Digoxin, an important cardiotonic drug of narrow therapeutic index, is cleared by both the kidney and liver, and exhibits a long half-life in vivo due to the large volume of distribution (Kramer et al., 1974; Rodin and Johnson, 1988). In the rat liver, digoxin is primarily metabolized by cytochrome P450 3a to the didigitoxoside and monodigitoxoside as well as digitoxigenin (Harrison and Gibaldi, 1976; Salphati and Benet, 1999) and is excreted unchanged into bile by the 170-kDa drug efflux pump, P-glycoprotein (Pgp) encoded by the multidrug resistance protein 1 (Mdr1) gene (Schinkel et al., 1995). The transport of digoxin into hepatocytes is by both passive diffusion and the rat organic anion transporting polypeptide 2 (Oatp2), which was expressed in Xenopus laevis oocytes (Noé et al., 1997; Guo and Klaassen, 2001; Hagenbuch et al., 2001) or LCC-PK1 cells (Shitara et al., 2002), and OATP-8 in man (Kullak-Ublick et al., 2001). Other members of the rodent and human OATP family, OATP-A, OATP-B, and OATPC (Noé et al., 1997; Hsiang et al., 1999; Kullak-Ublick et al., 2001), or members of the organic anion transporter (OAT) family (Kusuhara et al., 1999) do not transport digoxin. Significant interactions have been reported for digoxin and other drugs (Okudaira et al., 1988; Rodin and Johnson, 1988; Fromm et al., 1999), and many are attributed to the inhibition of Pgp-mediated efflux that can drastically increase drug accumulation in the brain (Schinkel et al., 1995). Hence, much attention has been devoted to adverse reactions arising from the concomitant administration of drugs with digoxin. Interactions of uptake of digoxin by rifampin, an Oatp2 inhibitor, had led to decreased digoxin clearance in the recirculating liver preparation (Lau et al., 2004), a finding that is consistent with reduced influx (Liu and Pang, 2005). Quinidine, an inhibitor of Pgp, resulted in greater metabolism and an increase in total digoxin clearance in the recirculating liver preparation (Lau et al., 2004); the increase in total hepatic clearance is inconsistent with reduced biliary excretion of the drug (Liu and Pang, 2005).

What are the other factors that may cause unexpected changes in digoxin clearance? One such factor may be transporter/enzyme heterogeneity. Another factor is that basolateral efflux was altered unexpectedly when metabolic or Pgp (Mdr1) inhibitors were used. It has been recognized that the metabolism of digoxin by CYP3a mostly occurs in the perivenous or centrilobular region of the rat liver (Oinonen and Lindros, 1995). Transporter localization studies further suggested that the distribution of Oatp2 was predominantly perivenous (PV) (Reichel et al., 1999), an observation that contrasts to that for the rat Oatp1 (Bergwerk et al., 1996; Abu-Zahra et al., 2000).

In this article, we reexamined the lobular distribution of Oatp2 and Pgp in enriched periportal (PP) and perivenous (PV) hepatocytes prepared from rat liver. Additionally, other determinants of hepatic drug clearance were assessed. For example, binding exerts an inhibitory effect on clearance (Pang and Rowland, 1977). Modest plasma protein binding (Belz et al., 2001) but a high distribution of digoxin into red blood cell (rbc) (Hinderling, 1984) have been reported, and the slow efflux from rbc further constitutes an impediment to drug removal (Goresky et al., 1975). Blood flow rate is another factor that affects clearance (Pang and Rowland, 1977). To address the factors of binding and flow rate, digoxin binding was studied in vitro, and digoxin clearances were compared in rat liver preparations perfused with Krebs Henseleit buffer (KHB) at 40 ml/min in the absence of bovine serum albumin (BSA) and rbc, and with KHB containing 1% BSA and 20% rbc at 10 ml/min. The recirculating design was chosen since a low hepatic clearance is predicted from the modest metabolic intrinsic clearance [V_max/K_m or (362 pmol/min/mg)/125 μM or 0.13 ml/min/g] (Salphati and Benet, 1999). We then fit the perfusion data to the compartmental and physiologically based, pharmacokinetic (PBPK) zonal liver models. The rate-limiting condition for tracer [³H]digoxin elimination: blood flow rate, vascular binding, transporter, metabolic enzyme, or Pgp activity and their accompanying heterogeneity were examined.

Materials and Methods

Materials

[³H]Digoxin (specific activity 19 Ci/mmol) and [¹⁴C]sucrose (specific activity 6.4 mCi/mmol) were purchased from PerkinElmer Canada (Mississauga, ON, Canada). [³H]Digoxin was 94% radiochemically pure as found by high-pressure liquid chromatography (gradient of 18–28% acetonitrile and water). Unlabeled digoxin (Dg3) was obtained from Sigma-Aldrich Canada (Mississauga, ON, Canada); digitoxigenin bis-digitoxoside (Dg2), digitoxigenin monodigitoxoside (Dg1), and digitoxigenin (Dg0) were kind gifts from Dr. Emil Lin (University of California, San Francisco, CA). Collagenase type II was obtained from Worthington Biochemicals (Freehold, NJ). All other reagents and solvents were of HPLC grade.

Digoxin Transport

Preparation of Zonal Rat Hepatocytes. Male Sprague-Dawley rats (301 ± 12 g; Charles River Canada, St. Constant, QC, Canada) were used. The rats were kept under a 12:12-h light:dark cycle and given food and water ad libitum. Studies were conducted in accordance to protocols approved by the Animal Committee of the University of Toronto. Enriched PP (zone 1) and PV (zone 3) hepatocytes that were used for the transport studies and Western blot analysis were isolated by the digitonin/collagenase perfusion technique of Lindros and Pentïlla (1985), with modifications (Tirona and Pang, 1999). Viability of the zonal hepatocytes exceeded 97 ± 2.2%, as assessed by trypan blue exclusion. All buffers were pregassed with carbogen [95% O₂, 5% CO₂ (v/v); Canox Gas, Mississauga, ON, Canada]. The enrichment of PP and PV cells was confirmed by use of enzyme markers; alanine aminotransferase (PP:PV ratio of 1.9 ± 0.7) was assayed by a Sigma diagnostics kit, and glutamine synthetase (PP:PV ratio of 0.029 ± 0.039) was measured by a standard UV method (Meister, 1985).

