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1 Faculty of Pharmacy, The hepatic transport of hippuric acid (HA), a
glycine-conjugated metabolite of benzoic acid that exhibits only modest
plasma albumin binding (binding association constant of 2.1 × 103
M
benzoic acid; L-lactate; influx and efflux coefficients; permeability-surface area product; carrier-mediated transport; monocarboxylic acid transporter; MCT2; plasma and tissue protein binding; rat liver perfusion
THE TRANSPORT OF ORGANIC anions across the basolateral
(sinusoidal) membrane of the liver has been extensively studied. Recent advances in molecular biology have revealed the existence in the liver
of ntcp, the Na+-dependent bile
acid (taurocholate) cotransporter (16, 17), and oatp, the multiple
organic anion transporter that mediates the transport of organic anions
(20, 21, 26, 27, 34) and cations (3). The carrier-mediated transport of
sulfobromophthalein (26, 27, 34) and its glutathione conjugate (13) and
sulfated estrone and bile acids and drug sulfate conjugates (11, 18, 33, 35) implicates a role for oatp or other as yet unknown transporters.
The transport of arylmonocarboxylic acids in the liver has not been
studied extensively (6, 31). The hepatic transport of the simple
arylcarboxylate anions aminohippurate and acetamidohippurate in rat
liver perfusion experiments was inhibited by probenecid (6). Transport
of the precursor, benzoate, into Caco-2 intestinal cells displayed a pH
dependence, suggesting the involvement of carrier proteins (38). In the
intestine, interaction was found between the transport of benzoate and
L-lactate (37). Transport of
L-lactate is ordinarily mediated
by the monocarboxylate transporter MCT1, which is present abundantly in
the intestine, erythrocytes, and cardiocytes (10, 36, 37). MCT2, which
is present in the liver, is responsible for the uptake of lactate and
pyruvate and is distinct from MCT1 (9). Whether the same substrate
specificity for MCT1 applies to MCT2 or whether MCT2 is capable of
transporting simple arylcarboxylic acids into liver cells is unknown.
In this study, we examined the hepatic uptake of hippuric acid (HA), a
simple organocarboxylic acid. HA is the glycine-conjugated metabolite
of benzoic acid found in almost all animal species, including humans
(4). It is present in herbivorous animals, and its existence is also
associated with its precursor, benzoate, a common food preservative.
The fate of hippurate has been studied in conjunction with benzoate in
the single-pass-perfused rat liver (5). Once formed, hippurate is
neither excreted nor further metabolized by the liver; only efflux to
the venous outflow occurs. Thus HA represents the simplest test
compound for the study of arylcarboxylic acids. Preliminary plasma
protein-binding experiments have demonstrated that HA is bound only to
albumin and not to red blood cells (RBC). We used the
multiple-indicator dilution (MID) technique to study the sinusoidal
transfer constants for HA in the single-pass in situ perfused rat liver
preparation at various steady levels of bulk unlabeled substrate. This
method entails the introduction of a bolus injection into the inflowing perfusate of both
[3H]HA and a set of
noneliminated reference indicators against a set of background
steady-state concentrations of unlabeled hippurate. We used
51Cr-labeled RBC as a vascular
reference, 125I-labeled albumin
and [14C]sucrose as
high and low molecular weight interstitial references, respectively
(14), and
2H2O
as a cellular reference (30). By kinetic analysis of the outflow
profile of the study substance,
[3H]HA, in relation to
those of the simultaneously introduced references, we obtained
estimates of parameters describing unidirectional tracer cellular
influx and efflux, using the barrier-limited model of Goresky et al.
(15). Competition of HA uptake by benzoate and
L-lactate was further examined.
Materials
ABSTRACT
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
1), was studied in the
single-pass perfused rat liver (12 ml/min), using the multiple
indicator dilution (MID) technique. The venous recovery of
[3H]HA on portal
venous injection of a MID dose containing a mixture of a set of
noneliminated reference indicators and
[3H]HA revealed a
survival fraction of unity, corroborating the lack of disappearance of
bulk HA from plasma. When the outflow recovery was fitted to the
barrier-limited model of Goresky et al. (C. A. Goresky, G. G. Bach, and
B. E. Nadeau. J. Clin. Invest. 52:
991-1009, 1973), the derived influx
(PinS ) and
efflux (PoutS )
permeability-surface area products were found to be dependent on the
concentration of HA (1-930 µM);
PinS and
PoutS were ~3.5 times the plasma flow rate at low HA concentration, but decreased with
increasing HA concentration. All values, however, greatly exceeded the expected contribution from passive diffusion, because the
equilibrium distribution ratio of chloroform to buffer for HA was
extremely low (0.0001 at pH 7.4). The tissue equilibrium partition
coefficient
(Pin/Pout,
or ratio of influx to efflux rate constants,
k1/k1)
was less than unity and decreased with concentration. The optimized
apparent Michaelis-Menten constant and maximal velocity were 182 ± 60 µM and 12 ± 4 nmol · s1 · g1,
respectively, for influx and 390 ± 190 µM and 29 ± 13 nmol · s1 · g1,
respectively, for efflux. In the presence of
L-lactate (20 mM), however,
PinS for the uptake
of HA (174 ± 3 µM) was reduced. Benzoic acid
(10-873 µM) was also effective in reducing hepatic uptake of HA
(5.3 ± 0.9 µM). These interactions suggest that MCT2, the monocarboxylate transporter that mediates the hepatic uptake of lactate
and other monocarboxylic acids, may be involved in HA transport.
INTRODUCTION
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
MATERIALS AND METHODS
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
Synthesis of [3H]HA. [3H]HA was synthesized from benzoyl chloride and [3H]glycine under aqueous and alkaline conditions (19). [3H]glycine (11.5 nmol or 500 µCi) was dissolved in 100 µl of 0.05 N sodium hydroxide. To this, 150 µl of an ethereal solution of benzoyl chloride (80 µM) were added, and 200 µl of 0.1 N sodium hydroxide were subsequently added drop by drop. After the reaction mixture was stirred for 1 h, 200 µl of 0.1 N hydrochloride and 100 µl of chloroform were added. The aqueous phase (top layer) was removed for purification by HPLC. After purification, the radiochemical purity estimated for HA by HPLC was >98%.
