Isolated hepatocytes are an important in vitro system for studying the disposition of drugs, reflecting both the key role of the liver in the elimination of foreign compounds and also the ability of isolation and maintenance procedures to retain the integrity of many functional hepatic components (Li et al., 1999; Soars et al., 2007). Pharmacokinetic models can be applied to study the movement of molecules in and out of cells and to quantify their intracellular binding and metabolism. This approach has been used extensively to study the kinetics of compounds within the whole organ (Goresky and Schwab, 1988; Sirianni and Pang, 1997; Liu and Pang, 2005) but can also be applied to derive a greater understanding of the behavior of drugs in isolated hepatocytes, thereby exploiting this model system.

Hepatocyte intrinsic metabolic clearance (CL_int,met) can be obtained from in vitro metabolism experiments by sampling a homogeneous hepatocyte suspension over time and either dividing the rate of metabolite formation by the initial substrate concentration (Houston et al., 2003) or by estimating the depletion rate of parent compound; for both methods, a correction is made to the clearance from the incubation (CL_inc) for the fraction unbound in the incubation (fu_inc). This latter approach has been used widely in the industry for the last 5 to 10 years (Ito and Houston, 2004, 2005; McGinnity et al., 2004; Riley et al., 2005; Soars et al., 2007) and is referred to as the “standard method” in the manuscript. For many highly permeable drugs, where the intracellular concentration of free drug can be assumed to be equal to that in the plasma, relatively simple liver models can be used to estimate intrinsic metabolic clearance in the liver (CL_int,L) from in vitro data (Houston and Carlile, 1997; Lau et al., 2002; McGinnity et al., 2004). CL_int,L can also be estimated from in vivo data by correcting plasma concentration-time data for plasma protein binding (Houston, 1994).

However, where the intracellular concentration of free drug is likely to be significantly different to that in the media (for example, diffusion-limited or uptake transporter protein mediated kinetics), more sophisticated in vitro experimental and modeling approaches are required (Evans, 1996; Webborn et al., 2007). The implications of perfusion- and diffusion-limited kinetics are described in the original publications of the well stirred liver model (Gillette, 1971; Rowland et al., 1973; Wilkinson and Shand, 1975), and, with the increased recognition of the role of uptake and efflux transporters, these models have been developed further (de Lannoy and Pang, 1987; Liu and Pang, 2005).

A number of models of drug disposition in hepatocytes have been reported in the literature to describe binding, permeation, and metabolism. Iwatsubo et al. (1999) described the uptake and metabolism of a polar base, YM796, modeling the cell and media data to estimate parameters for saturable uptake, metabolism, and binding. In contrast, Hallifax and Houston (2006) demonstrated, using a two-site model, that the kinetics of the lipophilic bases, propranolol and imipramine, are not controlled by active uptake but are dominated by intracellular binding. A model describing the distribution of the poorly permeable antibiotic teicoplanin into suspended rat hepatocytes has been proposed by Reinoso et al. (2001), and the partitioning into the cells and membrane permeability were found to be broadly comparable with in vivo data. Reinoso et al. made two important observations; first, that there was significant binding to the cell surface and second, that the effective surface area for drug uptake in suspended cells may be significantly higher than that in vivo. Pharmacokinetic models have also been successfully applied to the uptake and efflux of compounds in sandwich-cultured hepatocytes to evaluate the behavior of a drug-metabolite pair (Hoffmaster et al., 2004) and to elucidate mechanisms of biliary secretion (Turncliff et al., 2006).

This paper evaluates the utility of simultaneous fitting of cell and media concentration-time data to describe disposition in hepatocyte suspensions and to predict in vivo clearance, volume of distribution, and half-life. The disposition of atorvastatin, cerivastatin, and indomethacin, established substrates of rat hepatic basolateral uptake transporters (Shitara et al., 2004; Lau et al., 2006a), has been studied and evaluated in a model that describes drug binding, distribution, and elimination, with particular reference to estimation of the free intracellular concentration.

Materials and Methods

Chemicals. Cerivastatin and atorvastatin were purchased from Sequoia Research Products Ltd. (Oxford, UK). All other chemicals, including indomethacin and reagents were purchased from Sigma Chemical Co. (Poole, Dorset, UK), BDH (Poole, Dorset, UK) or Thermo Fisher (Loughborough, UK) unless otherwise stated and were of the highest grade available. Hepatocyte suspension buffer consisted of 2.34 g of Na HEPES, 0.4 g of d-fructose, 2 g of bovine serum albumin, 1 liter of powder equivalent of Dulbecco's modified Eagle's medium (Sigma, Gillingham, UK) diluted in 1 liter of water and adjusted to pH 7.4 with 1 M HCl.