Digoxin Uptake by Zonal Hepatocytes. After preincubation in an atmosphere of carbogen for 10 min at 37°C, 100 μl of a mixture of unlabeled digoxin, [³H]digoxin, and [¹⁴C]sucrose (an extracellular marker) in KHB buffer was added to 0.5 ml of hepatocyte suspension (2 × 10⁶ cells/ml in KHB, 5 mM glucose, and 1 mM HEPES) to result in 0.08 to 3.7 μM digoxin, 3.5 to 4.4 × 10⁶ dpm/ml [³H]digoxin, and 0.88 to 0.9 × 10⁶ dpm/ml [¹⁴C]sucrose. Samples (100 μl) of the incubation mixture were retrieved at 15-s intervals for up to 60 s and immediately centrifuged across the silicon oil layer (100 μl of density 1.02 g/ml) into the bottom layer of 50 μl of 3 N NaOH (Tirona and Pang, 1999). The tip, containing the hepatocyte pellet in 3 N NaOH, was removed into a 20-ml glass scintillation vial and left overnight. After the addition of 50 μl of 3 N H₂SO₄ to neutralize the base, the cellular content of [³H]digoxin (disintegrations per minute per milligram of protein) was determined by liquid scintillation spectrometry (model 5801; Beckman Coulter Canada, Mississauga, ON, Canada) after the addition of 10 ml of scintillation fluor (Ready Protein; Beckman Coulter Canada). The extracellular volume (mean value of 0.95 ± 1.4 μl) entrapped in the cellular compartment, found by the [¹⁴C]sucrose content, was used as a correction factor in the determination of cellular contents. The specific activity was used to calculate the rates of uptake. Protein content in the cell suspension was measured by the method of Lowry et al. (1951).

Western Blot Analysis of Oatp2, Oatp1, and Pgp in Rat Zonal Hepatocytes. Approximately 30 ml of ice-cold 0.1 M Na₂CO₃ and protease inhibitors was added to the pelleted zonal hepatocytes in a 50-ml conical tube for preparation of the crude membrane fraction. The cell suspension was homogenized at 4°C and then centrifuged at 4°C at 100,000g for 1 h. The supernatant was discarded, and the pellet was kept frozen overnight at -80°C before being sonicated for 10 to 30 s in ice-cold phosphate-buffered saline (200–400 μl) in Eppendorf tubes. Protein determination was performed by the Bio-Rad method (Bio-Rad, Hercules, CA). Western blotting was performed to determine the relative expression levels of Oatp2 and Pgp in PP and PV hepatocyte membranes. Oatp1, shown to be present homogeneously in rat liver (Abu-Zahra et al., 2000), was also examined in the same sample to serve as a comparison for Oatp2. Approximately 25 μg (Oatp2 and Oatp1) or 20 μg (Pgp) protein, in the same volume of sample buffer, was heated at 100°C for 7 min. Immunoblot was conducted with SDS-polyacrylamide gel electrophoresis (10% gel), and proteins were electrophoretically transferred to polyvinylidene difluoride membranes (Millipore Corporation, Billerica, MA). After blocking with nonfat milk solution, the membrane was incubated with antibody for 4 h before developing for luminescent detection (GE Healthcare, Little Chalfont, Bucking-hamshire, UK). For the immunodetection of Oatp2, 1:10,000 dilution of the primary rabbit polyclonal antibody toward Oatp2 [antibody was made corresponding to amino acids 650–661 at the carboxy terminus (CTEVLRSKVTED)] and 1:20,000 dilution of the secondary antibody, HRP-anti rabbit IgG (Bio-Rad), were used. For the immunodetection of Oatp1, a 1:2500 dilution of the primary rabbit polyclonal antibody toward Oatp1 [antibody was made to the peptide corresponding to amino acids 645–657 near the carboxyl terminus (EKESEHTDVHGSP)] and 1:20,000 dilution of the secondary antibody, HRP-anti rabbit IgG (Bio-Rad), were used. Both primary antibodies were raised to the KLH-linked peptide (Bergwerk et al., 1996). For immunodetection of Pgp, a 1:333 dilution of the primary mouse monoclonal antibody C219 (Signet Laboratories, Dedham, MA) and 1:20,000 dilution of the secondary antibody, HRP-anti mouse IgG (Bio-Rad), were used.

Immunofluorescent Confocal Microscopy. Immunofluorescence localization and confocal microscopy were performed as described previously, with modifications (Bergwerk et al., 1996; Novikoff et al., 1996). The liver was fixed in two ways: 1) perfusion through the portal vein with 4% paraformaldehyde/phosphate-buffered saline and then slicing the fixed liver into sections approximately 1 to 2 mm thick with further fixation by immersion; and 2) by slicing the unfixed liver tissue into sections approximately 1 to 2 mm thick and immersing the sections into the fixative. The fixed liver sections were then further sectioned with a microtome to obtain 10- to 20-μm sections that were then sequentially treated as follows: sodium borohydride, blocking serum, primary specific antibody (either to polyclonal anti-Oatp1 or anti-Oatp2), and fluorescent-labeled secondary antibody. Confocal microscopy was used to image the distribution of Oatp1 (previously described in the rat liver; Bergwerk et al., 1996) and Oatp2. Controls included microscopic examination of sections for autofluorescence and after substitution of the primary specific antiserum with nonspecific, primary serum.

Albumin Binding and rbc Distribution of Digoxin

Protein binding was conducted by equilibrium dialysis at digoxin concentrations of 10 to 100,000 nM (containing [³H]digoxin) in 1 or 2% albumin in perfusate. Preliminary studies had suggested that 4.5 h was required for equilibration between the buffer and plasma (drug-containing) compartments. The free or unbound fraction in perfusate plasma was given by the ratio of [³H]digoxin in buffer to drug-plasma compartment.

The rbc influx of digoxin and equilibration between plasma and rbc were examined. [³H]Digoxin and unlabeled digoxin were incubated in 1% albumin perfusate (without rbc) at 37°C for 30 min. Then, an equal volume of 40% rbc-1% albumin perfusate was added to result in digoxin concentrations of 20 to 20,000 nM in 20% rbc-1% albumin perfusate. The mixture was incubated in a rotating incubator at 37°C, and samples were retrieved and rapidly centrifuged to provide plasma during the next 20 min. The hematocrit (Hct) in the samples was determined. The [³H]digoxin contents in the original, plasma sample and for the 20% rbc (end sample) blood perfusate were assayed by a simple precipitation procedure with acetonitrile; a set of standards containing varying known amounts of [³H]digoxin were processed under identical conditions to provide the calibration curve. [³H]Digoxin in plasma was assayed directly by liquid scintillation spectrometry (model 5801; Beckman Coulter Canada).

