Monitoring in situ liver metabolism in rats using microdialysis. Comparison of microdialysis mass-transport model predictions to experimental metabolite generation data

Article abstract of DOI:10.1021/js970288z

The generation of metabolites from two model compounds, phenacetin and acetaminophen, included in the perfusion fluid of a microdialysis probe implanted into rat liver was studied. When 60 μM phenacetin was included in the perfusion fluid using a flow rate of 1.0 μL/min, acetaminophen and acetaminophen sulfate were recovered at concentrations that ranged between 0.4 and 1.6 μM. Acetaminophen sulfate ([AS](gain)) diffused back into the microdialysis probe on a micromolar percentage basis of 8.9 ± 2.4% (n = 3) when acetaminophen was passed through the probe at a concentration between 11 and 12 μM. When 220-240 μM acetaminophen was passed through the probe, the percentage of acetaminophen sulfate recovered was 4.8 ± 1.4% (n = 3) (P < 0.1 compared to the 11 μM group). No acetaminophen glucuronide was detected in the dialysate samples. A mathematical model that describes mass transport in microdialysis sampling was used to predict the concentration of metabolite that could be recovered into the dialysate after the loss of a substrate compound that undergoes metabolism. The model predicts a metabolite recovery of 23.6% using estimates for phenacetin metabolism and 21.5% using estimates for acetaminophen metabolism. The results presented here indicate that microdialysis has potential to be used to study local in situ metabolism and with further refinements of the microdialysis mass-transport model may be used to estimate in vivo metabolic formation rates.

Full text of DOI:10.1021/js970288z

Monitoring in Situ Liver Metabolism in Rats Using Microdialysis.
Comparison of Microdialysis Mass-Transport Model Predictions to
Experimental Metabolite Generation Data
§
JULIE A. STENKEN,*,†,‡ LARS STÅHLE,| CRAIG E. LUNTE,† AND MARYLEE Z. SOUTHARD
Contribution from Department of Chemistry and Center for Bioanalytical Research, University of Kansas,
Lawrence, Kansas 66045-0046, Department of Chemical and Petroleum Engineering and Center for Drug Delivery Research,
University of Kansas, Lawrence, Kansas 66045-2223, Department of Clinical Pharmacology, The Karolinska Institute,
Huddinge University Hospital, SE−141 86 Huddinge, Sweden
Received July 25, 1997.
Final revised manuscript received December 17, 1997.
Accepted for publication December 18, 1997.
concentration, Coutlet, and the far-field concentration, C∞ECF
,
Abstract 0 The generation of metabolites from two model compounds,
phenacetin and acetaminophen, included in the perfusion fluid of a
microdialysis probe implanted into rat liver was studied. When 60
µM phenacetin was included in the perfusion fluid using a flow rate
of 1.0 µL/min, acetaminophen and acetaminophen sulfate were
recovered at concentrations that ranged between 0.4 and 1.6 µM.
Acetaminophen sulfate ([AS]gain) diffused back into the microdialysis
probe on a micromolar percentage basis of 8.9 ± 2.4% (n ) 3) when
acetaminophen was passed through the probe at a concentration
between 11 and 12 µM. When 220−240 µM acetaminophen was
passed through the probe, the percentage of acetaminophen sulfate
recovered was 4.8 ± 1.4% (n ) 3) (P < 0.1 compared to the 11 µM
group). No acetaminophen glucuronide was detected in the dialysate
samples. A mathematical model that describes mass transport in
microdialysis sampling was used to predict the concentration of
metabolite that could be recovered into the dialysate after the loss of
a substrate compound that undergoes metabolism. The model predicts
a metabolite recovery of 23.6% using estimates for phenacetin
metabolism and 21.5% using estimates for acetaminophen metabolism.
