labeled RBC curve peaks first and then exhibits an approximately exponential decay with time; the labeled albumin, sucrose and water curves show progressively less steep upslopes, lower and later peaks and less steep downslopes; the areas under each are equal. For oxygen, the area under the curve, expressed in terms of that under the reference curves, is equal to the bulk unextracted fraction (it is the complement of the extraction). Several systematic differences can be observed between the tracer oxygen curves obtained in the different groups. In the high-hematocrit groups, regardless of the temperature of the perfusate, the oxygen curves peak relatively earlier and decay faster than the ones obtained from the low-hematocrit groups. The phenomenon is perhaps best perceived in the rectilinear plots of the data (Fig. 2). The forward shift of the curves in the data set with increase in hematocrit appears analogous to that previously observed with labeled xenon, where it was attributed to a RBC capacity effect. It is to be noted that in all cases the peak of the labeled oxygen curve was nevertheless delayed in time with respect to that of the labeled RBC curve. The second major effect discerned was the change with temperature change. The proportion of the oxygen label consumed (the decrease in area under the labeled oxygen curves, relative to that under the reference curves, which corresponds to the extraction) is much larger in the high-temperature instances than in the low-temperature cases. An accompanying shape change is also present in the labeled oxygen curves. In the low-temperature groups, regardless of the hematocrit of the perfusate, the oxygen curves apparently peak later and decay less steeply than do the ones obtained from livers perfused at normal temperatures. At a given temperature, the oxygen consumption in the high- and low-hematocrit groups is the same (Table 1); thus, since the oxygen carrying capacity varies almost directly with the hematocrit, the extraction in the high-hematocrit group is lower than that in the low-hematocrit group. Further insight into the behavior of the tracer oxygen can perhaps initially best be obtained by scrutiny of the shapes of the labeled oxygen curves in relation to those of the underlying, concomitantly injected reference substances. As background, the behavior of the reference set must be understood. The labeled RBCs serve as a vascular reference; in this instance they provide an index of the shape a labeled oxygen curve would have if all of the label remained bound to the hemoglobin during the time of passage and if all of it were delivered to the outflow, without loss. The three other reference substances behave differently; they undergo lateral flowlimited distribution into the extravascular space accessible to them (6,7). A symmetrical delay in their outflow times accompanied by a proportionate reduction in the magnitude of the corresponding parts of the outflow profile is found; this preserves the areas under the curves. The magnitude of the change is dictated by the

768

KASSISSIA ET AL.

0.10

HEPATOLOGY

0 S U U ~

rn Water

~

c8

Low hematocrit High temperature

0.01

i

F 0.00

f

-5

0.10

High hematocrit High temperature

High hematocrit Low temperature

0

c 0

E

U

0.Ql

0.W

0

10

20

30

4

0

0

10

20

30

40

Time after injection of tracers (s)

FIG.1. Semilogarithmichepatic venous normalized transport functions resultingfrom the simultaneousinjection of labeled RBCs, albumin, sucrose, water and oxygen into the inflow to the perfused rat liver at high and low temperatures and at high and low hematocrits. The time scale is corrected by the mean transit time of the catheters. At low temperature, regardless of the hematocrit,labeled oxygen curves enclose a proportionally larger area, peak later in time and decay relatively less steeply than do those perfused at a normal, higher temperature. Agam, in the high-hematocrit group, labeled oxygen curves peak relatively earlier in time and then decay faster than do the ones obtained from the low-hematocrit groups. At high temperature, the difference is more marked than at low temperature, where it is masked by the change in the curves with the decrease in oxygen consumption.

ratio of the space of distribution in the tissue (nonmoving) phase to that in the sinusoidal vascular (moving) phase. For labeled sucrose this space ratio is the ratio of the Disse (or interstitial) space to that of the sinusoidal plasma space, whereas, for labeled albumin it is the ratio of the accessible interstitial space (the complement of the polymer-excluded volume for albumin) to the sinusoidal plasma space. For labeled water, it is the ratio of the sum of the cellular plus interstitial water contents to the sum of the sinusoidal plasma plus RBC water contents. In relation to data acquired in the in uiuo dog liver, the labeled water dilution curves obtained in the perfused rat liver peak somewhat higher and earlier. This is because the vascular (RBC-accessible) space is approximately 50% higher in the perfused rat liver than in the experimental in situ dog liver (12, 13). This appears to be either a species- or perfusion-associated characteristic. The outflow labeled oxygen curves in Figures 1and 2 then must be interpreted in relation to what is known about oxygen behavior in blood and tissue and with respect to how they relate to the components of the set of reference materials. The first possibility that must be examined is that of RBC carriage. If the labeled oxygen