Preparation of Rat Hepatocytes. Rat hepatocytes were isolated from male Sprague-Dawley rats using the two-step in situ collagenase perfusion method of Seglen (1976) described in detail in Soars et al. (2007). Cells were resuspended in suspension buffer (without bovine serum albumin), and an estimation of hepatocyte yield and viability was obtained using the trypan blue exclusion method. Only cells with a viability of >80% were used.

Determination of CL_inc in Hepatocytes (Standard Method). The rate of turnover in hepatocyte suspensions (CL_inc) was estimated using a procedure that sampled the whole incubation. Ten microliters of DMSO stocks of atorvastatin, indomethacin, and cerivastatin (100 μM) was added to 490-μl aliquots of hepatocyte buffer (protein-free) and warmed to 37°C. Hepatocytes were diluted to 2 × 10⁶ cells/ml in protein-free hepatocyte buffer and warmed to 37°C. At time 0, 0.5 ml of cells was added to the appropriate substrate solution, mixed, and placed in a shaking water bath (37°C and 80 oscillations/min). Forty-microliter aliquots were removed at 5, 15, 30, 45, 60, 75, and 90 min and quenched into 80 μl of ice-cold methanol. Samples were mixed and frozen overnight. Prior to analysis, samples were spun at 2000g for 20 min at 4°C to pellet protein, and the supernatant was transferred to a 96-well Agilent plate (Agilent Technologies, Santa Clara, CA) for LC-MS/MS analysis. Parent peak area was plotted against time, and CL_inc was estimated by multiplying the incubation volume by the elimination rate constant.

Determination of Plasma Protein Binding. Rat plasma protein binding was measured using equilibrium dialysis at least twice for each compound. Atorvastatin, cerivastatin, and indomethacin (final concentration, 10 μM) were spiked into plasma and placed on one side of a dialysis cell; the other side contained only buffer. The compounds were dialyzed through a 50-kDa membrane in a Dianorm rotating unit (Diachema, Langnau, Switzerland) for 18 h at 37°C. Aliquots from the buffer and dialysate side of the membrane were then quenched in methanol and analyzed via LC-MS/MS as described below. The extent of plasma protein binding (fu_p) was calculated by dividing the concentration of compound in the absence of plasma (buffer side) by the concentration of compound in the presence of plasma (dialysate side).

Determination of fu_inc. Unbound fraction in hepatocytes (1 × 10⁶ cells/ml) was measured at least twice for atorvastatin, cerivastatin, and indomethacin at 1 μM by equilibrium dialysis over an 18-h time course. The method described above was followed with the exception that plasma was replaced with hepatocytes that had been metabolically inactivated by leaving at room temperature overnight prior to equilibrium dialysis (Austin et al., 2005).

Determination of Fraction Unbound in Liver Tissue. Unbound fraction in 25% liver homogenate was measured at least twice for atorvastatin, cerivastatin, and indomethacin at 1 μM by equilibrium dialysis over an 18-h time course following the method described above. Free fraction in whole liver was calculated by correcting for the homogenate dilution using the equation outlined and validated by Austin et al. (2002). where fu₂ in this case is the free fraction in whole liver, fu₁ is the measured free fraction in 25% homogenate, and C₁ and C₂ are the concentrations of the homogenate, that is, 25 and 100%, respectively.

Determination of Blood/Plasma Ratio. Atorvastatin, cerivastatin, and indomethacin at 100× final concentration were spiked into aliquots of fresh rat blood and plasma (0.5 ml) and incubated for 15 min at 37°C in a shaking waterbath followed by centrifugation in a MSE MicroCentaur centrifuge (Fisher Scientific, Loughborough, UK) at 11,000 rpm for 4 min. Aliquots of plasma from both the blood and plasma incubations were quenched into methanol and stored at -20°C for at least 1 h. Prior to analysis, samples were centrifuged at 2000g for 20 min, and the supernatant was transferred into high-performance liquid chromatography vials. Blood/plasma ratio was calculated by dividing the peak area from directly spiked plasma by the peak area from plasma isolated from spiked blood.

Determination of Uptake in Rat Hepatocytes. Uptake into suspended hepatocytes was determined using a centrifugal filtration technique through a silicone oil layer based on that of Petzinger and Fuckel (1992). Briefly, hepatocytes were resuspended in protein-free hepatocyte buffer at 2 × 10⁶ cells/ml and preincubated at 37°C in 0.5-ml aliquots. The final concentration of substrate was 1 μM, a concentration shown not to saturate metabolic processes in previous studies (data not shown). Cerivastatin, indomethacin, and atorvastatin solutions were prepared in hepatocyte buffer at 2 μM (2% DMSO) and equilibrated to 37°C. At time 0, substrate was added to cells and mixed. Aliquots were removed at 10, 20, 30, and 40 s and 1, 2, 5, 15, 30, 45, 60, and 90 min and dispensed into 0.4-ml microtubes containing 15 μl of cesium chloride (lower layer) and 150 μl of silicone oil and immediately centrifuged at high speed to separate cells from the media. An aliquot was taken from the upper media portion and quenched in methanol, and the lower pellet layer was removed by freezing in liquid nitrogen and cutting just below the oil/pellet interface. After addition of 300 μl of methanol/water (2:1) to the pellets, the samples were vortexed and centrifuged. Supernatants from both the media and cell portions were analyzed by LC-MS/MS, and the compound was quantified from appropriate standards curves.

