Estimation of specific hepatic arterial water space

Selma Sahin and Malcolm Rowland

School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester M13 9PL, United Kingdom

    ABSTRACT
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

The aim of this study was to estimate the specific arterial water space and associated blood flow using statistical moments of the frequency versus time outflow profile, with a model with specific spaces for hepatic arterial (HA) and portal venous (PV) flows in parallel with a common space. Studies were performed in the in situ dual-perfused rat liver (n = 6-10), using Krebs-bicarbonate buffer with constant PV flow (12 ml/min) and various HA flow rates (3-6 ml/min). An impulse input-output technique was employed, varying the route of input, using [14C]urea as the reference indicator. Regardless of flow conditions, the frequency outflow profile after HA input was flatter and broader and the mean transit time longer than after PV input. Excellent recovery of marker was obtained in all cases. Applying the above model, the specific arterial space was estimated to be 9.7 ± 2.3 of total water space and receives ~17% of the HA flow, with the remainder mixing with portal blood in the common space. The estimated total water content of liver (0.67-0.72 ml/g liver) agrees well with that determined by desiccation (0.72 ± 0.01 ml/g liver).

liver; urea; dual perfusion; specific space; moment analysis

    INTRODUCTION
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

UNLIKE MOST OTHER ORGANS of the body, the liver has a dual blood supply. Under physiological conditions, 25-35% of its blood is supplied by the hepatic artery (HA) with the remainder coming from the portal vein (PV). This dual nature of the afferent blood supply to the liver has prompted various investigators to define the anatomic and functional relationship between the two vessels by perfusing test substances either separately or simultaneously into the vessels (6, 7, 9, 17, 27, 29, 30). The observations obtained from such efforts favor the idea that there are both common and separate channels within the liver for arterial and portal blood. Although the majority of the sinusoids are perfused by the mixed blood, a small part of the vascular bed remains separate, at least in part, for the HA (14). The separation of these sinusoids is not necessarily anatomic but rather functional (24). However, few attempts have been made to quantify the proportion of the liver vascular (2, 9, 19) or water (27, 31) spaces that are specifically associated with the HA. The evidence from these investigations supports the idea that the arterial and venous blood streams share a very large proportion of the total hepatic vascular bed but that ~5-10% of the total vascular or water space remains specific to the HA, in both perfused dog and rat liver preparations.

The aim of the current research was to develop a new method, based on statistical moment theory, to estimate the specific water space associated with the HA in the rat liver and also to estimate the fraction of HA flow that irrigates this space. The in situ dual-perfused rat liver preparation was used under a variety of HA flow rates to determine the existence of such a specific space. An impulse input-output response technique was employed with [14C]urea chosen as the reference indicator for the estimation of this space.

    MATERIALS AND METHODS
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

Materials

[14C]urea (7.3 mCi/mmol) was obtained from Sigma Chemical and used without further purification. All other chemicals were of analytical grade (BDH Chemicals).

Perfusion Procedure

Male Sprague-Dawley rats were used as liver donors (319.0 ± 19.3 g, wet liver wt 13.5 ± 0.8 g, mean ± SE; n = 10). The perfusate consisted of Krebs-bicarbonate buffer containing 3 g/l glucose and 6 mg/l taurocholic acid. Single-pass dual perfusion of rat livers was performed as previously described (34). Briefly, after introduction of anesthesia, the bile duct was cannulated and loose ligatures were placed around the PV, ensuring exclusion of the HA. At this point, the abdominal contents were deflected to the animal's right and all branches of the celiac artery (i.e., left gastric artery, lineal artery) were tied very close to their junctions to the celiac artery. Only the HA was left patent after ligation of the gastroduodenal artery. After cannulation of the PV with a 16-gauge catheter (Argyle Medicut, OD 1.7 mm × 45 mm), the cannula was immediately connected to the tubing and the perfusion then started. Exsanguination of the liver was facilitated by inserting a PE-50 tubing into the thoracic vena cava via the heart. The HA was cannulated indirectly through the celiac artery using an 18-gauge (Argyle Medicut, OD 1.3 mm × 45 mm) or 20-gauge (Argyle Medicut, OD 1.1 mm × 45 mm) catheter. The second perfusion was then started, and the arterial cannula was fixed in place using tissue adhesive (Vetbond, 3M Animal Care Products). At the end of surgery all loose ligatures were tied securely, and then the HA cannula was connected to a mercury manometer (Fisons Scientific Equipment) by a side arm anterior to the arterial cannula, to monitor the perfusion pressure continuously. All operative procedures were completed within 20-30 min without interruption of flow to the liver. The exposed liver was kept moist with saline and covered with a piece of Parafilm to reduce dehydration. The preparation was then placed into a cabinet maintained at a temperature of 37 ± 2°C and stabilized for 20-30 min, using protein-free perfusate before the injection of [14C]urea. Viability of the liver was assessed from measurement of bile flow, perfusate recovery, and HA pressure and from gross appearance.

