Introduction

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It is important to predict hepatic metabolic clearance in humans because many drugs are eliminated from the body by metabolism in the liver. Rane et al. (1977) and Wilkinson (1987) introduced the approach to predict the in vivo metabolic clearance of drugs in rats from in vitro metabolism data obtained by using rat liver microsomes and/or hepatocytes based on pharmacokinetic models in which physiological and biochemical parameters such as Q_h and f_b are considered. In addition, it has already been reported that the aforementioned approach is suitable for many compounds metabolized by cytochrome P-450 (Sugiyama et al., 1988; Houston, 1994). We previously reported that this approach can be applied not only to rats but also to dogs and humans under linear conditions using (S)-(-)-2,8-dimethyl-3-methylene-1-oxa-8-azaspiro [4,5] decane-L-tartrate monohydrate (YM796) which is being developed as a drug to treat dementia (Iwatsubo et al., 1997c).

Some drugs such as propranolol exhibit nonlinear kinetics in vivo in humans even at therapeutic doses (Ludden, 1991). It is therefore important to establish a method with which the nonlinear metabolism of drugs can be predicted based on the in vitro data. The quantitative prediction of nonlinear hepatic metabolism is complicated, particularly for orally administered drugs, because the time profiles for the drug concentration in the portal vein varies as a function of k_a. In our study, we propose a method to predict the nonlinear hepatic availability of orally administered drugs from the in vitro metabolism data; based on a dispersion model, which is superior to well-stirred or parallel tube models for the prediction of F_h for compounds with high extraction ratio (Iwatsubo et al., 1997a). We could successfully predict the nonlinearity in the oral bioavailability by considering the k_a and metabolic parameters. As a model compound, we used YM796, because the kinetic parameters for the hepatic microsomal metabolism have been determined in vitro in rats, dogs and humans. In our study, AUC_oral values of YM796 in these animal species were predicted based on the in vitro data and compared with those obtained in vivo to examine the predictability under nonlinear conditions.

	Materials and Methods

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Chemicals and reagents. YM796 was synthesized in Yamanouchi Pharmaceutical Co., Ltd (Tokyo, Japan). Other reagents of analytical grade were purchased from Wako Pure Chemical Industries, Ltd (Osaka, Japan).

Plasma concentrations of YM796 in rats, dogs and humans. The doses used in the present study were 3.0 and 10.0 mg/kg for rats and dogs (n = 3), and 10, 20, 40 and 60 mg/subject for humans (n = 5 or 6). For human studies, healthy male volunteers were recruited and the study was carried out in the Kitasato University School of Medicine. The protocol had been approved by the Institutional Review Board of the university and written consent had been obtained from each subject prior to the study. Plasma concentration of YM796 in each species was determined according to the method reported previously (Iwatsubo et al., 1997c). At specified times after administration, blood specimens were collected. After centrifugation, plasma was separated and stored at -20°C until analysis. YM796 was extracted from plasma by liquid-liquid extraction and injected into a gas chromatography tandem mass spectrometry system (Iwatsubo et al., 1997c). The AUC values were calculated from the plasma concentration-time curves by the trapezoidal rule.

Prediction of dose-dependence in the bioavailability (F) or AUC_oral of YM796 in rats, dogs and humans from in vitro metabolic data. A simulation was carried out based on the dispersion model to predict the dose-dependent F_h using the kinetic parameters previously obtained from in vitro studies (Iwatsubo et al., 1997b, c). For the hepatic metabolism of YM796, a single saturable component was assumed for rats, although two saturable components and a single nonsaturable component were postulated for dogs and humans. The nonlinear dispersion model, therefore, can be given by equation (1) for rats and equation (2) for dogs and humans.

(1)

(2)

where D represents the axial dispersion coefficient which characterizes the degree of mixing or axial dispersion of a drug entering the portal vein, z represents the axial coordinate in the liver, C represents the concentration of solute at a distance z from the inlet to the liver, V_B represents the volume of blood space in the liver, V_h represents the apparent volume of distribution in the liver, v represents the linear velocity of blood in the liver (= Q_h/A = Q_hL/V_B), Q_h represents the hepatic blood flow rate, A represents the vertical area of the hepatic sinusoid, L represents the length from the inlet to the outlet of the liver, f_p represents the unbound fraction of YM796 in plasma and R_B represents the blood-to-plasma concentration ratio of YM796. Equations (1) and (2) can be restated in dimensionless terms,

(3)

(4)

where C_N = C/(dose/V_h), T = t/(V_h/Q_h), Z = z/L, D_N = D/(vL) = D/(LQ_h/A), K_mN = K_m/(dose/V_h), V_maxN = V_max/(Q_h·dose/V_h) and CL_nsN = CL_ns/Q_h. The initial and boundary conditions are given by equation (5).