The results presented here indicate that microdialysis has potential
to be used to study local in situ metabolism and with further
refinements of the microdialysis mass-transport model may be used
to estimate in vivo metabolic formation rates.
may vary depending upon the physiological and pharma-
cological conditions and the type of experiment that is being
performed. When microdialysis is used to sample neu-
rotransmitters such as dopamine, then Cinlet ) 0 and C∞ECF
equals a finite number. Since diffusion across the mem-
brane and in the tissue is symmetric to and from the probe,
it is possible to use microdialysis to locally administer a
compound by including it in the perfusion fluid. In this
case, Cinlet would be the concentration of the included
compound and C∞ECF would be zero.9
One of the principal advantages of using microdialysis
is the small size of the dialysis membrane and cannula. A
microdialysis probe can be placed into a distinct tissue
region because the outer diameter of the dialysis membrane
is between 220 and 500 µm. This allows for the study of
localized metabolic events in a specific tissue region using
microdialysis.
A few research groups have compared microdialysis
results with mathematical models. Microdialysis sampling
coupled with the use of a mathematical model that de-
scribed transport to and from microdialysis probes derived
by Bungay et al.10 and Morrison et al.11 has been used to
study ziduvodine (AZT) transport in rat brain.12 Addition-
ally, a mathematical model has been used in the study of
localized muscle blood flow in rats.13 The blood flow
through the tissue was determined by correlation of the
experimental results with a mathematical model that
describes the loss of ethanol to the tissue space based upon
diffusion of ethanol from the microdialysis probe and its
uptake into the capillaries. Capillary uptake of ethanol is
dependent upon blood flow rate and the experimental data
showing this result has been published.14
This paper describes the use of microdialysis sampling
coupled with a previously developed mathematical model15
to interpret experimental metabolism data obtained from
liver microdialysis experiments in which phenacetin and
acetaminophen were included in the perfusion fluid. The
development of a mathematical model that predicts the
concentration of metabolites formed after a local infusion
of a substrate requires a consideration of the multitude of
physiological processes that occur in the liver. The liver
is a highly perfused organ which is organized via an acinar
structure.16,17 The blood flow through the liver occurs
through blood spaces originating from the portal vein (75%)
and hepatic artery (25%).18 Blood from both inlets flows
through these spaces, which are called sinusoids, and is
combined at the outlet into the hepatic vein. The hepato-
cytes are aligned along the sinusoids in a one-unit layer of
cells. The drug-metabolizing activity of the liver varies
through three separate regions which are segregated into
zones (one, two, or three) and is dependent upon the oxygen
Introduction
Microdialysis is a well-known method for obtaining
protein-free samples from the extracellular fluid (ECF)
space of brain and has allowed many researchers to study
neurochemistry in localized brain regions.1,2 Microdialysis
has also been used as a method to sample the ECF of other
tissues3 including the liver.4-7 Analytes that diffuse freely
in the ECF to or from the implanted microdialysis probe
can be sampled. The efficiency of this diffusive process in
microdialysis is called recovery and is defined in eq 1.8
Coutlet - Cinlet
C∞ECF - Cinlet
Ed ) Recovery )
(1)
The values of the inlet concentration, Cinlet, the outlet
* Corresponding author. Phone: (518) 276-2045. Fax: (518) 276-
4887. E-mail: Stenkj@rpi.edu.
† Department of Chemistry and Center for Bioanalytical Research,
University of Kansas.
‡ Present address: Department of Chemistry, Rensselaer Polytech-
nic Institute, Troy, NY 12180-3590.
§ Department of Chemical and Petroleum Engineering and Center
for Drug Delivery Research, University of Kansas.
| Huddinge University Hospital.
© 1998, American Chemical Society and
American Pharmaceutical Association
S0022-3549(97)00288-8 CCC: $15.00
Published on Web 02/05/1998
Journal of Pharmaceutical Sciences / 311
Vol. 87, No. 3, March 1998

located in the endoplasmic reticulum of the hepatocytes and
have an estimated whole liver in vivo Vmax of 1000 nmol
min-1 per liver and a Km of 200 µM.18 The minor metabo-
lites of phenacetin metabolism include phenetidine, which
occurs via a deacetylation reaction; 2-hydroxyphenacetin,
which is an aromatic hydroxylation product; and 3-([5-
acetamido-2-hydroxyphenyl)thio]alanine, which is the cys-
teine conjugate of acetaminophen.23 The concentration of
these minor metabolites was not measured in these experi-
ments.