Desiccation of Liver

To obtain a physical estimate of total water content, the liver was quickly removed without exsanguination at the end of each experiment, weighed, cut into small pieces to increase the surface area for evaporation, and dried to a constant weight in an oven at 45°C. The liver was monitored up to 2 wk to ensure achievement of a constant weight.

Experimental Procedure

After the stabilization period, two different perfusion modes, dual and single, were utilized in the same liver preparation. Regardless of the perfusion mode, the perfusate was delivered into the PV at a constant flow rate (12 ml/min), whereas the HA flow rate (3, 4.5, and 6 ml/min) was varied. During the stabilization period all the livers were perfused bivascularly and then allocated into one of three groups. In group A (n = 5 livers), the HA flow was increased stepwise and then stopped so that the perfusion was via the PV only. In group B (n = 3 livers), the HA flow was decreased stepwise and then stopped. In group C (n = 2 livers), initially the liver was perfused only through the PV and then HA flow was increased stepwise.

After each alteration in the arterial flow the preparation was allowed to stabilize for ~10 min. Under each condition, a rapid bolus dose of [14C]urea (50 µl, 0.073 ± 0.036 µCi) was introduced, in a random order, into the injection port (extension set with T piece and Luer Lok; Venisystem, Abbott) of either the PV or HA, using a 100-µl Hamilton syringe with its tip positioned after the inflow of the perfusate to ensure adequate mixing, and then, after an appropriate interval (~5-10 min), into the alternate vessel. The injection solution also contained a small quantity of Evans blue dye to visually detect the efficiency of the injection. Immediately after an injection, the total effluent was automatically collected at 2- or 3-s intervals into wells of a locally made motor-driven carousel with 57 sampling holes for 2 or 3 min and thereafter (into test tubes) at increasing time intervals for a further 2 min. The radioactivity in 200 µl of outflow perfusate was determined on an LKB Wallac 1409 Rackbeta liquid scintillation counter after addition of 4 ml of scintillation fluid (Optiphase "Hisafe"II, Wallac) with results expressed as dpm.

Estimation of Nonhepatic Region Transit Time

The experimental system has two different regions, the liver and nonhepatic components. The input cannula and outflow tubing account for the nonhepatic region. The time delay in this region was determined in the absence of the liver. The PV and HA cannulas were connected and secured to the outflow tubing, and then the system was perfused with Krebs-bicarbonate buffer at different flow rates. Under each flow condition, a bolus dose of [14C]urea (50 µl, ~0.027 µCi) was administered into either the PV or HA cannula, and then after an appropriate interval (~5 min) into the alternate vessel. The total outflow was collected automatically at 1-s intervals for 30 s. The estimated mean transit times (MTT) in the nonhepatic region (MTTNH) of the arterial and venous systems were 2.9 and 2.6 s, respectively, for a total flow rate of 15 ml/min, 2.2 and 2.4 s, respectively, for a total flow rate of 16.5 ml/min, and 2.1 and 2.2 s, respectively, for a total flow rate of 18 ml/min. In the absence of HA flow, MTTNH for the venous system was 3 s.

Data Analysis

The frequency output [f(t), s-1] of the injected radiolabeled material at the midpoint time of the sampling interval was calculated using the following equation
<IT>f</IT>(<IT>t</IT>) = <FR><NU>C(<IT>t</IT>) ⋅ <A><AC>Q</AC><AC>˙</AC></A></NU><DE>D</DE></FR> (1)
where C(t) is the concentration of radioactivity, Q is the total perfusate flow (ml/s), and D is the injected dose (in dpm). A lag time, corresponding to the average transit time of [14C]urea in the nonhepatic region of the experimental system, was simply subtracted from the midtime of the sampling interval. The moments of the frequency outflow against midtime profiles were estimated by linear numerical integration, and then the parameters related to these moments [e.g., normalized variance (CV2)] were calculated using the following equations
AUC = <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C(<IT>t</IT>) ⋅ d<IT>t</IT> (2)
MTT = <FR><NU><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT> ⋅ C(<IT>t</IT>) ⋅ d<IT>t</IT></NU><DE>AUC</DE></FR> (3)
VTT = <FR><NU><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT><SUP>2</SUP> ⋅ C(<IT>t</IT>) ⋅ d<IT>t</IT></NU><DE>AUC</DE></FR> − (MTT)<SUP>2</SUP> (4)
where AUC is the area under the concentration versus time profile, MTT is the average time taken for a molecule to pass through the organ, and VTT is the variance of transit times, which is the temporal spreading or dispersion within the organ. These equations assume that Q is constant throughout and that solute is not eliminated, which is the case for urea. Theoretically, to obtain the VTT within the liver correction should be made for the VTT within the nonhepatic part of the system. In practice, for urea this correction proved so small as to be inconsequential.

CV2 is given by
CV<SUP>2</SUP> = <FR><NU>VTT</NU><DE>(MTT)<SUP>2</SUP></DE></FR> (5)
CV2 is a dimensionless parameter and has been used as a measure of relative dispersion of compound within the liver (32).

