Introduction

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The liver is the main organ in the body for the conversion of drugs, toxins, and body products into more water-soluble forms so as to facilitate excretion by the kidney and biliary system. Although the enzymes involved in this conversion have been widely studied, there is relatively limited information on how the liver transports drugs within its cells and why some drugs (e.g., propranolol) bind strongly to components in the cells.

This work is concerned with intrahepatocellular binding as a determinant of hepatic drug disposition, especially the "first pass effect". It is now known that, in the liver, ₁-acid glycoprotein (AAG) is a potentially important intrahepatocellular binding protein for cationic drugs (Mansor et al., 1991). Plasma concentrations of cationic drugs are often related to AAG concentrations, because these drugs normally bind strongly to AAG (Garrido et al., 2000).

Cationic drugs are of particular interest for a number of reasons: 1) they constitute 70 to 80% of all drugs (Steen et al., 1991; Moseley et al., 1992); 2) they often have a limited therapeutic ratio (e.g., cardiovascular, analgesic, and psychotherapeutic drugs); and 3) they constitute the majority of drugs showing a high first pass effect (Marzo, 1992; Tam, 1993). Many of the anticancer drugs are also cations (e.g., epirubicin). To our knowledge, this study is the first report to investigate the structure-hepatic disposition relationships for cationic drugs in the isolated perfused rat liver preparation. The results may lead to an understanding of the role played by intrahepatocellular binding of cationic drugs on their kinetics and trafficking within hepatocytes.

The structure-hepatic disposition relationships of model cationic drugs (atenolol, antipyrine, prazosin, labetalol, propranolol, and diltiazem) with varying lipophilicity (Table 1) were determined in isolated perfused rat liver preparations using multiple indicator dilution (MID) technique. The aim of this study was to relate parameters characterizing the hepatic distribution and elimination kinetics of cationic drugs to their lipophilicity. A heterogeneous (barrier-limited and space-distributed) transit time model was used to estimate the rate constants of hepatocellular influx, efflux, binding, and elimination for each solute. The model is in principle equivalent to the standard MID approach and has been successfully used to study the hepatocellular binding and disposition kinetics of diclofenac (Weiss et al., 2000). Model independent parameters (E, MTT, CV²) were determined by moments analysis.

	Materials and Methods

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Chemicals

Atenolol {4-[2-hydroxy-3-[(1-methylethyl)amino]propoxy]benzeneacetamide}, antipyrine {1,2-dihydro-1,5-dimethyl-2-phenyl-3H-pyrazol-3-one}, prazosin {1-(4-amino-6,7-dimethoxy-2-quinazolinyl)-4-(2-furanylcarbonyl)piperazine}, labetalol {2-hydroxy-5-[1-hydroxy-2-[(1-methyl-3-phenylpropyl)amino]ethyl]benzamide}, propranolol {1-[(1-methylethyl)amino]-3-(1-naphthalenyloxy)-2-propanol}, and diltiazem {(2S-cis)-3-(acetyloxy)-5-[2-(dimethyl amino)ethyl]-2,3-dihydro-2-(4-methoxyphenyl)-1,5-benzo-thiazepin-4(5H)-one} were obtained from Sigma Chemical Co. (St. Louis, MO), and were used without any further purification. [U-¹⁴C]Sucrose and [³H]water were obtained from Amersham (Buckinghamshire, UK).

In Situ Rat Liver Perfusions

The in situ perfused rat liver preparation used in this study has been described previously (Cheung et al., 1996). Briefly, male Wistar rats (weighing 300 g approximately) were anesthetized by interperitoneal injection of xylazine 10 mg kg¹ (Bayer Australia, Pymble, NSW) and ketamine-hydrochloride 80 mg kg¹ (Parnell Laboratories Australia, Alexandria, NSW). Following laparotomy animals were heparinized (heparin sodium; David Bull Laboratories Australia, Mulgrave, Victoria, 200 units) via the inferior vena cava. The bile duct was cannulated with PE-10 (Clay Adams, Franklin Lakes, NJ). The portal vein was then cannulated using a 16-gauge intravenous catheter and the liver was perfused via this cannula with 2% BSA MOPS buffer (Blanchard, 1984), which contains 15% (v/v) prewashed canine red blood cells (RBCs) at pH 7.4, and oxygenated using a silastic tubing lung ventilated with 100% pure oxygen (BOC Gases Australia, North Ryde, NSW). The perfusion system used was nonrecirculating and used a peristaltic pump (Cole-Palmer, Vernon Hills, IL). After perfusion was effected the animals were sacrificed by thoracotomy and the thoracic inferior vena cava was cannulated with PE-240 (Clay Adams). The animal was placed in a temperature-controlled perfusion cabinet at 37°C. Liver viability was assessed by macroscopic appearance, bile production, oxygen consumption, and perfusion pressure as described by Cheung et al. (1996).