bound to hemoglobin in the RBCs (most of the input labeled oxygen) were released relatively slowly, so that escape from the RBCs was limiting, the preponderant part of the oxygen label would be expected to travel with the labeled RBCs; the labeled oxygen curves would then be expected to exhibit an early large component peaking at the same time as or slightly earlier than that for the labeled RBCs, the latter because of the longer sinusoidal transit times of the late-appearing parts of the outflow curve (14).This does not occur, and so this possibility seems unlikely. This is not surprising, in view of the finding by Sirs (15) that bulk desaturation of RBCs with an oxygen-free, oxygen-consuming medium at 20" C is more than 50% complete at 50 msec. The second possibility that needs to be assessed is whether there is a substantial degree of resistance at the liver cell membrane. If the resistance at this site were great, the early upslope and peak of the diffusible tracer oxygen curve would again be expected to remain quite close to the reference RBC curve (because the preponderant part of the vascular plus interstitial extracellular tracer oxygen is associated with the RBCs), whereas the tracer oxygen that has entered the cells and escaped sequestration would be expected to appear as a delayed

769

TRACER OXYGEN BEHAVIOR IN RAT LIVER

Vol. 16, No. 3, 1992 0.15

Low hematocrit Low temperature 0 0 0

0.10

Low hematocrit High temperature

Rod Mood CrlA Albumin

sucrcm m Wmbr 0

1a

4

-acE -

om 0.15

0

c.

8

LL

0.10

L

L

0.05

om 0

10

20

30

40

0

10

20

30

40

Time after injection of tracers (8) FIG.2. Rectilinear representations of hepatic venous normalized transport functions.

component whose magnitude would vary inversely with the degree of sequestration (6, 16). On the other hand, if the resistance at the cell membrane is very small, so that the tracer oxygen distribution into the liver cells is flow limited, and if intracellular sequestration were occurring, a unimodal, more delayed curve would be expected, with neither an early nor a late component, and with its area reduced by the sequestration process (5, 14). Modeling analysis of the data under these circumstances should provide a quantitative appraisal of the degree of resistance at the liver cell membrane and of the magnitude of the sequestration process (and, with this, of the distribution space for oxygen in tissue). With this background, it is appropriate to review the experimental forms of the tracer oxygen curves, illustrated in figures 1and 2. On inspection, the first thing evident is that the tracer oxygen curves exhibit neither an early nor a late visually separable second component and that a late separable component is not seen even when the oxygen consumption is suppressed, at low temperature. The curves have a smoothly changing unimodal form. The lack of visual evidence of a second, later component to the tracer oxygen curves indicates that the permeability surface area product for tracer oxygen entry at the liver cell membranes is likely high enough that it is not limiting during flow through the liver; highly permeable, delayed, wave-flow-limited distribution with intracellular sequestration (1, 6) might thus describe these single-component curves.

We now turn to the situation in which the temperature is so low that metabolic utilization of tracer oxygen is suppressed and the recovery of tracer oxygen (the area under its dilution curve, in relation to that under the set of simultaneously injected reference substances) is only slightly less than complete. The forms of the curves thus correspond more or less to an apparently flow-limited extreme, but the relative space of distribution available to tracer oxygen in the tissue appears to vary with the hematocrit. In the flow-limited case, a derived space ratio, corresponding to the ratio of the nonmoving tissue content (in the absence of sequestration) to the moving sinusoidal vascular content (1, 61, has been useful. At high hematocrit (and low temperature), the form of the tracer oxygen curve is such that if it does undergo flow limited distribution the space ratio describingits relative space of distribution is similar to and perhaps slightly larger than that describing the curve for tracer sucrose. This does not mean that the space of distribution available in the liver to tracer oxygen corresponds to that for tracer sucrose. For sucrose, the space ratio is the ratio of the interstitial space to the sinusoidal plasma space. For tracer oxygen, the accessible sinusoidal vascular space includes not only the sinusoidal plasma space but also the sinusoidal RBC space, expressed in terms of an equivalent plasma space (17). Hence, because the sinusoidal RBC space available to tracer oxygen is a great deal larger than the plasma space, the tissue space available to tracer oxygen will be propor-