The recovery (F) is given by
F = <FR><NU>AUC ⋅ <A><AC>Q</AC><AC>˙</AC></A></NU><DE>D</DE></FR> (6)
The frequency outflow versus midtime profiles for each condition were transformed to the corresponding dimensionless plots by multiplying the frequency with, and dividing the time by, the relevant MTT.

Total Water Volume of Liver

Total water volume of the liver (VTW) was calculated by two different methods, physical and indicator dilution. The physical water volume of the liver was estimated by desiccation. The difference in weights (volume) of the wet (Wwet) and dry (Wdry) livers represents VTW, assuming the density of water to be 1. 
V<SUB>TW</SUB> = W<SUB>wet</SUB> − W<SUB>dry</SUB> (7)
Subsequently, results for this and all other volume terms were expressed in milliliters per gram of wet liver weight. The volume (VT) based on the indicator-dilution method, for both single- and dual- perfusion modes, was estimated as follows for single perfusion
V<SUB>T</SUB> = <A><AC>Q</AC><AC>˙</AC></A> ⋅ MTT (8)
and for dual perfusion (9)
V<SUB>T</SUB> = <A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB> ⋅ MTT<SUB>HA</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>PV</SUB> ⋅ MTT<SUB>PV</SUB> (9)
where MTTHA and MTTPV are the total transit times of solute through the liver after injection into the HA and PV, respectively, QHA is the HA flow rate, and QPV is the PV flow rate.

Estimation of Specific Water Space Associated With Hepatic Artery

Three different methods were used to estimate the specific water space associated with the HA (Vsa).

Desiccation method. The assumptions made in this method are as follows. 1) VTW represents the sum of the common space (Vc) and specific arterial space (Vsa). 2) In the absence of HA flow, PV flow does not have access to the Vsa.

On the basis of these assumptions, Vsa is then given by
V<SUB>sa</SUB> = V<SUB>TW</SUB> − V<SUB>PVs</SUB> (10)
where VPVs is the apparent volume of distribution obtained from the single (PV)-perfused rat liver preparation and estimated as the product of the corresponding MTT and QPV.

Serial model. This model was originally described by Field and Andrews (9) for the estimation of the specific arterial vascular space. Briefly, the total hepatic water space is considered to consist of three separate spaces, two specific spaces supplied solely by the HA and PV, each connected serially to a common space (Fig. 1). The model is based on several assumptions. To quote these investigators, "The common space receives mixed blood and the transit time of a solute through this space is the same for both the PV and HA. Even if the total space changes, the proportion of the total vascular space represented by any one of the specified spaces is assumed to remain constant." Therefore, this model predicts a linear relationship between the fractional arterial space (VHA/VT) and the fractional arterial flow (QHA/QT) expressed by
<FR><NU>V<SUB>HA</SUB></NU><DE>V<SUB>T</SUB></DE></FR> = <IT>a</IT> <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>T</SUB></DE></FR> + <IT>b</IT> (11)
where a is the slope of the regression line and the intercept on the ordinate (b) represents the fraction of the hepatic water space supplied solely by the artery; QT is the total flow rate (QHA + QPV), and VT is the total volume of the liver calculated using Eq. 9.


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Fig. 1.   Serial model depicting total hepatic water space of the liver (adapted from Ref. 9). Total flow rate (QT) comprises portal venous (PV) and hepatic arterial (HA) flow rates (QPV and QHA, respectively). Vsp, volume of specific PV space; Vsa, volume of specific HA space; Vc, volume of common space.

Parallel model. In this model the liver is envisaged as comprising a common water space and two specific water spaces. Unlike the serial model, here the specific spaces are arranged in parallel with the common space (Fig. 2). In this model the following assumptions are made. 1) The common space is supplied by both portal and arterial streams. 2) Regardless of the route of administration (HA or PV), the transit time of solute through the common space for a given flow rate is the same. 3) The fractional flows of HA and PV to the common and respective specific water spaces are independent of alterations in QHA and QPV. 4) The specific HA water space remains constant regardless of the QHA used.


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Fig. 2.   Proposed full model for total hepatic water space. f1 and f2, fractions of PV flow perfusing Vsp and Vc, respectively; f3 and f4, fractions of HA flow perfusing Vsa and Vc, respectively. f1 + f2 = 1; f3 + f4 = 1.

