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DRUG METABOLISM AND DISPOSITION
Copyright © 2000 by The American Society for Pharmacology and Experimental Therapeutics
DMD 28:577–581, 2000 /1795/819954
Vol. 28, No. 5
Printed in U.S.A.
ANALYSIS AND PREDICTION OF ABSORPTION PROFILE INCLUDING HEPATIC
FIRST-PASS METABOLISM OF N-METHYLTYRAMINE, A POTENT STIMULANT OF
GASTRIN RELEASE PRESENT IN BEER, AFTER ORAL INGESTION IN
RATS BY GASTROINTESTINAL-TRANSIT-ABSORPTION MODEL
TOSHIKIRO KIMURA, NORIO IWASAKI, JUN-ICHI YOKOE, SHUNJI HARUTA, YOSHIAKI YOKOO, KEN-ICHI OGAWARA,
KAZUTAKA HIGAKI
AND
Department of Pharmaceutics, Faculty of Pharmaceutical Sciences, Okayama University, Okayama (T.K., N.I., J.Y., S.H., K.O., K.H.); and
Technical Development Department, Suntory Ltd., Osaka (Y.Y.), Japan
(Received September 20, 1999; accepted January 14, 2000)
This paper is available online at http://www.dmd.org
The prediction method for the plasma concentration-time profile of
N-methyltyramine (NMT), a potent stimulant of gastrin release
present in beer after oral ingestion in rats was examined using the
previously developed Gastrointestinal (GI)-Transit-Absorption
Model, with the addition of a process of hepatic first-pass metabolism. Phenol red was used as a nonabsorbable marker for estimation of the GI transit rate constant for eight segments in the GI
tract. The first order absorption rate constant for each segment
was estimated by means of a conventional in situ closed loop
method. The results of in situ absorption experiments showed that
NMT is well absorbed in the small intestine, especially in the
duodenum and jejunum. Using the GI-Transit-Absorption Model, it
was demonstrated that more than 90% of orally ingested NMT is
absorbed in the small intestine, and that the substantial absorption
site for NMT in vivo is the lower jejunum and the ileum. However,
the observed bioavailability was only 39.0%. The in vitro metabolism study clarified that NMT is metabolized in the liver, but not in
the small-intestinal mucosa. With the hepatic intrinsic clearance
value (2.0 liters/h) calculated from the rate of metabolism in vitro,
the hepatic availability was estimated to be 0.510 on the basis of a
well stirred model, which was validated by two other methods to
calculate the hepatic availability of NMT. The plasma concentration-time curve and bioavailability of NMT after oral ingestion were
well predicted by the GI-Transit-Absorption Model with the hepatic
first-pass metabolism process.
Oral administration is one of the most convenient methods for drug
administration. Therefore, it is very important to be able to estimate
and predict the absorption behavior after oral administration. The
gastrointestinal (GI)1 absorption of orally administered drugs is determined not only by the permeability of GI mucosa but also by the
transit rate (residence time) in the GI tract. Because the difference in
the absorbability of drugs in each segment is found for several drugs
(Patel and Kramer, 1986; Tukker and Poelma, 1988), the drug amount
in each segment during the intestinal transit should be largely responsible for drug absorption. However, there have been few attempts to
analyze and predict the absorption behavior of drugs in the GI tract,
considering the site difference in drug absorbability. We have devel-
oped a novel method, the GI-Transit-Absorption Model, based on GI
transit kinetics for estimation of the absorption profiles of drugs
administered orally as an aqueous solution (Sawamoto et al., 1997).
The validity and utility of the prediction method have been demonstrated for model drugs with different absorption characteristics in
rats.
In this study, we tried to analyze the absorption kinetics of Nmethyltyramine (NMT; Fig. 1), and to predict its plasma concentration-time profile by the GI-Transit-Absorption Model. Because NMT
is a potent stimulant of gastrin release present in beer (Yokoo et al.,
1999), it is important to clarify and predict the absorption behavior of
NMT to investigate the actual role of NMT in the release of gastrin.