Recirculating Rat Liver Perfusion

Livers (9.1–13.8 g) from male Sprague-Dawley rats (290–360 g; Charles River Canada) were perfused in situ with recirculation of the perfusate. 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 were allowed free access to water and food ad libitum. Rat liver perfusion was carried out at 37°C as described previously (Tirona and Pang, 1996), with perfusate entering via the portal vein and exiting via the hepatic vein. Perfusate of varying composition was used: one perfusate consisted of KHB and 17 mM glucose (absence of rbc and albumin), and the other perfusate contained bovine erythrocytes (20% rbc), freshly obtained and washed (a kind gift of Ryding Meats, Toronto, ON, Canada), 1% BSA, and 17 mM glucose (Travenol Labs, Deerpark, IL) in KHB solution, pH 7.4. The perfusate was oxygenated with 95% oxygen, 5% carbon dioxide (Matheson Gas Company, Mississauga, ON, Canada). Two reservoirs were used for study. Reservoir 1 was used for equilibration of the liver, whereas reservoir 2 contained tracer concentrations of digoxin (initial concentration 256,600 ± 105,000 dpm/ml or 6.1 ± 2.5 nM in 150- or 200-ml volume) for recirculation of the liver. Perfusate samples (1 ml) were retrieved from reservoir 2 at 0, 2.5, 7.5, 12.5, 17.5, 22.5, 27.5, 35, 45, 55, 75, 105, 135, 165, and 180 min after initiation of perfusion. Bile was drained into prepared collection vials at the intervals 0 to 5, 5 to 10, 10 to 15, 15 to 20, 20 to 25, 25 to 30, 30 to 40, 40 to 50, 50 to 60, 60 to 90, 90 to 120, 120 to 150, and 150 to 180 min, such that the midpoint times coincided with the times for perfusate samplings. A sham experiment was also conducted in absence of a liver to ascertain the extent of binding of [³H]digoxin to the tubing of the perfusion apparatus; none was found.

Assay of Dg3 and Metabolites

Digoxin (Dg3 or digitoxigenin tridigitoxoside), Dg2, and other metabolites monodigitoxoside (Dg1) and the aglycone (Dg0) were quantified by HPLC. The HPLC procedure of Salphati and Benet (1999) was modified to separate radiolabeled Dg3 and all of the metabolites, Dg2, Dg1, and Dg0, within the same HPLC run. The chromatographic system (Shimadzu, Kyoto, Japan) consisted of two LC-10AT pumps, a SCL-10A system controller, a GT-104 degasser, FCV-10AL low-pressure mixing chamber, SIL-10A autoinjector, a SPD-10A UV detector set at 220 nm, and a Waters CB_18B μbondapak reverse-phase column (3.9 × 300 mm; particle size, 10 μm) and guard column (2.2 × 0.34 cm i.d.; particle size, 37–55 μm). A binary gradient consisting of water and acetonitrile was used. The initial condition of 18% acetonitrile was maintained at a flow rate of 1 ml/min. At 8 min, a linear gradient was used to increase the acetonitrile to 28% over the next 5 min and then kept there for 12 min. It was gradually returned to the original condition (18% acetonitrile) over 2 min and kept there for the next 10 min. Radiolabeled Dg3 and its metabolites eluting at the various intervals were predetermined upon determination of the 1-min radioelutions into 7-ml minivials. Five milliliters of scintillation cocktail (Ready Safe; Beckman Coulter) was added to each vial, and the radioactivity was quantified by a two-channel liquid scintillation spectrophotometer (model 5801; Beckman Coulter Canada). The emerging radiolabeled peak that was invisible due to the high specific activity of Dg3 was similar to those of the authentic standards; the run time was 37 min, and the retention times were Dg3, 28 min and Dg2, 23 min (Fig. 1).

KHB perfusate samples were centrifuged, and then 100 μl was used for direct counting and 180 μl was directly injected into the HPLC. A longer procedure was used to assay the blood perfusate samples. Unlabeled digoxin (25 nmol) was added to blood perfusate (400 μl) as an internal standard. Then, 2400 μl of acetonitrile was added, and the mixture was mixed well for deproteinization. After centrifugation, the supernatant was removed into a fresh glass tube and dried under nitrogen. The residue was dissolved in 120 μl of mobile phase (25% acetonitrile, 75% double distilled H₂O), and the reconstituted sample was centrifuged again before 60 μl was injected into the HPLC. Standards for calibration curves (varying amounts of [³H]digoxin) were processed under identical conditions. Bile was diluted with double distilled H₂O, and an aliquot was injected into the HPLC. Another aliquot of the diluted bile sample was counted directly. The extent of excretion of Dg3 and its metabolite(s) was quantified by the fractional disintegrations per minute of the species in the sample times the total counts of the sample.

Calculations and Modeling

Transport Studies. The cumulative amounts of digoxin (pico-moles per milligram of protein) that were taken up (after correction for the entrapped extracellular component) into hepatocytes within the first minute were regressed against the corresponding incubation time. The slope yielded an initial uptake rate, ν. Upon presenting the rate, ν, against [S], the substrate concentration, the data were fit to various curve models (general equation shown as eq. 1) for a single saturable component, for the sum of one saturable and one nonsaturable component, for two saturable components, or two saturable components plus a nonsaturable component. The general equation describes the various saturable systems which are characterized by the V_max,i and K_m,i, or the maximum capacity and Michaelis-Menten constant for each i^th saturable component, and a linear (nonsaturable) component for uptake, PS_uptake. The nonsaturable component for digoxin represents most likely passive diffusion for this lipophilic substrate.

rbc Partitioning and Plasma Protein Binding. The model that describes the exchange of digoxin between plasma and rbc in relation to the Hct is shown in Fig. 2. The blood concentration was estimated as the initial plasma concentration/2 when equal volumes of blank blood (40% rbc, 1% BSA) and plasma (1% BSA) were mixed. The concentration of digoxin in rbc was assessed from mass balance, knowing the concentration of drug in blood (C_b), in plasma (C_p) and the hematocrit. The unbound concentration in plasma, f_p, is the ratio of unbound to total drug in plasma.

