Increased Hepatocyte Permeability Surface Area Product for ^{86}Rb With Increase in Blood Flow
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Abstract
Abstract Liver cell recruitment (the equivalent of capillary recruitment in other organs) was explored by carrying out multiple indicator dilution experiments with labeled rubidium across the liver of the anesthetized dog under basal conditions and after bleeding with saline replacement infusion, which increases liver blood flow. A mixture of ^{51}Crlabeled red blood cells (a vascular reference), ^{22}Na (which immediately equilibrates in the extracellular space, the sum of the sinusoidal plasma and Disse or interstitial spaces, the expected distribution space for labeled rubidium in the absence of cellular entry), and ^{86}Rb was injected into the portal vein, and normalized outflow patterns, expressed as outflowing fractions of each injected tracer per milliliter versus time, were obtained. In relation to the labeled red blood cell curve, the labeled sodium curve is displaced by flowlimited distribution into the Disse or interstitial space; it is lower on the upslope, reaches a lower and delayed peak, and decays more slowly. The early part of the labeled rubidium curve lies within the labeled sodium curve; it reaches a much reduced peak, and the later return of tracer entering cells is so slow that it is obscured by recirculation. Modeling of the concentrative cellular uptake of rubidium from the Disse space provided an influx permeability surface area product for labeled rubidium. This increases with flow over the observed flow range, demonstrating that sinusoidal recruitment occurs with increase in hepatic blood flow.
The exchange capabilities of the microcirculation of in situ organs, in the in vivo situation, have generally been found to increase with flow. For instance, in the heart, the capillary permeability surface area product for labeled sucrose, an interstitial space label, increases with flow and then tends to level off at the highest flows encountered.^{1} ^{2} ^{3} In the lungs of exercising dogs, the labeled water space (ie, the accessible tissue) increases in the transition from rest to lowlevel exercise and then changes no further at higher flow rates. On the other hand, the capillary permeability surface area products for labeled norepinephrine and for benzoylPheGlyPro, a pharmacologically inactive angiotensinconverting enzyme substrate, increase continuously over the whole flow range encountered with exercise,^{4} ^{5} indicating that there is a concomitant continuous recruitment of capillary surface over the whole flow range.
The microcirculation of the liver is unique. Blood pours into the hepatic sinusoids primarily from the portal venule and bathes both faces of each segment of the liver cell plate, leaving the hepatic acinus via symmetrically placed hepatic venules. The sinusoids intercommunicate frequently, leading to a threedimensional labyrinthine kind of structure. Materials are carried to the exit by concurrent flow along the available channels. No anatomic structures are available that could lead to a short circuit or diffusion bypass of the vascular channels. Labeled water studies in the isolated perfused liver indicate that below flow levels of 0.7 mL·min^{–1}·g^{–1} (0.012 mL·s^{–1}·g^{–1}), the cellular water space accessible to labeled water diminishes as flow is decreased; above that level, the accessible cellular water space is invariant with flow.^{6} The question that arises is whether hepatic cellular uptake surface areas also change with flow and, if they do, in what fashion.
Labeled rubidium is an ideal tracer for the exploration of this question. In the liver, it is delivered directly to the sinusoidal faces of the hepatic parenchymal cells, a consequence of the open fenestra perforating the sinusoidal lining cells. At the surface of the hepatic parenchymal cells, it is transported into the cells in a highly concentrative fashion. As a consequence of this, tracer that enters the cells returns to the circulation very slowly; tracer carried along the sinusoids by flow, without entering the hepatic parenchymal cells, is joined early in time by only a very small proportion of the tracer that has entered the parenchymal cells. Good estimates of the permeability surface area product for the cell entry of labeled rubidium can then be obtained.^{7} Therefore, we designed a set of experiments in which this tracer was used to explore recruitment in the hepatic circulation.
Materials and Methods
In the present study, which was carried out in anesthetized dogs, we used the multiple indicator dilution approach. In each experiment, we injected three substances simultaneously: ^{51}Crlabeled red blood cells, a vascular indicator that does not leave the microcirculation; ^{22}Na, which freely enters the Disse space (the interstitial equivalent space) but does not significantly enter liver cells during the time of a single passage^{7} ; and ^{86}Rb, which undergoes rapid concentrative uptake by the liver cells.