Furthermore, as NMT was found to be subject to first-pass metabolism, a process of hepatic first-pass metabolism was introduced to the
GI-Transit-Absorption Model to predict the plasma concentrationtime profile and the bioavailability of NMT.
1
Abbreviations used are: GI, gastrointestinal; NMT, N-methyltyramine; ki, transit rate constant; kai, absorption rate constant; Fa, fraction absorbed; AUCra, area
under the absorption rate-time curve; CLint,h, hepatic intrinsic clearance; Fh,
hepatic availability; Qh, hepatic (portal) blood flow; fp, unbound fraction in plasma;
RB, blood-to-plasma concentration ratio.
Send reprint requests to: Prof. Toshikiro Kimura, Department of Pharmaceutics, Faculty of Pharmaceutical Sciences, Okayama University, 1-1-1 Tsushimanaka, Okayama 700-8530, Japan. E-mail: [email protected].
ac.jp
Experimental Procedures
Materials. NMT was supplied by Suntory Ltd. (Osaka, Japan), and phenylephrine (Sigma Chemical Co., St. Louis, MO) was obtained commercially.
Other chemicals and reagents were analytical grade commercial products.
Animals. Male Wistar rats weighing from 230 to 270 g were fasted for 24 h
before and during the experiment, but were allowed free access to water. Our
investigations were performed after approval by our local ethical committee at
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ABSTRACT:
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KIMURA ET AL.
where Qh, fp, RB and CLint,h represent hepatic (portal) blood flow, unbound
fraction in plasma, blood-to-plasma concentration ratio, and hepatic intrinsic
clearance, respectively. CLint,h was calculated using the following equation:
CLint,h ⫽ CLh (ml/h/mg protein)
FIG. 1. Chemical structure of NMT.
⫻ protein amount in the 1000g supernatant (mg/g liver)
Fh ⫽
Qh
Q h ⫹ f p/R B 䡠 CLint,h
(1)
⫻ liver weight (g)
Mean values of protein in the 1000g supernatant and liver weight were
151.12 mg/g liver and 9.68 g, respectively.
Determination of Plasma Protein Binding. A 10-␮l aliquot of phosphatebuffered isotonic solution containing NMT was added to a 1-ml aliquot of rat
plasma to give a concentration of 1 ␮g/ml. After incubation for 30 min at 37°C,
a 50-␮l aliquot was taken to measure the total plasma concentration, and the
remainder was transferred to an ultrafiltration tube (MPS-1; Amicon Co.,
Tokyo, Japan). The tubes were centrifuged for 5 min at 1000g, and NMT
concentration in the filtrate was determined as the unbound plasma concentration.
Determination of RB. The RB of NMT was determined using heparinized
whole blood. Aliquots (10-␮l) of phosphate-buffered isotonic solution containing NMT were added to 490-␮l aliquots of rat blood preincubated at 37°C
to give concentrations of 10, 20, and 50 ␮M. After incubation for 5 min at
37°C, the blood samples were centrifuged for 5 min at 1500g, and the plasma
concentration was measured. The RB value was calculated using the hematocrit
value of 0.458 (n ⫽ 4).
Analytical Methods. NMT concentration was determined by HPLC with an
electrochemical detector. An equal volume of methanol was added to the
plasma sample to deproteinize the sample. The HPLC system consisted of a
pump (LC-6A; Shimadzu, Kyoto, Japan), a column (4.6 mm i.d. ⫻ 150 mm)
packed with Capcell Pak C18 (5 ␮m; Shiseido, Tokyo, Japan), and an electrochemical detector (ECD-120; Sekisui Chemical Co., Tokyo, Japan). The
applied voltage was set at 750 mV. The degassed mobile phase consisted of
phosphate buffer (0.1 M, pH 6.0) containing EDTA (5 mg/ml) and 1-octansulfonic acid (500 mg/l)/methanol (4:1, v/v), and the flow rate was 1.0 ml/min.