Only the unbound species of digoxin in rbc and plasma are assumed to undergo equilibration. The on and off rate constants, k_pr and k_rp, respectively, denote the rate constant for movement of unbound digoxin from plasma to rbc, and from rbc to plasma. Inas-much as the binding of digoxin to rbc was uncertain, a modified rate constant, , which equals the product f_rbc (unbound fractions in rbc) and k_rp, was used.

The rates of change of digoxin concentrations in rbc (C_rbc) and plasma (C_p) are as follows, and the unbound fraction in blood (f_b) is related to f_rbc and f_p as shown below (Pang and Rowland, 1977), with the assumption that there is no concentrative transport of drug into the rbc.

The terms and k_pr have been shown to be related to the concentration ratio of rbc to plasma, where γ is the ratio of the interstitial or Disse space to the sinusoidal plasma space (Pang et al., 1988).

Rat Liver Perfusion Studies. Model-independent methods were used to calculate clearances. The area under the curve (AUC) of Dg3 in perfusate was calculated by trapezoidal rule and extended to time infinity (concentration of last sample/elimination rate constant) to estimate the total clearance, CL_liver,tot, by dose/AUC in both sets of studies. The cumulative amount of Dg3 excreted in bile over 3 h was summed and expressed as %dose. The amounts of Dg2 in bile and perfusate at the same time point were summed and the cumulative amount at 165 min was expressed as %dose. However, this amount would underestimate the total amount of Dg2 metabolite formed since minor levels of Dg1 and Dg0 were detected, and not all of the metabolites formed occurred in bile and perfusate; Dg2 and other metabolites may be trapped within the liver. The total recovery as Dg2 and Dg3 in bile and perfusate accounted for only 50 to 55%, and a substantial amount of radioactivity was indeed found in the liver at 180 min.

Compartmental Modeling. Compartmental models, either with elimination from the central compartment (Fig. 3A) or peripheral compartment (Fig. 3B), were used for fitting of Dg3 perfusate and bile data. Both models are equally consistent to describe the biexponential decay of Dg3 in perfusate. Since the summed amounts of Dg2 occurring in perfusate and bile may not represent total metabolism due to residual ³H radioactivity in liver, the summed Dg2 amount was not used for fitting. Rather, the rate constant for metabolism, k_m [as (k₁₀ - k_e)or(k₂₀ - k_e)] and the total amount of metabolite formed were estimated from modeling (Fig. 3).

PBPK Zonal Liver Modeling. For the description of data based on the physiological variables, a PBPK zonal model consisting of three compartments in series to represent zones 1, 2, and 3 in the liver (Tirona and Pang, 1996; Abu-Zahra and Pang, 2000) was used (Fig. 4). In this model, physiological variables such as flow rate and tissue and blood volumes were used. Moreover, the PBPK zonal model encompasses zonal transport, metabolism, and excretion of Dg3 in the PP, midzonal, and PV regions (Fig. 4A) as well as rbc binding, namely, the transport into and out of red cells, and albumin binding (Fig. 4B) in the rat liver preparation. It is assumed that the free species is the one that is transported, metabolized, or excreted. This model describes heterogeneity in basolateral influx transport, denoted as CL_in1, CL_in2, and CL_in3 within zones 1, 2, and 3, respectively. Likewise, CL_ef1, CL_ef2, and CL_ef3 are the clearances for basolateral efflux; CL_int,sec1, CL_int,sec2, and CL_int,sec3 for biliary excretion; and CL_int,met1, CL_int,met2, and CL_int,met3 for metabolism within zones 1, 2, and 3, respectively.

Fitting

The program SCIENTIST version 2 (MicroMath Inc., Salt Lake City, UT) was used for all fittings and simulations. Fitting was performed with various weighting schemes of unity, 1/observation and 1/observation². The model selection criterion (MSC), a modified Akaike information criterion, was used as a discriminator for the optimal model.

Hepatocyte Uptake.Equation 1 was used for fitting of the digoxin uptake data. The total uptake clearance (CL_uptake) under first-order conditions was given by the ratio V_max,i/K_m,i, of the various transporter systems + the nonsaturable uptake clearance.

rbc and Albumin Binding. Data for plasma protein binding were used to estimate the f_P as unbound plasma concentration/total plasma concentration. Then, data (n = 3) for red cell binding were averaged, and the mean data for C_rbc and C_p for Dg3 blood concentrations ranging from 20 to 20,000 nM were fitted to eqs. 3 and 4.

Compartmental Modeling. A set of differential equations (see Appendix A) was used for data fitting to the compartmental models (Fig. 3). The intercompartmental rate constants, k₁₂ and k₂₁; the excretion rate constant, k_e; and k₁₀ (or k₂₀) were fitted; k_m was found by difference (k₁₀ - k_e or k₂₀ - k_e). The hepatic clearance (CL_liver,tot) was calculated from the derived parameters: k₁₀V₁ (volume of reservoir) for elimination from the central compartment, or k₂₀V₁× k₁₂/(k₂₁ + k₂₀), when elimination takes place in the peripheral compartment. The biliary (CL_liver,ex) and metabolic (CL_liver,met) clearances are denoted as k_eV₁ and k_mV_1, respectively, when Dg3 is eliminated from the central compartment; or k_eV₁ × k₁₂/(k₂₁ + k₂₀) and k_mV₁ × k₁₂/(k₂₁ + k₂₀), respectively, when Dg3 elimination occurs in the peripheral compartment. The hepatic extraction ratio, E, is estimated as CL_liver,tot/flow rate.

PBPK Zonal Liver Modeling. Data of Dg3 in reservoir and in bile were fit by mass balance differential equations for first-order conditions (see Appendix B). The designated flow rates, volumes, and hematocrit from rat liver perfusion study were known constants. The fitted parameters on the rbc partitioning (k_pr and ) and protein binding (f_p), obtained from the in vitro binding study, were assigned as constants. The uptake clearance, CL_in, was obtained by scale-up of the in vitro hepatocyte uptake data: the experimentally determined in vitro V_max/K_m, added to the nonsaturable uptake clearance, yielded 12.1 ml/min/g after scale-up for the average of the PP and PV transport data. The value was divided by three so that CL_in1 = CL_in2 = CL_in3 since even distribution of Oatp2 was found. An initial estimate of the total, hepatic intrinsic clearance (CL_int) was calculated, based on simplified equations shown below for the “well stirred” (eq. 7) or “parallel tube” (eq. 8) model (Pang and Rowland, 1977). The equation is valid when the influx and efflux transport of digoxin across the hepatocytes membrane is fast, and metabolism and excretion are slow. The assumption is valid for Dg3. The total intrinsic clearance was divided by three to provide a crude estimation of the zonal, intrinsic clearance.