Data were fitted to the model (Fig. 1) (CL_int,efflux set to zero) with a 1/predicted y² weighting using WinNonlin (version 3.2; Pharsight, Mountain View, CA) to obtain parameters for CL_int,uptake, CL_int,pass, CL_int,met, and k_mem. The fraction in the medium at 60 min (f_med,60) was determined by dividing the amount of compound in the medium at 60 min (assumed to be pseudo-steady state) by the total amount of compound in the incubation (cells plus media) at 60 min.

In Vivo Studies. All in vivo work was subject to internal ethical review and conducted in accordance with Home Office requirements under the Animal Scientific Procedures Act (1986) and allowed a minimum of 1-week acclimatization. Healthy virus antibody-free male Sprague-Dawley rats were obtained from Charles River (Margate, Kent, UK). They were housed in a light-controlled room and kept at a temperature of 19°C ± 2°C and 55% ± 10% humidity. They received a Teklad 2021 diet (Harlan, Indianapolis, IN) and had access to water ad libitum.

Intravenous Bile Duct Cannulation Studies. Rats (250–350 g) were surgically prepared under nonrecovery isoflurane anesthesia. The bile duct was cannulated, and cannulae were implanted into the jugular vein (dosing cannula) and carotid artery (blood sampling cannula). Atorvastatin was prepared at 1 mg/ml in water/dimethylacetamide (60:40), cerivastatin, and indomethacin at 1 mg/ml in saline. Infusion protocols were designed to achieve steady-state concentrations within 4 h. Atorvastatin was infused initially as a loading dose (720 μg/min/kg) for 10 min, then the infusion rate was reduced to 18 μg/min/kg for the remaining 4 h and 50 min. Cerivastatin was initially dosed at 330 μg/min/kg for 10 min, then the infusion rate was reduced to 11 μg/min/kg out to 5 h. Indomethacin was given as a bolus dose at 1 mg/kg. Bile was collected up to 7 h at 0 to 60 min, then every half hour thereafter. Serial blood samples (200–300 μl) were taken at the midpoint of the bile collections and were centrifuged to obtain plasma (1110g for 10 min). Urine was collected by periodically draining the bladder, and the liver and sartorius muscle were taken at termination. Liver, plasma, and bile concentrations at steady state (pseudo-steady state for indomethacin) were determined, and clearance was estimated for the infused animals by dividing the infusion rate by plasma concentration at steady state. Indomethacin clearance was determined by noncompartmental analysis using WinNonlin. Intravenous bile duct cannulation studies were performed on two rats (atorvastatin and indomethacin) or three rats (cerivastatin).

Intravenous Pharmacokinetic Studies. For the pharmacokinetic studies, atorvastatin, indomethacin, and cerivastatin (minimum of three rats each) were dosed at 1 mg/kg as a bolus to the tail vein in saline/DMSO (3:1) to conscious male rats. Serial blood samples (200–300 μl) were taken and centrifuged to obtain plasma. The liver and sartorius muscle were taken at termination. Pharmacokinetic parameters (clearance, Vss, and terminal half-life) were estimated from the concentration-time profile by noncompartmental analysis using WinNonlin.

In Vivo Sample Preparation. Plasma was dispensed into 50 μl aliquots, and 150 μl of methanol (containing internal standard) was added and mixed. Bile and urine were diluted in water prior to analysis. Liver and muscle were weighed, diluted with water, and homogenized. Homogenate was dispensed into 50 μl aliquots in triplicate and processed as per plasma. Appropriate standard curves and quality control samples prepared in the equivalent blank tissue were used for each analysis.

Sample Analysis. Samples were analyzed using an HP1100 high-performance liquid chromatography system (Hewlett Packard, Palo Alto, CA) linked to a Quattro Ultima mass spectrometer (Micromass; Waters, Milford, MA) in negative or positive electrospray ionization mode with data analysis on Quanlynx software (version 4.0; Micromass). Cone voltage and collision energy were optimized for each compound. In these analyses, chromatographic separation was achieved using a Waters Symmetry C8 3.5-μm (2.1 × 30 mm) column using 10 μl of each sample. The mobile phase consisted of an aqueous phase of water with 0.1% (v/v) formic acid and an organic phase of methanol with 0.1% (v/v) formic acid. Samples were quantified using appropriate calibration curves and quality controls.