Prediction of the concentration of metabolite (Cdial) that
returns to the microdialysis probe after metabolism of a
substrate requires metabolite kinetics to be incorporated
into a previously developed mathematical model.15 Here,
we use a model we have previously developed based on the
work of Bungay et al. and Morrison et al.10,11 The experi-
mental results are compared with predictions calculated
using this theoretical model that predicts metabolite back-
extraction into the microdialysis probe. Although several
groups have used mathematical models to describe mi-
crodialysis recovery10,11,13 and others have studied in situ
liver metabolism,4,5,25 there have been no applications of a
theoretical model to describe metabolite back-extraction in
microdialysis sampling.
Figure 1sA schematic diagram illustrating the pathway that a substrate must
pass from the microdialysis probe to the tissue space. The substrate must
diffuse through the dialysis membrane and the cell lipid bilayer prior to
metabolism. The metabolites must diffuse back through the lipid bilayer and
through the probe dialysis membrane prior to analysis.
gradient through these zones.19 Zone 1 is the closest to
the entry of the periportal region (where the hepatic artery
and portal vein enter the liver), zone 2 is in the middle,
and zone 3 is closest to the exit, which is the perihepatic
region. Between the sinusoids and the hepatocytes lies the
space of Disse, which allows for equilibrative exchange
between the sinusoid and the hepatocytes.
Most drugs form different metabolites after a dose is
given. This known result indicates clearly that drug-
metabolizing enzymes within the liver act concurrently.
Therefore, the complexity of xenobiotic metabolism cannot
be completely understood in vivo from individual in vitro
studies of single drug-metabolizing enzymes.20 The extent
of drug metabolism in the liver has often been studied using
the isolated perfused liver technique.21 Different models
have been developed to predict metabolite formation based
on blood flow patterns in the liver.22
In the experiments described here, phenacetin and
acetaminophen were included in the microdialysis perfu-
sion fluid at a known concentration and are used as
substrates to be metabolized in the liver. The microdialysis
probe may be thought of as an artificial blood vessel which
allows diffusive exchange across its semipermeable wall.2
The direction of transport of the drug and metabolite are
opposite that in the liver perfusion studies. Here we are
putting the hepatocytes in direct contact with the sub-
strate. Enzymatic heterogeneity still exists, but will now
depend on the probe implantation site, rather than the
length down the sinusoid. Since the probe is much wider
(500 µm) and longer (4 mm) than the acinus (300 µm), it is
reasonable to consider this situation a well-stirred case and
assume that enzymes are randomly spaced around the
microdialysis probe.
A substrate gets metabolized only after it diffuses
through the dialysis membrane into the ECF and through
the cell membrane of the hepatocyte in order to reach the
metabolic enzymes found inside the hepatocyte as il-
lustrated in Figure 1. Phenacetin is oxidized to acetami-
nophen via an O-deethylation catalyzed by cytochrome
P450, CYP1A2, which accounts for 80-90% of its metabo-
lism.23 Acetaminophen can be sulfated, glucuronidated, or
oxidized to the quinoneimine.24 Sulfation of phenolic
substrates occurs via high-affinity, low-capacity cytosolic
sulfotransferase enzymes, which have an estimated re-
ported whole liver in vivo Vmax value of 500 nmol min-1
per liver and a Km of 10 µM.18 Glucuronidation of phenolic
substrates occurs via the glucuronyltransferases, which are
Materials and Methods
Th eor ysA concentration profile of the substrate calculated at
different radial points is the first step to modeling metabolite
return into a microdialysis probe. We have recently shown how
a
developed finite-difference model can be used to calculate
concentration profiles in liver15 on the basis of the work of
Bungay10 and Morrison.11 The substrate concentration profile is
needed to calculate the metabolite concentration profile. Once the
metabolite concentration profile is calculated, then the concentra-
tion of the metabolite that diffuses into the probe can be calculated.