For the well stirred model, and for the parallel tube model, The basolateral efflux clearance (CL_ef), metabolic intrinsic clearance (CL_int,met), secretory intrinsic clearance (CL_int,sec), and the unbound tissue binding (liver tissue unbound fraction, f_t) were estimated from fitting. Each of the zonal clearances was expressed as a percentage of total intrinsic clearance. For example, the metabolic activity of Cyp3a was perivenous, and could be described by 10, 30, and 60% of the total metabolic intrinsic clearance (CL_int,met) dispersed in the periportal (zone 1), midzonal (zone 2), and perivenous (zones 3) regions, respectively. Alternately, the activities may be assigned to be evenly distributed among all three zones, that is, CL_int,met1 = CL_int,met2 = CL_int,met3 = CL_int,met/3. This was assumed for Pgp as found from Western blot analysis, and each zonal secretory intrinsic clearance is CL_int,sec/3.

Simulations. The parameters obtained after fitting of data from the rbc-alb-perfusion studies (Table 4, middle column) were used for further simulations with the PBPK, zonal model shown in Fig. 4B. The first set of simulations was based on an even distribution of CL_int,met, and the simulations were made to demonstrate the changes in digoxin disposition (metabolism and excretion) when the flow rate was altered from 10 to 40 ml/min, when the binding of digoxin to rbc, then to albumin was set as zero, sequentially (, f_p = 1), and when the influx, efflux, secretory, or metabolic intrinsic clearances were doubled. Only one change was made at any one time. In these simulations, the concentration-time profiles of Dg3 in perfusate, the cumulative amount in bile, and the total formation of Dg2 were simulated. The CL_liver,tot (dose/AUC), CL_liver,ex (total Dg3 excreted amount in bile/AUC) and CL_liver,met (total Dg2 formation/AUC) were estimated for each condition.

To address whether enzyme heterogeneity and transporter heterogeneity would result in any unexplained observations in digoxin clearance, such as increased hepatic clearance upon inhibition of Pgp (Lau et al., 2004), a second set of simulations was performed. In this instance, the total activity for transport or metabolism was divided among zones 1, 2, and 3. An even distribution in zones 1, 2, and 3 (1:1:1) was designated with the distribution “A”. A preferential PV distribution was assigned (1:3:6), meaning that 10, 30, and 60% of the total activity resided in zones 1, 2, and 3, respectively, and was assigned a “B” distribution. The reverse pattern, a preferential PP distribution (6:3:1) meaning that 60, 30, and 10% of the total activity resided in zones 1, 2, and 3, respectively, was assigned the distribution of “C”. Each model was described by three letters, with the first letter describing the parallel distribution patterns of influx and efflux clearances (CL_in and CL_ef). The second and third letters described the distribution patterns of the metabolic (CL_int,met) and secretory (CL_int,sec) intrinsic clearances, respectively. The various distributions resulted in 27 possible combinations. All of the possible distribution patterns were used to simulate digoxin disposition with the PBPK, zonal model shown in Fig. 4B. Again, the parameters from rbc-alb-perfused liver (Table 4) were used initially to evaluate the effect of zonal metabolic and transporter heterogeneity on clearance with the model. Several other sets of simulations were made to explore the effects of the relative values of the intrinsic clearances, CL_int,met and CL_int,sec, to the transport clearances, CL_in and CL_ef. Since values of the CL_int,met and CL_int,sec were much lower than those for CL_in/CL_ef, values of the CL_int,met and CL_int,sec were increased to 5- and 50-fold of the original values, respectively, or 100- and 500-fold, respectively, to examine the influence of enzymatic and excretory activities when these values were comparable with those for basolateral influx and efflux. Last, the CL_int,sec was reduced to 10% of the original value to examine the condition of inhibition of Pgp efflux on metabolism. The concentration time-profiles for Dg3 in the reservoir, and the cumulative amounts of Dg3 in bile as well as the total amount of Dg2 formed were used to estimate the areas under the curve, and in turn, the total, metabolic, and biliary excretory clearances. The values of the clearances according to the various distribution patterns were subsequently ranked.

Statistical Analysis

For comparison of data, a one-way analysis of variance was performed. The data were expressed as mean ± S.D. A P value of 0.05 was set as the level for statistical significance.

Results

Uptake of Digoxin by Isolated Zonal Rat Hepatocytes

The time course for digoxin accumulation into cells (amount per milligram of cells versus time plot) was linear over 1 min (data not shown). These values provide the initial uptake velocities of digoxin for the various concentrations used. Digoxin uptake was best described as the sum of a saturable component and a nonsaturable component (Fig. 5). The K_m and V_max and the nonsaturable linear uptake clearance, PS_uptake, were obtained with the optimal weighting of 1/observation². Differences in parameter estimates were insignificant among PP and PV zonal hepatocytes (Table 1). The fitted K_m is low (180 and 390 nM), suggesting a high-affinity but readily saturable process, whereas the nonsaturable component was appreciable, although it constituted about 10% of the transport clearance under first-order conditions. In view of the lipophilic character of digoxin, this component is most likely due to passive diffusion.

Distribution of Oatp2 and Pgp in Zonal Rat Hepatocytes and in Rat Liver

The intensities of immunodetectable Oatp2, Oatp1 (Fig. 6), and Pgp (Fig. 7) by Western blots of PP and PV cells showed similar zonal distributions. The relative intensities of Oatp2 in PP and PV cells were 1260 ± 423 and 1620 ± 303 arbitrary units (525 ± 70 and 572 ± 138 arbitrary units in PP and PV cells for Oatp1), respectively (P > 0.05), whereas the relative intensities of Pgp in PP and PV cells were 1850 ± 700 and 2800 ± 750 arbitrary units, respectively (P > 0.05), suggesting that all three proteins were present homogeneously throughout the acinus of the rat liver. Confocal immunofluorescent microscopy revealed that rat Oatp2 was present in hepatocytes located in portal, midzonal, and central areas of the hepatic lobule, although their appearance may not be contiguous (Fig. 6). We consistently observed variable fluorescence intensities within and between the areas. The distribution of Oatp2 in rat liver was the same regardless of the fixation protocol employed. Oatp2 was distinctly present in the PP region as well as the PV region. These results mirrored that of Oatp1, which was distributed homogeneously throughout the liver lobule (Bergwerk et al., 1996; Abu-Zahra et al., 2000).