Data Analysis.In Vitro. In the present analysis, a hepatocyte incubation model similar to that used by Reinoso et al. (2001) has been constructed that includes medium, cellular, and cell membrane compartments (Fig. 1). The volume of the whole incubation (V_inc) is the sum of the medium and cell volumes, V_med and V_cell, respectively, with the volume of the cell membrane assumed to be negligible. Sinusoidal bidirectional passive permeation and active uptake/efflux occurs between the medium and cellular compartments. The passive components of influx and efflux were parameterized as a distribution clearance CL_int,pass rather than as influx and efflux permeability-surface area products and therefore were assumed to be equivalent in the model. A single clearance mechanism is incorporated (CL_int,met), although multiple mechanisms can be considered. It is assumed that only unbound drug is able to pass across the cell membrane, and binding to the cell membrane is assumed to be so fast as to be at steady state with respect to movement across the cell membrane as proposed by Reinoso et al. (2001).

Following the addition of a test compound, the overall rate of change of amount of drug in the system at steady state can be expressed as follows: where the subscripts cell and med refer to the cell (excluding the membrane) and medium compartments, respectively, X is the amount of drug, C is the total drug concentration, and fu is the free fraction of the corresponding compartment. CL_med is the clearance from the medium, and CL_int,met is the unbound metabolic intrinsic clearance from the cell. Albumin was not present in the cell suspension; therefore, fu_med was assumed equal to 1.

Hence, where Ψ represents the ratio of the free concentration inside the cell to the free concentration in the medium at steady state.

The model in Fig. 1 was fitted to the two measured concentrations of drug in medium and total concentration in hepatocytes (C_hep) simultaneously using WinNonlin. Drug concentration in hepatocytes comprised both drug within the cell and that bound to cell membrane. The amount of drug bound to the cell membrane (X_mem) is directly proportional to the unbound concentration of drug in the medium. where k_mem is the proportionality constant between amount in membrane and free concentration in medium and has units of volume. In this model, the initial concentration in the medium is given by: where dose is total amount of drug added to the suspension.

The unbound fraction of drug within the cells (fu_cell) is an important parameter as it represents the free fraction of drug to which the metabolizing enzymes are exposed. Furthermore, fu_cell will be the same for both the in vitro and in vivo case. Hallifax and Houston (2006) have derived an expression for the unbound fraction of drug within hepatocyte cells, assuming that intracellular binding represents the major mechanism. In this present analysis, a more comprehensive approach was used that takes into account drug bound to the cell membrane. An expression for the fu_cell was obtained by considering the relationship between the experimentally measured fu_inc and the amounts in the medium, cell, and cell membrane when no active processes are occurring (eq. 6). And, because fu_cell is equal to the free concentration in the cell (equals concentration in medium) divided by the total cell concentration then:

To remove active processes, incapacitated hepatocytes were used to measure incubational binding (fu_inc) of test drug. Incubational binding may also be estimated using the algorithm proposed by Austin et al. (2005). The cellular volume (V_cell) used in calculations was assumed to be 4 μl/10⁶ cells, based on previous estimates by Reinoso et al. (2001) and Petzinger and Fuckel (1992). Inclusion of k_mem accounts for the component of binding to the cell membrane and is estimated from the model fit to both the medium and hepatocyte data. When binding to cell membrane is significant, fu_cell estimated according to eq. 7 can be many times larger than fu_cell estimated, assuming that intracellular binding represents the major mechanism.

By converting the differential equations for the model in Fig. 1 to their Laplace transforms and subsequent use of matrix algebra, expressions for clearance from the medium, hepatocytes, and incubation can be obtained (for derivations, see Supplemental data).

Equation 8 expresses the clearance from the medium in terms of passive, uptake, efflux, and metabolic intrinsic clearances. This is analogous to the general expression for the overall apparent intrinsic clearance described by Shitara et al. (2005). Because clearance from medium is a composite of intrinsic clearance terms, the authors believe that the term CL_med is more appropriate than an intrinsic clearance. CL_med was estimated for atorvastatin, cerivastatin, and indomethacin by substituting the intrinsic clearances obtained from the model fit into eq. 8 with the assumption that efflux was negligible. These results were compared with the observed CL_med obtained from the area under the medium concentration-time curve.

Hence, from eqs. 3 and 8, the ratio of the free concentration inside the cell to the free concentration in the medium (Ψ) can be expressed as follows:

CL_inc is obtained from the standard method (i.e., sampling from the hepatocyte/medium suspension) for the determination of incubational clearance. Clearance from the incubation was either estimated from the slope of the natural log (concentration in incubation)-time plot or from eq. 10.