Bolus Studies

Perfusions were made at 15 ml/min in each liver. After a 10-min perfusion stabilization period, a solution (50 µl of perfusion medium) of a particular concentration of the cationic drug (4 mM atenolol/propranolol, 5 mM antipyrine, 3 mM prazosin/labetalol, 2 mM diltiazem approximately) containing [³H]water (3 × 10⁶ dpm) and [U-¹⁴C]sucrose (1.5 × 10⁶ dpm) was injected into the liver with outlet samples collected via a fraction collector over 4 min (1 s × 20, 4 s × 5, 10 s × 5, 30 s × 5). In each liver a maximum of six injections was made with the order of injection randomized and no repeat of the same injection in the same rat. A stabilization period of 10 min was afforded between two injections. The total perfusion time for each liver was less than 2 h. These samples were centrifuged and aliquots (100 µl) of supernatant (containing [³H]water and [U-¹⁴C]sucrose) were taken for scintillation counting using a MINAXI beta TRI-CARB 4000 series liquid scintillation counter (Packard Instruments, Meriden, CT). The residue was vortexed and prepared for high performance liquid chromatography (HPLC) analysis to determine the outflow concentration of each cationic drug.

Analytical Procedure

HPLC Instrumentation. HPLC generally used a system consisting of a Waters 616 Quaternary Pumping system (Waters, Milford, MA); a Waters 717-plus autoinjector; a Waters Symmetry C18 3.9 × 150-mm steel cartridge column; a Waters 474 fluorescence detector for atenolol, antipyrine, prazosin, labetalol, and propranolol detecting (excitation 300 nm/emission 375 nm); a Waters 996 PhotoDiode array detector monitoring at 210 nm for diltiazem detecting; and a Waters Millennium 2010 Chromatography Manager data system. The mobile phase used for atenolol, antipyrine, prazosin, labetalol, and propranolol was 100 mM KH₂PO₄ buffer with 25% acetonitrile, at pH 3.0 (flow rate 1.0 ml/min). The mobile phase used for diltiazem was 100 mM KH₂PO₄ buffer with 30% acetonitrile, at pH 5.1 (flow rate 1.0 ml/min). The mobile phase was filtered and degassed under vacuum through a Millipore HVLP 47-mm-diameter filter membrane with 0.45-µm pore size before use.

Extraction Procedure. The standards and samples (buffer with canine RBCs) were prepared for HPLC analysis according to the following extraction procedure. 1) Atenolol, antipyrine, prazosin, labetalol, and propranolol: 100-µl aliquots of sample were mixed with 25 µl of 20 mg/l pronethalol (internal standard) in methanol and 50 µl of 10% trichloroacetic acid in an Eppendorf tube. The tubes were vortexed for 1 min and centrifuged and 50 µl of the resulting supernatant was injected onto the column. 2) Diltiazem: 100-µl aliquots of sample were mixed with 100 µl of 5 mg/l desmethylimipramine (internal standard) and 500 µl of phosphate buffer (0.05 M KH₂PO₄, 0.05 M Na₂HPO₄, pH 7.5). The samples were extracted by shaking vigorously for 5 min with 9 ml of hexane: isoamyl alcohol (99:1) in a polypropylene tube. After centrifugation, the organic phase was pipetted to a 10-ml polypropylene tube, leaving at least 5-mm depth of organic phase to avoid getting contamination from the aqueous phase, and extracted by vortexing with 0.2 ml 0.05 M HCl for 1 min. After a further centrifugation, the organic phase was aspirated and injecting 100 µl of the resulting supernatant onto the column.