(5)

where k_aN = k_a/(Q_h/V_h) and k_a represents the first-order absorption rate constant after oral administration. The K_m and V_max values for rats were 13.4 µM and 520 nmol/min/g liver. The K_m1, K_m2, V_max1, V_max2 and CL_ns values were 8.1 µM, 890 µM, 10.9 nmol/min/g liver, 570 nmol/min/g liver and 0.65 ml/min/g liver, respectively, for dogs, and 1.7 µM, 650 µM, 1.3 nmol/min/g liver, 79 nmol/min/g liver and 0.06 ml/min/g liver, respectively, for humans (Iwatsubo et al., 1997b, c). The f_p and R_B values were 0.694 and 1.10 for rats, 0.707 and 1.07 for dogs, and 0.700 and 1.11 for humans, respectively (Iwatsubo et al., 1997c). A Q_h value of 0.95 ml/min/g liver (Bischoff et al., 1971; Dedrick et al., 1973; Montandon et al., 1975) and a D_N of 0.17 (Roberts and Rowland, 1986; Iwatsubo et al., 1997b, c) were used. The V_h value was estimated to be 1.5 ml/g liver based on the f_p and R_B mentioned above and the unbound fraction of YM796 in the tissue (f_T = 0.41) obtained using isolated rat hepatocytes (V_h = f_p/R_B/f_T). In the calculation of outflow concentrations of YM796 from the liver, rapid equilibrium of the drug between blood and hepatocytes and the absence of any active transport of the drug through the sinusoidal membrane were assumed so that the unbound concentrations of the drug in the liver were equal to those in blood at any point throughout the liver. By solving partial differential equation (3) or (4) numerically with the Napp based on the finite difference method (Hisaka et al., 1994), the time profile of unchanged drug concentrations (C) at a distance of z from the inlet of the liver was obtained. The drug concentrations at the outlet from the liver (hepatic vein) were integrated from time zero to infinity to obtain the AUC. Then, the calculated AUC was multiplied by the Q_h to obtain the total amount of unchanged drug that entered the circulating blood. Finally, the F_h was calculated by dividing the aforementioned amounts by the dose.

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

Effects of the absorption rate of YM796 on bioavailability (F) in rats. The apparent absorption rate after oral administration of a drug is considered to be rate-determined by GE when its absorption through the intestinal membrane is rapid, unless it is absorbed directly from the stomach. The GE process is known to be described by the first-order kinetics and its rate constant has been reported to be approximately 0.1 min¹ for humans (Oberle et al., 1990). Based on these considerations, F values were simulated by the aforementioned method as a function of k_a with the maximum value of 0.1 min¹.

	Results

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Plasma concentrations of YM796 in rats, dogs and humans. All parameters obtained from the plasma concentration-time profiles after oral doses of YM796 in rats, dogs and humans are summarized in table 1. The previously reported parameters at the lowest dose for rats, dogs and humans (Iwatsubo et al., 1997b, c) are also shown in table 1 for comparison. Plasma concentrations of the unchanged drug reached a maximum at 0.50, 0.50 and 0.08 hr after oral administration of YM796 at doses of 1, 3 and 10 mg/kg, respectively in rats (fig. 1). In dogs and humans, the T_max values were slightly greater being .5~1.3 hr and 1.2~2.0 hr, respectively (figs. 1 and 2). Both C_max and AUC_oral were increased almost in proportion to the dose indicating linear pharmacokinetics both in dogs and humans (figs. 1 and 2). The AUC_oral normalized by the dose (AUC_oral/dose) remained almost constant at 87.7~105×10⁶ hr/ml·kg in dogs and 1260~1768×10⁶ hr/ml·kg in humans, respectively, although in rats, the AUC_oral/dose was increased markedly from 5.0×10⁶ to 33×10⁶ hr/ml·kg as the dose increased (fig. 3). Similarly, a marked increase in F from 3.4 to 22.3% was also observed in rats when the dose was increased, whereas F remained almost constant at 16.1×19.0% irrespective of dose in dogs (fig. 3).

View larger version (19K): [in this window] [in a new window]   Fig. 1.   Plasma concentration time profiles of YM796 after oral administration in rats and dogs. Each point represents the mean ± S.D. of three animals. : 1 mg/kg; : 3 mg/kg and : 10 mg/kg.

View larger version (22K): [in this window] [in a new window]   Fig. 2.   Plasma concentration time profiles of YM796 after oral administration in humans. Each point represents the mean ± S.D. of five or six subjects. : 5 mg/body; : 10 mg/body; : 20 mg/body; : 40 mg/body and : 60 mg/body.