On the basis of these assumptions, the following equation holds after HA input (see APPENDIX)
MTT<SUB>HA</SUB> = <FR><NU>V<SUB>sa</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB></DE></FR> + <FR><NU>V<SUB>c</SUB></NU><DE>(<A><AC>Q</AC><AC>˙</AC></A><SUB>2</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>4</SUB>)</DE></FR> (1 − f<SUB>3</SUB>) (12)
where MTTHA is the total transit time of the solute through the liver after injection into the HA, Q2 and Q4 are the flow rates to the common space from PV and HA inputs, respectively, and f3 is the fraction of HA flow perfusing the specific space. Assuming that there is no specific portal space (Q2 = QPV), recasting Eq. 12 into experimental variables then yields
MTT<SUB>HA</SUB> = <FR><NU>V*<SUB>sa</SUB> ⋅ W</NU><DE>Q<SUB>HA</SUB></DE></FR> + <FR><NU>MTT<SUB>PVs</SUB> ⋅ <A><AC>Q</AC><AC>˙</AC></A><SUB>PVs</SUB>(1 − f<SUB>3</SUB>)</NU><DE>[<A><AC>Q</AC><AC>˙</AC></A><SUB>PV</SUB> + (1 − f<SUB>3</SUB>) ⋅ <A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB> ]</DE></FR> (13)
where V*<SUB>sa</SUB> is the volume of the specific arterial space per gram of liver, W is liver weight, MTTPVs and QPVs are the MTT and corresponding QPV after PV administration when operating in the single PV-perfusion mode, and QPV is the portal flow rate when operating in the dual-perfusion mode. In the current experiment the PV flow rate was maintained the same in both the single- and dual-perfusion modes. Mean values of V*<SUB>sa</SUB> and f3 were estimated by fitting Eq. 13 to the entire experimental data using mixed-effect regression analysis (NONMEM; Ref. 4), with equal weighting of the data.

Estimation of HA Perfusion Resistance

The HA resistance (RHA, mmHg · ml-1 · min) of the preparation was determined from the HA perfusion pressure (PHA, mmHg) and QHA (ml/min; Ref. 37) given by
<IT>R</IT><SUB>HA</SUB>=P<SUB>HA</SUB>/<A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB> (14)

Statistical Analysis

The results are presented as means ± SE and compared by means of a one-way analysis of variance. A P < 0.05 was taken as significant.

    RESULTS
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Materials & Methods
Results
Discussion
Appendix
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Hemodynamic Parameters

During perfusion, the liver maintained its uniform light brown color and stable bile production (5.7 ± 0.5 µl/min). Regardless of the flow conditions, the volumetric recovery of the total effluent was always >95% (96-98%) of the input flow rate. The HA perfusate pressure increased with an increase in the HA flow (i.e., 57 ± 4, 83 ± 12, and 96 ± 13 mmHg for QHA of 3, 4.5, and 6 ml/min, respectively). However, for a given flow rate, the pressure remained stable on commencement of the injection, indicating the constancy of the flow rate during the administration. The arterial resistance remained relatively constant (17.2 ± 2.6 to 19.8 ± 3.1 mmHg · ml-1 · min) irrespective of the QHA employed.

Outflow Profiles and Tracer Transit Times

Representative frequency (f) outflow versus midtime profiles for [14C]urea after injections into the PV and HA under different flow conditions are depicted in Figs. 3-5.


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Fig. 3.   Linear plots of fractional rate of efflux of [14C]urea from the same liver preparation obtained after independent bolus administration into HA and PV of a dual-perfused rat liver. Total perfusate flow rate = 16.5 ml/min. f, Frequency outflow.


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Fig. 4.   A: linear plots of fractional rate of efflux of [14C]urea from a representative liver obtained after bolus administration into HA of a dual-perfused rat liver preparation with arterial flow rates of 3.0 (HA1), 4.5 (HA2), and 6.0 (HA3) ml/min and a fixed portal flow rate (12 ml/min). B: linear plots of fractional rate of efflux of [14C]urea from a representative liver, obtained after bolus administration into the PV (12 ml/min) of a single (PVs)-perfused rat liver and dual-perfused rat liver preparation with arterial flow rates of 3.0 (PV1), 4.5 (PV2) and 6.0 (PV3) ml/min.


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Fig. 5.   A: dimensionless outflow profiles of [14C]urea from a representative liver obtained after bolus administration into HA of a dual-perfused liver preparation with arterial flow rates of 3.0 (HA1), 4.5 (HA2), and 6.0 (HA3) ml/min. B: dimensionless outflow profiles of [14C]urea from a representative liver obtained after bolus administration into PV (12 ml/min) of a single (PVs)-perfused rat liver and dual-perfused liver preparation with arterial flow rates of 3.0 (PV1), 4.5 (PV2), and 6.0 (PV3) ml/min. MTT, mean transit time.

After HA injection, urea emerged slightly earlier but the peak was diminished [e.g., maximum frequency (fmax) = 0.021 ± 0.002 s-1 for HA and 0.028 ± 0.002 s-1 for PV] and the curve was flatter and broader than after PV input (Fig. 3). With an increase in HA flow rate, the outflow profiles after intra-arterial injections were displaced to earlier times [time to reach maximum frequency (tmax) from 27 to 23 s] and gave slightly higher peaks (e.g., fmax from 0.020 to 0.023 s-1; Fig. 4A). In contrast, the effect of increased HA flow on the outflow profiles after PV input was not that pronounced; although the fractional output at the peak increased slightly (e.g., fmax from 0.029 to 0.032 s-1) with an increase in HA flow, the curves peaked almost at the same time (e.g., tmax ~21 s; Fig. 4B). Figure 5A shows the urea profiles normalized to the corresponding MTT in the same liver preparation after HA administrations. Regardless of the perfusate flow rate (15, 16.5, and 18 ml/min) after normalization, in each case, the HA profiles were superimposable. Similar observations were also observed for the PV profiles (Fig. 5B).