Calibration and Assay Validation. Calibration samples were obtained by dissolving particular cationic drug in methanol. Increasing amount of this methanolic solution was added to perfusate medium to generate calibration curves over the range of 0 to 5000 ng/ml. For all the drugs in this work, HPLC standard curves were linear within the range of concentrations studied, with linear regression analysis yielding r² values >0.999. The within-day coefficients of variation (CV) for the various cationic drugs were determined by establishing and running three separate standard curves on the same day. Identical unknown samples were also run and the exact concentration determined using the separated standard curves. The CV was determined by dividing the standard deviation of the determined unknown solute concentration by the mean of these concentrations. The within-day coefficients of variation for all the drugs studied in this work were within the range of 0.6 to 4.4% (n = 3). Detection limit (atenolol/antipyrine/labetalol = 50 ng/ml, prazosin = 25 ng/ml, propranolol = 5 ng/ml, diltiazem = 10 ng/ml) was established by injecting decreasing concentrations of particular cationic drug extracted standards (prepared in perfusate medium) onto the column.

Perfusion Medium Binding

These experiments were carried out in 2% BSA MOPS buffer (pH 7.4), which contains 15% (v/v) prewashed canine RBCs, and incubated at 37°C water bath for 30 min to attain the required temperature. A 500 µM solution of each cationic drug was prepared in this perfusate.

The unbound fraction (f_uB) of cationic drug was investigated using an ultra-filtration method. A 1.0-ml aliquot sample (in triplicate) was placed in an ultrafiltration tube (MPS-1, micro-partition system; Amicon, Beverly, MA) and centrifuged at 3000g for 10 min. The ultra-filtrate was then assayed by HPLC. The f_uB was determined as the ratio of the free concentration to total concentration of solute.

Data Analysis

The two-phase organ model, which describes intracapillary mixing, transfer across a permeability barrier, and the intracellular distribution and elimination kinetics (Weiss and Roberts, 1996; Weiss et al., 1997), was previously applied to the disposition of diclofenac in the isolated perfused rat liver assuming "slow" hepatocellular binding, i.e., reversible sequestration (Weiss et al., 2000). Here the model was used in a reparameterized form introducing an additional class of intracellular binding sites. Briefly, the model (Fig. 1) assumes drug transfer across the permeability barrier (plasma membrane) with influx and efflux rate constants k_in and k_out, respectively. The model recognizes that solute concentrations change in space and time in both phases. The stochastic approach represents the transit of a molecule through the organ as a series of sojourns in one of the two regions described by density functions. The distribution of successive sojourn times in the tissue region, i.e., the density of cellular residence times [_y(s)] describes the hepatocellular distribution and elimination kinetics. We started with the assumption of two cellular binding sites characterized by a rapid (R) and slow (S) dissociation process, respectively. In fitting the data we observed that the dissociation rate constant of the rapid process was extremely high. Thus, we simplified the model using the solution for k_{off, R}  , i.e., assuming an instantaneous equilibration process characterized by K_R = k_{on, R}/k_{off, R,} the equilibrium amount ratio characterizing the rapidly equilibrating binding sites. (Note that "binding" is used for all of reversible sequestration processes into cellular pools or storage compartments.)

View larger version (37K): [in this window] [in a new window]   Fig. 1.   Schematic overview of hepatocellular drug transport in the stochastic space-distributed liver model. kon and koff represent the intracellular binding and unbinding rate constant, respectively. KS is the equilibrium amount ratio characterizing the slowly equilibrating binding sites. KR is the equilibrium amount ratio characterizing the rapidly equilibrating binding sites. VC is the cellular water volume. kin, kout, and ke represent the permeation, efflux, and elimination rate constant, respectively. Also represented in the model are lysosomes and mitochondria, sites for ion trapping of cationic drugs.

The sojourn time distribution f_y(t) of a molecule after a single excursion in the cellular space for the resulting two-compartment cell model can be obtained by standard methods in the Laplace domain, _y(s) = L¹[f_y(t)], as described earlier (Weiss, 1999; Weiss et al., 2000):

(1)

where the permeation rate constant k_in = CL_pT/V_B is the permeation clearance per extracellular volume V_B (note that CL_pT = f_uBPS; PS is the permeability-surface product, f_uB is the free fraction of solute in the perfusate), k_on and k_off representing the intracellular binding and unbinding rate constant, respectively, determining the equilibrium amount ratio K_S = k_on/k_off characterizing the slowly accessible pool, and the elimination rate constant k_e = CL_int/V_C is the intrinsic elimination clearance normalized per cellular volume V_C.

This approach is comparable with the liver MID model proposed by Schwab et al. (1990) and the model applied by Audi et al. (1998) to the isolated perfused rabbit lung assuming multiple intracellular binding sites. Note that due to the assumption of two intracellular storage compartments the definition of k_on and k_off differs from the model previously used for diclofenac (Weiss et al., 2000).