View larger version (12K): [in this window] [in a new window]   Fig. 3.   Dose-dependence of observed bioavailability (A) and AUCoral/dose of YM796 in rats, dogs and humans. Each point represents the mean ± S.D. of three animals for rats and dogs and 5~6 subjects for humans. : bioavailability or AUCoral/dose in rats; : bioavailability or AUCoral/dose in dogs and : AUCoral/dose in humans.

Effects of the absorption rate of YM796 on bioavailability (F) in rats. The F values of YM796 at each dose, simulated using the previously obtained in vitro metabolism parameters for rats, are shown in figure 4. The F value at a high dose (10 mg/kg) was markedly affected by a change in k_a from 0 to 0.1 min¹ and was found to be 3.2~28.4%, although no pronounced change in F was observed at low doses (1 and 3 mg/kg) if the k_a was changed. When k_a was 0.1 min¹ (the maximum value), the predicted F values at the dose of 1, 3 and 10 mg/kg were estimated to be 5.0, 7.7 and 28.4%, respectively. With a k_a of 0.07 min¹, the predicted values of F were 4.8, 6.3 and 23.4%, comparable with those obtained in vivo (3.4, 5.0 and 22.3%) at each dose.

View larger version (14K): [in this window] [in a new window]   Fig. 4.   Effects of the absorption rate on bioavailability of YM796 in rats. The solid lines are the simulation curves of in vivo bioavailability after oral dose at 1, 3 and 10 mg/kg of YM796 calculated from the parameters obtained in vitro based on the dispersion model assuming the first-order absorption. In the calculation, a dispersion number (DN) of 0.17, the unbound fraction of YM796 in plasma (fp) of 0.7 and the hepatic blood flow (Qh) of 0.95 ml/min/g liver were used.

Prediction of dose-dependence in the bioavailability (F) or AUC_oral of YM796 in rats, dogs and humans from in vitro metabolic data. Because the predicted F values were most similar to those in vivo if k_a was 0.07 min¹ in rats, prediction of the dose-dependence of F and AUC_oral in all animal species was attempted by using the metabolism parameters (K_m, V_max) obtained from the in vitro studies and a k_a value of 0.07 min¹. The predicted AUC_oral values after oral administration of 1, 3 and 10 mg/kg YM796 to rats and dogs were 5.5, 31.1 and 412, and 94.2, 323 and 1143 ng·hr/ml, respectively, which were comparable with the in vivo values in both animal species (5.0, 22.2 and 333, and 87.7, 316 and 1041 ng·hr/ml for rats and dogs, respectively) (fig. 5). Similarly, the predicted values of AUC_oral in humans (130, 201, 532, 1539 and 2197 ng·hr/ml) were also comparable with those observed in vivo (117, 180, 408, 1010 and 1482 ng·hr/ml) after oral administration of YM796 at doses of 5, 10, 20, 40 and 60 mg/subject, respectively, although the AUC_oral values at higher doses were overestimated to some extent (fig. 5). In addition, the F values in rats and dogs at each dose from in vitro metabolism data were successfully predicted. The predicted F in humans was 71.7~81.0% which was larger than that in rats and dogs and was not as markedly affected by dose.

View larger version (15K): [in this window] [in a new window]   Fig. 5.   Comparison of the predicted values and the observed values for AUCoral (A) or bioavailability (B) of YM796 in rats, dogs and humans. The solid lines represent the predicted curves based on the kinetic parameters obtained from the in vitro metabolism studies reported previously (Iwatsubo et al., 1997b, c). In the calculation, a dispersion number (DN) of 0.17, the unbound fraction of YM796 in plasma (fp) of 0.7, the hepatic blood flow (Qh) of 0.95 ml/min/g liver and ka of 0.1 min were used. Each point represents the mean ± S.D. of three experiments. : observed data for rats; : observed data for dogs and : observed data for humans.

	Discussion

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As shown in figure 3, AUC_oral of YM796 normalized by the dose (AUC_oral/dose) was found to be almost constant irrespective of the dose in dogs and humans, whereas in rats it increased markedly from 5.0×10⁶ to 33×10⁶ hr/ml·kg as the dose increased. As a consequence, F in rats was determined as low as 3.4% at the low dose and increased markedly as the dose increased, whereas F in dogs was also almost constant (16~19%) independent of dose. F is given as the product of 1) F_a, 2) F_g and 3) F_h. Considering the facts that approximately 92% of the radioactive dose was recovered in urine and bile after oral administration of ¹⁴C-YM796 (0.5 mg/kg) to rats and that the fraction of unchanged YM796 absorbed from the intestinal tract after administration of 1 mg/kg of YM796 into the rat intestinal loop was 88% (Iwatsubo et al., 1997c), the marked first-pass metabolism in the liver [factor 3)] should be the predominant factor to account for the low F in rats at a low dose, and the nonlinearity in F may be ascribed to saturation of first-pass metabolism in liver.