The experiments were carried out in mongrel dogs weighing 13 to 26 kg that had been anesthetized with pentobarbital (on average, 25 mg/kg). A catheter for injection was placed in the portal vein, and a collection catheter was placed in the left main hepatic venous reservoir in such a fashion that no outflow obstruction resulted.^{8} The abdomen was closed to allow its contents to return to a normal temperature. The injection mixture was rapidly introduced to produce crosssectional mixing in the portal vein, and hepatic venous samples were pumped from the hepatic vein, at a rate of ≈75 mL/min.
The injection mixture was made up of blood, with a hematocrit matching that of the animal. The following special materials were used: [^{51}Cr_{2}]Na_{2}O_{7} solution, 6 Ci/mmol (Charles E. Frosst); [^{22}Na]Cl, 5 mCi/mmol (Radiochemical Centre, Amersham); and [^{86}Rb]Cl, 50 μCi/mmol (New England Nuclear Corp). The quantities of radioactivity injected were approximately as follows: ^{51}Crlabeled red blood cells, 20 μCi; ^{22}Na, 3 μCi; and ^{86}Rb, 150 μCi. The ^{86}Rb was added to the injection mixture just before the experimental run, so that all of the tracer was in the plasma phase. Since canine red blood cells are deficient in Na^{+},K^{+}ATPase,^{9} red blood cell entry rates would, in any case, be slow. Standards were prepared from the injection mixture by the addition, in serial dilution, of blood obtained before the experiment. Volumes of 0.5 mL of sample or standard, diluted with 1.0 mL of saline and then centrifuged, were assayed in a twochannel welltype scintillation crystal gamma ray spectrometer (Nuclear Chicago) or a threechannel Cobra gamma ray spectrometer (Packard Instrument Co) for gamma rays of appropriate energy (for ^{22}Na, the segment above 1.16 MeV was used; for ^{86}Rb, the 1.08MeV region; and for ^{51}Cr, the 0.32MeV region). The activity due to each species was determined by use of appropriate standards containing only one of the radioactive species and, where necessary, a decay factor. At least 1000 counts were ordinarily recorded in the lowest activity channel.
Experiments were carried out in 17 animals with normal hematocrit values and in 6 animals in which the hematocrit was reduced by bleeding with replacement of ≈20% more than the lost volume by saline. The latter maneuver has the effect of substantially increasing liver blood flow.
Model analysis was used to secure from the outflow dilution curves a set of parameters describing exchange in the sinusoidal bed. It has previously been shown that in relation to the labeled red blood cells, labeled sodium is distributed into the space of Disse in a flowlimited fashion; ie, it enters this space as rapidly as it is presented, because with the fenestra perforating the sinusoidal lining cells, there is no resistance to exchange between the sinusoidal plasma and the space of Disse. This has the consequence that the labeled sodium impulse propagates along the sinusoid in both the sinusoidal plasma and Disse spaces; it travels less rapidly than the labeled red blood cells, which are carried within the sinusoids by flow, so that the labeled sodium impulse emerges later.^{7} ^{8} The distribution of transit times in the large vessels and sinusoids is such that virtually all of the heterogeneity occurs in the sinusoidal bed (this is the predominant part of the contained blood in the liver). With this, when outflow profiles are normalized in relation to the amount of tracer injected, the relation between the labeled sodium and labeled red blood cell profiles is described by the following relation^{8} ^{10} : where C_{Na}(t) and C_{RBC}(t) are the labeled sodium and labeled red blood cell outflow profiles as a function of time t, γ is the ratio of sodiumaccessible Disse space to the plasma space in the sinusoids, and t_{0} corresponds to the largevessel transit time. The sense of the equation is that the labeled sodium curve, with appropriate transformation, will superimpose on the labeled red blood cell curve, and an optimal superimposition will provide estimates of γ and t_{0}. The superimposition maneuver consists of increasing the labeled sodium values by (1+γ) and diminishing the time beyond t_{0} by the factor 1/(1+γ).