The MTT after arterial administration was longer than that after venous administration (Table 1). With an increase in QHA, the MTT obtained after HA injection was decreased. In the case of PV injections, the MTT were comparable irrespective of both perfusion mode and flow rate. The CV2 for labeled urea was very similar whether injection was into the HA or PV, indicating that relative spreading of urea within the liver is independent of the route of administration. Excellent recovery of [14C]urea was obtained for all cases.

                              
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Table 1.   Results obtained after bolus injections of [14C]urea into portal vein and hepatic artery of dual perfused and into portal vein of single perfused rat liver preparation

Total Water Volume of Liver

Estimates of VTW by two different methods are depicted in Fig. 6. In the desiccation experiment, a constant dry weight was achieved within a week. The values obtained by desiccation (0.72 ± 0.01 ml/g, n = 10 livers) and transit time methods after dual perfusion under different flow conditions [0.67 ± 0.03 ml/g (n = 10) for Q1, 0.71 ± 0.03 ml/g (n = 8) for Q2, and 0.72 ± 0.06 ml/g (n = 6) for Q3, where Q1 = 15.0 ml/min, Q2 = 16.5 ml/min, and Q3 = 18.0 ml/min] were in good agreement. In contrast, the value based on the transit time after single perfusion was only 74% of the physical volume.


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Fig. 6.   Total water volume of liver estimated from desiccation (DESIC) and MTT methods after single (VPVs) and dual perfusion with total flow rates of 15.0 (VT1), 16.5 (VT2), and 18.0 (VT3) ml/min.

Specific HA Water Space

The results for V*<SUB>sa</SUB> and the fractions of HA flow perfusing this space and the common space are summarized in Table 2.

                              
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Table 2.   Specific hepatic arterial water space, estimated by various methods, and fractions of hepatic arterial flow perfusing specific hepatic arterial water space and common space, estimated by transit time method

Desiccation method. This method showed considerable variation, with results ranging from 12.6 to 43.2% and an average value of 29.8 ± 4.4% (mean ± SE, n = 9 livers) of the total water space. Only 1 of 10 experiments was rejected because of a negative value obtained for Vsa. The results differed significantly from both the serial and parallel models (P < 0.001).

Serial model. The V*<SUB>sa</SUB> calculated by this method provided a mean value of 13.7 ± 4.6% of the total water space.

Parallel model. This model yielded a V*<SUB>sa</SUB> of 0.070 ± 0.014 ml/g liver corresponding to 9.7 ± 1.9% of the total water space estimated from desiccation. The fraction of HA flow that perfuses the specific space (f3) was 0.173 ± 0.074, with the remainder supplying the common space.

The values of the specific arterial space obtained from the serial and parallel models agreed well, with no significant difference between them.

    DISCUSSION
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

Choice of Compound

Tritiated water is the standard marker used for estimation of total organ water space, but it suffers from the problems of errors caused by its volatility, involvement of labeled water in various biochemical reactions in cells, and the ability of 3H atoms to exchange with hydrogen atoms of organic materials in the body (20, 36). In the present study [14C]urea was selected as an alternative marker; it is a small, hydrophilic, and electrostatically neutral molecule that behaves very similarly to water, having a volume of distribution, and hence MTT, equal to 96-97% of that of tritiated water in dog and rat liver (12, 25). In addition, urea is not expected to be metabolized during single passage through the liver, and hence total 14C activity is equivalent to [14C]urea.

Outflow Profiles and Transit Times

Regardless of the route of administration, unimodal outflow profiles for urea were always observed. In contrast, Reichen (31) reported some bimodal patterns of dilution curves after arterial input for various reference markers (e.g., erythrocytes, albumin, sucrose), and attributed these to two populations of portal tracts being perfused at different velocities. However, no other investigator has reported such biphasic profiles after arterial administration.

It is generally believed that the majority of the sinusoids are common channels for both the HA and PV streams and receive mixed blood. If this is so, regardless of the route of administration, very similar hepatic outflow profiles would be expected. The distinctly different outflow profiles (e.g., Fig. 3) after venous and arterial administrations do not favor this idea. A similar observation was made earlier, using 125I-albumin in dog liver (7) and, more recently, using erythrocytes, albumin, and sucrose in the rat liver (18). Pang et al. (27) attributed the slightly delayed and attenuated peak after HA injection to a much greater delay in the arterial catheter. Although the nonhepatic region (e.g., catheters) of the experimental system is known to have an effect on the outflow profile of a compound, especially for vascular and extracellular markers that have short MTT values (13), this should not be the case in our experiments, because the MTT of urea (e.g., 48 s for HA and 35 s for PV; Table 1) is much greater than the MTT of the nonhepatic region of both HA and PV systems (e.g., 2.9 vs. 2.6 s). Furthermore, rapid washout of Evans blue dye from the injection site rules out the possibility of stagnation in the catheter. All these factors suggest that the arterial outflow profiles are more likely to be distorted within the liver rather than by the nonhepatic regions of the experimental system.

