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## Pii: s0378-5173(99)00147-7

International Journal of Pharmaceutics 186 (1999) 119 – 125
A compartmental absorption and transit model for
a

*Glaxo Wellcome Inc*.,

*Fi*6

*e Moore Dri*6

*e*,

*Research Triangle Park*,

*NC *27709,

*USA*
b

*College of Pharmacy*,

*The Uni*6

*ersity of Michigan*,

*Ann Arbor*,

*MI *48109,

*USA*
Received 2 November 1998; received in revised form 16 April 1999; accepted 19 April 1999

**Abstract**
This report describes a compartmental absorption and transit model to estimate the fraction of dose absorbed and
the rate of drug absorption for passively transported drugs in immediate release products. The model considerssimultaneous small intestinal transit flow and drug absorption. Both analytical and numerical methods were utilizedto solve the model equations. It was found that the fraction of dose absorbed can be estimated by

*F *= 1 − (1 + 0.54
is the human effective permeability in cm/h. A good correlation was found between the fraction
of dose absorbed and the effective permeability for ten drugs covering a wide range of absorption characteristics. Themodel was able to explain the oral plasma concentration profiles of atenolol. 1999 Elsevier Science B.V. All rightsreserved.

*Keywords*: Drug absorption kinetics; Fraction of dose absorbed; Permeability; Compartmental modeling

**1. Introduction**
mechanistic models have been discussed in a re-cent review article (Yu et al., 1996a). Although
Estimating intestinal drug absorption kinetics
gastric emptying and small intestinal transit flow
can greatly facilitate lead drug candidate selection
can influence the rate and extent of drug absorp-
and support formulation strategies. Quantitative
tion after oral administration, none of the previ-
and mechanistic approaches have been developed
ous models have fully considered these factors.

since the traditional approach to treat the entire
The aim of this report was to develop a compart-
gastrointestinal tract as a single-compartment
mental absorption and transit (CAT) model for
‘black box’ does not suffice (Ho et al., 1983;
estimating the fraction of dose absorbed and the
Dressman et al., 1984; Sinko et al., 1991). The
rate of drug absorption based on the transit mod-
utilities and limitations of these quantitative and
els (Yu et al., 1996b; Yu and Amidon, 1998). Wederived an equation to correlate the fraction ofdose absorbed with the human effective perme-
* Corresponding author. Tel.: + 1-919-4830445; fax: + 1-
ability. The CAT model was related to compart-

*E*-

*mail address*: lxy33016@glaxo.com (L.X. Yu)
mental pharmacokinetic models to evaluate the
0378-5173/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 5 1 7 3 ( 9 9 ) 0 0 1 4 7 - 7

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*International Journal of Pharmaceutics *186 (1999) 119 – 125
effect of gastric emptying on plasma concentra-

**2. Theoretical**
where

*M *is the amount of drug in the stomach,

*M *is the amount of drug in the colon,

*M *is the
Fig. 1 illustrates the CAT model to account for
amount of drug in the

*n*th compartment,

*t *is the
the transit flow in the stomach, duodenum, je-
time,

*K *,

*K *, and

*K *are the rate constants of
junum, and ileum, and the passive absorption in
gastric emptying, small intestinal transit, and in-
the duodenum, jejunum, and ileum. The gas-
trinsic absorption, respectively. In Eq. (2), when
trointestinal tract is divided into three segments:

*n *= 1, the term

*K M *is replaced by

*K M *. The
stomach, small intestine, and colon. The transit
rate of drug absorption from the small intestine
flow in the human small intestine can be described
by seven compartments, where a drug transfers
from one compartment to the next one in a
first-order fashion (Yu et al., 1996b). The colon is
considered only as a reservoir and the colonic
where

*M *is the amount of drug absorbed. From
transit flow was not considered in this model. The
1. Absorption from the stomach and colon is
insignificant compared with that from the
As

*t *,

*M *and

*M *’s approach zero, so
2. Transport across the small intestinal mem-
The fraction of dose absorbed,

*F *, can then be
4. A drug moving through the small intestine can
be viewed as a process flowing through a series
of segments, each described by a single com-
partment with linear transfer kinetics from one
to next, and all compartments may have dif-
Coupling with Eqs. (1) and (2), the analytical
ferent volumes and flow rates, but have the
same residence times (Yu and Amidon, 1998).