Furthermore, figure 4 shows that F at a high dose (10 mg/kg) was markedly changed (3.2~28.4%) by the increase in k_a, whereas no pronounced change in F was observed at low doses (1 and 3 mg/kg) by changing k_a values. These results may be accounted for by considering that the unbound YM796 concentrations in the portal vein become greater than the K_m value as k_a increases at the dose of 10 mg/kg, whereas at the 1 and 3 mg/kg doses, they are less than K_m even when k_a is 0.1 min¹. Indeed, the maximum concentrations of unbound YM796 in the portal vein were estimated by computer simulation [equations (3) and (5)] to be 3.8, 11.4 and 38.0 µM at the doses of 1, 3 and 10 mg/kg, respectively, when k_a was 0.1 min¹.

The F values of YM796 in humans predicted from the in vitro metabolism data were as high as 72~81%, and no marked nonlinearity in AUC_oral was predicted at doses of 5 to 60 mg/man. Indeed, no nonlinearity in F and/or oral clearance (dose/AUC_oral) was observed in humans in vivo (figs. 3 and 5; table 1), although the K_m value for the high-affinity component estimated previously from the in vitro studies with liver microsomes was lowest in humans (rat: 13.4 µM, dog: 8.1 µM, human: 1.7 µM) and the maximum concentration of unbound YM796 in the portal vein was estimated to be 4.1 µM at the highest dose (60 mg/man) when k_a was assumed to be 0.07 min¹. For this reason, the following possibilities can be considered.

1)The maximum plasma unbound concentrations of YM796 in circulating blood at the highest dose in rats, dogs and humans were calculated to be 568, 395 and 186 ng/ml (1.6, 1.1 and 0.53 µM), respectively, taking into account the unbound fraction in the plasma of each species (0.694, 0.707, 0.700). Because these values were lower than the K_m values for the high-affinity component in each species (13.4, 8.1 and 1.7 µM, respectively, Iwatsubo et al., 1997b, c), the elimination of YM796 entering the circulating blood, after the first-pass through the liver after oral administration, can be assumed to be linear.

2)Because the V_max of the high-affinity component for humans was approximately 1/450 that of rats and 1/9 that of dogs, the hepatic intrinsic clearance (V_max/K_m) was also the lowest among the species studied. Therefore, the predicted F value for humans was close to unity (0.72~0.81) so that the hepatic availability was not considered to change very much even when saturation of the first-pass metabolism in liver occurs. For these reasons, no pronounced nonlinearity in the oral clearance should have been observed in humans despite the low K_m value.

For dogs, the maximum concentration of unbound YM796 in the portal vein was estimated to be 34.7 µM at the highest dose (10 mg/kg) when k_a was 0.07 min¹. This value was greater than the K_m value for the high-affinity component but much less than that for the low-affinity one. At this concentration, the intrinsic metabolic clearances for the high-affinity component, low-affinity component and nonsaturable component were 0.255, 0.616 and 0.650 ml/min/g liver, and the latter two components primarily contributed to the metabolism of YM796. This may be why no nonlinearity in F and/or oral clearance (dose/AUC_oral) was also observed in dogs (figs. 3 and 5; table 1).

In this way, the method for prediction used in our study seems useful to guide the development of a new drug in its preclinical stages and help one decide whether to conduct clinical studies with a drug when F in experimental animals has been found to be low.

Furthermore, this method of prediction may be used in the dose escalation in the clinical studies. The dose escalation is often performed with reference to the AUC or C_ss which produces the desired pharmacological effect and is predicted from preclinical studies using animals and/or in vitro metabolism studies. In the case where AUC and C_ss change in a nonlinear manner as the dose increases, it is difficult to find the appropriate dose for the pharmacological effect and much more care is required when carrying out dose escalation studies. Even when nonlinear metabolism is observed, our study suggests that the quantitative prediction of in vivo pharmacokinetics after oral administration of a drug based on the parameters obtained from in vitro metabolism studies is possible (fig. 5). Such prediction of pharmacokinetic parameters under nonlinear conditions will make it possible to increase the dose more safely and efficiently to obtain the desired pharmacological effect.

In conclusion, the predictability of the AUC_oral and F of YM796 from in vitro data was good for all species suggesting that, even when nonlinear metabolism is observed, quantitative prediction of in vivo pharmacokinetics after oral administration of a drug is possible using the parameters obtained from in vitro metabolism studies, taking into consideration the rate of drug absorption into the portal vein.