Reports on the MTT for markers injected into both the PV and HA have been ambivalent. Some authors have observed different MTT after PV and HA injections (7, 10, 19), whereas others reported no difference (2). Despite a sharper peak after PV injection (for 125I-albumin), Cohn and Pinkerson (7) reported smaller MTT values for red blood cells and albumin after intra-arterial administration. In contrast, Gascon-Barre et al. (10) and Kassissia et al. (19) observed longer MTT values after HA injections. In the present study, irrespective of the flow conditions, the MTT values for urea after arterial administration were longer than after venous administration. When urea was administered via the PV, the MTT were very similar regardless of both the perfusion modes (single or dual) and QHA, indicating that distribution of PV-administered urea is minimally affected by the presence of HA inflow. This observation is in accordance with Pang et al. (27), who recently reported unchanged vascular, interstitial, and cellular distribution volumes after PV administrations for different HA-to-PV flow ratios.

Total Water Volume of Liver

The desiccation method offers a direct approach for estimation of the absolute amount of water in the whole body (8, 20, 36) and in various tissues, including liver (11) and heart (10). Whole body studies (8, 20, 36) suggest that the isotope-dilution method, using tritiated water, overestimates the total water content of the body compared with the desiccation method. Nevertheless, Goresky (12) found a good agreement between these two methods in the PV-perfused dog liver. The current study extends this knowledge to the dual-perfused liver preparation. Desiccation of the liver was performed by heating for an extended period (~2 wk) at a relatively low temperature (45-50°C) to minimize the possibility of release of other volatile substances in addition to water. In the dual-perfused rat liver, the values obtained from the indicator dilution method (0.67-0.72 ml/g) agreed very well with the value (0.72 ml/g) obtained by desiccation. Regardless of the method employed, the estimates of water volume lie within the range of values reported in the literature (18, 25, 28, 31, 33) and agree well with the tentative value of 75% of liver weight given by Greenway and Stark (14).

In the absence of arterial input, urea is not expected to distribute into the entire water space of the liver because ~10% of the total water space is specific to the arterial input. However, the estimated value (74% of total) was less than the expected value (90% of total), probably because of a reduction in the total perfusion rate from 15 to 12 ml/min. An increase in the volume of distribution of tritiated water with an increase in the perfusate flow rate (e.g., from 0.51 to 0.65 ml/g for the flow rates of 15 and 30 ml/min; Ref. 18) clearly shows the effect of perfusion rate on the observed volume of distribution and may be taken as an indication of poor perfusion of the liver at low flow rates. Similar observations were also made by Pang et al. (26).

Specific HA Space

In the current analysis it is assumed that there is no specific portal space, nor, unlike the case of a specific arterial space, is there any support for, or suggestion of, a specific portal space in the literature. Theoretically, the presence of a specific portal space should be detected by predicted differences in the output profiles after PV input operating in the dual- and single-perfusion modes. In practice, we could discern no such difference between these perfusion modes, which could mean that either there is no specific portal space or it is too small to be detected under the experimental conditions. This was not the case for the HA-specific space.

Although the dual-perfusion studies support the idea that a small fraction of the sinusoids remains separate in favor of HA input, the degree of mixing between the HA and PV inflows at the microscopic level is still controversial. Field and Andrews (9) were the first to calculate the proportion of the specific arterial vascular space; from the linear relationship between the fractional HA flow and fractional space, they estimated that 10% of the total vascular space in dog liver is perfused solely by the HA. Their method was later applied by Nakai et al. (Ref. 24; using Evans blue dye), and then by Ahmad et al. (Ref. 2; using labeled red blood cells). Although Nakai et al. (24) failed to demonstrate the existence of such a specific space, Ahmad et al. (2) obtained an almost identical value (11%) in the rat liver as that reported by Field and Andrews (9). More recently, Kassissia et al. (19) took the product of HA flow and the difference between arterial and venous transit times as a close approximation of the specific arterial vascular space, which provides values of 6.7% of the total sinusoidal space in normal liver and 7.8% in the cirrhotic liver. Both Reichen (31) and Pang et al. (27) reported a slightly larger water space (5%) after arterial than after portal administration.

In the present study three different methods, desiccation, serial, and parallel methods, were employed for the estimation of specific arterial water space. Of these, the desiccation method is based on the volume difference between the physical and indicator-dilution estimates. Although the method is very easy to perform, two types of error may be associated with its application; one error is the temperature effect on the estimation of physical water volume and the other is the error involved in the estimation of the volume of distribution from application of moment analysis caused by extrapolation and low perfusion rate. The effect of temperature can be easily avoided by desiccating at relatively low temperature (e.g., 50°C) or alternatively by employing another drying method (e.g., freeze drying). The estimates of specific arterial water space using this method were relatively high compared with the estimates obtained with the serial and parallel models. This is attributed to a slight underestimation of urea volume of distribution, caused by the inadequate perfusion of the liver in the absence of HA flow. The other two methods (serial and parallel) are very similar with regard to the assumptions made in the development of the models but differ structurally. In the serial model the specific spaces are serially connected to the common space, whereas in the parallel model these are in parallel with the common space. Although both models consider HA flow segregation, only the parallel model provides an estimate for the degree of the arterial flow segregation. It may be argued that neither a serial nor a parallel model truly reflects reality. However, the PV and HA perfusion studies suggest that some of the arterial blood drains directly into the terminal hepatic venules, thus completely bypassing the sinusoidal bed. Furthermore, some of the vessels draining the peribiliary plexus may form direct connections to the terminal hepatic venule (35). These findings tend to support the existence of a similarly connected specific arterial space.