Therefore, for a non-degradable drug dosed in
an immediate release dosage form, the absorption
and transit in the gastrointestinal tract can bedepicted as follows.

Fig. 1. A schematic diagram of the CAT model with lineartransit and passive absorption kinetics. This model accounts
for the transit in the stomach, duodenum, jejunum, and ileum,
and the absorption in the duodenum, jejunum, and ileum.

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*International Journal of Pharmaceutics *186 (1999) 119 – 125
The transit rate constant

*K *can be estimated from

**3. Methods**
the mean small intestinal transit time (Yu et al.,1996b):
Model 1 – 3 and 13 – 15 are a typical initial value
problem of an ordinary differential equation sys-tem. This system was numerically solved by the
The absorption rate constant

*K *is proportional
ADAPT pharmacokinetic and pharmacodynamic
to the effective permeability,

*P *, (Sinko et al.,
modeling package (D’Argenio and Schumitzky,
1992). A subroutine was written to accommodate
3.2.

*Estimating fraction of dose absorbed*
where

*R *is the radius of the small intestine. Thesubstitution of Eqs. (9) and (10) into Eq. (8) gives
Ten compounds covering a wide range of ab-
sorption characteristics, from enalaprilat (the least
permeable) to ketoprofen (the most permeable),
were chosen to evaluate the predictability of themodel. The permeability data were obtained from
Substitution of

*T * of 3.32 h (Yu et al., 1996b)
regional perfusion studies in humans using the
and the radius of 1.75 cm (Lennernas et al., 1992)
regional intestinal perfusion technique (Lennernas
et al., 1994; Amidon et al., 1995; Fagerholm et al.,1995; Lennernas et al., 1995; Amidon, 1996; Lin-
dahl et al., 1995). The fraction of dose absorbeddata were obtained from the literature (Paterson
where the human effective permeability

*P*
et al., 1970; Mason et al. 1979; Eichelbaum et al.,
expressed in cm/h. If there is no first pass effect,
1982; Davies, 1984; Kubo and Cody, 1985; Tse et
Eq. (4) can be related to intravenous pharmacoki-
al., 1992; Ponto and Schoenwald, 1993; Benet et
netic models to estimate oral plasma concentra-
al., 1996; American Hospital Formulary Service,
tion profiles. For example, in the case of the
1998 Edition). The fraction of dose absorbed data
three-compartment open model with central com-
were corrected for first pass effects, if any. Table
partment elimination (Wagner, 1993), we have the
3.3.

*Estimating rate of drug absorption*
In conjunction with the compartmental phar-
macokinetics model Eqs. (12) – (15), the CAT
model was used to simulate oral plasma concen-
tration profiles of atenolol. Atenolol is a b -selec-
tive b-adrenergic receptor blocking agent andessentially undergoes no first-pass metabolism
(Riddell et al., 1987). Two simulations were car-
ried out with respect to gastric emptying (mono-exponential and biphasic gastric emptying). The
where

*V *is the volume of the central compart-
effective permeability of atenolol was found to be
ment 1, and

*C *,

*C *, and

*C *are the plasma con-
0.19 cm/h (Amidon et al., 1995). The volume of
the central compartment and microscopic rate
respectively.

*k *,

*k *,

*k *,

*k *, and

*k*
constants were taken from the intravenous phar-
macokinetics study by Mason et al. (1979).

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*International Journal of Pharmaceutics *186 (1999) 119 – 125
dicted fraction of dose absorbed is 34%, slightly
Summary of the literature data of permeability and fraction of
below the experimental observations. The model
predicted the fraction dose absorbed to be 48, 50,
84, and 95% for terbutaline, atenolol, metoprolol,
and propranolol, respectively, based on the per-
meability data. The predicted results are in agree-
ment with the experimental data (Paterson et al.,
1970; Mason et al., 1979; Davies, 1984; Benet et
al., 1996; American Hospital Formulary Service,
1998). Fluvastatin, antipyrine, naproxen, and ke-
toprofen are completely absorbed (Eichelbaum et
al., 1982; Benet et al., 1996; Tse et al., 1992), as
4.2.