Protein Binding and rbc Distribution of Digoxin

The f_p of digoxin in plasma from the in vitro binding study was 0.64 ± 0.03 (Table 2). Binding to 1% albumin was modest, and the unbound fraction was constant even when the albumin concentration was doubled to 2% (Fig. 8). The fit of the rbc partitioning data (Fig. 9) to the model (Fig. 2) yielded values of k_pr (0.468 ± 0.021 min^-1) and (1.81 ± 0.12 min^-1), showing that the on rate constant (k_pr) was lower than the apparent off rate constant () (Table 2). The f_b at equilibrium, calculated as f_p/(C_b/C_p), equaled 0.615.

Digoxin Disposition in KHB and rbc-Albumin Perfused Rat Liver Preparations

Dg3 underwent an initial rapid distribution, and then a protracted decline in livers perfused with KHB at 40 ml/min, in a distinctly biexponential decay profile (Fig. 10A). Only Dg2 was found in perfusate, and Dg1 and Dg0 levels were very low or nonexistent (Fig. 10B). Both Dg3 and Dg2 were excreted into bile in comparable quantities (Fig. 10). However, the unbound biliary clearance of Dg3 (excretion rate of Dg3/midtime unbound Dg3 concentration in perfusate or 0.05 ± 0.02 ml/min/g liver) was significantly lower (P < 0.05) compared with the apparent biliary clearance of Dg2 (excretion rate of Dg2/midtime Dg2 concentration in perfusate or 1.10 ± 0.72 ml/min/g liver) (plot not shown).

Comparable results were observed when Dg3 in 20%-rbc and 1%-BSA medium recirculated through the liver at 10 ml/min (Fig. 11). A more shallow distribution phase of digoxin was observed in the presence of the lower flow rate and vascular binding elements such as rbc and albumin in the rbc-alb-perfused livers (Fig. 11A) in comparison with the KHB-perfused livers (Fig. 10A). The metabolite Dg2 was found in perfusate and was excreted avidly into bile; other metabolites, Dg1 and Dg0 were present at very low levels (Fig. 11B). The apparent excretion clearance of Dg2 (0.44 ± 0.04 ml/min/g liver) was significantly greater (P < 0.05) than the unbound biliary clearance of Dg3 (0.02 ± 0.04 ml/min/g liver) (plot not shown). The hepatic clearances calculated from dose/AUC from trapezoidal method were 0.192 ± 0.049 versus 0.123 ± 0.061 ml/min/g, respectively, for the KHB-perfused liver and rbc-alb-perfused livers (P > 0.05). Upon correction for f_b, the clearance values (CL_liver,tot/f_b) become virtually identical (Table 3).

Compartmental Fitting

Compartmental fits of data from individual experiments and to the averaged data were performed. Fits obtained for individual experiments provide mean values (Table 3) that were similar to the parameters obtained for the fit of the average data (data not shown). For fits to the model that assumed elimination from the central compartment, no difference was found in k₁₂, k₂₁, and k₁₀, due to the large variability among the preparations; however, k_e and the total clearance (0.114 ± 0.057 versus 0.244 ± 0.082 ml/min/g) were significantly lower for the rbc-alb-perfused livers in comparison with those for the KHB-perfused livers (P < 0.05). For fits to the model with elimination from the peripheral compartment, significant differences were found for k_m and k₂₀, and E (P < 0.05) but not for the total hepatic clearance between KHB-perfused and rbc-alb-perfused livers, regardless of correction for the f_b (Table 3). After normalization of CL_liver,tot by f_b, values of CL_liver,tot/f_b provided by compartmental fitting were similar for the KHB-perfused and rbc-alb-perfused livers, when elimination occurred from central (0.244 ± 0.082 versus 0.185 ± 0.093 ml/min/g; P > 0.05) or peripheral compartment (0.198 ± 0.111 versus 0.191 ± 0.083 ml/min/g; P > 0.05) (Table 3). In all of the fits, the predicted amounts of Dg2 formed were higher than the summed amount of Dg2 obtained from the perfusate and bile (Figs. 10B and 11B).

Generally, good fits were obtained for the models encompassing elimination from the central or peripheral compartments (Figs. 10A and 11A). The biliary excretion data seemed to be better predicted during the earlier times by the peripheral compartment. But the small difference (observed only with semilogarithmic plot) failed to alter the overall fit as to whether or not removal occurred from the central or peripheral compartment. This was shown by the similar MSC values and sum of squared residuals (P > 0.05; Table 3). It was not possible to discern whether elimination occurred in the central or peripheral compartment. Moreover, the fit failed to reveal unequivocally the underlying reason for the difference in the clearance of digoxin estimated with compartmental modeling-binding of digoxin to BSA or rbc, or the flow rate.

PBPK Zonal Liver Modeling

When the mean data were fit to the PBPK zonal models (Fig. 4, A and B), the CL_ef, CL_int,met, CL_int,sec, and f_t were found not to differ between KHB-perfused and rbc-alb-perfused livers (P > 0.05; Table 4). Good fits were obtained (Fig. 12, A and B), and the parameters were found to be similar regardless of whether heterogeneous or evenness in CL_int,met was considered (Table 4). That presence of heterogeneity in metabolic activity did not exert an effect on the overall clearance of digoxin that was poorly extracted. The digoxin removal within the liver would fail to evoke a steep sinusoidal or intracellular concentration gradient in the liver lobule. Under this condition, the enzymes are recruited in the entirety by the substrate (Pang and Stillwell, 1983), and enzymatic heterogeneity became irrelevant. When the data were forced fit to provide a common set of CL_int,met, CL_int,sec, CL_ef, and f_t, the fits were not as good as those when data of the KHB- and rbc-livers were fit separately (fits not shown). But generally, the parameters obtained from forced-fitting were similar to those furnished from separate fits to data of KHB-perfused and rbc-alb-perfused livers (Table 4).