Agreement between the current results for the specific arterial space (9.7%) and the literature values (10-11%; Refs. 2, 9) is noteworthy. Furthermore, close similarity between the MTT values after PV administration in the absence and presence of the HA input imply that PV input is minimally affected by the presence of the HA flow. This latter observation agrees well with that by Pang et al. (27), who recently reported that the excess space associated with the HA is independent of total-to-arterial flow ratio and that the distributional volumes after PV administration are unaffected by the presence of arterial input. These observations strongly support the assumption made in the development of the parallel model.

Together, these results suggest that regardless of the space of interest and methods used, there are two separate spaces for the HA input; one is a common space shared with the PV, and the second is a specific space. Some authors (see, e.g., Refs. 2, 24) have suggested that separation of these sinusoids is not necessarily anatomic but functional; others (27, 31) have related this excess space almost exclusively to the peribiliary capillary plexus, whereas still others (19) do not distinguish between these characteristics. The PV and HA branches run parallel within the liver, and their terminal branches supply blood to the sinusoids. In the rat, unlike the PV, the HA flow drains into the sinusoids via various pathways including arteriovenous anastomosis, arteriosinusoidal twigs, and the peribiliary capillary plexus (5, 15, 22, 23). Of these, the peribiliary plexus, which receives the majority of its afferents from the HA (15, 16), may provide an additional anatomic space in favor of arterial input. On the other hand, flow in the sinusoids is not unidirectional but can be reversed (3, 21). The angle at which arterioles join the sinusoids and also sphincter activity (22) determine not only direction of blood flow through the sinusoids but also the degree of mixing (5). Therefore, sinusoids that were previously perfused by both the PV and HA may on another occasion be perfused solely by the HA (i.e., functionally separate sinusoids). All these suggest that both anatomic and functional spaces contribute to the total HA specific space. Nevertheless, the contribution of each to the total cannot be separated using the methods employed in this study. If we assume that 5% of the total specific space is due to peribiliary capillary plexus, as suggested by Reichen (31) and Pang et al. (27), the remainder (~4-5%) is due to functional characteristics of the arterial input.

The knowledge obtained from the existence of a specific HA water space and its flow fraction can be extended to make predictions about the fate of an eliminated substance after arterial administration. Such a prediction may have relevance to the systemic exposure of compounds after HA administration, as sometimes arises during the treatment of hepatic carcinomas, many of which reside predominantly on the arterioles (1). If the enzyme distribution responsible for elimination is the same as in the common space, the route of administration should have no effect on the disposition of a substance within the liver. In contrast, if there is no enzyme in the specific HA space, up to 17% of the HA dose will escape extraction, on the basis of the assumption that separation of the dose is a function of the flow, the upper limit being reached with compounds whose extraction ratio after PV input is in excess of 0.90-0.95 (2).

    APPENDIX
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

Derivation of Model Equation for Calculation of Specific HA Water Space

In the derivation it is assumed that
<A><AC>Q</AC><AC>˙</AC></A><SUB>T</SUB> = <A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>PV</SUB> (A1)
where QT, QHA, QPV are the total outflow and HA and PV flow rates, respectively.

The fractional flows of the common and specific water spaces are given by
f<SUB>1</SUB> = <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>1</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>PV</SUB></DE></FR> ; f<SUB>2</SUB> = <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>2</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>PV</SUB></DE></FR> = 1 − f<SUB>1</SUB>; f<SUB>3</SUB> = <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>3</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB></DE></FR> ;
f<SUB>4</SUB> = <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>4</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>HA</SUB></DE></FR> = 1 − f<SUB>3</SUB> (A2)
where Q1 and Q2 are the PV flows to the specific portal and common water spaces and Q3, and Q4 are the HA flows to the specific arterial and common water spaces, respectively.

Because the derivation of the equations for both arterial and venous injections is the same, only that after HA injection is now considered.