*Estimating the rate of drug absorption*
Fig. 3 gives the theoretical prediction (dotted
lines) for rate of drug absorption, based on mono-
exponential gastric emptying and the mean gastric
residence time of 0.25 h for all three doses. The
theoretical prediction is in fair agreement with the
experimental data. The double peaks in the exper-
a The oral bioavailability metoprolol is about 38% (Benet et
imental plasma concentration profiles would not
al., 1996). After oral dose, about 50% of dose appears to
be expected from the simulation, however. Mason
undergo first-pass metabolism in the liver (AHFS Drug Infor-mation, 1998, pp. 1369). Thus, the fraction of dose is about0.88.

b The oral bioavailability of propranolol is about 26%.

However, the drug is completely absorbed following oral doses(Paterson et al., 1970).

c The fraction of dose absorbed of fluvastatin is 0.93–0.98
although the oral bioavailability is only 19–29% due to exten-sive first-pass effect (Tse et al., 1992).

**4. Results and discussion**
4.1.

*Estimating fraction of dose absorbed*
Fig. 2 shows the predicted values. The fraction
of dose absorbed for enalaprilat in laboratoryanimals was estimated to be only 5 – 12%; in hu-mans, oral absorption of radiolabelled enalaprilatwas probably less than 10% (Kubo and Cody,1985). The model predicted the fraction of doseabsorbed to be 26% for enalaprilat, higher than
Fig. 2. The fraction of dose absorbed as a function of the
the experimental value. The fraction of dose ab-
human effective permeability, where ( — ) represents the pre-
sorbed for furosemide varies from 37 to 83% in
diction of the compartmental absorption and transit model,
healthy volunteers and the mean value is around
(---) represents the single compartment model, and (···), the
55% (Ponto and Schoenwald, 1993). The pre-

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*International Journal of Pharmaceutics *186 (1999) 119 – 125
almost two hours of no emptying. The remainingdrug was completely cleared from the stomach inthe second phase of the emptying, producing thesecond peak in the plasma concentration profile.

Nevertheless, no gastric emptying for 2 hours isphysiologically questionable although not impos-sible despite the fact that the biphasic gastricemptying model is better than the monoexponen-tial model for fitting the experimental data.

Several approaches to predicting the fraction of
dose absorbed have been discussed in the litera-ture (Yu et al., 1996a). Ho et al. (1983) developeda dispersion model and proposed an anatomicalreserve length concept. The dispersion model isphysically more plausible than the CAT model.

However, the current dispersion model is proba-
Fig. 3. Prediction of plasma concentration profiles of atenolol
bly unable to account for gastric emptying and to
at the 25, 50, and 100 mg oral doses, where dotted lines
simulate the effect of gastric emptying on absorp-
represent the prediction with monoexponential gastric emp-tying, solid lines represent the prediction with biphasic gastric
tion (Yu et al., 1996b). The dispersion model also
emptying (two intervals of monoexponential emptying, inter-
appears to be difficult to incorporate into phar-
rupted by an interval with no emptying), and symbols repre-
macokinetic models to estimate plasma concentra-
sent the experimental results from Mason et al. (1979).

Sinko et al. (1991) developed a macroscopic
et al. (1979) postulated that the biphasic gastric
mass balance approach and showed the relation-
emptying contributed to the double peaks.

ship between the fraction of dose absorbed and
In the next simulation, therefore, we assumed
the absorption number (effective permeability)
that the drug was emptied from the stomach in a
under steady-state conditions. Two flow models
biphasic fashion. The simulation results are also
were considered in the mass balance approach:
shown in Fig. 3. Evidently, there exist double
the single mixing tank model and the plug flow
peaks in the simulated curves (solid lines). Based
model. The single mixing tank model, as the name
on the