The internal standard was phenylephrine. For quantitative calculations, a
Shimadzu C-R6A data module was used. Protein concentration was determined by the method of Lowry et al. (1951), using BSA as a standard.
Statistical Analysis. Statistical significance was evaluated using ANOVA.
Results are expressed as mean ⫾ S.E. of more than three experiments.
Results
The permeability of GI mucosa to NMT was examined by an in situ
closed loop method, and it was clarified that the absorption from each
segment follows the first order kinetics. In addition, no concentration
dependence of the kai value was observed in the range of initial
concentration used in this study, except in the lower jejunum (Table
1). As is evident from the table, the permeability in the stomach and
the cecum is relatively small, and this compound seems to be absorbed
mainly from the small intestine. The site specificity in the small
TABLE 1
GI-transit rate constants (ki, h⫺1) and absorption rate constant (ka , h⫺1) of NMT for each segment in rats
Data are cited from Sawamoto et al. (1997). The ki value for each segment was obtained from the fitting of the experimental data to GI-Transit-Kinetic Model. The kai value for each
segment was obtained from conventional in situ loop studies. Results are shown as the mean ⫾ S.E. with the number of experiments in parentheses.
Parameter
Stomach
ki (h⫺1)
0.1 mg/mlb
2.031
—c
1.0 mg/mlb
kai
10 mg/mlb
0.105
⫾0.031 (6)
—c
Mean
0.105
Duodenum
Upper Jejunum
Lower Jejunum
Upper Ileum
Lower Ileum
Cecum
28.748
1.640
⫾0.248 (7)
1.362
⫾0.156 (6)
1.394
⫾0.082 (3)
1.466
18.066
1.531
⫾0.252 (9)
1.160
⫾0.048 (6)
1.249
⫾0.079 (3)
1.313
4.206
2.116
⫾0.171 (6)
1.411*
⫾0.094 (6)
0.628**
⫾0.031 (3)
1.385
1.162
0.899
⫾0.149 (3)
1.079
⫾0.101 (6)
1.234
⫾0.133 (6)
1.071
0.464
1.134
⫾0.220 (3)
1.359
⫾0.084 (8)
0.910#
⫾0.123 (3)
1.134
—a
—c
0.291
⫾0.082 (6)
—c
0.291
Statistically significant differences are indicated as follows: *P ⬍ .01; **P ⬍ .001 (compared with 0.1 mg/ml); #P ⬍ .05 (between 1.0 and 10 mg/ml). aNot calculated. b Initial concentration
in absorption experiments. c Not examined.
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Okayama University and in accordance with Interdisciplinary Principles and
Guidelines of the Use of Animals in Research.
Determination of Absorption Rate Constant (kai) for Each Segment (i).
The absorption experiments were performed for each segment by a conventional in situ closed loop method (Schanker et al., 1957; Kakemi et al., 1970).
Whole GI tract was divided into eight segments, i.e., stomach, duodenum,
upper jejunum, lower jejunum, upper ileum, lower ileum, cecum, and large
intestine. Each size (length) was as follows: stomach (whole organ), duodenum, ca. 6 cm; upper and lower jejunum, ca. 20 cm; upper and lower ileum,
ca. 20 cm; cecum (whole organ), large intestine (colon to anus). Initial
concentrations of NMT were 0.1, 1.0, and 10 mg/ml, pH 6.5, and the first order
absorption rate constant was estimated by the rate of the disappearance from
each segment at 30 min.
In Vivo Oral, i.v., and Intraportal Administration Studies. Under ether
anesthesia, the right femoral artery of rats was cannulated with vinyl tubing
(i.d., 0.5 ⫻ 0.8 mm; Dural Plastics and Engineering, Dural, Australia) for
collecting the blood samples. In the case of oral administration, the solution of
NMT was administered intragastrically at the dose of 20 mg/2.5 ml/kg. For i.v.
administration, NMT solution was administered into the left femoral vein at the
dose of 10 mg/ml/kg. The dosed rats were kept in restraining cages, with free
access to water. Intraportal administration was performed after opening the
abdomen under urethane anesthesia. The i.v. administration study was carried
out under the same conditions as the intraportal administration study after
sham operation. Blood samples were periodically taken from the cannulated
femoral artery.