Considering mass balance
D = <A><AC>Q</AC><AC>˙</AC></A><SUB>T</SUB> ⋅ <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>T</SUB></SUB> ⋅ d<IT>t</IT> (A3)
where CoutT is the total outflow concentration after injection into the hepatic artery. The net rate of outflow is the sum of that from the specific arterial supply (Q3 · Coutsa) and that from the common space [(Q2 + Q4) · CoutC]. So that
<A><AC>Q</AC><AC>˙</AC></A><SUB>T</SUB> ⋅ C<SUB>out<SUB>T</SUB></SUB> = <A><AC>Q</AC><AC>˙</AC></A><SUB>3</SUB> ⋅ C<SUB>out<SUB>sa</SUB></SUB> + (<A><AC>Q</AC><AC>˙</AC></A><SUB>2</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>4</SUB>) ⋅ C<SUB>out<SUB>c</SUB></SUB> (A4)
where Coutsa and Coutc are the outflow concentrations of the specific arterial and common water spaces after injection into the HA. Integrating Eq. A4 over the interval t = 0, infinity  gives
<LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>T</SUB></SUB> = <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>3</SUB></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>T</SUB></DE></FR> ⋅ <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>sa</SUB></SUB> ⋅ d<IT>t</IT> + <FR><NU>(<A><AC>Q</AC><AC>˙</AC></A><SUB>2</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>4</SUB>)</NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>T</SUB></DE></FR> ⋅ <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>c</SUB></SUB> ⋅ d<IT>t</IT> (A5)
The MTT after an HA injection (MTTHA), after appropriate substitution, is given by
MTT<SUB>HA</SUB> = <FR><NU><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT> ⋅ C<SUB>out<SUB>T</SUB></SUB> ⋅ d<IT>t</IT></NU><DE><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>T</SUB></SUB> ⋅ d<IT>t</IT></DE></FR>
= <FR><NU><A><AC>Q</AC><AC>˙</AC></A><SUB>3</SUB> <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT> ⋅ C<SUB>out<SUB>sa</SUB></SUB> ⋅ d<IT>t</IT> + (<A><AC>Q</AC><AC>˙</AC></A><SUB>2</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>4</SUB>) <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT> ⋅ C<SUB>out<SUB>c</SUB></SUB> ⋅ d<IT>t</IT></NU><DE><A><AC>Q</AC><AC>˙</AC></A><SUB>3</SUB> <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>sa</SUB></SUB> ⋅ d<IT>t</IT> + (<A><AC>Q</AC><AC>˙</AC></A><SUB>2</SUB> + <A><AC>Q</AC><AC>˙</AC></A><SUB>4</SUB>) <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>c</SUB></SUB> ⋅ d<IT>t</IT></DE></FR> (A6)

By definition, the MTT through the specific HA space (MTTsa) and common space (MTTc) are given by
MTT<SUB>sa</SUB> = <FR><NU><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT> ⋅ C<SUB>out<SUB>sa</SUB></SUB> ⋅ d<IT>t</IT></NU><DE><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>sa</SUB></SUB> ⋅ d<IT>t</IT></DE></FR> (A7)
MTT<SUB>c</SUB> = <FR><NU><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> <IT>t</IT> ⋅ C<SUB>out<SUB>c</SUB></SUB> ⋅ d<IT>t</IT></NU><DE><LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>c</SUB></SUB> ⋅ d<IT>t</IT></DE></FR> (A8)
Furthermore, after arterial administration, the doses associated with the specific HA and common spaces (Dsa and Dc) are
D<SUB>sa</SUB> = f<SUB>3</SUB> ⋅ D = Q<SUB>3</SUB> ⋅ <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>sa</SUB></SUB> ⋅ d<IT>t</IT> (A9)
D<SUB>c</SUB> = (1 − f<SUB>3</SUB>) ⋅ D = (Q<SUB>2</SUB> + Q<SUB>4</SUB>) ⋅ <LIM><OP>∫</OP><LL>0</LL><UL>∞</UL></LIM> C<SUB>out<SUB>c</SUB></SUB> ⋅ d<IT>t</IT> (A10)
Substituting Eqs. A7-A10 into Eq. A6 then provides
MTT<SUB>HA</SUB> = MTT<SUB>sa</SUB> ⋅ f<SUB>3</SUB> + MTT<SUB>c</SUB> ⋅ (1 − f<SUB>3</SUB>) (A11)
Finally, by replacing MTTsa and MTTc with their respective volumes and flow terms, one obtains
MTT<SUB>HA</SUB> = <FR><NU>V<SUB>sa</SUB></NU><DE>Q<SUB>HA</SUB></DE></FR> + <FR><NU>V<SUB>c</SUB></NU><DE>(Q<SUB>2</SUB> + Q<SUB>4</SUB>)</DE></FR> ⋅ (1 − f<SUB>3</SUB>) (A12)
where Vsa and Vc are the volumes of the specific HA and common spaces, respectively.

    ACKNOWLEDGEMENTS

The help of Ziad Hussein in the data analysis is acknowledged.

    FOOTNOTES

S. Sahin thanks the Turkish Government for a studentship. This research was supported by a grant from the Wellcome Trust.

Present address of S. Sahin: Fac. of Pharmacy, Hacettepe Univ., 06100-Ankara, Turkey.

Address for reprint requests: M. Rowland, School of Pharmacy and Pharmaceutical Sciences, Univ. of Manchester, Manchester M13 9PL, UK.

Received 20 August 1997; accepted in final form 6 April 1998.

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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

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