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tionately much larger than that available to tracer sucrose. At low hematocrit (and low temperature), the relative tissue space of distribution becomes substantially larger than in the high-hematocrit case (this is also what was found in the studies carried out with xenon [81; a proportionately larger change with change in hematocrit is, however, expected with labeled oxygen because of the larger degree of association of oxygen with hemoglobin). This is manifested by the change in the form of the tracer oxygen curve at the lower hematocrit. The tracer oxygen curve lags behind the sucrose curve on its upslope, reaches a lower peak, and decays less quickly; the downslope of the tracer oxygen curve crosses the labeled sucrose curve. At high temperatures, one can utilize the inferences gained from the foregoing to visualize how the increased metabolic sequestration at higher temperature affects the outflow profiles for labeled oxygen. In the highhematocrit (and the higher temperature) case illustrated, the apparent space ratio for tracer oxygen is apparently slightly smaller than that for labeled sucrose (but larger than that for labeled albumin). The labeled oxygen curve leads the labeled sucrose curve on the upslope and decays within the labeled sucrose curve on the downslope; the rate of decay of the downslope is larger than that for both the labeled sucrose and labeled albumin, on the semilogarithmic representation. The pattern of change suggests that with respect to a suitable reference material for tracer oxygen, with a space ratio between that for labeled albumin and sucrose, the process of metabolic sequestration (which is more evident at the higher normal temperature) removes proportionately more of the emerging tracer oxygen at later-in-time points along the curve (a phenomenon previously observed for tracer ethanol with respect to labeled water, as its reference substance 151). At the lower hematocrit, with its lower oxygen-carrying capacity, and at a high temperature, similar effects are evident in figures 1and 2.The tracer oxygen curve now corresponds in the tracer set to a hypothetical reference curve with an apparent space ratio much larger than that accessible to labeled sucrose; the fractional extraction of oxygen tracer, at the higher temperature, is much greater. The progressive change in the form of outflow data in toto, in which the peak of the diffusible tracer oxygen curve shifts to later times with a decrease in hematocrit (that is, in the relative intravascular volume of distribution), suggests strongly that flow-limited rather than barrier-limited transport of tracer oxygen occurs in the liver but does not document that this is the case. A more quantitative approach is needed. Modeling the Distribution and Sequestration Processes. In exploring the kinds of modeling that might provide a description of the data, we first examined the case in which transfer of oxygen between blood and hepatocytes is not instantaneous but is subject to barrier limitation. The modeling used was that previously developed to describe the behavior of tracer galactose in the liver (18)but with the interstitial space set equal to zero because, in the absence of a binding protein for oxygen in this space, the amount of oxygen present in

HEPATOLOGY

the space will be comparatively quite small. The appropriate reference in this case is the labeled RBC curve. The parameters one would expect to be able to optimize with this approach are the rate constant for the entry of tracer oxygen into the hepatocyte; the rate constant for its reflux back into the blood; the rate constant for the sequestration of tracer oxygen by conversion into its end product, water; and the ratio of the apparent volumes of distribution of oxygen between hepatocytes and blood. When we attempted to fit this barrier-limited modeling to the data, convergence of the fitting algorithm could not be achieved; the rate constants for the transfer of tracer oxygen between blood and hepatocytes increased with each successive iteration until they reached such high values that the calculations led to overflow in the computer. This result is the one expected when distribution of label is flow limited because, as previously shown (3), flow-limited behavior is the highpermeability extreme of the barrier-limited case, which is approached when the permeability of the barrier becomes too high to perceive by this approach. In view of these findings, we proceeded to model the distribution of tracer oxygen into the liver as a flowlimited process. In the modeling, tracer oxygen distribution into the extravascular space, including the cellular space, is treated as flow limited, and metabolic uptake of tracer within the liver cells is considered a unidirectional process. The modeling is similar to that utilized previously to describe the handling of monohydric alcohols by the liver (5). In the case of tracer oxygen, we developed this in detail. It is necessary to include, in the development, a description corresponding to the differential binding of oxygen in the RBC. Two basic assumptions are necessary and provide the physical basis for the modeling (19). 1. Diffusion over the short distances radial to the sinusoid is assumed to take place so rapidly that in the flow-limited case the concentration at each point along the length is equal to the concentration in the vascular space. 2. The mechanism transporting material along the length of the sinusoid is assumed to be only flow. Longitudinal diffusion is assumed to be negligible. Outflow dispersions of each of the reference substances (labeled RBCs, interstitial substance and water), relative to their mean, are essentially identical (8) and are accounted for, in the modeling, at a multicapillary level. Consider a sinusoid of length L, in which blood flows with a velocity, W. Let the concentration of tracer in the RBCs in space and time be y(x,t); in plasma, u(x,t); in Disse space, u(x,t); and in the hepatic cellular space, z(x,t); and let the relative water space ratios for RBCs, Disse space and liver cells with respect to the sinusoidal space be p, y, and 8. It can be shown (17) that the conservation equation for a substance not removed along the length of a single sinusoid is au at