When there is no active uptake/efflux (Ψ= 1), eq. 10 becomes the more familiar expression for incubational intrinsic clearance.

The right side of eq. 11 is obtained by substituting eq. 6.

In addition to expressions for clearance, many other useful expressions can be obtained from this analysis. The steady-state volume of distribution as viewed from the medium (Vss_med) can be expressed as follows:

Vss_med was either estimated from eq. 12 or from a noncompartmental analysis of the concentration in the medium-time plot. Vss_med may appear an inconsequential parameter; however, it links clearance from the medium to clearance from the incubation as follows:

Equation 13 becomes more intuitive when linked to the fraction of drug in the medium at steady-state.

Therefore, when V_med approximates to V_inc, the ratio of the clearance from the incubation to clearance from the medium equals the fraction in the medium at steady state.

When the fraction in the medium at pseudo-steady-state approximates to f_med,ss, the CL_med can be simply obtained by dividing the measured incubational clearance from the standard method (CL_inc) by the measured fraction in the medium.

In Vivo. A seven-compartment physiological model (Fig. 2) was constructed to describe sinusoidal bidirectional passive permeation and active uptake/efflux in the liver. The model has been designed to be analogous to the in vitro model shown in Fig. 1. Drug dosed to the blood compartment can distribute to tissues (T) and interstitial fluid (I) in the body as well as distribution to the vascular (LV), cell membrane (L,mem), interstitial fluid (LI), and cellular (L,cell) components of the liver. Sinusoidal bidirectional passive permeation and active uptake/efflux occurs between the liver vascular and cellular compartments and is described by the in vivo intrinsic clearances: CL_int,L,pass, CL_int,L,uptake, and CL_int,L,efflux. Drug is eliminated from the cellular compartment with in vivo intrinsic clearance (CL_int,L).

By converting the differential equations for the model in Fig. 2 to their Laplace transforms followed by the use of matrix algebra, expressions for blood clearance, Vss, and MRT can be obtained (for derivations, see Supplemental data). where Q_L and fu_B are hepatic blood flow and free fraction in the blood, respectively and

The expression for blood clearance in eq. 16 is analogous to the expressions for clearance derived by Sirianni and Pang (1997) and Liu and Pang (2005), and similar equations can be derived for alternative and multiple clearance mechanisms.

However, an expression for the blood Vss (and hence MRT) that incorporates the impact of hepatic uptake has not been published. An expression for blood Vss is shown in eq. 18 and is written as the sum of four components, namely, the standard contribution from blood, body tissue, and body interstitial fluid plus a term for the liver. where fu is the free fraction of drug in the compartment denoted by the subscript, and k_L,mem is the proportionality constant between free blood concentration and the amount of drug in the cell membranes of the liver. MRT can be obtained from the expressions for clearance and Vss and can be found in Supplemental data. Summary of abbreviations and definitions can be found in Appendix 1 and Appendix 2.

Predicting in Vivo from in Vitro. The seven-compartment in vivo model was used to predict the in vivo plasma, liver, and body tissue levels and to predict the clearance, Vss, and half-life of atorvastatin, cerivastatin, and indomethacin in rat. Body tissue volume was assumed to be equal to the sum of muscle, skin, gut, kidney, lung, and heart cellular volumes as obtained from Khor and Mayersohn (1991). Body tissue blood flow rate was assumed equal to muscle and along with liver blood flow rate obtained from Brightman et al. (2006). Tissue volumes in the liver were also taken from Khor and Mayersohn (1991), where V_LV, V_LI, and V_L,cell were 1.29, 1.68, and 7.33 ml, respectively, considering a liver weight of 10.3 g (250-g rat) (Bernareggi and Rowland, 1991). The fu_I was calculated according to McNamara et al. (1983) using a plasma/interstitial space albumin concentration ratio of 0.5 (Khor and Mayersohn, 1991). The fraction unbound in body tissue (fu_T) was assumed to be equal to the fu_L. This assumption was based upon the observation that unbound partition coefficient (K_pu) measurements for several body tissues including the liver and muscle were within 2-fold for a series of barbituric acids (Ballard et al., 2003); as mentioned earlier, fu_L,cell in vivo equals fu_cell in vitro.