The transit time density function (s) of drug molecules across the liver can then be derived in terms of the extracellular transit time density of nonpermeating reference molecules (s) [in this study sucrose _sucr(s)], and the density function of successive sojourn times _y(s) of the drug molecules into the cellular space:

(2)

The fractional outflow versus time data were fitted in the time domain using a numerical inverse Laplace transformation of the appropriate transit time density function applying the nonlinear regression program SCIENTIST (MicroMath Scientific Software, Salt Lake City, UT). Data were analyzed by a sequential procedure. First, the fractional outflow curve C_sucr(t) of the extracellular marker [U-¹⁴C]sucrose was fitted by eq. 3, whereby _cath(s) accounts for the catheter and _B(s) includes the large vessel transit time:

(3)

and the transit time density of the nonpermeating indicator is given by the following equation:

(4)

with

(5)

Equation 5 is the Laplace transform of the inverse Gaussian density function with mean MT_i and relative dispersion CV. [It was shown previously that eqs. 3 through 5 adequately describe the transit time density of vascular markers in perfused rat livers (Weiss et al., 1997, 1998).]

The catheter transit time density was determined in the same way, i.e., by an independent experiment fitting eqs. 4 and 5 to the outflow profile of the catheter system. The four parameters describing _cath(s) were then fixed in fitting the liver outflow data. It should be also noted that in contrast to the Goresky approach (Schwab et al., 1990) the delay due to the nonexchanging liver vessels (t₀) was not determined directly; however, the inverse Gaussian density accounts for a lag time (for CV²  1 the apparent lag-time increases with decreasing values of CV²; Weiss, 1997). This model, however, also corrects for the differences in the first appearance time of sucrose and water.

The mean transit time of the extracellular reference, MTT_B =  tf_B(t)dt, is given by the following equation:

(6)

V_B = MTT_BQ(1  hematocrit), is the volume, accessible to sucrose, i.e., the sum of the sinusoidal plasma space and the Disse space, V_B = V_Plasma + V_Disse [Q(1  hematocrit) denotes the plasma flow rate]. Since sucrose does not distribute into erythrocytes, this extracellular space value has to be corrected for hematocrit (Varin and Huet 1985). Also, using this information the outflow concentration data of the permeating drugs, C(t), were analyzed, i.e., the parameters MT_i, CV (i = 1, 2), and p of the individual fits of [U-¹⁴C]sucrose data were substituted as fixed parameters in _B(s) of the model (eq. 2):

(7)

and the parameters k_in, k_out, k_on, k_off, K_R, and k_e were estimated.

The cellular distribution volume of water was estimated in the same way, i.e., by fitting the [³H]water outflow data with eq. 7 using the density function for water _W(s) instead of (s). The latter differ only with regard to the respective tissue residence time densities _y(s); assuming no cytoplasmic binding of water and k_{out, w} = k_{in, w}v_{c, w} where v_{c, w} denotes the normalized cellular water volume eq. 1 for well mixed intracellular distribution reduces (Weiss et al., 2000):

(8)

and is substituted in eqs. 2 and 7.

Nonparametric estimates of hepatic availability (F), mean transit time (MTT), and normalized variance (CV²) were determined from the outflow concentration (C) versus time (t) profiles for the reference from eqs. 9 through 12 using the parabolas-through-the-origin method (extrapolated to infinity) with the assistance of the Moments Calculator 2.2 program for Macintosh computer (Purves, 1992).

(9)

AUC = C(t)dt is the area under the solute concentration versus time curve, Q is the perfusate flow rate, and D is the dose of solute administered. All concentrations used were expressed in molar equivalents. Hepatic extraction ratio (E) equals to 1  F.

(10)

(11)

where

(12)

Statistical Analysis

All data are presented as mean ± standard deviation unless otherwise stated. The model selection criterion provided by SCIENTIST, a modified Akaike Information Criterion (normalized to the number of data points), is defined by the following formula:

(13)

where w_i are the weights applied to each concentration data point, n is the number of points, C_obsi are the observed concentrations, C_cali are the values predicted by the model, _obs is the weighted mean of the observed data, and p is the number of estimated parameters. This equation is used to compare the models with regard to "goodness of fit"; the most appropriate model, from a pure statistical point of view, is that with the largest model selection criterion. Information on parameter statistics was obtained from the approximate coefficients of variation of each estimate and the correlation matrix. A high coefficient of variation and/or correlation between parameters suggests unreliable estimates.