Distribution of HA Between Chloroform and Perfusate
The distribution of HA into Krebs-Henseleit bicarbonate solution (KHB) and chloroform was studied at HA concentrations of 3, 30, and 300 µM. Because the equilibrium distribution ratio was expected to be low, any impurity of [3H]HA, albeit representing a very small percentage of the total radioactivity, posed a complication for quantitation. For this reason, only unlabeled HA was used in the determination of the distribution ratio. The partitioning of HA in 20 ml of KHB (pH 7.4) and 20 ml of chloroform was studied. After the mixture was shaken in a capped 50-ml test tube and subsequently centrifuged, 10 ml of the chloroform phase was removed and assayed for HA. The lowest concentration of HA in chloroform (3 µM) was below the detection limit of the HPLC procedure. For the other two concentrations (30 and 300 µM), the ratio of chloroform to buffer was found to be constant (0.0001 ± 0.000015; n = 3).Protein Binding of HA and Distribution into RBC
Plasma protein binding.
The binding of HA to albumin was studied with ultrafiltration (10,000 mol wt cutoff, filter no. YM10; Amicon). Hippurate (0.5-500 µM)
containing [3H]HA was
prepared in perfusate plasma (5% BSA) and subjected to ultrafiltration
at 1,000 g (M2-J centrifuge; Beckman,
Mississauga, ON) for 20 min at room temperature. The total HA
concentration in plasma (Cp) was
determined by HPLC and liquid scintillation spectrometry, and the
unbound concentration (Cp,u) in
the ultrafiltrate was quantified by virtue of the radioactivity and the
specific activity of the original plasma sample. The binding constants were initially estimated by expressing the concentration ratio of bound
to free, or (Cp 
Cp,u)/Cp,u,
vs. the free HA concentration, Cp,u. Fitting of the data was
subsequently performed by regression of the following expression, for
one class of binding sites
![C<SUB>p</SUB> = <FR><NU><IT>n</IT>[P<SUB>t</SUB>]C<SUB>p,u</SUB></NU><DE><IT>K</IT><SUB>d</SUB> + C<SUB>p,u</SUB></DE></FR> + C<SUB>p,u</SUB>](/content/vol274/issue1/fulltext/G10/img001.gif)
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(1) |
Distribution into RBC.
The distribution of HA into RBC was investigated by mixing plasma
perfusate (5% albumin) containing varying concentrations of HA (up to
883 µM), [3H]HA, and
[14C]sucrose (a
reference that does not enter RBC) with an equal volume of blank blood
perfusate containing 40% RBC (vol/vol) and 5% albumin. The admixture
resulted in a composition identical to that used for perfusion studies
(20% RBC, vol/vol, and 5% albumin). The samples were incubated at
37°C in a rotating water bath for 30 min. Aliquots of perfusate
plasma solution, before and after admixture, were assayed for
[14C]sucrose and
[3H]HA by liquid
scintillation spectrometry, whereas unlabeled HA was assayed by HPLC.
The concentration ratio of
[3H]HA in RBC to the
unbound [3H]HA in
plasma water, 
, was estimated by a formula developed earlier (29),
and was found to be essentially zero.
Binding of HA to intracellular components (tissue binding). Tissue binding was studied in both liver homogenate (1:5 dilution) and the 9,000 g supernatant. The liver was first homogenized with 4 vol of ice-cold KHB (homogenizer by Ultraturrax T25; Janke & Kunkel IKA-Labortechnik), and then a 1:10 dilution of the homogenate was centrifuged at 9,000 g for 20 min at 4°C to provide the S9 fraction. Bulk HA and [3H]HA were added to the homogenate and S9 supernatant such that the concentrations of HA varied from 1.1 to 511 µM (10,000-20,000 dpm/ml [3H]HA); 1.0 ml of the homogenate and S9 solution was used for ultrafiltration (10,000 mol wt cutoff; Centricon; Amicon) at 1,000 g for 20 min at room temperature. Preliminary investigation showed that the leakage of liver protein in the ultrafiltrate, prepared in the manner outlined above, was <1% of the total protein present. Protein was evaluated by the method of Lowry et al. (24). The radioactivities in homogenate and S9 before ultrafiltration (Ct) and in the ultrafiltrate (Ct,u) were measured, and the concentrations of bulk HA in both the homogenate and S9 fractions were assayed by HPLC.
Rat Liver Perfusion
Male Sprague-Dawley rats weighing 274-375 g (Charles River, St. Constant, PQ; livers were 8.3-13.3 g) were used for liver perfusion. The animals were housed in accordance with approved protocols of the University of Toronto Animal Committee, kept under artificial light on a 12:12-h light-dark cycle, and allowed access to water and food ad libitum. The perfusate contained 20% freshly obtained, washed bovine RBC (Ryding Meats, Toronto, ON), 5% BSA, and 17 mM glucose (Travenol Labs, Deerpark, IL) in KHB buffered to pH 7.4. The perfusate was oxygenated with 95% O2-5% CO2 (Matheson, Mississauga, ON) and O2 (BOC Gases, Whitby, ON) and was maintained at pH 7.4 by an online flow-through pH electrode (Orion, Boston, MA). Perfusion was carried out at 37°C in a single-pass fashion as previously described (5), with perfusate (12 ml/min) entering via the portal vein and exiting via the hepatic vein. The hepatic artery was ligated.Single-pass perfusion. Previous liver perfusion studies had confirmed the lack of removal of HA when it is formed from benzoic acid; only trace levels of hippurate were found in bile (5). Moreover, preliminary studies showed that a constancy in the perfusate outflow and biliary excretion was reached by 20 min after perfusion commenced. Single-pass studies were conducted at 12 ml/min for 60 min for all studies. Only one concentration of HA (1-930 µM) was used per rat liver. For the first set of competition experiments, HA (~200 µM) and 20 mM L-lactate were kept constant in the inflowing perfusate. For the second set of competition studies, 5 µM HA and benzoate (varying from 10 to 873 µM) were present in the inflowing perfusate; in this set of studies, the HA in the outflow was expected to exceed that entering the liver due to its formation from benzoate.