Su bstr a te Con cen tr a tion P r ofilesECFsAll analytes that
are either sampled or delivered via the microdialysis probe will
diffuse through the extracellular fluid space (ECF) of the tissue
in which the microdialysis probe is implanted. In addition to
diffusion, kinetic processes such as uptake, metabolism, and
capillary permeability will remove the analyte from the ECF in
the tissue. The transient concentration time profile for this process
is described by eq 2.
∂CECF(r,t)
∂t
∂CECF(r,t)
∂r
1 ∂
) ΦECFDECF
r
- ΦECFkLCECF(r,t)
r ∂r ( (
))
(2)
Equation 2 accounts for the diffusive (DECF, cm2/min) and kinetic
processes that occur in the tissue space. For simplicity kL (min-1
)
is used, where kL is a lumped kinetic rate constant that includes
the summation of rate constants for tissue metabolism (km),
exchange between the intracellular and extracellular space (kei,
kie), or permeation across capillary walls (kep), and r (cm) is the
radial distance from the probe. ΦECF is the aqueous volume
fraction of the tissue space and is used in this equation to remind
the reader that diffusion is assumed to occur only in the ECF water
space. In the solved mathematical model kL is subdivided into
the individual kinetic processes mentioned above such as metabo-
lism, capillary permeation, or uptake.26 The z axis (length of the
probe) is averaged in the final numerical solution and is therefore
not included in the above partial differential equation. The extent
of tissue binding for acetaminophen and phenacetin in the liver
is an unknown quantity and it has not been included in the model
formulation. A partition coefficient between the ECF and ICF is
assumed to be unity.
Equation 2 does not account for convection around the microdi-
alysis probe. Inclusion of convection into the diffusion model adds
much complexity to the modeling process. The possibility of
convection around the probe exists especially in a tissue such as
the liver, where the respiration of the rat moves the liver. The
volumetric flow rate of any convection and whether the convection
process has laminar flow are difficult parameters to obtain in vivo.
312 / Journal of Pharmaceutical Sciences
Vol. 87, No. 3, March 1998

MembranesIn the membrane, only diffusion (Dmem, cm2/min)
is allowed to occur. An effective diffusion coefficient is used that
takes into account diffusion through the membrane pores and
polymer. For most dialysis membranes, it is reasonable to assume
that the majority of the mass transport occurs through the water
space within the membrane pores. Diffusion through the water
space in the pores provides less resistance to mass transport than
polymer diffusion. The mass balance for the substrate in the
membrane becomes
Dd[Cmem - Cd]
ri - rc
dC
dr
35
13
DmemΦmem
(r,t)|r
)
(8)
(
)
i
In eq 8 the term Dd/(ri - rc) (rc is the inner cannula radius) has
the same form as a mass transfer coefficient and can then be used
to relate membrane and dialysis flux in the model as was shown
by Bungay et al. for their steady-state model (see eq A1 in their
paper).10
Equations 2-4 are solved simultaneously using the boundary
conditions listed above at various time points by using a developed
FORTRAN program to obtain the substrate concentration exiting
the probe and the substrate concentration profile away from the
probe.28 The partial differential equations which describe the
mass balances in the dialysate, the membrane, and the tissue are
solved by using an implicit finite-difference scheme which can be
found in a numerical methods textbook.27 For this numerical
model, an initial guess must be made for the concentration of the
dialysate, and the program uses a relaxation technique to reach
the final answer.28
After calculating the steady-state substrate concentration pro-
file, the concentration of the metabolite in the ICF is calculated
by using eq 5. With this calculation the metabolite concentration
in the dialysate can be found by using eqs 3, 4, and 6. It is possible
to solve this model transiently to predict the outlet concentration,
∂Cmem(r,t)
∂t
∂Cmem(r,t)
∂r
1 ∂
) ΦmemD
r
(3)
mem r ∂r ( (
))
where Φm and Dm are the membrane volume fraction and diffusion
coefficient, respectively.