	Results

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The experimental parameters associated with the perfusion studies were (mean ± S.D., n = 6) rat weight = 298 ± 18 g, liver weight = 8.45 ± 1.24 g, bile flow = 1.54 ± 0.09 µl · min¹ · g¹ of liver, oxygen consumption = 1.14 ± 0.12 µmol · min¹ · g¹ of liver, and perfusion pressure = 11.45 ± 2.13 cm of H₂O. These values, reflecting liver viability, are comparable to those reported by Varin and Huet (1985) in a similar type of preparation.

The estimated model parameters for extracellular volume (determined by [U-¹⁴C]sucrose), cellular volume (determined by [³H]water), and ratio of cellular volume to extracellular volume were V_B = 0.49 ± 0.15 ml g¹ of liver, V_C = 1.30 ± 0.44 ml g¹ of liver, and v_c (V_C/V_B) = 2.65 ± 0.90 (n = 6), respectively. The value of v_c is in good agreement with the value of the fractional intracellular water space of 3.0 reported by Pang et al. (1988, 1990, 1991).

Figure 2 shows the typical outflow profile (logarithmic scale) and data fitting result (regression line) for [U-¹⁴C]sucrose with the corresponding cationic drug. [U-¹⁴C]Sucrose was coadministered as an extracellular reference solute with each cationic drug bolus injection. The fit was obtained by eqs. 3 to 5 for [U-¹⁴C]sucrose and eqs. 1 to 7 for cationic drug. It is apparent that this model fitted the data robustly. The more lipophilic the drug, the lower will be the peak high (higher hepatic extraction) and the slower decline will be the curve (longer mean transit time) for all cationic drugs studied in this work. The sucrose curves show a similar pattern among various bolus injections.

View larger version (15K): [in this window] [in a new window]   Fig. 2.   Typical outflow profiles for the model cationic drugs and [U-14C]sucrose (data weighted, 1/yobs2) in the regressions. A, atenolol with sucrose; B, antipyrine with sucrose; C, prazosin with sucrose; D, labetalol with sucrose; E, propranolol with sucrose; and F, diltiazem with sucrose. The solid circles () represent cationic drug experimental data. The open circles () represent sucrose experimental data. The lines represent the fits of the profiles using eqs. 3 to 5 for [U-14C]sucrose and eqs. 1 to 7 for cationic drugs.

Table 1 presents the f_uB, molecular weight, log P_app, and pK_a values of model cationic drugs. It is apparent that f_uB decreases with increasing lipophilicity of drug.

Table 2 lists the results of nonparametric moments analysis for model cationic drugs studied in this work. It shows that the E value increases with the lipophilicity of drug [E = 0.255 + 0.191 log P_app (r² = 0.971), from 0.30 for atenolol to 0.92 for diltiazem]. The MTT value also increases with the lipophilicity of drug [MTT = 5.299 + 18.869 log P_app (r² = 0.645), from 14.34 s for atenolol to 105.32 s for diltiazem]. The CV² value for the drugs did not appear to be related to lipophilicity.

Table 3 summarizes the parameters estimated using the stochastic two-phase model of hepatic drug disposition. The k_on value increases significantly with the lipophilicity of drug [log k_on = 1.249 + 0.252 log P_app (r² = 0.944), from 0.05 s¹ for atenolol to 0.35 s¹ for diltiazem]. In contrast, the k_off value decreases with the lipophilicity of drug [log k_off = 1.012  0.185 log P_app (r² = 0.953), from 0.081 s¹ for atenolol to 0.021 s¹ for diltiazem]. The partition ratio of k_in and k_out, k_in/kout, increases with increasing pK_a value of the drug [log k_in/k_out = 0.079 + 0.091 pK_a (r² = 0.914), from 1.72 for antipyrine (pK_a = 1.45) to 9.76 for propranolol (pK_a = 9.45)]. The permeation and elimination kinetics parameters PS, CL_pT, and CL_int increase with the lipophilicity of drug [log PS = 1.180 + 0.183 log P_app (r² = 0.864), from 14.59 ml · min¹ · g¹ of liver for atenolol to 90.54 ml · min¹ · g¹ of liver for diltiazem; log CL_pT = 1.045 + 0.098 log P_app (r² = 0.899), from 10.80 ml · min¹ · g¹ of liver for atenolol to 25.35 ml · min¹ · g¹ of liver for diltiazem; log CL_int = 0.936 + 0.257 log P_app (r² = 0.993), from 10.08 ml · min¹ · g¹ of liver for atenolol to 67.41 ml · min¹ · g¹ of liver for diltiazem]. The steady-state distribution parameters K_S and K_R are also related to log P_app [log K_S = 0.239 + 0.438 log P_app (r² = 0.992), from 0.61 for atenolol to 16.67 for diltiazem; log K_R = 0.517 + 0.121 log P_app (r² = 0.769), from 0.36 for atenolol to 0.95 for diltiazem]. There is no significant difference in the V_C values (data not shown) determined from the water outflow data administered simultaneously with the cationic drugs, i.e., V_C was not affected by the drug injected.