For these two reference substances, the primary dilution curve (the activity resulting from first passage, not contaminated by recirculation) finishes early in time, and the areas under the curves can be determined by linear extrapolation of the downslopes on a semilogarithmic plot.^{8} Hence, since with normalization, the amount of tracer injected is a unit amount, flow F can be calculated by use of the following relation^{8} : where the expression in the denominator is the area under the curve. Since the area under the curve for each reference substance is expected to be the same,^{7} flow may be determined from either labeled red blood cell or labeled sodium dilution curves.
The liver vascular space was calculated as the product of blood flow and the mean transit time (the time integral of the product of time and activity divided by the area under the curve) for the labeled red blood cells. The sodium accessible interstitial space was calculated as the product of the plasma flow and the difference between the labeled sodium and labeled red blood cell mean transit times.
Labeled rubidium enters the liver cells from the Disse space in a highly concentrative fashion. Since biliary excretion of tracer will be small, virtually all of the tracer that has entered the liver cells would be expected to emerge subsequently from the liver cells to plasma, if there were no recirculation of tracer. For labeled rubidium, the expected form of its first passage curve (ie, the curve if there were no recirculation), with respect to that for labeled sodium, is as follows^{7} ^{11} : where C_{Rb}(t) is the predicted labeled rubidium outflow profile; k_{1} is the influx permeability surface area product for labeled rubidium, divided by the cellular volume, equivalent to the influx transport rate constant; k_{2} is the efflux permeability surface area product for rubidium, divided by the cellular volume, equivalent to the efflux transport rate constant; θ is the ratio of the cellular space to the sinusoidal plasma space for rubidium; and τ is the dummy variable of integration. Fitting this expression to the data will give a value for k_{1}θ/(1+γ) that corresponds to the ratio of the influx permeability surface area product for labeled rubidium divided by the space from which the flux comes, which is the sum of the sinusoidal plasma and interstitial (Disse) spaces, and, potentially, a value for k_{2}, if the later part of the first passage curve is accessible.
In carrying out the superimposition of the labeled sodium curve on the labeled red blood cell curve and finding the best parameters for calculated labeled rubidium curves, weighted nonlinear leastsquares fits were performed, using a modified LevenbergMarquart algorithm (IMSL Library, Sugar Land, Tex). An analysis of the sources of experimental error revealed that the largest part of the error is due to radioactivity counting, which follows a Poisson distribution. Hence, a reasonable choice is to set the weights proportional to the inverse of the values, which is approximately the inverse of the variances.^{12} Parameter estimates were evaluated statistically.^{12} The Jacobian matrix (matrix of sensitivities) obtained from the fitting program was used to calculate the variances and covariances of fitted parameters. The square roots of the variances, the standard deviations of the fitted parameters, were calculated for each single experiment, representing the uncertainty in the determination of the parameter from the data of the experiment (as opposed to that for parameters from different experiments, representing interindividual variability).
The input and collection catheters impose delay and distortion on the curves. Goresky and Silverman^{13} have shown that when the transfer functions of the catheters have been characterized and that even though all of the indicators are sampled simultaneously through the same system, deconvolution of the transfer functions results in somewhat increased values for γ and t_{0}^{13} and for the rate constants describing labeled rubidium exchange.^{7} Therefore, it is necessary to derive parameter values from data derived by deconvolution of the catheter transfer function.