The in vitro parameters CL_int,pass, CL_int,uptake, and k_mem were scaled to their in vivo analogs CL_int,L,pass, CL_int,L,uptake, and k_L,mem using standard rat biological scaling factors (120 million cells/g liver). However, using standard biological scaling factors to scale in vitro CL_int,met generated in isolated human hepatocytes suggests a systematic underprediction of in vivo CL_int,L (Ito and Houston, 2005; Riley et al., 2005). A similar systematic bias of approximately 5-fold has been observed in the rat data in this laboratory (Grime and Riley, 2006) and can be found in the rat CL_int,met data presented by some academic laboratories (Naritomi et al., 2001) but not others (Ito and Houston, 2004). Several likely explanations for this have been discussed (Ito and Houston, 2005; Riley et al., 2005). It is widely appreciated that incubation conditions can strongly influence rates of drug metabolism in vitro, and it remains a strong possibility that this too may play a part in the underprediction. Therefore, CL_int,met was scaled to in vivo CL_int,L by applying a rat biological scaling factor 5 times the standard.

Clearance and Vss were estimated using eqs. 16 and 18. Plasma, liver, and body tissue levels were simulated from the seven-compartmental model with the assumptions that the rate of binding to liver cell membrane and flow into interstitial fluid is much faster than any other process.

Results

In Vitro. Measured in vitro parameters for atorvastatin, cerivastatin, and indomethacin are summarized in Table 1. fu_inc determined in rat hepatocytes was similar for all three compounds; 0.61, 0.69, and 0.78 for cerivastatin, atorvastatin, and indomethacin, respectively. Plasma protein binding measurements varied between the compounds, with indomethacin demonstrating very high protein binding (0.2% free), whereas atorvastatin and cerivastatin were less bound, with free fractions of 3.25 and 2.6%, respectively. In contrast, binding to liver tissue for the three compounds was high, with free fractions ranging from 1.8% for cerivastatin to 7.6% for indomethacin. Blood/plasma ratios differed between the compounds, and it was surprising (for an acid) that the blood/plasma ratio for atorvastatin was greater than 1 (1.26 ± 0.23), although this is consistent with the value of 1.47 determined by Lau et al. (2006b). Cerivastatin and indomethacin were both determined to be 0.7.

CL_inc values were determined directly by measuring depletion of parent from a hepatocyte suspension (Table 1). Values for CL_int,uptake, CL_int,pass, CL_int,met, and k_mem were derived from fitting cell and medium concentration data to the model shown in Fig. 1, where CL_int,efflux was assumed to be 0. This was considered a reasonable assumption on the basis that the authors know of no evidence that any of the three compounds are substrates for sinusoidal efflux transporters, and indomethacin and cerivastatin do not undergo significant canalicular efflux, as judged by their biliary clearances in this study. Atorvastatin does undergo canalicular efflux in the rat, but biliary clearance constitutes only 20% of the hepatic clearance, and the functionality of canalicular efflux transporters in suspended hepatocytes is unlikely to approach the in vivo activity (Bow et al., 2008). The derived parameters are listed in Table 2, and typical fits are shown in Fig. 3. Interestingly, although indomethacin exhibited the largest CL_int,uptake (599 ± 101 μl/min/10⁶ cells), because of the very high passive clearance (237 ± 63 μl/min/10⁶ cells), the impact on the overall elimination was small. Derivation of these parameters allowed estimations of CL_inc to be made (eq. 10; these estimated CL_inc values were in good agreement with the direct determinations: 10 ± 7 versus 15 ± 5.6, 3.0 ± 2.8 versus 6.0 ± 3.0, and 4.0 ± 2.3 versus 6.7 ± 1.9 μl/min/10⁶ cells for atorvastatin, cerivastatin, and indomethacin, respectively, giving confidence in the utility of this model).

CL_med for the three compounds was determined directly from the disappearance of parent from medium (dose divided by area under the curve) and also predicted using the parameters derived from the in vitro model using eq. 8. The predicted CL_med was comparable with the measured values: 68 versus 85, 17 versus 26, and 7 versus 13 μl/min/10⁶ cells for atorvastatin, cerivastatin, and indomethacin, respectively.

fu_cell, representing unbound fraction within the cell excluding the membrane, could not be measured directly but was estimated using the derived parameter k_mem and eq. 7. fu_cell was similar for the two statins (0.01 and 0.008 for atorvastatin and cerivastatin, respectively) but higher for indomethacin (0.05). The f_med,60 values (representing fraction in the media at pseudo-steady state) of atorvastatin and cerivastatin were both low (0.1 and 0.14, respectively) and considerably lower than their respective fu_inc values of 0.69 and 0.61, indicating significant uptake into hepatocytes. In contrast, indomethacin f_med,60 was higher at 0.45 and within 2-fold of the fu_inc value of 0.78, indicating less overall uptake into hepatocytes. Predicted values of f_med,ss using eq. 14 are shown in Table 2 and are in good agreement with the directly measured values (Table 1).