	Discussion

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Barrier-limited tissue distribution is conventionally used in most organ models of solute disposition such as the two-compartment dispersion model (Roberts et al., 1988, 1990; Yano et al., 1989) and "Goresky" model (Goresky et al., 1973). However, it is well recognized that the two-compartment dispersion model inadequately describes the tail part of outflow curves (Schwab et al., 1990; Luxon and Weisiger, 1992; Pang et al., 1995; Weiss et al., 1997, 2000; Tirona et al., 1998). The two-phase stochastic model of drug transport (Weiss and Roberts, 1996; Weiss et al., 2000) was used in this work to integrate cytoplasmic binding kinetics into the conventional barrier-limited tissue distribution model. Consequently, this model perfectly fitted the data from the peak to the tail part of outflow curves. Audi et al. (1998) have used a similar approach to report the binding of cationic drugs in the isolated perfused lung. In general, models using vascular references as a basis for drug disposition in perfused organs are generally comparable but mathematically not identical. In addition to the two-phase stochastic model used in this work, other approaches include the Goresky model (Schwab et al., 1990), the "slow diffusion" model of Luxon and Weisiger (1992), the convection-dispersion model, and transit density functions (Roberts et al., 1988; Yano et al., 1989; Chou et al., 1995; Hung et al., 1998a,b; Roberts and Anissimov 1999; Roberts et al., 2000). Although an integrated cytoplasmic binding, barrier-limited, and two-phase stochastic distribution model was able to describe the drug kinetic data in the present work, an integrated slow diffusion (instead of "slow binding") model failed to fit our data. A comparison of alternative models of cytoplasmic drug distribution (slow binding versus slow diffusion) can be found elsewhere (Weiss, 1999; Weiss et al., 2000).

The present article has shown that the hepatic extraction ratio (E) values for model cationic drugs studied in this work increased with lipophilicity. We have also shown that a homologous series of O-acyl salicylate esters (Hung et al., 1998a) and diflunisal esters extraction also increased with lipophilicity (Hung et al., 1998b). The finding that the hepatic extraction of the cationic drug is dependent on lipophilicity is consistent with reports in the literature for various families of compounds. It is well recognized that hepatic extraction increases with lipophilicity for barbiturates (Yih and Van Rossum, 1977; Toon and Rowland, 1983; Hiura et al., 1984; Watari et al., 1988), tetracyclines (Toon and Rowland, 1979), -adrenoceptor blocking agents (Hinderling et al., 1984), aminosteroidal neuromuscular blocking agents (Proost et al., 1997), phenolic compounds (Mellick and Roberts, 1999), and in general (Goldstein et al., 1974). However, Chou et al. (1993) reported that other than for n-pentyl 5-ethyl barbituric acid, the extraction of the barbiturates by the liver was negligible in a single-pass, in situ perfused rat liver preparation using RBC-free, protein-free perfusate. The difference in extraction between the work of Chou et al. (1993) and that of others may be due to the low flow rate of 15 ml/min and RBC-free perfusate used by Chou et al. (1993), being inadequate for maximal barbiturate extraction. Hickey et al. (1996) reported that oxygen supply played a vital role for propranolol extraction in the isolated perfused cirrhotic rat liver.

Both the permeation and intrinsic elimination clearances of liver CL_pT and CL_int increase with log P_app (Table 3). In general, hepatic extraction is a function of hepatic clearance (CL_pT and CL_int), hepatic permeability (PS), fraction unbound in the perfusate (f_uB), flow rate (Q), and vascular dispersion (Roberts et al., 1988, 1990). Because CL_pT and CL_int increase with lipophilicity to a greater extent than f_uB decreases with lipophilicity with flow rate and vascular dispersion being constant, the observed increase in E with increasing the lipophilicity of drug is expected.