The transfer functions of the catheters have previously been characterized in terms of both analytical form and the parameters characterizing a particular experimental situation.^{13} In the present experiments, the outflow catheter and the attached pump were the same as in Reference 13^{13} . In that study, the catheter transfer function was approximated by a delay, followed by a decreasing exponential. The catheter mean transit time was ordinarily of the order of 2.5 seconds. The distortion due to the exponential part of the catheter transfer function was handled in the following way during the fitting procedure: A spline function^{14} was fitted to the labeled sodium curve. Catheter distortion was deconvoluted from this curve using the following relation: where C̃_{Na}^{Deconvoluted}(s) and C̃_{Na}(s) are the Laplace transforms of the deconvoluted and measured sodium curves, respectively, and H̃(s) is the Laplace transform of the transfer function of the catheter. Using a decreasing exponential function as transfer function h(t)=αe^{–αt}, the undistorted reference curve in the time domain is as follows: Since a spline is a piecewise polynomial, the derivative is easily obtained analytically. Trial values of γ and t_{0} were used to linearly transform the deconvoluted curve using Equation 1; the resultant transformed labeled sodium curve was then convoluted with the catheter transfer function using the following equation: The transformed curve was then fitted to the observed labeled red blood cell curve. Best fit values for γ and t_{0} were obtained with a minimum χ^{2} criterion. This choice, in terms of the approach to deconvolution, has the advantage that the originally observed data with their uncertainties are available for the fitting. Since the process of deconvolution accentuates irregularities in the curves, this approach also has the general advantage that fitting is carried out with the original smoother set of observations. The sinusoidal mean transit time is, then, by definition, t̄_{RBC}−t_{0}.
In fitting the labeled rubidium outflow curves, the t_{0} value obtained above was used. A onebarrier model was fitted to the data, as described by Equation 3. The parameters potentially obtained by fitting to the data are k_{1}θ/(1+γ) and k_{2}. However, the form of the data is such that recirculation interrupts the later part of the impulse response to the system, making the estimation of k_{2}, which depends on the later part of the curve, problematical. To make accommodations for this, the ratio k_{1}θ/[k_{2}(1+γ)] was assumed to be equal to 40, a value corresponding to the expected ratio of cellular to plasma sinusoidal and Disse space rubidium contents in steady state,^{15} ^{16} and the parameter k_{1}θ/(1+γ) was obtained from the fitting. In the fitting, the catheterdeconvoluted, splined, labeled sodium curve served as the reference curve. A modelpredicted labeled rubidium curve was generated from this, by means of Equation 3, and then convoluted with the catheter transfer function. The resultant curve was then fitted to the experimentally observed labeled rubidium curve, again with a minimum χ^{2} criterion.
The influx permeability surface area product for labeled rubidium, P_{in}S, is then derived from the fitted parameter k_{1}θ/(1+γ) in the following way: Since, by definition, k_{1}θ/(1+γ) is the influx permeability surface area product (P_{in}S) divided by the sum of the sinusoidal and Disse spaces of distribution of the labeled rubidium and since the rubidium is distributed in the plasma space of blood, P_{in}S can be calculated by multiplying k_{1}θ/(1+γ) by the space of distribution, F(1−Hct)(¯t_{Na}−t_{0}); ie, where ¯t_{Na} is the mean transit time for labeled sodium, Hct is hematocrit, and if F(1–Hct) is expressed as mL plasma ·s^{–1}·g^{–1}, P_{in}S is expressed in similar units.
Results
Rpresentative sets of experimental data from lowflow and relatively highflow experiments are presented in Fig 1⇓. The data are represented in semilogarithmic, linear, and cumulative formats in the upper, middle, and lower panels, respectively. An estimate of measurement standard deviation, which includes radioactivity counting and sample volume measurement error, is shown whenever it is larger than the symbol used for the plot. The semilogarithmic format displays the relations between the curves, especially as values become lower; the linear format displays the relative magnitudes of the curves; and the cumulative format displays cumulative outflow profiles. The outflow fraction per milliliter for labeled red blood cells rises to the earliest and highest peak and decays rapidly. The values for labeled sodium are lower on the upslope, the peak is delayed and is lower, the downslope decays much more slowly, and recirculation is delayed. Both reference curves are corrected for recirculation by linear extrapolation on the semilogarithmic plot. The areas under the labeled red blood cell and sodium reference curves are higher at the lower flow and smaller at the higher flow, as expected. The initial part of the labeled rubidium curve is contained within the labeled sodium curve. With time, it departs progressively from the labeled sodium curve on the semilogarithmic plot. The peak of the labeled rubidium curve is lower and slightly earlier, and the downslope of this early component of the curve decays more rapidly than that of the labeled sodium curve. The later part of the response is concealed by recirculation; however, tracer rubidium that has entered the liver cells will be expected to exit slowly to plasma with the passage of time. The cumulative outflow survival of tracer rubidium is illustrated in the lower panel. At higher flows, more of the tracer emerges early in time. Conversely, the proportional cellular uptake of tracer early in time is higher at lower flow.