au ax

av at

az at

-+w-ty-te-+p

(Z-tw-

=o

(2)

The RBC W r tracer is found only in the RBCs. Its conservation expression is therefore described by the expression in brackets on the left hand side of equation

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771

2, set equal to zero. The outflow solution for this (at for oxygen consumption, moderated by the activity of the electron transport chain; K , is the Michaelis constant of the system; and [OJ is the total oxygen concentration at the site of consumption. amount of activity injected), is Now assume that the tracer oxygen undergoes instany(L,t) = -8 t - (3) taneous equilibrium partition between RBCs, plasma, F, qo Disse space and hepatocytes at each point along the where F, is the flow of RBCs. The labeled RBCs length (that is, y = h p ; u = u; and z = Ahpu;where Ac, propagate along the sinusoid with flow at the velocity W. is the ratio of erythrocyte/plasma oxygen concentration The RBCs effectively fill the sinusoids and deform the and hh is the ratio of hepatocyte/plasma oxygen conendothelial cells during flow, segmenting flowing plasma centrafion, as indicated by our qualitative analysis of the data. The solution to equation 5 for an impulse input is, between them. Labeled sucrose does not penetrate the RBCs or the as described previously (5, 8, 16), liver cells but does instantaneously equilibrate into the Disse space, so that concentrations in plasma and accessible Disse space are equal at each point along the length (that is, u = v). Accordingly, the single-sinusoid where qo is the amount of tracer injected, Fbis sinusoidal outflow profile for labeled sucrose is found to be (61, blood flow, kses is the form of the rate constant which appears in the integrated equation,

x = L), in response to an impulse function or Dirac delta function qoS(x)introduced at the origin (where qo is the

i 3

(4)

where F, is the sinusoidal plasma flow. The tracer sucrose travels as a delayed wave with velocity W/[l + y S J . The parameter y,, is the space ratio (interstitial space/sinusoidd plasma space) for labeled sucrose. An approximation is utilized here- that the moving sinusoidal plasma, to which the sucrose space is referred, has the same transit time and dispersion as the labeled RBCs because there is no way to account for any slip layer beyond the confines of the RBC-accessible space. Tracer oxygen distribution is assumed to occur in a steady state with respect to bulk oxygen. Modeling of tracer oxygen transport must include at least two more variables; the partitioning into the RBCs and uptake by the hepatocytes. Two more assumptions are made: 3. that oxygen consumption can be represented as first order and 4. that partition of oxygen between hepatocytes and plasma and between plasma and RBCs is constant along the length of the sinusoid. Obviously, these assumptions are not strictly true; they are somewhat too simple (they do not include the RBC oxygen-saturation curve or the presence of a potentially saturating binding site in the liver cells, which would have made the equations nonlinear and dimcult or impossible to solve analytically). The model, as developed, however, fits the data within small error, and can be regarded as a first approximation. Given the assumptions, the conservation equation for tracer oxygen becomes, in analogy to the equation previously developed for tracer xenon (81,

(7)

and (8)