The inflow and outflow samples were collected at steady state (between 15 and 55 min), and the average (3-5 samples) was used to determine the input (Cin) and output (Cout) plasma concentration of unlabeled HA. Bile was collected from 20 min onward, at 5-min intervals. At the end of each perfusion experiment, the livers were perfused with 25 ml of ice-cold KHB, removed, weighed quickly, and homogenized with an equivalent volume of KHB (1:1, wt/vol). The homogenates were stored at 20°C until analysis.Multiple-indicator dilution. A MID dose was introduced into the portal vein 20 min after initiation of all perfusion studies. Sham experiments (without liver) were conducted to characterize the dispersion due to the inflow and outflow catheters. MID was conducted as described previously (13). The injection mixture (0.23 ml), containing 51Cr-labeled washed bovine RBC (0.4 ± 0.14 µCi), 125I-labeled albumin (3.7 ± 1.7 µCi), [14C]sucrose (2.1 ± 2.5 µCi), [3H]HA (1.9 ± 1.1 µCi), 2H2O (0.099 ± 0.032 ml), and unlabeled HA, in a composition otherwise identical to that of the perfusate, was introduced into the inflow system by an electronically controlled HPLC injection valve. Simultaneously, outflow samples were rapidly collected at successive 1-, 2-, and 3-s intervals for a total of 180 s by a fraction collector. Bile was collected at 5-min intervals after MID injection for the next 40 min. The hematocrit of the blood perfusate and dose was determined for each experiment with the use of a hematocrit centrifuge (MB microhematocrit centrifuge; International Equipment Company Division, Fisher Scientific).
Quantitation of Radiolabels or Stable Isotopes
The 51Cr and 125I radiolabels in blood outflow perfusate samples (25-200 µl) and in the 1:10 diluted dose were assayed by gamma counting (Cobra II; Canberra-Packard, Mississauga, ON); the [14C]sucrose and [3H]HA in plasma perfusate (50-200 µl) and in the 1:10 diluted plasma dose were assayed by liquid scintillation counting (Scintillation Counter 5801; Beckman), as previously described (13). 2H2O was assayed by Fourier transform infrared spectrometry (model 1600; Perkin Elmer, Rexdale, ON) over a frequency interval of 2,300-2,700 cm1 (30).
Recovery of 51Cr,
125I,
14C, and
3H radiolabels and
2H2O
in outflow samples was virtually complete.
Assay of Unlabeled HA in Plasma and Bile
The concentrations of unlabeled HA in plasma samples and bile were assayed by HPLC, as previously described (5). The HPLC method was used for the quantitation of the HA in the S9 fraction and liver homogenate.Data Treatment
For the MID data, outflow radioactivity for each indicator was expressed as a fraction of the radioactivity of injected mixture per milliliter of blood (13). The concentration of radiolabels at the end of the collection (180 s) was <0.1% of peak values. Recoveries were calculated as the product of the time integrals of the fractional recovery and blood flow. Fractional recovery integrals were approximated by summing the products of fractional recoveries and sample intervals; fractional recovery activity-time integrals [area under the curve (AUC)] and integrals of the product of fractional recovery and time [AUC at midintervals (AUMC)] were calculated similarly (13, 32). The ratio of AUMC to AUC yielded the mean transit time.Modeling.
A scheme (Fig. 1) was developed to describe
the kinetic events underlying the disposition of HA in the perfused rat
liver preparation. HA in the plasma space is present as bound and
unbound forms, and only the unbound HA in the plasma compartment
(assumed to be the same for sinusoidal plasma and interstitial space)
is assumed to exchange with that in the hepatocellular compartment. Rapid equilibrium between bound and unbound forms was assumed. It
should be noted that, since albumin is excluded from part of the Disse
space (14), the space of distribution for bound HA is identically
diminished. Transfer rates depend on the rate constants for entry into
(k1) and efflux
from
(k1) the
hepatocytes, as defined in Table 1. The
rate constants, when multiplied by the accessible cellular water space
(Vcell), yield the
permeability-surface area products for transport
(PinS or
PoutS ). The rate
constant for HA removal solely by excretion
(kseq) is
virtually zero and is neglected in the modeling of the
[3H]HA curve. With
these assumptions, preliminary studies showed that an adequate fit to
the data was attained with the barrier-limited model of Goresky et al.
(13, 15, 32).
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Superposition of noneliminated references and appraisal of influx
and efflux coefficients.
Superposition of the noneliminated reference indicators (labeled
albumin, sucrose, and
2H2O)
was performed. We used the relationship between the outflow recovery
(concentration/dose) for the noneliminated tracer,
C(t), or the
convolution of the organ transport function
h(t) with the outflow profile
[Ccath(t)] of the sham experiment that defines the dispersion of the inflow and outflow catheters (for details, see
APPENDIX, Eqs.
A1-A3). The
procedure provided values of
t0, a common
large vessel transit time, and 
, a space ratio. For the interstitial
space tracers 125I-albumin and
[14C]sucrose, is
the ratio of the accessible albumin or sucrose Disse space to the
sinusoidal plasma space, and for
2H2O
this ratio is the sum of the accessible Disse and hepatic cellular
water spaces and that in the sinusoid (in RBC and plasma). Equation A3 indicates that, after
t0 (transit time
of large vessel) and the transit time of the input and collecting
systems, each point on the
125I-albumin,
[14C]sucrose, or
2H2O
curves will be delayed in time, relative to the corresponding point on
the RBC curve, by the factor (1 + ), and its magnitude will be
correspondingly attenuated by the factor 1/(1+ ).
[3H]HA outflow dilution
curves.