The parameters derived from the data and their analyses are presented in Tables 1⇓ and 2⇓. The average ratio of the recovery of labeled red blood cells to that of labeled sodium was 0.99±0.06 (mean±SD). Values for times have been corrected for catheter transit times. Values for vascular volume are in the normal range^{17} ; ie, they do not correspond to the reduced values found in a sympathetically stimulated preparation. Values for the interstitial or Disse space tend to be higher than expected^{17} in the salineinfused animals.
Fits to the labeled rubidium data of the representative experiments are shown in Fig 2⇓. The data are shown in semilogarithmic format in the top panels and in rectilinear format in the lower panels. The predicted outflow response for the labeled rubidium consists of two parts: (1) tracer that passes through the microcirculation without entering liver cells, a throughput component that, in this instance, is the preponderant part of the recorded early outflow response (the first term of Equation 3), and (2) tracer that has entered the liver cells to return later in time, the returning component (the second term of Equation 3). The illustration shows that the returning component is proportionally larger in the lowerflow experiment, where the proportion of the label that has entered the liver cells was larger. However, the returning component was so small in magnitude in each case, early in time, that it was easily perceptible only on the semilogarithmic plot. The continuation of the fit, beyond times of the collected samples, was used to extend the cumulative plots in Fig 1⇑. This demonstrates that return of tracer that has entered liver cells is expected to occur very slowly. To assess the quality of the fits, the normalized residuals (R_{i} values) are shown in the lower panels of Fig 2⇓, which are defined as follows: where C_{Rb}^{i} is the ith measurement, C_{Fit}(t_{i}) is the fitting function value at the corresponding time; and ς_{i} is ana priori estimate of standard deviation for point i. The definition for the fractional recoveries being where ξ_{Rb}^{i} and ξ_{Rb}^{Injected} are the radioactive counts per sample for point i and for the injection mixture, respectively. Since the counts for the injection mixture are much higher than for the point i, the standard deviation for C_{Rb}^{i} is mainly due to counting error for the latter, so that The a posteriori estimate of standard deviation (ς̂) is as follows: where DF is degrees of freedom and has a value of 2.0 for each of these experiments, indicating that the experimental error was initially underestimated. Averaged over all experiments, the proportion of residuals lying between −ς̂ and +ς̂ is 67±10%, which is consistent with a normal distribution of the residuals with a variance of ς̂^{2}. The maximum residual (in absolute value) for each individual is 2.6ς̂±0.5ς̂, and the overall maximum residual (in absolute value) is 3.8ς̂.
We have performed WaldWolfowitz runs tests (SYSTAT, Inc) on all fits and found that in 9 of 23 experiments, systematic deviations from the fit occur. We attribute these to the use of a parsimonious model (see “Discussion”). Also, because of the limited number of data points for each experiment, runs tests are not very reliable.
Although the fits to the data are acceptable and the system behaves as expected, one of the questions that arises is how dependent the estimate of k_{1}θ/(1+γ) is upon the estimate for k_{1}θ/[k_{2}(1+γ)]. To assess this, we also fitted the data with k_{1}θ/[k_{2}(1+γ)] estimates of 20, 80, and ∞ and compared the results with those arising from the original estimate k_{1}θ/[k_{2}(1+γ)] of 40. For the k_{1}θ/[k_{2}(1+γ)] estimate of 20, the average value for k_{1}θ/(1+γ) was 1.3% larger, with a maximum difference of 2.7%; when 80, the average was 0.6% smaller, with a maximum decrement of 1.4%; and when ∞, the average was 1.2% smaller, with a maximum decrement of 2.8%. The value for k_{1}θ/(1+γ) thus appears fairly well defined. However, the standard deviations for k_{1}θ/(1+γ) are likely underestimates of the true standard deviations because of uncertainty on k_{1}θ/[k_{2}(1+γ)].