Simulations with PBPK Zonal Liver Model

Flow or Binding on Digoxin Clearance. The fitted parameters for the rbc-alb-perfused of CL_liver,tot/f_b provided by compartmental fitting were similar in KHB-perfused and rbc-alb-perfused liver preparation (flow = 10 ml/min with rbc and albumin binding; Table 4, middle) were used for simulations. When the blood flow rate was increased from 10 to 40 ml/min, it was apparent that flow failed to perturb the concentration-profile and decay processes of digoxin, and both excretion and metabolism of digoxin remained similar (Fig. 13A). Whereas when red cell binding was set as nonexistent , the decay profile of digoxin was more rapid, and all clearance values: excretory and metabolic, were increased. When albumin binding was further set as zero (f_p = 1), steeper changes in decay were observed, and all of the clearance values were increased further (Fig. 13B; Table 5).

Changes in CL_in, CL_ef, CL_int,met, and CL_int,sec. To investigate the interrelationship of the transporters and the metabolic enzymes, the intrinsic clearance, CL_in, CL_ef, CL_int,met, or CL_int,sec was doubled in individual simulations. Upon doubling of CL_in, the decay of digoxin was much faster, and CL_liver,tot, CL_liver,ex, and CL_liver,met all increased, with digoxin being more highly excreted and metabolized (Fig. 14A; Table 5); whereas with a doubling of CL_ef, the decay of digoxin was much slower, and CL_liver,tot, CL_liver,ex, and CL_liver,met all decreased (Fig. 14B; Table 5). An increase of CL_int,met increased CL_liver,met and CL_liver,tot but decreased the alternate (competing) clearance, CL_liver,ex, and the decay of digoxin was much faster (Fig. 14C; Table 5). The increase in CL_int,sec only slightly hastened the disappearance of digoxin, increasing the CL_liver,tot slightly, although the CL_liver,ex was increased and CL_liver,met decreased slightly (Fig. 14D; Table 5). Only small differences in excretion existed in the last two situations because metabolism was the major removal pathway of digoxin.

Transporter and Enzyme Heterogeneity. The clearances for the 27 combinations of zonal patterns (1:1:1, 1:3:6, and 6:3:1, denoted by A, B, and C, respectively) for influx/efflux, metabolism, and secretion were estimated with simulations. The best three (highest clearances) and the worst three (poorest clearances) conditions are listed in Table 6. The best condition for total clearance CL_liver,tot existed when the influx/efflux, metabolism, and secretion intrinsic clearances were evenly distributed (distribution pattern of AAA), and the even distribution of CL_in/CL_ef, allowed access of substrate into the cell for metabolism or excretion. The worst condition was when the CL_in/CL_ef versus CL_int,met or CL_int,sec exhibited opposite distributions (CBB or BCC), and persisted regardless of the values of CL_int,met and CL_int,sec. The metabolic clearance, CL_liver,met, was highest when parallel distributions existed between CL_in/CL_ef and CL_int,met, the dominant removal pathway, and this occurred when CL_in/CL_ef or CL_int,met displayed distribution A or C. The CL_liver,met was lowest when CL_int,met displayed distribution B. For the biliary clearance, CL_liver,ex, higher values existed when the CL_int,sec exhibited distribution A or C, and when CL_liver,met was of distribution B, representing a lower metabolic clearance. The CL_liver,ex was lowest when the CL_in/CL_ef and CL_int,sec were of opposite distributions (B versus C, or C versus B). These general patterns were consistent over the parameter space examined, and when the biliary intrinsic clearance was reduced to 10% of the original value (Table 6). Moreover, the varying distribution patterns of CL_in/CL_ef, CL_int,met, and CL_int,sec did not change the trend in the total clearance when CL_int,sec was inhibited. The metabolic clearance was increased, whereas the biliary and total clearances were decreased with inhibition of Pgp (effectively, a reduction in CL_int,sec).

Discussion

The uptake of digoxin has been attributed to the Oatp2 in the rat liver (Noé et al., 1997; Hagenbuch et al., 2001; Shitara et al., 2002) and OATP-8 in humans (Kullak-Ublick et al., 2001) based upon transport studies performed in Xenopus oocytes (Noé et al., 1997; Hagenbuch et al., 2001) or LCC-PK1 cells (Shitara et al., 2002) expressing these proteins. However, we were unable to confirm Oatp2-mediated digoxin uptake in stably transfected HeLa cells in which Oatp2 expression was under control of a Zn²⁺-activated methallothionein promoter, similar to studies we performed for rat Oatp1 (Pang et al., 1998). The observed digoxin uptake rate was high but represented nonsaturable transport that was also present in HeLa cells that had not been stimulated with Zn²⁺ (A. W. Wolkoff and K. S. Pang, unpublished data,). Our failure to demonstrate that digoxin is an Oatp2 substrate may be attributed to use of mammalian cells versus X. laevis oocytes. It could also be further argued that, for the mammalian LCC-PK1 cells that were transfected with rat Oatp2, the digoxin transport rates were very low and existed at levels similar to those for background transport (Shitara et al., 2002).

Expression of Oatp2, present at the basolateral plasma membrane of the rat hepatocyte (Kullak-Ublick et al., 1994; Meier and Stieger, 2002), was reported to be higher in the perivenous region (Reichel et al., 1999), as also found for Oatp4 (Cattori et al., 2001). The findings contrasted which those for Oatp1, which was homogeneously distributed in rat liver (Bergwerk et al., 1996; Abu-Zahra et al., 2000). Upon induction with phenobarbital, immunoreactive Oatp2 in the perivenous region increased disproportionately over the periportal region, and hepatocyte uptake of digoxin in phenobarbital treated rats was 4-fold greater than untreated rats, a finding that was consistent with increased Oatp2 expression (Hagenbuch et al., 2001). By contrast, the distribution of Oatp2 found by Western blots in our PP and PV cells and our digoxin transport studies revealed the homogeneous presence of Oatp2 in both PP and PV cells (Figs. 5 and 6). Moreover, confocal immunofluorescence microscopy revealed that Oatp2 was present in periportal, midzonal, and perivenous cells, although the presence was spotty and not contiguous (Fig. 6). All of the data suggest that Oatp2 is also present in the PP region. Moreover, the transport of digoxin, in absence or presence of inhibitors with freshly prepared PP and PV hepatocytes, was similar (Tirona et al., 2000). The extents of transport inhibition by various digoxin inhibitors among the rat zonal hepatocytes were also similar (Tirona et al., 2000). Equal extents of inhibition of digoxin uptake were observed with taurocholate, estradiol 17β-glucuronide, and bromosulfophthalein, Oatp1 or Oatp2 substrates as well as the diuretics bumetanide and ethacrynic acid in PP and PV hepatocytes; however, salicylate and tetraethylammonium, OAT, and organic cation transporter substrates, respectively, were devoid of effect (Tirona et al., 2000).