DialysatesFinally transport in the dialysate must be accounted
for by
∂Cd
∂t
∂Cd(r,t)
∂z
∂Cmem(ri,z)
∂r
) Qd
- 2πriDmemΦmem
(4)
where Cd is the averaged substrate concentration in the dialysate
and z is the axial position along the probe in the direction of flow,
Qd is the dialysate flow rate (µL/min), ri is the inner membrane
radius (cm), and Φm is the volume fraction of the membrane since
it is assumed that transport primarily occurs through membrane
pores.
Metabolite Concentration ProfilesA metabolite generation term
is needed to obtain the metabolite concentration profile in the
tissue space. This term is shown below in eq 5
C
outlet, of the substrate and metabolite at each time point.
Calculation of transient Coutlet for the substrate and metabolite
would increase computation time and is not the focus of this paper,
since the experiments performed here were steady-state.
Linear Kinetics AssumptionssThe model to predict the sub-
strate concentration profile is based on linear kinetics. The
reasoning behind using linear kinetics is multifold. Although most
biologically relevant rates are saturable, they can be approximated
as first-order rates by assuming the substrate concentration is low
enough that it reduces the Michaelis-Menten equation to a first-
order equation.29 The more important modeling reason is that
incorporation of nonlinear kinetics into the mass-balance equations
(2 or 6) adds much complexity to the coding and implementing of
the computational solution. The task of incorporating the non-
linear kinetics into the mathematical model is important and is
ongoing in our laboratories. Finally, although it is intuitively
expected that nonlinear kinetics would affect Ed, i.e., by lowering
GICF ) km,subCICF,sub(r)
(5)
where CICF,sub(r) is the concentration for the substrate predicted
by the model for a particular radial point, r, and km,sub is the
metabolic rate constant for the degradation of the substrate. The
mass balance of the metabolite in the tissue space then becomes
∂CECF,met(r,t)
∂t
dCECF,met(r,t)
1 ∂
) ΦECFD
r
+
(
)
ECF,met r ∂r
dr
E
d as the concentration of the substrate leaving the probe becomes
Φ
ICFGICF(r) - ΦECFkL,metCECF,met(r,t) (6)
greater than Km, in the liver there are multiple kinetic processes
that affect the removal of compounds from the microdialysis probe.
In particular, the effect of capillary permeability has been shown
to have a much greater influence on the Ed than metabolism, even
when metabolic processes are inhibited. Keeping this in mind,
error in the prediction of Ed will occur for any substrate concentra-
tion greater than the enzymatic Km that describes the removal of
a substrate, but this error will be low because of the large capillary
permeability, kep, in the liver that dominates the kinetic removal
of substances in the liver, as was shown in ref 15. However, this
argument will most likely not hold for Ed predictions with
saturable kinetics in tissues such as the brain or the skin, where
the capillary permeation rate constant, kep, is much lower than in
the liver.
Note that DECF,met and kL,met for the metabolite may be different
than the values for the substrate.