In Vivo. In vivo pharmacokinetic parameters were measured in the rat, and these are summarized in Table 3. Data were collected using tissue and plasma samples from bolus or an infused bile duct cannulated rat animal model, as described under Materials and Methods. There was good agreement between the noncannulated and cannulated animal models in the clearances measured for all three compounds (47 and 43, 27 and 17, and 0.51 and 0.25 ml/min/kg for atorvastatin, cerivastatin, and indomethacin, respectively). This gave confidence that the surgery had not compromised the animals and allowed all parameters to be determined using the cannulated animals, with the exception of Vss and half-life, and these were determined using the noncannulated animals. Of the three compounds studied, only atorvastatin showed significant biliary clearance, but this was still less than 20% of total clearance, with a biliary excretion rate of 3.2 μg/min/kg. No significant renal clearance was observed. The Vss observed ranged from 0.19 for indomethacin to 3.0 l/kg for cerivastatin. The Vss values tracked the liver levels observed, which were high for atorvastatin and particularly for cerivastatin, especially when compared with indomethacin. Along with lower plasma levels, this gave rise to a much higher liver/plasma ratio for these compounds (52 and 65 for atorvastatin and cerivastatin, respectively, compared with 0.22 for indomethacin). Muscle levels were similar for the three compounds.

Prediction of in Vivo Parameters.Table 4 summarizes predicted in vivo pharmacokinetic parameters using the hepatocyte uptake assay and the data analysis previously described. Also, the standard method and in-house scaling approach (Grime and Riley, 2006) with homogeneous sampling of the hepatocyte incubation was used to predict metabolic clearance only. For the purposes of this exercise, values estimated within 2-fold of the observed were regarded as being well predicted. Prediction of in vivo metabolic clearance from the standard method and the in-house scaling approach underpredicted the observed in vivo clearance for atorvastatin and cerivastatin by approximately 4-fold. Clearly, without applying a 5 times the standard rat biological scaling factor correction (Grime and Riley, 2006), the underprediction would have been greater. The estimate of the metabolic clearance of indomethacin was slightly greater than that observed using this approach. An improved prediction was seen when the scaled parameters obtained from the uptake assay, in conjunction with eq. 16, were used to predict clearance. Atorvastatin and cerivastatin are well estimated, i.e., are now within 2-fold of that observed, and the indomethacin prediction is in excellent agreement with the clearance obtained from the i.v. bile duct cannulation study. Using eq. 18, predictions of Vss are overpredicted for atorvastatin and under-predicted for cerivastatin, but both are predicted to be higher than might be expected for an acid compound, and this is what was observed. Indomethacin Vss is well estimated. The projected half-lives are in very good agreement with those measured (0.82 and 1.2, 3.4 and 2.9, and 8.2 and 4.6 h for atorvastatin, cerivastatin, and indomethacin, respectively). Plasma and liver levels are well simulated using the seven-compartment model for all three compounds, with the exception of the predicted plasma levels of cerivastatin (within 3-fold). Predicted body tissue levels are approximately 4 times greater than measured muscle levels for atorvastatin and cerivastatin and very similar for indomethacin. This is not surprising because muscle makes up a significant component of body tissue. The seven-compartment model was also used to predict the all-important free liver cellular levels to which the metabolizing enzymes are exposed. Simulation of the full in vivo profiles for liver, body tissue, and plasma are shown in Fig. 4 for atorvastatin, cerivastatin, and indomethacin.

Discussion

The dispositions of atorvastatin, cerivastatin, and indomethacin, established substrates of rat hepatic basolateral uptake transporters, have been evaluated in suspended hepatocytes. The results presented here augment the view that the three compounds are indeed transported but also show that although indomethacin undergoes a similar degree of uptake, a high passive permeability limits the impact on the pharmacokinetics because the ability to increase the ratio of the intracellular to extracellular free concentrations, Ψ, is diminished (eq. 9).

There is some lack of clarity in the literature in the nomenclature of intrinsic clearances used to describe elimination from in vitro metabolism systems. The term has been used to describe turnover in hepatocyte suspensions (with or without protein-containing media) and also, more correctly, to describe the in vitro rate of metabolism, corrected for binding and/or uptake. In this paper, we propose a new term to describe the uncorrected rate of turnover in an in vitro incubation (CL_inc) obtained from homogeneous sampling of a hepatocyte suspension. This is a clearance term (not intrinsic clearance), which describes clearance from the system as a whole, prior to any definition of binding or transport within the system.

The relationship between CL_inc and CL_med when active uptake/efflux processes are occurring has been derived. Both the theory and the limited results presented here suggest that CL_med can be simply obtained by dividing CL_inc by the fraction in the medium at pseudo-steady-state. This is analogous to obtaining the metabolic intrinsic clearance by dividing the CL_inc by the free fraction in the incubation when no active processes occur.

k_mem describes cell surface binding and is estimated primarily from intercepts on the y-axis in media and cell concentration-time plots. k_mem is potentially corrupted by binding to the incubation tube in the media analysis. However, this is not the case in the cell analysis, and because the two end points gave similar k_mem estimates, tube binding is not likely to be significant for the compounds studied.