The logarithmic permeability-surface area product (log PS) is linearly related to log P_app (Fig. 3). This linear relationship is consistent with that first described by Chou et al. (1995) and extended by Mellick and Roberts (1999). The intercept in this study (1.18) is similar to that of 1.53 reported by Mellick and Roberts (1999). The slightly low slope found in this study (0.18) relative to that of 0.44 reported by Mellick and Roberts (1999) probably reflects the perfusion conditions used. This study used RBCs containing perfusate at 15 ml/min, whereas Mellick and Roberts (1999) used RBC-free perfusate at 30 ml/min.

View larger version (10K): [in this window] [in a new window]   Fig. 3.   Logarithmic relationship of permeability-surface area product (log PS, mean, n = 6) and lipophilicity (log Papp) for various cationic drugs. The line and solid circles () represent the log PS linear regression line (log PS = 1.180 + 0.183 log Papp, r2 = 0.864, p < 0.05) and data.

The putative nature of the slowly equilibrating binding sites described in this work has yet to be determined. The model used in this work cannot distinguish between binding to cytosolic binding sites, binding sites on cellular membranes, entry into the matrix of intracellular organelles such as mitochondria and lysosomes, or dissolution in the lipid bilayer of cellular membranes (Proost et al., 1997). Figures 4 and 5 showed that log k_on, log K_S, and log K_R values are related to log P_app, consistent with binding to both the slowly and rapidly equilibrating binding sites being related to the lipophilicity of drug. The decrease in log k_off value with increasing lipophilicity of drug (Fig. 4) is consistent with the slow-equilibrating binding site being lipophilic. Accordingly, the equilibrium amount ratio characterizing the slowly equilibrating binding sites K_S = k_on/k_off increases with drug lipophilicity, whereas the fraction of solute unbound in the cells (f_uC) decreases with increasing lipophilicity of drug. In summary, the extent of uptake of the various cationic drugs by the two binding sites (K_S, K_R) is greater for the more lipophilic drugs.

View larger version (12K): [in this window] [in a new window]   Fig. 4.   Logarithmic relationship of intracellular binding rate constant (log kon, mean, n = 6), intracellular unbinding rate constant (log koff, mean, n = 6), and lipophilicity (log Papp) for various cationic drugs. The solid line and solid circles () represent the log kon linear regression line (log kon = 1.249 + 0.252 log Papp, r2 = 0.944, p < 0.05) and data. The long dash line and open circles () represent the log koff linear regression line (log koff = 1.012-0.185 log Papp, r2 = 0.953, p < 0.05) and data.

View larger version (11K): [in this window] [in a new window]   Fig. 5.   Logarithmic relationship of equilibrium amount ratio characterizing the slowly equilibrating binding sites (log KS, mean, n = 6), equilibrium amount ratio characterizing the rapidly equilibrating binding sites (log KR, mean, n = 6), and lipophilicity (log Papp) for various cationic drugs. The solid line and solid circles () represent the log KS linear regression line (log KS = 0.239 + 0.438 log Papp, r2 = 0.992, p < 0.01) and data. The long dash line and open circles () represent the log KR linear regression line (log KR = 0.517 + 0.121 log Papp, r2 = 0.769) and data.

The ratio k_in/k_out is determined by the clearances into and out of the hepatocyte via the sinusoidal membrane and by the distribution spaces for the unbound cationic drugs between the hepatocyte and the perfusate. Given that uptake by binding sites has already been accounted for by the model, the increase in the k_in/k_out ratio for the various cationic drugs relative to antipyrine (1.72 ± 0.73) (which is un-ionized over the range of physiological pH values) is possibly a reflection of ion trapping or asymmetric transport. Such effects are expected to be greater for cationic drugs with higher pK_a values and, hence, a higher fraction ionized over the range of physiological pH values. Figure 6 showed that log k_in/k_out values for the cationic drugs increased with increasing pK_a value of the drug, suggesting that ion trapping or asymmetric transport may be involved.

View larger version (10K): [in this window] [in a new window]   Fig. 6.   Logarithmic relationship of partition ratio of influx and efflux rate constant (log kin/kout, mean, n = 6) and pKa (the negative logarithm of the ionization constant) for various cationic drugs. The line and solid circles () represent the log kin/kout linear regression line (log kin/kout = 0.079 + 0.091 pKa, r2 = 0.914, p < 0.05) and data.