Boundary Conditions and Numerical SolutionsThe metabolite
model solution requires the substrate concentration to be at a
steady-state. The program then calculates the metabolite con-
centration using the same mass balance equations listed above
along with the boundary conditions listed below for the substrate
concentration. A second assumption made is that a rapid equi-
librium exists for both substrate and metabolite between the ECF
and the intracellular fluid space (ICF) as was used by Morrison
et al.11
∂Cmem
∂r
∂CECF
∂r
Michaelis-Menten KineticssTwo versions of the model program
that calculate the concentration of the metabolite entering the
probe have been coded with different assumptions. The first
assumes that metabolism rate constants for the generation term
described in eq 5 are linear. The second model uses Michaelis-
Menten kinetics in the generation term. This is not as arduous a
task to code as in the first model case that predicts the substrate
J mem ) J ECF
DmemΦmem
) DECFΦECF
(7)
The following boundary conditions were used to obtain the
solution to the equations. The far-field concentration, C∞ECF, is
zero since the nonendogenous substrate is delivered to the tissue
space by inclusion in the perfusion fluid. This is a reasonable
assumption since the concentration will be highest near the probe
membrane and will drop exponentially farther from the probe
because of kinetic processes such as metabolism and capillary
permeation that remove substrate from the tissue. The inlet
dialysate concentration is known. It is assumed that substrate
concentrations outside the probe are lower than inside the probe
because the tissue has kinetic processes that remove the substrate
in addition to diffusion, whereas in the dialysate and membrane
no kinetic processes occur. The conservation of flux across the
membrane/ECF interface is defined in eq 7. Φm is included in eq
7 because it is possible that diffusion can occur though the polymer.
Flux must be conserved between the membrane and the dialysate
which is defined in eq 8.10
Coutlet
. In this second model program, the Michaelis-Menten
terms are included in a separate matrix and are simply multiplied
by the parent concentration found by model program 1. In this
case, the computer program calculates the CECF,met in each radial
space based on the Michaelis-Menten kinetic terms and the value
calculated for the substrate concentration, CECF,sub
. This is not
possible in the first program since the computer must calculate
the CECF,sub and that would require extensive iteration at each
radial step since a Michaelis-Menten kinetic term would include
CECF,sub in the denominator.
Modeling Parameter ChoicesThe rationale for choosing the
aqueous diffusion coefficient values (Dd) for phenacetin and
acetaminophen has been previously described.15 To find DECF
corrected for tortuosity in the tissue space, Dd was divided by the
Journal of Pharmaceutical Sciences / 313
Vol. 87, No. 3, March 1998

CMA/150 temperature monitor (CMA/Microdialysis AB, Stock-
holm, Sweden) during all experiments.
Table 1sValues Used for Model Analysis of Metabolite Generation
inner radius (cm) (r)
0.020
0.025
7.5 × 10-6
1.5 × 10-6
3.3 × 10-6
0.2
i
Micr od ia lysis P r obe Im p la n ta tion sThe details of the mi-
crodialysis probe implantation have been previously described.15
Briefly, the liver was exposed by making an incision perpendicular
to the midline of the animal approximately 1 cm from the xyphoid
process. The lower lobe (right) was then secured to the abdominal
wall by a suture through the skin and lobe. This prevented
excessive movement of the liver lobe. A second suture was then
prepared to secure the microdialysis probe. A 23-gauge needle
was used to gently pierce the outside of the liver tissue to allow
for careful insertion of the dialysis probe through this hole toward
the head and parallel to the midline. The cannula was secured
to the skin by a third suture to prevent excessive probe movement
during respiration. A large piece of tape was used to cover the
incision to prevent tissue dehydration.
After probe insertion, a wash-out period of 1 h was used to clear
the ECF space of substances released due to cellular damage
caused by the implantation procedure. After the wash-out period,
samples were collected every 15 min using a perfusion rate of 1
µL/min. A puncture wound accompanies the implantation of the
microdialysis probe; however, previous histology studies for mi-
crodialysis in the liver indicate that once the microdialysis probe
is implanted the tissue area around the microdialysis probe is in
intimate contact with the microdialysis probe.35
Dialysate blanks were collected for 1 h prior to changing the
perfusion fluid with a liquid switch (CMA-111, CMA/Microdialysis
AB, Stockholm, Sweden) to the phenacetin (60 µM) or acetami-
nophen solutions (12, 120, and 240 µM). The dialysates were
analyzed for total phenacetin and its metabolites acetaminophen
and acetaminophen sulfate. Measuring phenacetin, acetami-
nophen, and acetaminophen sulfate in the same chromatographic
run was found to be impractical because phenacetin is much more
highly retained than acetaminophen. A gradient chromatographic
system was not available to alleviate the problem of phenacetin
having a retention time of greater than 2 h with the isocratic
chromatographic conditions necessary to resolve acetaminophen
from acetaminophen sulfate. For this reason and because the
model as currently formulated does not provide for the sequential
metabolism observed with phenacetin, a second set of experiments
using acetaminophen in the perfusion fluid were performed.