We used the relationship between the outflow recovery
(concentration/dose) for the diffusible substance (HA),
Cdiff(t),
or the convolution of the organ transport function,
hdiff(t),
with the outflow profile of the inflow and outflow catheters,
Ccath(t) (see APPENDIX, Eq. A10), and that of the noneliminated reference, sucrose
[Csuc(t),
see Eq. A1]. A quantitative
analysis of the [3H]HA
outflow profile was carried out with a model developed previously (15,
32). Because binding of HA to RBC is negligible, the hypothetical
reference that described the extracellular behavior of
[3H]HA was constructed
based on the unbound fraction of HA in plasma (fu) and very rapid exchange
between bound and free forms (Eq. A5). A similar strategy was used for salicylamide
sulfate (39) and the glutathione conjugate of bromosulfophthalein (13).
The calculated parameter ref
(Eq. A5) provides a value for the
interstitial space ratio of a hypothetical reference that, outside the
cells, behaves in a manner identical to that for HA. It is expected to change with HA concentration, as binding of HA to albumin
(fu) changes. The unbound
fraction fu is calculated with the
known binding parameters
Ka and
n obtained from the binding studies (40)
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',
and efflux,
k'1,
defined in Table 1 were provided by the fitting procedure. The first
term represents material that propagates through the system without
entering the liver cells, or the throughput component. The second term
represents material that enters the liver cells and returns later and
exits via the vascular pathway, or the returning component. As
defined by Goresky et al. (15),
k1 and
k1 are the
permeability-surface area products for influx and efflux across the
hepatocyte membrane, respectively, per milliliter of cell water
(Vcell) (see Table 1).
To obtain
k1, the product
fuk1'
is divided by fu
(Eq. 2) and the space distribution
ratio, ', or the ratio of
Vcell to the extracellular
distribution space for HA (Eq. A9). Alternatively, the influx
permeability product
PinS was obtained
with Eq. A11. Normally, the influx
parameters are related to the logarithmic average of the unbound input
and output concentrations (12, 13, 40). Because there was a lack of
hippurate elimination, the unbound concentration in the plasma
(Cu) is constant throughout the
sinusoids and is given by
finCin,
the product of the unbound fraction in input plasma
(fin) and the steady-state input
concentration (Cin), or
foutCout,
the product of the unbound fraction in output plasma
(fout) and the steady-state
output concentration (Cout).
The efflux rate constant,
k1, was
obtained by dividing
k'seq
by ft, the unbound fraction of HA
in liver tissue. The unbound tissue concentration,
Ct,u, was calculated from the
tissue partition equilibrium ratio,
k1/k1,
which equals
Ct,u/Cu.
Superposition and MID fitting procedures. From the fractional outflow recovery curve of the vascular reference (the labeled RBC curve), the transport function of the injection and collection system of the outflow profile for the sham experiments conducted with injection of an MID dose into the inflow and outflow catheters, without the presence of a liver, was deconvoluted (13). A linear flow-limited transformation of the deconvoluted RBC curve was then carried out to generate a calculated first pattern for each diffusible reference, by selection of trial values for the ratio of the extravascular to vascular distribution spaces and of t0, the common large-vessel transit time. The resulting curve was convoluted with the system transport function. The generated diffusible reference curve (for labeled albumin, sucrose, or water) was compared with that obtained experimentally, and the parameter values were repetitively refined until a best fit was obtained using a least-squares procedure (International Mathematics Statistical Library, Visual Numerics, Houston, TX). The classical weighted least-squares approach to parameter estimates, as discussed by Landaw and DiStefano (22), was used as the criterion for fitting. A weighting strategy was carried out according to counting statistics noise, assuring an error variance proportional to the magnitude of the observation (7, 22). The Jacobian matrix (matrix of sensitivities) obtained from the fitting program was used to calculate variances and covariances of the fitted parameters. The square roots of the variances and the standard deviations of the fitted parameters for each experiment represented the uncertainty in the parameter estimate.
With these values in hand, a similar process was used to gain best fit values for influx and efflux coefficients for HA. The outflow dilution data were fitted to Eq. A8 by variation of fuk1', and
k'1,
as described previously (13, 32), using the same fitting procedure as
above. The tracer HA outflow profile was further resolved into
throughput and exchanging (returning) components. The dependence of the
parameters on HA concentration was taken into account in that the
nonlinear binding to albumin over the concentration range was
considered (the fraction of unbound HA increased from 0.39 to 0.56 when
the input concentration of HA varied from 1 to 930 µM).
Statistics
All data are means ± SD. Student's t-test statistic was used, and a P value
0.05 was viewed as
significant.
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RESULTS |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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Protein binding of HA.
The binding of HA to albumin was concentration dependent. One class of
binding site was found (n = 1.03),
with a Ka of 2.1 × 103
M1 (Fig.
2). Within the concentration range used for
the MID studies, the unbound fraction of HA in plasma varied from 0.39 to 0.56. The extent to which HA was bound to liver homogenate or
S9, however, did not vary with HA
concentration (1.1 to 500 µM); values for the unbound fraction of HA
in diluted homogenate and S9 were 1 ± 0.012 and 0.99 ± 0.02 (n = 5), respectively. The values suggest a lack of binding of HA to tissue
proteins.
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Hepatic extraction and biliary excretion of HA. When perfusate containing increasing bulk plasma concentrations of HA (1.3 to 930 µM) was used for perfusion, the steady-state hepatic extraction ratio of unlabeled HA remained virtually zero. Only trace amounts of HA were found in bile; the biliary excretion of HA was 0.35 ± 0.14% of the total dose. Given the extremely low excretion rate of HA, the use of a model without sequestration appeared justified.