An estimate of the extent of ion trapping may be obtained from the consideration of the pH values and fractional volumes of the various cellular components, assuming that distribution is instantaneous and the resulting steady-state ratios are reflected in the observed ratios from dynamic (nonsteady-state) studies. When the unbound drug concentration is assumed to be identical in both the intracellular and perfusate compartments, the intracellular-to-perfusate concentration ratio for a drug with a given pK_a is given by (1 + 10^{pK_a pHi})/(1 + 10^{pK_a pHp}) (Goldstein et al., 1974), where pHi is the intracellular pH and pHp is the perfusate pH. In the simplest case, based on a perfused normal rat liver intracellular pHi of 7.27 (Le Couteur et al., 1993) and perfusate pHp of 7.4, then the concentration ratios for the cationic drugs studied in this work ranged from 1 to 1.35 (Table 4), suggesting a maximum ion trapping of 35%. A more profound pH-partitioning ion-trapping effect will be apparent for cations partitioning into organelles such as mitochondria and lysosomes where pH values of 6.67 (fasted) (Soboll et al., 1980) and 4.70 (Myers et al., 1995), respectively, have been reported. Apparent steady-state mitochondria/perfusate and lysosomes/perfusate concentration ratios based on these pH values and assuming fractional cytoplasmic volumes of 1 and 20% for lysosomes and mitochondria, respectively (Rhoades and Pflanzer, 1996), are shown in Table 4. Using the k_in/k_out for antipyrine, a basic drug un-ionized under physiological conditions, the predicted overall unbound cytoplasmic-to-perfusate concentration ratios can be used to estimate a predicted k_in/k_out ratio for each cationic drug. The predicted k_in/k_out values are similar (and not statistically different) to the experimental ratios obtained for k_in/k_out (Table 4). It is recognized that the predicted k_in/k_out values are only approximate because a range pH values has been reported for intracellular pH (7.19-7.29) (Le Couteur et al., 1993; Burns et al., 1999; Pietri et al., 2001), mitochondria pH (6.7-7.0) (Soboll et al., 1980), and lysosomal pH (4-5) (MacIntyre and Cutler, 1988; Myers et al., 1995; Proost et al., 1997) as well as differing lysosomal fractional volumes (0.68-1%) (Weibel et al., 1969; Rhoades and Pflanzer, 1996). Interpretation of the ion-trapping effect may be further complicated by binding or aggregation of basic drugs in lysosomes (Ishizaki et al., 2000) and by asymmetric exchange, since the interior of a hepatocyte is negatively charged relative to the extracellular space. Asymmetric exchange may also occur across the sinusoidal membrane as a result of cation transport by one or more of the reported cationic transporters (Zhang et al., 1998). In summary, intracellular, mitochondria, lysosomes, and perfusate pH differences and respective volume fractions enable the differing k_in/k_out values for the cations to be partly accounted for by a pH-partitioning ion-trapping effect. However, overall, the contribution of k_in/k_out as an explanation of differences in cationic drug disposition in the liver is small. Lipophilicity differences tend to dominate as determinants of hepatic extraction as is evident in a comparison of the k_in/k_out values of 8.00 and 7.35 for atenolol and diltiazem (Table 3) to their overall hepatic extraction ratios (E) values of 0.3 and 0.92 for atenolol and diltiazem (Table 2), and their corresponding octanol-water partition coefficients of 0.14 and 3.53 for atenolol and diltiazem (Table 1), respectively.

It is concluded that the structure-hepatic disposition relationships for cationic drugs is characterized by transmembrane exchange (permeability barrier) and the cytoplasmic binding process. The outflow curves of model cationic drugs were well described by a two-phase stochastic model of drug transport. The parameters E and MTT derived from moments increase with the lipophilicity of drug, whereas CV² did not differ significantly for any of the drugs studied in this work. In general, lipophilic drugs also have lower f_uB values. The derived pharmacokinetic parameters k_on, K_S, K_R, CL_int, CL_pT, and PS values increased with log P_app, whereas k_off value decreased with log P_app and V_C remained constant. Hence, increasing the lipophilicity of a cationic drug leads to a greater retention in the liver due to a more rapid uptake into the liver (higher PS), higher cytoplasmic binding, and slower dissociation rate off binding sites. However, the more lipophilic solutes are also associated with a higher permeation and intrinsic elimination clearance in the liver.