LC An a lysessA Shimadzu LC-6A pump was used with a
Shimadzu variable wavelength detector set to 254 nm. A Phe-
nomenex (Torrence,CA) C-8 spherex 3 mm column (150 mm × 2.0
mm(i.d.)) was used at a flow rate of 0.22 mL/min. A mobile phase
consisting of 97/3 (v/v%) 0.5 M sodium phosphate pH 2.7 and
acetonitrile was used. An underfill injection of 7 µL was performed
manually with a syringe that had a Cheney adapter. Standard
curves were prepared using phenacetin, acetaminophen, acetami-
nophen sulfate and acetaminophen glucuronide.
outer radius (cm) (ro)
2
estimated (D ) (cm /s)
d
2
estimate membrane (cm /s) (Dm)
estimate extracellular fluid DECF with tortuosity included
volume fraction of liver ECF (ΦECF
)
estimated (ICF) (min-1) (km) [phenacetin f APAP]
1.8a
estimated (ICF) (min-1) (km)[APAP f APAP-SO ]
5.0a
4
estimated (ICF) (min-1) (km)[APAP f APAP-glucuronide]
estimataed rate of ECF/plasma exchange (min-1)
(kep)[capillary exchange]
0.5a
2.0
membrane length (mm)
flow rate of dialysate (mL/min) (Q)
4.0
1.0
a The first-order kinetic rate constants were determined as listed in the
methods section of the text.
tortuosity of the tissue space, which has been suggested to be 2.25
for brain tissue.30 A tortuosity value for liver tissue has not been
reported, but was assumed to be 2.25. The volume fraction of the
liver is reported to be approximately 0.2.17
The tortuosity of the tissue increases the relative aqueous
diffusion coefficient of any analyte by increasing the path length
that an analyte must travel. Although tortuosity and liver volume
are difficult to measure, they are important parameters to consider
for any in vivo diffusion process.31 It is the tortuosity and volume
fraction in the in vivo tissue which makes it difficult to compare
results to an in vitro experiment.
The substrate and metabolite diffusion coefficients in the
membrane (Dmem,sub and Dmem,met) are found by multiplying the
estimated aqueous diffusion coefficient (7.5 × 10-6 cm2/s) by a
multiplication factor which accounts for membrane volume fraction
and tortuosity and has been reported to be 0.2 for the polycar-
bonate membrane used in these experiments.10
Table 1 shows the various constants and their values used in
the model to predict Ed values for phenacetin and acetaminophen
and their probe outlet metabolite concentration. All diffusivity
and kinetic rate constant model values for acetaminophen and
phenacetin were identical except for the estimated metabolic rate
constant, km. The phenacetin rate constant was evaluated from
its microsomal clearance (a measure of metabolism) reported as
33 mL/min/mg microsomal protein, and then multiplied by a
constant 45 mg protein/g liver.32 This product was then multiplied
by an estimate of the liver density of 1.2 g/mL to obtain the
estimated phenacetin km value of 1.8 min-1
. In vivo disposition
predictions from microsomal data have been previously de-
scribed.33
Km and Vmax values for acetaminophen sulfation and glucu-
ronidation have been reported to be 10 µM, 500 nmol/min/liver,
and 200 µM, 1000 nmol/min/liver, respectively.18 These data are
estimated from perfused liver experiments which used flow rates
of 10 mL/min. Vmax in units of µM/min becomes 50 µM/min for
sulfation and 100 µM/min for glucuronidation. Assuming the
concentration of the substrate is less than Km, the substrate
Ch em ica lssPhenacetin, acetaminophen, and acetaminophen
glucuronide were obtained from Sigma (St.Louis, MO). Acetami-
nophen sulfate was a gift from the McNeil Consumer Products
Co. (Ft. Washington, PA). Ketamine and xylazine were obtained
from the local animal care facility at the University of Kansas.