The rate constant k,, is expected to have the form V,, (now derived from ehe enzyme activity,*integrated from entrance to exit), divided by (Y, + [O,]), where [OJ is the logarithmic average bulk oxygen concentration {[O,(O)I - [O,(L)l}/{ln [O,(O)l - In [O,(L)l}, [O2(O)l and [02(L)lare the bulk oxygen concentrations at the entrance and exit from the sinusoid and the Zn[021 values are the corresponding natural logarithms of the oxygen concentrations (20). Equation 6 can be viewed as an analog of the Crone expression (211, in which sequestration takes the place of the permeability surface area product. It is assumed that tracer oxygen distributes into the Disse space in the same fashion as labeled sucrose. It could have a slightly larger space of distribution if there were an excluded volume phenomenon for sucrose relative to oxygen. A quantitatively important effect of this kind is unlikely to be present, however, because for labeled sodium, a tracer much smaller than sucrose, outflow dilution curves essentially coincide with those for sucrose (1). The possibility is therefore neglected. This single-sinusoid response can now be coupled to a model of the distribution of large and small (exchanging) vessels to obtain the organ response of the whole liver, as described previously (9). Additional assumptions au au av - + w- + y+ 8'-az +- p' + O'k'-z = 0 (5) utilized at this point in the development follow. at ax at at 5. There is essentially a single common large vessel where p' and 8' are the ratios of the volumes of the RBC transit time, represented by to (9).This is another way and hepatocytic spaces to the sinusoidal plasma space, of saying that essentially all of the dispersion in the respectively, and klseq is the rate constant for uni- reference RBC curve is due to the variation in the transit directional oxygen sequestration per unit of cell space. times of the sinusoids (this likely arises because such a The sequestration rate constant k'seqcan be construed large proportion of the liver is sinusoidal blood [121). to have the form V,-/(Y, + [O,]), where V,, is the Axial dispersions in individual vessels are not differenlocal enzymic capacity of the cytochrome oxidase system tiated. 6. There is no net diffusional interaction between

112

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KASSISSLG ET AL.

sinusoids of unequal transit time. The latter two assumptions have been used to account for the experimental finding that, with a single common tovalue, the curve for each of the compartmental reference labels (albumin, sucrose and water) is found, on transformation with a single parameter (utilized to diminish the time scale and increase the fractional recovery), to superimpose on the labeled RBC, or vascular reference, curve (1).We assume that the opportunity for intersinusoidal interactions for labeled oxygen will be more or less like that for labeled water because the sequestration of the tracer oxygen is far from complete. The corresponding theoretical description for the whole organ outflow response (9) is, for labeled RBCs,

fashion, becoming smaller as the hematocrit increases. This corresponds to the behavior observed experimentally. Finding Parameters fkom the Tracer Outflow Dilution Curves.As a background to later calculations, optimized values for, ,y and towere determined, by use of equation 10, from the relationships between the labeled RBC and sucrose curves (8). The next problem resolves into that of securing optimized estimates of the parameters characterizing the tracer oxygen behavior. Equation 11provides a way of relating the tracer oxygen behavior to the labeled RBC curve. At the same time, the superposition relation expressed by equation 10 also makes it possible to relate the outflow tracer oxygen curve to that of the interstitial compartment reference, labeled sucrose. Because from the data it has become clear that the space ratio of the reference for the labeled oxygen curve is close to that for labeled sucrose and the use of the labeled sucrose curve as the reference for the labeled oxygen curve provides more points and therefore where n(LIW) describes the distribution of sinusoidal slightly better fitting statistics, we chose to use the transit times, t' is t - to and F is total organ blood flow. labeled sucrose curve as the reference curve for our From the definition of fractional recovery, the amount of fitting calculations. This choice does not mean that we tracer injected is a unit amount. have abandoned the use of the labeled RBC curve as the For labeled sucrose, appropriate reference to which to relate the tracer oxygen data, as expressed in equation 11. We simply used a set of equivalent relations that allowed us to obtain the best possible estimates of the parameters in equation 11. From the previously derived relationships between the curves, equation 11 becomes r.1+

Yaucl

For labeled oxygen, C02(t) =

To use this equation we need to proceed further. The inference of our use of bulk input and output oxygen contents in the definition of the fractional recovery per milliliter of blood for tracer oxygen is that the cumulative outflow recovery of tracer matches that of bulk (11) oxygen- that is, that

J')dk)

t' - e-kseq8"t'

[1 + Yo,]

Bulk outflow recovery of oxygen =

In the foregoing, note that

Co2(t)dt

(12)

-

The expression is the product of keeqand the proportion of the total oxygen space in which the removal process is taking place. The space ratio parameter yo2, describing the partition of tracer oxygen between tissue and blood, is

em

FJ, C,,(t)dt

lo=

C,uc(t")e-ksege"(t* - to)dtn

-

(16)

(13) where

From the definition of p', this is ?sue

Yo,

1

+

A

k',e'

+

= C

Hct P

=

(14) m

where Hct is the hematocrit of the blood. Thus 'yo, is expected to vary with hematocrit in a nonlinear