Prediction of Absorption Kinetics, Transit Kinetics, and Plasma Concentration-Time Profile of Orally Administered NMT. These predictions
were performed by the convolution method using the GI-transit rate constant
(ki) and kai in each segment, based on the GI-Transit-Absorption Model (see
Appendix) (Sawamoto et al., 1997).
Determination of Metabolic Clearance of NMT. The rates of metabolism
of NMT in the homogenates of rat small-intestinal mucosa and liver were
estimated in vitro. Whole homogenates of small-intestinal mucosa and liver
were prepared with 4 volumes of pH 7.4 phosphate-buffered isotonic solution.
After centrifugation at 1000g for 5 min, the supernatant fraction was used for
the experiments. NMT (initial concentration: 0.01, 0.1, 1.0, and 5.0 mM) was
incubated with the supernatant at 37°C. The metabolic reaction was stopped by
the addition of methanol, and the rate of metabolism was estimated by the
disappearance of incubated NMT in 30 min. Hepatic availability (Fh) was
calculated according to the following equation reported by Rane et al. (1977):
(2)
PREDICTION OF ABSORPTION PROFILE OF N-METHYLTYRAMINE
FIG. 2. Calculated amount of NMT in each segment of GI tract after oral
administration in rats.
intestine is not so predominant, but the permeability in the duodenum
and jejunum is slightly larger than that in the ileum.
Figure 2 shows the time course of NMT amount (percentage of the
dose) available for absorption (Xi-time profile) in each GI segment
after oral administration, which was calculated by using the mean
values of kai and ki determined previously (Table 1). Although nonlinearity of NMT absorption was found only in the lower jejunum, we
used the mean kai values of 0.1, 1, and 10 mg/ml for the following
calculation because of small difference in kai and convenience for
calculations. This figure gives the information about the drug amount
remaining in each segment and its transit from the stomach through
the cecum. As can be seen from the figure, NMT is well absorbed in
the small intestine and only about 7% of the dose reaches the cecum.
Pharmacokinetic parameters for these curves are summarized in Table
2. Figure 3 shows the absorption rate-time profiles for NMT calculated from the Xi-time profiles (Fig. 2) and kai values (Table 2). Just
after administration, the main absorption sites might be stomach,
duodenum, and upper jejunum. After that, lower jejunum, upper
ileum, and lower ileum are mainly in charge of absorption of NMT,
dependent on time after dosing. The area under the absorption ratetime curve (AUCra) gives the fraction absorbed (Fa) in each segment;
the values are shown in Table 2. Although the kai for NMT is largest
in the upper jejunum, the contribution of this region to the total
absorption in vivo is small, and the substantial absorption sites in vivo
are from lower jejunum to lower ileum.
Prediction of the plasma concentration of orally administered NMT
was performed by means of the convolution method. The total absorption rate-time data and pharmacokinetic parameters after i.v.
administration correspond to the input and weight functions, respectively. Plasma concentrations Cp of NMT after i.v. administration
were expressed as Cp ⫽ 152.7e⫺190.15t ⫹ 11.8e⫺25.45t at the dose of
10 mg/kg. The dotted line in Fig. 4 shows the predicted plasma
concentration-time curve for NMT after oral administration at the
dose of 20 mg/kg. From the AUC of this curve, the Fa value was
estimated to be 0.974. The “predicted” curve showed a higher plasma
concentration than the “observed” curve, suggesting that NMT might
be subject to first-pass metabolism or presystemic elimination in the
small intestine and/or liver.