*F*-test, the pharmacokinetic model with
suggests, considers the small intestinal tract a
biphasic gastric emptying was found to be a sig-
mixed tank with uniform concentration. The plug
nificant improvement over the model with mono-
flow model considers the small intestinal tract a
uniform tube without axial mixing. In the case of
The parameters in the biphasic gastric emptying
the single mixing tank model, the mass balance
include two rate constants and the interval be-
tween the two phases (Clements et al., 1978, type
3). The first phase of the biphasic gastric emp-
tying was assumed to have the same rate constantas the monoexponential emptying. The values of
In the case of the plug flow model, the mass
the second emptying phase and the interval were
determined by curve fitting. In a typical simula-

*F *= 1 − e−3.87

*P*eff.

tion, approximately 77% of the dose was evacu-ated from the stomach during the first phase. The
Fig. 2 shows the fraction of dose absorbed
emptying was then interrupted by an interval of
calculated by Eqs. (16) and (17). The single com-

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*International Journal of Pharmaceutics *186 (1999) 119 – 125
partment model underestimates the fraction of
D’Argenio, D.Z., Schumitzky, A. 1992. Adapt II: Mathemat-
dose absorbed whereas the plug flow and the
ical Software for Pharmacokinetics/PharmacodynamicsSystems Analysis, University of Southern California, Los
CAT models give a much closer fit to the data.

We have shown that the CAT based pharmacoki-
Davies, D.S., 1984. Pharmacokinetics of terbutaline after oral
netic model was able to incorporate gastric emp-
administration. Eur. J. Resp. Dis. Suppl. 134, 111 – 117.

tying and predict plasma concentration profiles.

Dressman, J.B., Fleisher, D., Amidon, G.L., 1984. Physico-
This appears to be difficult to achieve by the plug
chemical model for dose-dependent drug absorption. J.

flow model because of its steady state assumption.

Eichelbaum, E., Ochs, H.R., Roberts, G., Somogyi, A., 1982.

Pharmacokinetics and metabolism of antipyrine after in-travenous and oral administration. Arzneim-Forsch. 32,

**5. Conclusions**
Fagerholm, U., Borgstrom, L., Ahrenstedt, O., Lennernas,
This report describes a compartmental absorp-
H., 1995. The influence of net water absorption on thesmall intestinal permeability of terbutaline, studied in
tion and transit model to estimate oral drug ab-
vivo in man. J. Drug Target. 3, 191 – 200.

sorption of passively transported drugs. A simple
Ho, N.F.H., Park, J.Y., No, P.F., Higuchi, W.I., 1983. Ad-
equation was derived which predicts the fraction
vanced quantitative and mechanistic approaches in inter-
of dose absorbed reasonably well. The CAT
facing gastrointestinal drug absorption studies in animals
model offers the advantages of being able to
and humans. In: Crouthanel, W., Sarapu, A.C. (Eds.),
estimate the rate of drug absorption and couple
Animal Models for Oral Drug Delivery in Man: In Situand In Vivo Approaches. American Pharmaceutical Asso-
ciation, Washington, DC, pp. 27 – 106.

models. The simulation study showed that gastric
Kubo, S.H., Cody, R.J., 1985. Clinical pharmacokinetics of
emptying could cause double peaks in oral plasma
the angiotensin converting enzyme inhibitors. Clin. Phar-
Lennernas, H., Ahrenstedt, O., Hallgren, R., Knutson, L.,
Ryde, M., Paalzow, L.K., 1992. Regional jejunal perfu-sion, a new in vivo approach to study oral drug absorp-

**Acknowledgements**
tion in man. Pharm. Res. 9, 1243 – 1251.

Lennernas, H., Ahrenstedt, O., Ungel, A.-L., 1994. Intestinal
The authors would like to thank Avis Bridgers,
drug absorption during induced net water absorption in
Ambrish Vyas, and Mark Sacchetti for reviewing
man: A mechanistic study using antipyrine, atenolol andenalaprilat. Br. J. Clin. Pharmacol. 37, 589 – 596.

Lennernas, H., Knutson, L., Knutson, T., Lesko, L.,
Salmonson, T., G.L. Amidon, G.L. 1995. Human effec-tive permeability data for furosemide, hydrochlortiazide,

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