Cumulativetracer oxygen recovery Cumulative referencerecovery

-

-

(1 + Yo,) (1 + Y d

k 0"-

k-gAhpe'

(1 + ysuc)(l + &P')

(17)

and, in the transformation to obtain the upper integral,

773

TRACER OXYGEN BEHAVIOR IN RAT LrVER

Vol. 16,No.3, 1992

temperature than in the low-temperature groups, but it was not related to hematocrit. No difference in yauc was found between the groups, but yoz was signifiwhere exponential extrapolation beyond the last sample cantly higher in the low-hematocrit groups compared is used to obtain the areas under the curves. Because with the high-hematocrit groups. The rate constant + A,,)p’] was significantly higher in the bulk recovery is known, the parameter k’sQ” was found k A,,O’/[(l from equation ( 16)by iterative Newtonian interpolation. h3-temperature groups compared with the lowThe value reported for the rate constant, in the tables, temperature groups; it was lower with high hematocrits than with low hematocrits, as expected. Sinusoidal blood is volumes and interstitial spaces were not different between the groups. (19) (1 + Y,“,i(t

t” :

(1 + Yo,)

~

t”)

i

to

(18)

DISCUSSION

This is independent of (1 + y,,,,). With the value determined for the rate constant, equation 15 was used to obtain optimized values for the parameter (1 + yo,) from the relationships between the tracer sucrose and tracer oxygen curves. The optimizing procedure was, for both the tracer sucrose and oxygen curves, guided by a least-squares algorithm provided by International Mathematical and Statistical Libraries (Houston, TX), which was programmed in Fortran 77 on a Hewlett-Packard 9000 Series 500 computer (Hewlett-Packard Corp., Fort Collins, CO). Standard deviations of the optimized parameters were obtained as described by Landau and DiStephano (22). Coefficients of variation and coefficients of determination were calculated for the fit to the data, as previously described by Goresky et al. (18). The sinusoidal blood volume (the space accessible to RBCs) was calculated by multiplying the difference between the mean transit time of the RBCs and the common large vessel transit time toby the flow of blood, and the hepatic interstitial space, by multiplying the difference between the mean transit times of labeled sucrose and RBCs by the flow of plasma. Experimental Results and Fitted Parameters. Table 1 shows the primary data and derived parameters from all experiments over the four groups, together with the calculated S.D.s for the fitted parameters and the coefficients of variation and determination for the fits. The estimated S.D. for the fitted coefficients, expressed as fractions of the value of the coefficient were on average, for ysu0 0.095; for yoz, 0.195; and for kseq Ahp0’/(l + X,p’), 0.125. The modeling was found to fit the expermental data, within experimental error. The average coefficient of variation for the transformation of the labeled sucrose curve to fit the labeled RBC curve was 0.083; that for the fit of the computed to the experimental labeled oxygen curve was 0.083. The average coefficient of determination for the transformation of the labeled sucrose was 0.994; that for the fit to the labeled oxygen curve was 0.988. The fit showed no systematic deviations from the experimental data. At constant flow rate, oxygen extraction is expected to be a function of both temperature and hematocrit; such was the case in these experiments. No significant differences were seen in flow rate per gram of liver between the four groups. ANOVA was carried out to discern the effects of temperature and of hematocrit on the oxygen consumption and the fitted parameters. Total liver oxygen consumption was sigdicantly higher in the high-