The seven-compartmental physiological model describes the pharmacokinetics in terms of blood, interstitial, liver, and all other tissues. All other tissues are lumped into one compartment, and the liver is split into four as postulated by Reinoso et al. (2001). Splitting the liver into four compartments allows the separation of cellular liver from other components. This then allows the prediction of the all-important concentration in the cellular component of the liver to be predicted. It is also analogous to the in vitro hepatocyte model, with the anticipation that the hepatocyte data may be scaled to the physiological situation. The model has limitations in that it lumps body tissues (except liver) into one compartment and assumes that there is no uptake into nonhepatic tissues. These assumptions adequately describe the pharmacokinetics of atorvastatin, cerivastatin, and indomethacin but may not be appropriate for all drugs.

The scaling approach used here is both simple and pragmatic in that all in vitro parameters are scaled using standard rat biological scaling factors (120 million cells/g liver), with the exception of metabolic intrinsic clearance, which uses an extra factor of 5-fold. This additional empirical factor has been required within this laboratory for the successful scaling of metabolic intrinsic clearance of numerous substrates (Grime and Riley, 2006), importantly, where it is believed that no uptake occurs. Although the approach used here is quite simple, it has afforded reasonable predictions of the physiological observations albeit with a limited set of compounds.

Monitoring of drug levels in cells and media and subsequent modeling enabled estimation of the intracellular free drug concentration and prediction of the hepatic clearance within a factor of 2 of the observed. What may be surprising is that predictions from the standard method, which do not include any consideration of active uptake, are only 2-fold lower. For example, in the case of atorvastatin, the predicted clearances based on the seven-compartment model and the standard method are 24 and 12 ml/min/kg, respectively, yet the intracellular free drug concentration/media concentration ratio at steady state is 18:1. This small difference in the predictions from the two assays can be rationalized by estimating the maximum intracellular free drug concentration. The media concentration of atorvastatin when the cell concentration is at a maximum is approximately 0.1 μM and has reached steady state (Fig. 3). This corresponds to a free intracellular concentration of only ∼1.8 μM. This is the concentration determining the rate of elimination from the system. In the standard method, the maximum intracellular free concentration is assumed to be the initial media concentration corrected for binding (fu_inc). For atorvastatin, in this example, this is 0.69 μM, only 2- to 3-fold less than the actual intracellular concentration, determined using the physiological-based pharmacokinetic model. This observation, that high intracellular free drug concentration/media concentration ratios may only achieve small increases in intracellular free drug concentration relative to the total incubation concentration, has profound implications for the use of hepatocytes in CYP inhibition studies. The effect is particularly marked for atorvastatin because of its high intracellular binding. Conversely, for highly polar compounds with very low intracellular binding, large increases can be achieved.

An estimate of fu_cell is a crucial parameter because it represents the free fraction of drug within the hepatocyte cell and is the same in both the in vitro and in vivo cases. The approach used recognizes the importance of separating binding driven by the intracellular free concentration and the binding to the cell membrane, which is in equilibrium with the medium. Therefore, a good estimate of fu_cell is reliant on an accurate value of k_mem. It is possible to obtain k_mem from either the medium or the hepatocyte concentration data; however, fitting to both sets of data simultaneously affords greater accuracy. A value of fu_cell combined with a prediction of the physiological cellular liver concentration gives an estimate of the free levels exposed to the metabolizing enzymes once steady state has been reached. This would be most useful in the prediction of drug-drug interactions for both inhibition and induction.

The impact of hepatic uptake on clearance has been well documented, but little has been published with respect to Vss and hence MRT (Shitara et al., 2005). The three compounds that have been studied are all acidic drugs and would normally be expected to have low steady-state volume of distribution (0.1–0.3 l/kg typical for acids); however, hepatic uptake has increased the liver levels, thus leading to a major contribution to the volume of distribution. In fact, for atorvastatin and cerivastatin, the amount of drug in the liver represents ∼80% contribution to the total Vss, whereas other tissues have very little contribution due to the high plasma protein binding relative to tissue binding. Both the theory and measured pharmacokinetics described here indicate that uptake has equal impact (increase) on both hepatic clearance and the hepatic component of Vss; therefore, half-life will remain constant as long as the overall extraction from the liver is low, and there is minimal peripheral distribution (as commonly observed with acidic compounds). If, however, these compounds were basic, the hepatic uptake would only have a small contribution to the total Vss. In summary, using the approaches outlined in this paper for predicting the impact of hepatic uptake on clearance, Vss, half-life, and the free liver cellular concentration may lead to more accurate predictions of the pharmacokinetics of hepatic uptake substrates.