From Fig 1⇑ it is seen that, with k_{1}θ/[k_{2}(1+γ)]=40, the amount of tracer returning from the cellular to the vascular space within the sampling period is negligible. The data do not allow us to distinguish this situation from the case where k_{1}θ/[k_{2}(1+γ)]=∞, when the tracer will never return from the cellular to the vascular space. Thus, values for k_{1}θ/[k_{2}(1+γ)], although able to be estimated from steady state biological data, and for k_{2} are not determinable from individual experimental data, with the present truncated data sets.
Fig 3⇓ illustrates the change in the throughput component as a function of flow, expressed as a fraction of the total. The error bars represent the uncertainty in the throughput component (standard deviation) due to the variation in k_{1}θ/(1+γ). Different symbols were used to distinguish low hematocrit experiments, where dogs were bled and given saline, from normal hematocrit ones. Performing separate linear regressions on each set of experiments shows that the two regression lines are not statistically different^{18} (P>.05). Hence, only one line is used to fit the whole data set. Also, using a curvature test,^{18} the data appear best fitted using a straight line (P>.1). Since the error bars shown on Fig 3⇓ do not account for most deviations from the fit, unweighted regression is used. The best fit line is where T is the throughput component, F is blood flow in mL·s^{–1}·g^{–1}, and r is the Pearson correlation coefficient for the fit. This corresponds to a significant correlation between throughput and flow (P>.999).^{18}
The change in the vascular volume with flow is illustrated in the upper panel of Fig 4⇓. If linear regression is used, separate lines are needed in order to fit normal and low hematocrit data sets (the probability that the two sets can be fitted by a single line is P<.01^{18} ). The best fit lines are where V_{vasc} is the vascular volume in milliliters per gram liver. Again, unweighted fit was performed. If the difference between the two lines is attributed to the difference in flow range, the data can be treated as a single set and, hence, be fitted with a unique function. A saturating exponential has been fitted to the data, over the range of the observations. The best fit was The combined low and normal hematocrit data appear to increase more or less linearly over the low flow range, from 0.01 to 0.03 mL·s^{–1}·g^{−1}, and then begin to level off over the higher flow range. Previously, data have been available over the linear low flow range^{17} ^{19} ^{20} ^{21} ; the demonstration of an apparent maximum is new.
The variation in the influx permeability surface area product for labeled rubidium with flow is displayed in the lower panel of Fig 4⇑. A single straight line is sufficient to fit the data (the probability that the two hematocrit data sets belongs to the same set is P>.3). The combined data increase with flow over the range studied. The probability that there is no correlation between influx permeability surface area product and flow is P<.01. The data display no significant curvature^{18} (probability that the data is linear is P>.5). However, the three highest flow points lie below the fitted line, and in the flow range 0.027<F<0.041, most of the points are above the fit (five points above and one below); this suggests a tendency for the influx permeability surface area product to reach a maximum as flow increases. Though a larger data set may be needed to find a significant curvature, the data are fitted with a saturating exponential function as well as with a single line. The equations for the best unweighted fit are where P_{in}S is the influx permeability surface area product in milliliters per second per gram liver. One can conclude that, over the observed range of flows, there is a recruitment of liver cell surface with flow.
Discussion
In choosing a model for evaluating the data for the present study, we faced a dilemma between an unbiased representation of the data and a parsimonious description of the essential physiological phenomena. The model used in the present study is based on simplifying assumptions. For example, the transit time of the nonexchanging (“large”) vessels, t_{0}, is assumed to be uniform and identical for sodium and rubidium. The membrane permeability for rubidium and the diameter of sinusoids are also assumed uniform. These simplifications may be responsible for small but systematic deviations of the model from the experimental data. Moreover, temporal fluctuations of liver blood flow due to the breathing movements of the animals may have led to minor distortions of the outflow profiles. Since for a majority of the animals, systematic deviations were not significant, the values obtained for the permeability surface area product may be regarded as valid approximations for the liver averages in all cases.