Linear superposition by use of the delayed-wave model. Recoveries of labeled RBCs, albumin, sucrose, and 2H2O, including [3H]HA, in hepatic venous blood were complete within experimental errors. Representative outflow profiles for the labeled substances injected into the portal vein of the liver are shown in Figs. 3 and 4. The labeled RBC emerged first and reached the highest and earliest peak; the RBC outflow curve had the steepest upslope, and the downslope decayed most rapidly. The 125I-albumin curve rose slightly less quickly and decayed with a slightly reduced slope, showing a lower and later peak. In comparison to the labeled albumin curve, the [14C]sucrose curve showed a slightly more delayed upslope, a slightly lower and later peak, and a more prolonged downslope. The greatest dispersion was seen with 2H2O, whose upslope and downslope were very delayed and whose peak occurred much later with a much lower magnitude, due to its permeation of the cellular as well as vascular and interstitial spaces.
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(Table
2). The average t0 value (3.7 ± 1.3 s) was similar to those obtained for other perfused livers
(12, 13). The values for the interstitial substances (for labeled
albumin and labeled sucrose) and for
2H2O
(Alb = 0.65 ± 0.22, Suc = 1.1 ± 0.5, and
= 5.2 ± 1.5) were similar to those estimated in a similar fashion
in other perfused rat liver preparations (12, 13). After the approximation of the AUMC and AUC for the noneliminated indicators with
cubic splines, the average mean transit times were estimated by moment
analysis and were converted to their respective volumes after
multiplication by appropriate flows (Table 2). The mean transit times
for the noneliminated indicators were generally similar to those
obtained in other perfused rat liver MID studies.
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Evaluation of MID results: outflow profile for HA. The rising upslope of [3H]HA was slightly delayed with respect to that of labeled albumin, but it slightly preceded the labeled sucrose curve (Fig. 3). The [3H]HA curve crossed over the labeled sucrose curve, then peaked lower and earlier than the labeled sucrose curve, as expected, due to binding of HA to albumin. During its decay, the [3H]HA curve again crossed over the labeled sucrose curve and exhibited a more delayed downslope (Fig. 4). Fits to representative experiments are shown in Fig. 4. The tracer [3H]HA outflow profile was further resolved into the throughput and exchanging (returning) components. The throughput component increased from 40 to 60% of the total dose over the unbound concentration range studied (Fig. 5).
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rel, the influx coefficient
fuk1',
and the cellular efflux coefficient
k'seq are summarized in Table 3.
PinS estimated with
Eq. A11 was 3.5 ± 0.6 times that
of the plasma flow rate (0.017 ± 0.002 ml · s1 · g1)
at the lower HA concentration used, and these values decreased with
increasing concentration, demonstrating saturability (Fig. 6A). The
corresponding k1
values were also concentration dependent (Fig.
6B). Fitting of these values to
Vmax/(Km + Cu) yielded the apparent
constants for uptake: with
PinS,
Km = 162 ± 53 µM and Vmax = 19 ± 6 nmol · s1 · g1,
and with k1,
Km = 182 ± 60 µM and
Vmax = 12 ± 4 nmol · s1 · g1
(mean ± SD of parameter estimate); a slight but insignificant difference in these estimates existed due to the reliance of
k1 on
Vcell and subsequently '.
Saturation was also displayed for PoutS and
k1; the
latter was equal to the efflux coefficient, since the unbound fraction
in tissue, ft, was found to be
unity (Fig. 7; Table 3). Fitting these
values to the estimated tissue unbound concentration,
Ct,u, yielded very similar kinetic
constants (Km = 330 ± 140 and 390 ± 190 µM;
Vmax = 42 ± 16 and 29 ± 13 nmol · s1 · g1)
for efflux. The tissue equilibrium partitioning ratios,
k1/k1, were slightly lower than unity, and the values were similar to that
found in the liver of the hairless guinea pig (24). The values were
highest at the lower HA concentrations (average value of 0.82 ± 0.19) but gradually decreased with increasing concentration (Fig.
8).
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Interactions with L-lactate and
benzoate.
The hepatic transfer of HA in the presence of
L-lactate (20 mM) and benzoate
(from 10 to 873 µM) is summarized in Table
4. The values of
PinS for HA uptake
at ~180 µM (for controls see Table 3, preparations
11-13) were statistically different from those
in the presence of L-lactate,
although the changes in
PoutS, k1 and
k1 were
not significant. In the presence of benzoate (10 µM), the outflow HA
concentrations increased to 13 µM, whereas for benzoate
concentrations >200 µM, HA outflow concentration varied from 81 to
103 µM, due to HA formation from the various concentrations of
benzoate. The accrued HA concentration was expected not to evoke
changes in transport, since the influx and efflux parameters had
remained rather constant at input HA concentrations <200 µM (see
Figs. 6 and 7). The changes observed were therefore induced by
benzoate. PinS and
PoutS and
k1 and
k1 for HA uptake were decreased in the presence of benzoate (see Table 3, preparations 1-10 for controls).
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DISCUSSION |
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Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
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Hippuric acid, similar to its precursor benzoic acid (5), is found to
exhibit poor binding properties to albumin
(n = 1, Ka = 2.1 × 103
M1) and does not
distribute into RBC. As expected with these binding constants, the
unbound fraction of HA increased only slightly, from 0.39 to 0.56, over
the wide input plasma concentration range of HA studied (1-930
µM). Binding of HA to intracellular (tissue) components was also
found to be absent.
A negligible extraction ratio of HA was observed, confirming the previous observation that HA was poorly excreted by the perfused rat liver preparation (5). To gain insight into the transfer processes, we estimated the transfer coefficients and transfer rate constants from the MID experiments, since the events underlying the handling of hippurate were revealed in its outflow behavior in relation to the outflow behavior of other reference materials. We found that the transport parameters for influx and efflux (transfer clearances or rate constants) were relatively constant for HA input concentrations below 200 µM but eventually decreased with increasing concentration. The transfer processes are, however, quite rapid for hippurate: PinS was three to four times that of the plasma flow rate at low concentrations and one to two times that of the plasma flow rate at higher concentrations. Efflux was equally as fast (Table 3). The lack of hepatic excretion of HA is due purely to its poor candidacy for excretion and is not a result of poor penetration.