We have secured the first observations of tracer oxygen behavior in the liver. The use of lower temperature perfusion provided a dramatic tool for examining tracer oxygen distribution in a situation in which consumption of oxygen and, hence, sequestration of tracer, was much reduced. The tracer data and the results of our modeling are consistent with flow-limited distribution of tracer oxygen in the isolated perfused liver. The data provide an index of the space of distribution available to tracer oxygen and of the rate constant for consumption and provide evidence for their dependence on hematocrit. Before the details of this and of the relationship between oxygen supply and hepatic metabolism are discussed, it is important to address the potential limitations of the preparation and of the modeling. Suitability of the Preparation. Most of the blood flow to the hepatic sinusoids of the in situ rat liver arises from portal venules. The arterial flow to the rat liver, which provides a minor part of the whole, also reaches the sinusoids, by three differing routes: drainage into peribiliary sinusoids after supply of the periductal capillary network, through arterial twigs that directly enter sinusoids in the central part of the acinus or through direct arterial-portal venous anastomoses. We expect, however, that provision of all the oxygen through the portal vein - although it might result in a less-thanoptimal oxygen supply to the biliary apparatus-will provide an adequate supply of oxygen to the hepatocytes, which constitute the bulk of the liver parenchyma. Most of the net oxygen supply of the i n situ liver can be calculated to arise, in uzuo, from the hepatic artery (23). The oxygen consumption of the portally perfused isolated liver is somewhat lower than that of the in uiuo, normally perfused liver. This was initially attributed to lack of a circulating hormone stimulating liver metabolism (241, but it is likely due to lack of substrate in the perfusion fluid; it is associated with a decrease in the potential across the hepatocyte cell plasma membrane (25).One would expect most of the oxygen consumption of the isolated liver to be associated with oxidative phosphorylation, which normally accounts for 70% to 85% of the oxygen consumption (26, 27); this in turn would be expected to reflect the rate of energy demand by the cell. Oxygen use is thus expected to reflect the metabolism of other substrates, rather than being controlled of itself. suitability of the Model. The oxygen consumption of the isolated rat liver, perfused in the usual manner

774

KASSISSIA ET AL.

(without substrates known to increase oxygen consumption), has been found to be constant and relatively independent of flow (13,28,29) at flow values sufficient to recruit all of the liver tissue (13). The values are, experimentally, independent of the hematocrit used in the perfusion (this study and [291). It is thus clear from the above data and from in uitro RBC unloading rates (15) that oxygen consumption in the perfused liver is not limited by oxygen supply. We used a first-order rate constant to describe the intracellular sequestration of tracer oxygen. The model provided excellent fits to the tracer data. In the light of the expected dependence of the consumption of oxygen on the consumption of other substrates, this can be construed to reflect, essentially, a first-order consumption of the other substrates. In this situation the tracer oxygen consumption is not simply a function of the oxygen species concentration because it can be increased dramatically by increasing the supply of other materials that increase oxygen demand. The characterization of the process is different from the usual case, in which the consumption varies only with the underlying bulk concentration of the substance (30). Absolute confidence in the suitability of the simple approach as a reasonable first approximation can be obtained only by constructing a much more elaborate model including the effects of nonlinear hemoglobin-oxygen binding. The problem is challenging and has not yet been solved. Nevertheless, the simple model appears to reflect a good approximation to reality, and the optimized parameters change in the expected directions with the two interventions. The data and the analysis confirm the flow-limited nature of oxygen transport in the liver, the main conclusion to be derived from this study. It is possible that the rate of oxygen consumption could be heterogeneously distributed along the sinusoid, as proposed by Kekonen, Jauhonen and Hassinen (31). In the flowlimited case, outflow analysis alone can provide no insight into this. Effkcts of Temperature and Hematocrit. Variation in temperature and hematocrit were chosen as the two interventions that we expected to independently affect the rate of oxygen sequestration and the relative space of distribution, respectively. Higher temperature increased the oxygen consumption and the sequestration rate constant, as expected, but temperature did not have an independent effect on the space of distribution available to oxygen. We found no effect of hematocrit on the rate of oxygen consumption, but the sequestration rate constant decreased as the hematocrit increased. The relative space of distribution available to oxygen in tissue was larger at the lower hematocrit than the higher hematocrit. Extravascular Maas of Tracer Oxygen. It would be useful in this instance if one could in some independent fashion determine the intracellular space of distribution available to tracer oxygen, with the objective of determining the magnitude of the parameter hh Oxygen is moderately lipid soluble (it partitions into o%veoil from water in the concentration ratio 5 :1[321); thus it has a