The hepatic transport of digoxin by PP and PV hepatocytes (Fig. 5) showed that the saturable transport system is of high affinity (Table 1); the K_m values were similar among PP and PV hepatocytes (P > 0.05), and these values are similar to that found for Oatp2 by Noé et al. (1997). Upon expression of the uptake data in terms of the V_max/K_m + nonsaturable clearance, the values of the summed uptake clearances of digoxin for both PP and PV hepatocytes are extremely rapid, averaging about 100 μl/min/mg protein (Table 1) or 12 ml/min/g liver (Table 4). The metabolic intrinsic clearance of digoxin, derived from the K_m (125 μM) and V_max (362 pmol/min/mg microsomal protein) for digoxin metabolism (Salphati and Benet, 1999), is 0.13 ml/min/g liver (using the scaling factor of 44.8 mg of microsomal protein per gram of liver), and is comparatively smaller. Because of the rapid exchange of digoxin between the sinusoid and hepatocyte at basolateral membrane (large CL_in and CL_ef), CL_int,sec, and CL_int,met or vascular binding are important determinants of digoxin hepatic clearance. The same may be speculated for the human liver in which the metabolic intrinsic clearance of digoxin is poor, and sinusoidal transport is likely very fast due to the lipophilicity of digoxin.

In terms of modeling of the transport, metabolic, and binding data, a simplified, mathematical relationship for CL_in, CL_ef, CL_liver,tot, CL_liver,ex, and CL_liver,met that encompasses vascular binding on organ clearance has been established for the well stirred model (Sirianni and Pang, 1997). However, it was shown the PBPK zonal model is more apt to reveal the influence of the determinants on clearance as well as heterogeneity factors, as found for enalapril removal (Abu-Zahra and Pang, 2000; Liu and Pang, 2005). The PBPK zonal model is also superior over the compartmental model to demonstrate the pertinent factors that influence the clearance of digoxin. For example, the PBPK zonal model showed that the differential flow rates in the rbc (Q = 0.811 ml/min/g) and KHB-perfused livers (Q = 3.58 ml/min/g) played a minor role in the clearance of digoxin, a low extraction drug. Based on simulations with the PBPK zonal model, vascular binding and not flow affected the kinetics of the digoxin (Fig. 13). Considering the large amounts of erythrocytes in blood, it is important to assess the effects of rbc binding/distribution on digoxin clearance (Hinderling, 1984). Because of the slow equilibrium time of digoxin between plasma and rbc (Fig. 9), red cell binding is slow and will affect the equilibration time of digoxin in liver. There was slow influx of digoxin from plasma to rbc (k_pr of 0.468 min^-1) and relative rapid efflux of digoxin from rbc to plasma (k′_rp of 1.81 min^-1). This was predicted in the unbound clearance (CL_liver,tot/f_b) versus time plot when the same parameters (forced fit) were used to simulate the amounts of Dg3 in perfusate and bile. The resultant simulated data revealed that a longer time was needed to reach the same asymptotic value for CL_liver,tot/f_b when rbc binding exists (simulation not shown).

Moreover, the PBPK zonal liver model better describes the heterogeneity in transporter and metabolic functions within the liver. The simulations showed general patterns for clearance estimates with heterogeneity in transporter, metabolic, and excretion activities (Table 6). The even distribution of transporters is optimal for the achievement of highest organ clearance, whereas transporter and intrinsic clearances of opposite distributions provide the poorest organ clearance. As expected, a greater overlap in influx transporter activity and the intrinsic clearance, either for metabolism or excretion, also provides a greater metabolism or excretion. The converse is also true. The lesser overlap in influx transporter activity and the intrinsic clearances brings about decreased metabolism or excretion (Table 6). The PBPK zonal model further addresses whether decreased inhibition of Pgp would evoke increased metabolism as well as total clearance of digoxin (Lau et al., 2004). From the present simulations which mimic the inhibition of Pgp (10% CL_int,sec), zonal heterogeneity cannot account for the observation of increased clearance, although it is expected that metabolism of Dg3 should increase. The trend paralleled that of Liu and Pang (2005) who also examined these relations in a simplified, PBPK model. The clearance of Dg3 would increase when the Pgp inhibitor further decreased the basolateral efflux (Fig. 14). This type of investigation, including both transport and enzyme heterogeneity (Abu-Zahra and Pang, 2000), is quantitative in revealing the determinants of clearance and the nature of competitive pathways. These concepts are universal in predicting the changes in metabolism and excretion which are competing pathways among elimination organs. Although there are the usual recognizable species differences between rat and man in terms of the transport and metabolism of digoxin in the liver (Doherty and Perkins, 1962; Wirth and Frolich, 1974), the poor hepatic clearance and metabolism, the red cell and albumin binding, and the high lipophilicity suggest a similar role of red cell and albumin binding on the hepatic clearance of digoxin in human.

Appendix A

Two-Compartment Model with Elimination from Central Compartment

For the rate of change of Dg3 in compartment 1,

For the rate of change of Dg3 in compartment 2,

For the cumulative amount of Dg3 excreted into bile,

For the cumulative amount of Dg3 metabolized,

Two-Compartment Model with Elimination from the Peripheral Compartment

For the rate of change of Dg3 in compartment 1,

For the rate of change of Dg3 in compartment 2,

For the cumulative amount of Dg3 excreted into bile,

For the cumulative amount of Dg3 metabolized,

Appendix B

Mass Balance Equations of the PBPK Zonal Liver Model That Described the Disposition of Dg3 in rbc-Albumin Rat Liver Preparations (Fig. 4B) with Even Distribution of CL_int,met

For the rate of change of Dg3 in reservoir (whole blood, rbc, or plasma),

For the rate of change of Dg3 in zone 1 (rbc, plasma, or liver tissue),

For the rate of change of Dg3 in zone 2 (rbc, plasma, or liver tissue),

For the rate of change of Dg3 in zone 3 (rbc, plasma, or liver tissue),

For the cumulative amount of Dg3 excreted into bile,

For the cumulative amount of Dg2 metabolized,