Consistently, the magnitude of
PinS (or influx
clearance per gram liver) and
k1 (Fig. 6) and
their efflux counterparts
PoutS and
k1 (Fig.
7) was reduced with rising concentrations. The increasing throughput
component (Fig. 5) and the declining partition coefficient (Fig. 8)
conform to the assumption that a carrier protein is involved, since
saturation is evident (12, 13). The alternate mechanism of passive
diffusion, however, is untenable, since the distribution ratio
(equilibrium partitioning of drug into chloroform and buffer at pH 7.4)
was extremely low (0.0001). A similarly low value was also obtained by
Lanman et al. (23). The
Km for influx is
quite high (160-180 µM), and this explains why the transport
remained virtually first order for input plasma concentrations of 200 µM (corresponding to 100 µM unbound concentration). The
Km for efflux is
even higher (330-390 µM). The rate of distribution of hippurate
into the tissue thus appears to be limited by the sinusoidal permeation
of HA molecules from blood to tissue.
That carrier proteins are involved in the transsinusoidal transfer of
HA was evident, since the uptake and efflux displayed saturation. The
anion transport protein oatp expressed in HeLa cells (34) was, however,
not involved in hippurate or benzoate uptake (K. S. Pang and A. W. Wolkoff, unpublished observations). There was demonstrable competition
by L-lactate and benzoate
(10-873 µM), which depressed
PinS and
PoutS. The reduction
in PS products for HA influx and efflux by
L-lactate suggests the putative
role of the hepatic monocarboxylate transporter, MCT2 (9, 10); the
natural substrate is likely to be
L-lactate (8). The interaction between L-lactate and benzoate
has been thoroughly studied in the cloned and expressed MCT
transporter, MCT1, in hamster and rabbit intestine (9, 10, 36, 37).
Reduction of L-lactate but not
D-lactate transport by benzoate
and inhibition by 
-cyanocinnamide were observed (37).
Carrier-mediated transport of benzoic acid was found to occur within
Caco-2 cells; a pH dependence was further identified (38). Fast
disappearance of benzoate from peritoneal fluid, suggestive of
carrier-mediated uptake by the peritoneum, was recently reported (28).
All of these findings point to transport of benzoic acid by MCT. The
present data suggest that hepatic transport of the carboxylates by this
transporter may be extended to hippurate in the rat liver.
| |
APPENDIX |
|---|
|
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
|
|---|
The model used for interpreting the data in this study was the barrier-limited, space-distributed, variable transit time model developed by Goresky et al. (15). It describes the relationship between the dose-normalized outflow profiles for the substance under study, Cdiff(t), and those of the interstitial reference substances (sucrose or albumin). Because HA binds to plasma proteins but not RBC, a hypothetical reference accounting for partial binding, similar to that proposed for enalaprilat (32), is defined with respect to the proportion bound to labeled albumin and that which is unbound. In the absence of binding and uptake, the latter would behave like labeled sucrose.
The single path (or single sinusoid) model. The sinusoid is thought to be a single pathway with adjacent sheets of hepatocytes, from which the irreversible biliary excretion occurs. Within the sinusoid, with the small lateral dimensions, diffusion in the lateral direction is assumed to be instantaneous; the sinusoid is so long, however, that diffusion in the longitudinal direction will not contribute significantly to transfer from entrance to exit over the time scale involved, and this is therefore neglected. With these assumptions, space can be described by a single variable, x, denoting position along the sinusoid flow path, and it is possible to find an analytical solution in time and space describing the behavior of tracer within the vasculature and tissue and at the outflow from a sinusoid.
To evaluate the experimentally obtained outflow profiles, the dispersion of the injected bolus by the injection apparatus and the inflow and outflow catheters must be considered, as previously described in detail (13). For example, the experimental sucrose curve, CSuc(t), is the convolution of the organ sucrose transport function (catheter-corrected outflow profile or impulse response), hSuc(t), with the outflow profile obtained from the apparatus in the absence of a liver, Ccath(t)
|
(A1) |
|
(A2) |
, and the common large-vessel transit time
t0, were found by
first calculating the RBC transport function,
hRBC(t),
by deconvolution as mentioned above and then calculating the organ
sucrose transport function,
hSuc(t),
from the organ RBC transport function,
hRBC(t),
according to the following equation
|
(A3) |
|
(A4) |
ref is the ratio of
extravascular to vascular distribution space of HA. The value of this
ratio is
|
(A5) |
|
(A6) |
|
(A7) |
ref)/(1 + Suc) or the ratio of the
total sinusoidal plasma plus interstitial spaces of distribution for
HA, in relation to that for labeled sucrose, further defines (1 + rel), which was used to
describe the appropriate interstitial space reference for the data. The
organ transport function for HA was then calculated according to the
barrier-limited space-distributed variable transit time model, using
the following equation
(13)
|
|
![×<LIM><OP>∑</OP><LL><IT>n</IT> = 1</LL><UL>∞</UL></LIM> <FR><NU>[(f<SUB>u</SUB><IT>k</IT><SUB>1</SUB><IT>&thgr;′k</IT>′<SUB>−1</SUB>)(&tgr;′ − <IT>t</IT><SUB><B>0</B></SUB>)]<SUP><IT>n</IT></SUP>(<IT>t</IT> − &tgr;′)<SUP><IT>n</IT> − 1</SUP></NU><DE><IT>n</IT>!(<IT>n</IT> − 1)!</DE></FR> d&tgr;′](/content/vol274/issue1/fulltext/G10/img019.gif)
|
(A8) |
1
are transfer coefficients for entry into and efflux from the
hepatocytes, and
k'seq
is the sequestration coefficient describing removal of HA, which was
set to zero in the present case; 
' = (1 + ref) and = x/vF,
where x is the distance and
vF is the linear
velocity of sinusoidal blood. The ratio of cellular to extracellular
distribution spaces for HA, ', is obtained from
|
(A9) |
is the ratio of Vcell to
plasma water space (Vp) and
ref is the ratio of the
extravascular to the vascular distribution space of HA
(Eq. A5).