HEPATOLOGY

lipid distribution space. If, in addition, oxygen binding to cytochromesm3and P450show up as a binding space ( 5 ) for tracer oxygen (beyond that available to dissolved oxygen) the parameter Ahp is expected to be larger than 1.0. To gain insight, we calculated from the measured input and output blood oxygen contents the logarithmic average oxygen content and, from this, an average hemoglobin saturation and plasma PO,. From the results of the dilution-curve analysis, sinusoidal RBC and plasma oxygen contents were calculated. From the interstitial water content, calculated from the tracer sucrose curve, and the cellular water content, estimated from the liver weight and the results of previous tracer water studies (lo), the equilibrium interstitial and cellular oxygen contents expected on the basis of their water contents can be calculated. The tracer oxygen studies themselves provide, from the value for yo,, an estimate of the total equilibrium extravascular oxygen content. By subtraction of the interstitial space oxygen content, this gives an experimental estimate of the cellular oxygen content. The ratio of this to the expected value can then be found; for our experiments this value was on average 2.91 mVml. This value corresponds to hhpe'/O if, as calculated previously (81, O'/O = 1.11and Xhp = 2.62 d m l . The value indicates that the equilibrium association of oxygen with 1ml of liver cells is 2.62 times that with 1ml of plasma; expressed in terms of liver weight it would be 2.46 d g m . The comparative values for xenon are 1.93 mVml and 1.79 d g m (8).The association of oxygen with liver tissue appears slightly greater than that of xenon. Implications of Flow-limited Oxygen Transport in the Liver. Oxygen uptake is independent of liver blood flow at flows of about 0.9 mVmin/gm liver or greater. Below this level, oxygen uptake and galactose elimination decline in spite of venous PO,S above 20 mm Hg in both isolated perfused rat and pig livers (26, 291, apparently because of tissue derecruitment (13).When the critical PO, of isolated mitochondria is estimated in vitro under state 3 conditions, values less than 1 mm Hg are obtained. On the other hand, the apparent critical PO, of whole cells in close-to-physiological conditions or of whole organs tends to be much higher. Despite these inferences, it is clear that in most situations more oxygen is supplied to the liver than can be used; the overall rate of metabolism and of oxygen utilization reflects the energy metabolism of the cell and substrate supply rather than the rate of oxygen supply. This fits together with our finding that no barrier limitation exists to the distribution of tracer oxygen in the liver. This behavior is quite different from that in the heart, where there is resistance to transfer of tracer oxygen at the capillary level with low tissue oxygen levels due to consumption beyond the barrier. Thus, in line with this, it has been found that coronary blood flow can affect oxygen consumption (33).The data generally show that when local oxygen consumption and flow are both low, an increase in coronary flow is associated with both an increase in oxygen consumption and an improvement in performance. The change is construed to reflect a

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volume, Disse space, intracellular water space, and drug extraction concomitant capillary recruitment with increase in flow in the perfused rat liver preparation: characterization by the (4), mediating more effective tissue delivery, in this multiple indicator dilution technique. J Pharmacokinet Biophartransfer-limited system. marnut 1988;6:595-632. The comparison between the liver and the heart 14. Goresky CA, Bach GG, Rose CP. Effects of saturating metabolic uptake on space profiles and tracer kinetics. Am J Physiol provides additional insight. Whereas in the liver flow1983;244:G215-G232. limited distribution of tracer oxygen occurs, and in the Sirs JA. The egress of oxygen from sheep erythrocytes. Biochim heart the process is barrier limited, the distances from 15. Biophys Ada 1966;112:538-549. blood to parenchymal cells are not very different. The 16. Goresky CA, Bach GG, Nadeau BE. On the uptake of materials by major difference is the structure of the space. In the the intact liver: the transport and net removal of galactme. J Clin Invest 1973;52:991-1009. heart there is an intervening capillary wall and inter17. Goresky CA, Bach GG, Nadeau BE. Red cell carriage of label: its stitial space, whereas in the liver there is only a freely limiting effect on the exchange of materials in the liver. Circ Res accessible interstitial space. It is therefore likely that the 1975;36:328-351. continuous capillary wall provides the resistance in the 18. Goresky CA, Bach GG, Wolkoff AW, Rose CP, Cousineau D. Sequestered tracer outflow recovery in multiple indicator dilution heart. The interstitial space of the liver does not impose experiments. HEPATOLOGY 1985;5:805-814. an equivalent resistance; instead, the resistance is so low Bassingthwaighte JB. A concurrent model for extraction during that the tracer distribution process for oxygen is flow 19. transcapillary passage. Circ Res 1974;35:483-503. limited. 20. Dupuis J, Goresky CA, Ryan JW,Rouleau JL, Bach GG. Pulmonary angiotensin-converting enzyme substrate hydrolysis Acknowledgments: We thank Eva Ibrahim and Kay during exercise. J Appl Physiol 1992;72:1868-1886. Lumsden for their expert technical assistance and 21. Crone C. Permeability of capillaries in various organs as determined by use of the “indicator diffusion” method. Acta Physiol Elizabeth Capon for typing this manuscript.

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