To investigate the first-pass metabolism of NMT, the in vitro
experiments using homogenate of rat small-intestinal mucosa and
liver were examined. The marked metabolism of NMT in the liver was
observed, but the metabolism in the small-intestinal mucosa was
negligible (93.5 ⫾ 4.9% remaining after 30-min incubation at the
concentration of 0.1 mM), suggesting that the first-pass metabolism of
NMT would occur mainly in the liver. Kinetic study on the hepatic
metabolism showed the linearity of its metabolism in the range of
initial concentration used in this study (Fig. 5) and the CLint,h was
calculated to be 2043 ⫾ 55 ml/h.
To obtain the Fh according to eq. 1, we determined fp (0.423 ⫾
0.003) and RB (1.53 ⫾ 0.08). We cited Qh, 588 ml/h, from a reference
(Davies and Morris, 1993). Using these parameters, including CLint,h,
the Fh value was calculated to be 0.510. To confirm the validity of Fh
obtained above, Fh for NMT was also estimated from the difference
in AUC of plasma concentration between after i.v. injection (AUCi.v.)
and intraportal vein injection (AUCi.p.). Because the abdomen was
incised for intraportal vein injection, AUCi.p. (1.78 ␮g/ml 䡠 h) were
compared with AUCi.v. (4.19 ␮g/ml 䡠 h) after i.v. injection in rats with
abdominal incision at a dose of 10 mg/kg. AUCi.p./AUCi.v. gave an Fh
value of 0.425, which is close to the Fh in the in vitro study.
By introducing the Fh value into the GI-Transit-Absorption Model,
the plasma concentration-time profile for orally administered NMT
was predicted again. The GI-Transit-Absorption Model with the hepatic first-pass metabolism process (solid line, Fig. 4) predicted the
plasma concentration-time curve of NMT after oral administration
very well.
Discussion
The GI-transit rate, in addition to the permeability of GI mucosa, is
an important factor to determine the absorption kinetics of orally
administered drugs. We have developed a novel method based on GI
transit kinetics for estimation of the absorption profiles of drugs
administered orally as an aqueous solution (Sawamoto et al., 1997).
The validity and utility of the prediction method have been demonstrated for model drugs with different absorption characteristics without first-pass metabolism in rats. In this study, we tried to predict the
plasma concentration-time profile and bioavailability of NMT. It is
known that alcoholic beverages produced by alcoholic fermentation,
but not by distillation, contain powerful stimulants of gastric acid
secretion (Teyssen et al., 1997). NMT has recently been isolated from
beer and determined as a potent stimulant (Fig. 1) (Yokoo et al.,
1999). Therefore, the clarification and the prediction of its absorption
kinetics is important to estimate the pharmacological effect of NMT.
The permeability of each GI segment to NMT, estimated by the in
situ closed loop technique (Table 1), indicated that this compound is
absorbed mainly from the small intestine and that permeability to
NMT is largest in the duodenum and jejunum (Table 1). However, the
contribution of this region to the total absorption in vivo is found to
be small according to the Fa values we calculated (Table 2). The
substantial absorption sites in vivo were suggested to be the regions
from lower jejunum to lower ileum (Fig. 3; Table 2). Those regions,
having values comparable to ka, have longer residence times than
duodenum and upper jejunum, which should be responsible for the
substantial absorption. This is almost the same as the in the case of
cephalexin reported previously (Sawamoto et al., 1997; Haruta et al.,
1998), and it was supported that the GI-transit rate is important as a
factor in determining the absorption site in vivo. The in situ closed
loop study also showed the nonlinearity of NMT absorption in the
lower jejunum (Table 1). A preliminary study showed no effect of
quinidine, choline, and tetraethylamine on the absorption of NMT
(data not shown); additional study would be necessary to refer to the
nonlinearity and the mechanisms of NMT absorption as well as the
nonlinearity in lower ileum.
As shown in Fig. 4, it was recognized that NMT should be subject
to the first-pass elimination from the difference between the plasma
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A, stomach; B, duodenum; C, upper jejunum; D, lower jejunum; E, upper ileum;
F, lower ileum; G, cecum.