VSuc is sinusoidal sucrose space,
and Vcell and
VSuc are estimated from their mean
transit times.
The calculated HA outflow profile,
CHA(t),
is obtained by convolution of
hHA(t)
with the outflow profile obtained from the apparatus in the absence of
a liver,
Ccath(t)
|
(A10) |
',
k'1,
and rel. From the fitted value
of
fuk1',
k1 was calculated
using ', obtained using Eq. A8 and Eq. A10.
Finally, PinS was
obtained from the fitted value of
fuk1',
as follows
|
(A11) |
| |
ACKNOWLEDGEMENTS |
|---|
We thank Dr. Allan W. Wolkoff of the Marion Bessin Liver Research Center, Albert Einstein College of Medicine, Bronx, NY, for kind assistance in the uptake studies of hippurate by oatp in HeLa cells.
| |
FOOTNOTES |
|---|
This work was supported by National Institutes of Health Grant GM-38250, the Fast Foundation, and the Medical Research Council of Canada (MT-11228).
This work was presented in part at the Annual Meeting of the American Society of Pharmacology and Experimental Therapeutics, San Diego, CA, 1997.
Present address of T. Yoshimura: Dept. of Drug Metabolism and Pharmacokinetics, Eisai Tsukuba Preclinical Research Laboratories, Tsukuba City, Ibaraki 300-26, Japan.
Address for reprint requests: K. S. Pang, Faculty of Pharmacy, Univ. of Toronto, 19 Russell Street, Toronto, Ontario, Canada M5S 2S2.
Received 2 June 1997; accepted in final form 5 August 1997.
| |
REFERENCES |
|---|
|
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References
|
|---|
1.
Bassingthwaighte, J. B.
Circulatory transport and convolution integral.
Mayo Clin. Proc.
42:
137-154,
1967[Medline].
2.
Beck, J. V.,
B. Blackwell,
and
J. C. Clair.
Inverse Heat Conduction: Ill-Posed Problems. New York: Wiley Interscience, 1985.
3.
Bossuyt, X.,
M. Müller,
B. Hagenbuch,
and
P. J. Meier.
Polyspecific drug and steroid clearance by an organic anion transporter of mammalian liver.
J. Pharmacol. Exp. Ther.
276:
891-896,
1996
4.
Bridges, J. W.,
M. R. French,
R. L. Smith,
and
R. T. Williams.
The fate of benzoic acid in various species.
Biochem. J.
118:
47-51,
1970[Medline].
5.
Chiba, M.,
K. Poon,
J. Hollands,
and
K. S. Pang.
Glycine conjugation of benzoic acid and its acinar localization in perfused rat liver.
J. Pharmacol. Exp. Ther.
268:
416-419,
1994.
6.
Despopoulos, A.
Congruence of excretory functions in liver and kidney: hippurates.
Am. J. Physiol.
210:
760-764,
1966.
7.
DiStefano, J. J., III,
and
E. M. Landaw.
Multi-exponential, multi-compartmental, and non-compartmental modeling. I. Methodological limitations and physiological interpretations.
Am. J. Physiol.
246 (Regulatory Integrative Comp. Physiol. 15):
R651-R664,
1984.
8.
Edmund, G. L.,
and
A. P. Halestrap.
The kinetics of transport of lactate and pyruvate into rat hepatocytes.
Biochem. J.
249:
117-126,
1988[Medline].
9.
Garcia, C. K.,
M. S. Brown,
R. V. Pathak,
and
J. L. Goldstein.
cDNA cloning of MCT2, a second monocarboxylate transporter expressed in different cells than MCT1.
J. Biol. Chem.
270:
1843-1849,
1995
10.
Garcia, C. K.,
J. L. Goldstein,
R. V. Pathak,
R. G. W. Anderson,
and
M. S. Brown.
Molecular characterization of a membrane transporter for lactate, pyruvate and other monocarboxylates: implications for the Cori cycle.
Cell
76:
865-873,
1994[Medline].
11.
Gärtner, U.,
T. Goeser,
A. Stiehl,
R. Raedsch,
and
A. W. Wolkoff.
Transport of chenodeoxycholic acid and its 3- and 7-sulfates by isolated perfused rat liver.
Hepatology
12:
738-742,
1990[Medline].
12.
Geng, W. P.,
K. Poon,
and
K. S. Pang.
An understanding of flow- and diffusion-limited versus carrier-mediated hepatic transport: a simulation study.
J. Pharmacokinet. Biopharm.
23:
347-378,
1995[Medline].
13.
Geng, W. P.,
A. J. Schwab,
C. A. Goresky,
and
K. S. Pang.
Carrier-mediated uptake and excretion of bromosulfophthalein-glutathione in perfused rat liver: a multiple indicator dilution study.
Hepatology
22:
1188-1207,
1995[Medline].
14.
Goresky, C. A. Initial distribution and rate of uptake
of sulfobromophthalein in the liver. Am. J. Physiol. 207: 1964.
15.
Goresky, C. A.,
G. G. Bach,
and
B. E. Nadeau.
On the uptake of materials by the intact liver. The transport and net removal of galactose.
J. Clin. Invest.
52:
991-1009,
1973.
16.
Hagenbuch, B.,
H. Lubbert,
B. Stieger,
and
P. J. Meier.
Expression of the hepatocyte Na+-bile acid cotransport system.
Proc. Natl. Acad. Sci. USA
88:
10629-10633,
1991
17.
Hagenbuch, B.,
and
P. J. Meier.
Molecular cloning, chromosomal localization, and functional characterization of a human liver Na+/bile acid cotransporter.
J. Clin. Invest.
93:
1326-1331,
1994.
18.
Hassen, A. M.,
D. Lam,
M. Chiba,
E. Tan,
W. Geng,
and
K. S. Pang.
Uptake of sulfate conjugates by isolated rat hepatocytes.
Drug Metab. Dispos.
24:
792-798,
1996[Abstract]. [Erratum 24: 925, 1996.]
19.