The recruitment of liver cell surface with flow occurs within the set of volume changes that occur in the liver with flow and has been interpreted within the structure of these changes. The substance of the liver is contained within an elastic capsule, and with increase in flow, plethysmography shows that the whole expands.^{19} ^{20} Liver pump perfusion with exact recording of inflow and outflow^{21} and multiple indicator assessment^{17} have demonstrated that the chief components of the change are an increase in vascular volume and an increase in Disse space with flow. The increase in blood volume with blood flow is linear across the normally encountered flow range (the lower flow range of the present experiments); extrapolation of the relation to zero flow yields a value that has been termed the unstressed volume.^{20} Sympathetic stimulation reduces the blood volume in the liver.^{17} ^{21} The unstressed volume is reduced, but the slope of the volumetoflow relation is unchanged; with major sympathetic stimulation, the vascular volume decrease is of the order of 0.05 mL/g.^{17} A similar set of changes is found for the Disse space.^{17} In the present set of experiments, the values for vascular volume and interstitial or Disse space fall into the expected normal range of change, except after saline infusion, when the Disse space values tend to be increased, perhaps because of increased venous pressure; there are no low values in the range suggesting sympathetic stimulation. The volume changes across the lower range of flows are therefore more or less as expected. On the other hand, over the upper flow range, there is a substantial change in the response. The vascular volume increases less steeply with flow and, at the highest flows, tends to level off. The influences of recruitment and distension appear to have maximized. The modeling used to analyze the tracer rubidium curve builds in the influence of changes in transit time, vascular volume, and interstitial space over the whole range of flows.
The throughput component of the labeled rubidium curve increases with flow, as illustrated in Fig 3⇑. The observed rate of increase is less than would have been expected if the structural system were rigid and cellular permeability surface area products were unchanging with flow. The corresponding function, the initial rate of removal of tracer rubidium, increased with flow more than expected, and analysis indicated that this flow induced amplification was due to recruitment of liver parenchymal cell sinusoidal surface, as exemplified by the change in calculated permeability surface area product for labeled rubidium with flow, illustrated in Fig 4⇑. Over the normal and higher flow regime, the recruitment may be due to easier access to previously inaccessible segments of the sinusoidal vasculature as the sinusoidal volume increases with flow; a contribution may also be due to a decrease in the temporary trapping of leukocytes, so that the degree to which their segmental residence interferes with flow is diminished. At very low flow, an additional phenomenon has been observed in the isolated perfused liver. This may also be presumed to occur in vivo, under similar circumstances. This is a recruitment of tissue with increase in flow. In indicator dilution experiments designed so that labeled water curves will provide an estimate of intracellular water space,^{6} the cellular water space, expressed as a fraction of blotted liver weight, is found to be constant above a flow level of 0.7 mL·min^{–1}·g^{–1} (0.012 mL ·s^{–1}·g^{–1}), whereas below this level, the accessible cellular water space decreases with decreasing flow. Over this very low flow range, decrease in flow leads to derecruitment of tissue, and increase in flow leads to recruitment of tissue. In the present experiments, flow values in this low flow range were not observed. It appears appropriate to conclude that this phenomenon will ordinarily be of importance only in lowflow situations in vivo, since the flow ranges over which it occurs are not ordinarily otherwise encountered. The corollary of this is that over ordinary ranges of flow, all of the parenchymal cells, including those beyond the first layer encountered, will be accessible to labeled water. With the highly concentrative cellular uptake for labeled rubidium, on the other hand, the tracer rubidium will not penetrate rapidly beyond the first layer of accessible cells. The simultaneous labeled rubidium data thus indicate that all of the parenchymal cell uptake surfaces are not immediately accessible from the vascular space, at the flow values ordinarily encountered. The density of perfusion is such that some of the sinusoidal segments do not ordinarily receive flow. With increase in flow to high flow values, additional sinusoids and additional parenchymal cell surface are recruited.