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KIMURA ET AL.
TABLE 2
Pharmacokinetic parameters for GI transit and extent of absorption (Fai) of NMT in each segment
Calculations were carried out from 0 to 4 h by using the data obtained by simulation studies.
Parameter
Stomach
Duodenum
Upper Jejunum
Lower Jejunum
Upper Ileum
Lower Ileum
Cecum
AUCra (% 䡠 h)
MRT (h)
VRT (h2)
Fai (%)
46.827
0.467
0.216
4.917
3.409
0.503
0.217
4.995
5.232
0.557
0.219
6.870
16.953
0.736
0.250
23.480
31.867
1.175
0.424
34.129
22.623
1.732
0.626
25.655
16.902
2.597
0.700
4.919
FIG. 3. Calculated absorption rate of NMT in each segment of GI tract after
oral administration in rats.
A, stomach; B, duodenum; C, upper jejunum; D, lower jejunum; E, upper ileum;
F, lower ileum; G, cecum.
FIG. 4. Prediction of plasma concentration of NMT after oral administration
based on GI-Transit-Absorption Model with and without addition of hepatic
first-pass metabolism.
Dose of NMT was 20 mg/kg. Closed circles are the experimental results and are
expressed as the mean ⫾ S.E. of four experiments. Solid and dotted lines are the
plasma concentration-time curves calculated from absorption and transit rate constants in each segment based on GI-Transit-Absorption Model with and without
addition of Fh, respectively.
concentration-time curve calculated without any first-pass elimination
and the observed profile. Therefore, we introduced the first-pass
elimination process into the GI-Transit-Absorption Model to predict
the plasma concentration-time profile and the bioavailability of NMT
by using the Fh value determined by in vitro study. From the in vitro
metabolism study, it was clarified that the site of first-pass metabolism
of NMT is the liver, but not the small-intestinal mucosa, although the
metabolic pathways of NMT remain to be determined. The in vitro
metabolism study using rat liver 1000g supernatant predicted the Fh
value to be 0.510. This modified model using the Fh value calculated
from the in vitro metabolism study can predict the plasma concentration-time curve of NMT after oral administration very well, as the
solid line shown in Fig. 4. The Fh value, 0.425, was also estimated
from AUCi.p./AUCi.v.. Moreover, as the Fa and the bioavailability of
NMT were estimated to be 0.974 and 3.90 ⫾ 0.043 from the AUC
calculated by the GI-Transit-Absorption Model without the first-pass
elimination process and the AUC observed, respectively, the presystemic availability (1 ⫺ presystemic extraction ratio) was calculated to
be 0.400. This method to calculate the presystemic availability has
been validated already in the case of propranolol (Sawamoto et al.,
1997). Because three different methods gave the similar Fh values, the
GI-Transit-Absorption Model with first-pass metabolism process
could be useful also to predict the bioavailability of the compound
subject to hepatic first-pass metabolism.
As described above, the modified GI-Transit-Absorption Model
allowed us to predict the in vivo absorption kinetics, including the
first-pass metabolism by using the Fh value obtained by in vitro study
with the 1000g supernatant of liver homogenate. However, this may
not be the case for the drug showing nonlinear pharmacokinetics,
especially nonlinear presystemic elimination. Furthermore, the in
vitro system and the range of drug concentration to estimate the
metabolism of drug should be selected carefully, dependent on each
drug to be investigated, because the usage of an inadequate system
and/or drug concentration could result in the under- or overestimation
of in vivo metabolism.
In conclusion, the GI-Transit-Absorption Model could be really
available for the prediction of plasma concentration-time profile and
bioavailability for drugs with hepatic first-pass metabolism.
Appendix
GI-Transit-Absorption Model (Sawamoto et al., 1997). GI-Transit-Absorption Model is the model that can predict absorption kinetics
containing GI transit and absorption of drugs administered orally. This
model is based on the assumption that the whole GI tract is divided
into eight segments (stomach, duodenum, upper jejunum, lower jejunum, upper ileum, lower ileum, cecum, and large intestine), and: 1)
the drug distribution in each segment can be defined as the well stirred
condition; 2) the drug absorption in each segment is assumed to be an
apparent first order kinetic process, and absorbability is represented
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FIG. 5. In vitro hepatic metabolism of NMT.