Ingersoll, W.,
and
S. H. Babcock.
Organic Syntheses, Collective Index. New York: John Wiley & Sons, 1943, p. 328-330.
20.
Jacquemin, E.,
B. Hagenbuch,
B. Stieger,
A. W. Wolkoff,
and
P. J. Meier.
Expression of the hepatocellular chloride-dependent sulfobromophthalein uptake system in Xenopus laevis oocytes.
J. Clin. Invest.
88:
2146-2149,
1991.
21.
Jacquemin, E.,
B. Hagenbuch,
B. Stieger,
A. W. Wolkoff,
and
P. J. Meier.
Expression of a rat liver Na+-independent organic anion transporter.
Proc. Natl. Acad. Sci. USA
91:
133-137,
1994
22.
Landaw, E. M.,
and
J. J. DiStefano III.
Multiexponential, multicompartmental, and noncompartmental modeling. II. Data analysis and statistical considerations.
Am. J. Physiol.
246 (Regulatory Integrative Comp. Physiol. 15):
R665-R677,
1984.
23.
Lanman, R. C.,
C. E. Stremsterfer,
and
L. S. Schanker.
Absorption of organic anions from the rat small intestine.
Xenobiotica
1:
613-619,
1971[Medline].
24.
Lowry, O. H.,
N. J. Rosebrough,
A. L. Farr,
and
R. J. Randall.
Protein measurement with the Folin phenol reagent.
J. Biol. Chem.
193:
265-275,
1951
25.
MacPherson, S. E.,
C. N. Barton,
and
R. L. Bronaugh.
Use of in vitro skin penetration data and a physiologically based model to predict in vivo blood levels of benzoic acid.
Toxicol. Appl. Pharmacol.
140:
436-443,
1996[Medline].
26.
Min, A. D.,
T. Goeser,
R. Liu,
C. G. Campbell,
P. M. Novikoff,
and
A. W. Wolkoff.
Organic anion transport in HepG2 cells: absence of high affinity, chloride-dependent transporter.
Hepatology
14:
1217-1223,
1991[Medline].
27.
Min, A. D.,
K. L. Hohansen,
C. G. Campbell,
and
A. W. Wolkoff.
The role of chloride and intracellular pH on the activity of the rat hepatocyte organic anion transporter.
J. Clin. Invest.
87:
1496-1502,
1991.
28.
Nakashima, E.,
R. Matsushita,
N. Kanada,
and
F. Ichimura.
Kinetic evidence for facilitated peritoneal transport of benzoic acid in rats.
J. Pharm. Pharmacol.
48:
347-350,
1996[Medline].
29.
Pang, K. S.,
I. A. Sherman,
A. J. Schwab,
W. Geng,
F. Barker III,
J. A. Dlugosz,
G. Cuerrier,
and
C. A. Goresky.
Role of the hepatic artery in the metabolism of phenacetin and acetaminophen: an intravital microscopic and multiple indicator dilution study in perfused rat liver.
Hepatology
20:
672-683,
1994[Medline].
30.
Pang, K. S.,
N. Xu,
and
C. A. Goresky.
D2O as a substitute for 3H2O, as a reference indicator in liver multiple-indicator dilution studies.
Am. J. Physiol.
261 (Gastrointest. Liver Physiol. 24):
G929-G936,
1991
31.
Rollins, D. E.,
J. W. Freston,
and
D. M. Woodbury.
Transport of organic anions into liver cells and bile.
Biochem. Pharmacol.
29:
1023-1028,
1980[Medline].
32.
Schwab, A. J.,
F. Barker III,
C. A. Goresky,
and
K. S. Pang.
Transfer of enalaprilat across rat liver cell membranes is barrier-limited.
Am. J. Physiol.
258 (Gastrointest. Liver Physiol. 21):
G461-G475,
1990
33.
Schwenk, M.,
and
V. L. del Pino.
Uptake of estrone sulfate by isolated rat liver cells.
J. Steroid Biochem.
13:
669-673,
1980[Medline].
34.
Shi, X.,
S. Bai,
A. C. Ford,
R. D. Burk,
E. Jacquemin,
B. Hagenbuch,
P. J. Meier,
and
A. W. Wolkoff.
Stable inducible expression of a functional rat liver organic anion transport protein in HeLa cells.
J. Biol. Chem.
270:
25591-25595,
1995
35.
Sundheimer, D. W.,
and
K. Brendel.
Metabolism of harmol and transport of harmol conjugates in isolated rat hepatocytes.
Drug Metab. Dispos.
11:
433-440,
1983[Abstract].
36.
Takanaga, H.,
T. Tamai,
S.-I. Inaba,
Y. Sai,
H. Higashida,
H. Yamamoto,
and
A. Tsuji.
cDNA cloning and functional characterization of rat intestinal monocarboxylate transporter.
Biochem. Biophys. Res. Commun.
217:
370-377,
1995[Medline].
37.
Tamai, I.,
H. Takanaga,
H. Maeda,
Y. Sai,
T. Ogihara,
H. Higashida,
and
A. Tsuji.
Participation of a proton-cotransporter, MCT1, in the intestinal transport of monocarboxylic acids.
Biochem. Biophys. Res. Commun.
214:
482-489,
1995[Medline].
38.
Tsuji, A.,
H. Takanaga,
I. Tamai,
and
T. Terasaki.
Transcellular transport of benzoic acid across Caco-2 cells by a pH-dependent and carrier-mediated transport mechanism.
Pharmaceut. Res.
11:
30-37,
1994[Medline].
39.
Xu, X.,
A. J. Schwab,
F. Barker,
C. A. Goresky,
and
K. S. Pang.
Salicylamide sulfate cell entry in perfused rat liver: a multiple-indicator dilution study.
Hepatology
19:
229-244,
1994[Medline].
40.
Xu, X.,
P. Selick,
and
K. S. Pang.
Nonlinear protein binding and enzyme heterogeneity: effects on hepatic drug removal.
J. Pharmacokinet. Biopharm.
21:
43-74,
1993[Medline].
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