Analogous phenomena have been seen in other organs, appearing in different ways. In indicator dilution experiments carried out in the lungs, for instance, extravascular water space accessible from this lowpressure circulation is found to increase in the transition from rest to low level exercise. At higher levels of exercise and cardiac output, the accessible extravascular water was found not to vary further with flow. At higher flows, all of the parenchymal tissue becomes accessible to labeled water introduced into the blood perfusing the organ.^{4} ^{5} The accessible capillary surface area has been assessed simultaneously by examining processes carried out by the pulmonary capillary endothelial cells: the uptake and processing of labeled norepinephrine by the capillary endothelial cells of the lung^{4} and the intravascular cleavage of the labeled pharmacologically inactive angiotensinconverting enzyme substrate, benzoylPheGlyPro, by the angiotensinconverting enzyme associated with the pulmonary capillary endothelial cell surface.^{5} These processes are expected to occur when the tracer first meets the capillary surface; distribution further into tissue is not expected. In the transition from rest to firstlevel exercise, where tissue recruitment is observed, capillary recruitment is found. At higher levels of exercise, when the accessible extravascular water space remains unchanging with flow, a further recruitment of pulmonary capillary surface is found, with the increase in flow. The increase does not approach a maximum at the highest levels of exercise achieved.^{4} ^{5} A parallel set of observations of the pulmonary diffusion capacity also suggests a continuing recruitment of capillary surface over the whole attainable flow range. The pulmonary diffusing capacity for carbon monoxide increases across the whole range of flows encountered with exercise; it also continues to increase in the exercising pneumonectomized dog, over the whole flow range achieved, to the highest flow to tissue perfusion levels yet encountered.^{22}
In the heart, recruitment of capillary surface with increase in flow has also been well defined. In this organ, the essential elements of the tissue are capillaries, interstitial space, and muscle. The most convenient substance for the examination of tissue recruitment in this organ is tracer sucrose, which enters the interstitial space and does not penetrate the muscle. Indicator dilution experiments with labeled sucrose show that all of the interstitial space is accessible at the lowest levels of flow found in the functioning in vivo heart and that the sucrose accessible interstitial space does not change further with increase in flow.^{23} ^{24} In the closedchest dog under anesthesia, in the basal state, and after a variety of stimuli designed to increase flow (cardiac pacing, plasma expansion, and carotid occlusion), the capillary permeability surface area product for labeled sucrose, on the other hand, is found to increase with flow over a common locus, which begins to level off (ie, to saturate) at the highest flow levels encountered.^{1} ^{2} ^{3} Analysis of the tracer data indicates that there is not only capillary recruitment with increase in flow but also a decrease in heterogeneity, as flow increases. The two phenomena serve together to amplify the exchange characteristics of the capillary bed with increase in flow.
The sinusoidal recruitment demonstrated in the liver is thus part of a general phenomenon. In the liver, it results in an increase in the density of perfusion and partly compensates for the decreased transit times accompanying increased flow by increasing the efficiency of blood tissue exchange.
Acknowledgments
This study was supported by grants from the Medical Research Council of Canada, the Quebec Heart Foundation, and the Fast Foundation. The authors wish to thank Dr Lawrence Joseph for helpful suggestions concerning statistical analysis, Kay Lumsden and Bruce Ritchie for their technical assistance, and Mary Ann Adjemian for typing this manuscript.
Footnotes

Reprint requests to Dr Andreas J. Schwab, University Medical Clinic, Room C10.157, Montreal General Hospital, 1650 Cedar Ave, Montreal, QC, Canada H3G 1A4.

↵1 Dr Goresky died March 21, 1996.
 Received January 5, 1996.
 Accepted December 19, 1996.
 © 1997 American Heart Association, Inc.
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 Increased Hepatocyte Permeability Surface Area Product for ^{86}Rb With Increase in Blood FlowCarl A. Goresky, André Simard and Andreas J. SchwabCirculation Research. 1997;80:645654, originally published May 19, 1997https://doi.org/10.1161/01.RES.80.5.645
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