Results are expressed as means with S.E. of four experiments. Vertical bars are
within the symbol.
581
PREDICTION OF ABSORPTION PROFILE OF N-METHYLTYRAMINE
by the kai; and 3) the drug transit from one segment (i) to the next (i
⫹ 1) is assumed to follow first order kinetic process (ki).
The absorbable drug moves from a segment (i) to the next segment
(i ⫹ 1) with segmental absorption (first order absorption). For a
nonabsorbable drug (kai ⫽ 0), gastric emptying rate and intestinal
transit rate for each segment are represented by eqs. 3 and 4, respectively.
total absorption rate-time data obtained in Step 3 and pharmacokinetic
parameters after i.v. administration correspond to the input function
and the weight function, respectively. Laplace transform of the plasma
concentration after oral administration C̃pp.o.(s) is expressed using
Laplace transform of the plasma concentration after i.v. administration C̃pi.v.(s) as follows:
冘
ce
dX s/dt ⫽ ⫺共k s ⫹ ka s兲 䡠 X s
(3)
C̃p (s) ⫽ 共D p.o./D i.v.兲共f̃as(s)⫹
p.o.
where at t ⫽ 0, Xs ⫽ Dp.o. (the dose of the orally administrated drug).
dX i⫹1/dt ⫽ k i 䡠 X i ⫺ 共k i⫹1 ⫹ ka i⫹1兲 䡠 X i⫹1
(4)
f̃ai(s))C̃pi.v.(s)
(8)
i⫽d
Multiplication of eq. 8 with Fh, calculated from the in vitro metabolism study gives the Laplace transform of the plasma concentration
for a drug with hepatic first-pass metabolism (eq. 9).
The subscripts s and i indicate stomach and each intestinal segment,
respectively.
Prediction of Plasma Concentration Profile by the Convolution
Method. An outline of the prediction method using convolution
analysis is as follows.
In Step 1, the profile of the amount of drug against time (Xi-time
profile) in each segment is calculated by the convolution method. The
Laplace transform of the amount of drug in segment i ⫹ 1 X̃i ⫹ 1 (s))
is described by eq. 5:
The inverse Laplace transformation of eqs. 8 and 9 give the predicted drug concentrations in the plasma after oral administration
without and with first-pass elimination in the intestinal epithelium
and/or in the liver, respectively.
X̃ i⫹1共s兲 ⫽ k i 䡠 X̃ i共s兲/共s ⫹ k i⫹1 ⫹ ka i⫹1)
References
That is, the fraction of the dose available for absorption in segment i
⫹ 1 (Fi ⫹ 1) can be given by eq. 6 using its Laplace transform
f̃i ⫹ 1(s)):
f̃ i⫹1共s兲 ⫽ k i 䡠 f̃ i共s)/(s ⫹ k i⫹1 ⫹ ka i⫹1兲
(6)
In Step 2, the profile of absorption rate against time in each segment
is calculated by using the Xi-time profile obtained in Step 1 and the kai
in each segment. The fraction of the dose absorbed (absolute absorption) from segment i (Fai) can be given by eq. 7 using its Laplace
transform f̃i(s)).
f̃ai(s) ⫽ ka i 䡠 f̃ i共s)
(7)
In Step 3, the profile of total absorption rate against time in the
whole GI tract is calculated as the sum of the absorption rate-time
profiles obtained in Step 2.
In Step 4, prediction of the plasma concentration of orally administered drug is performed by means of the convolution method. The
C̃p (s) ⫽ 共D p.o./D i.v.兲 F h共 f̃a s共s兲 ⫹
f̃a i(s))C̃pi.v.(s)
(9)
i⫽d
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