metabolism rate constant, km,sub found by using the ratio Vmax
/
Km, reduces to 5.0 min-1 for sulfation and 0.5 min-1 for glucu-
ronidation. The kep for both drugs and their metabolites was
estimated to be 2.0 min-1, which is the estimated flow limited
value for a high-clearance drug such as acetaminophen.34
Micr od ia lysissCMA-10 microdialysis probes with an exposed
4 mm polycarbonate membrane (i.d. 400 µm, o.d. 500 µm), (CMA/
Microdialysis, Acton, MA) and outlet tubing cut to a length of 3
cm were used for liver experiments with a perfusion flow rate of
1.0 mL/min with a Ringer’s solution containing 147 mM NaCl, 4
mM KCl, and 2.3 mM CaCl2. Prior to use, the probes were rinsed
with ethanol to remove the glycerol used in the manufacturing
process. The recovery is determined by using eq 1 with the value
of C∞ECF set to zero.
P r ep a r a tor y Su r gica l P r oced u r essMale Sprague-Dawley
rats (220-280 g) were obtained from a local breeding colony at
the University of Kansas. Rats were anesthetized with 200 mg/
kg ketamine and 15 mg/kg xylazine, im. All animal experimental
procedures were approved by the local ethical committee at the
University of Kansas. Rats were allowed food and water ad
Results and Discussion
The amount of phenacetin lost from the microdialysis
probe at 1.0 µL/min along with the concentration of
acetaminophen and acetaminophen sulfate gained back
into the perfusion fluid is shown in Table 2 and Figure 2
for an individual rat. A steady-state loss of phenacetin and
gain of the metabolites was approached within 45 min as
shown in Table 2. At steady-state, approximately 10% of
the total concentration of phenacetin lost was recovered
as either the converted acetaminophen or acetaminophen
sulfate metabolite. The 10% recovered conversion of the
phenacetin metabolites will be termed the metabolite
fraction, Mfraction, for clarity. Phenacetin eluted 2 h after
acetaminophen with the chromatographic conditions neces-
sary to resolve acetaminophen from acetaminophen sulfate.
The rapid conversion of acetaminophen to acetaminophen
sulfate after delivery of phenacetin complicated the model
analysis originally intended for these experiments. The
libitum and were on
a 12 h on/off lighting cycle. The core
temperature of the animal was maintained at 37 °C by using a
314 / Journal of Pharmaceutical Sciences
Vol. 87, No. 3, March 1998

Table 2sPhenacetin (60 µM) Delivery to a Rat at 1.0 µL/mina
time (min)
[phenacetin], µM, lost from probe
[APAP-SO ], µM gained
[APAP], µM gained
total APAP metabolites (µM)
M
fraction
4
15
30
45
60
75
90
15.4
23.6
28.7
27.7
29.1
25.5
0.38
0.79
1.29
0.99
1.21
1.06
1.06
1.58
1.42
1.59
1.51
1.89
1.44
2.37
2.71
2.58
2.72
2.95
9.35
10.04
9.44
9.31
9.35
11.6
model results
[phenacetin], µM, lost from probe
[APAP], µM gained
M
fraction
kep,met, kep,sub ) 2.0 min-1
24.46
25.72
5.78
3.29
23.6
12.8
k
ep,met, kep,sub ) 5.0 min-1
a Recovery of the metabolites acetaminophen and acetaminophen sulfate are reported in µM. Each sample represents a collection time of 15 min, which began
after the collection of blanks for 1 h. The model predictions for two different kep,met and kep,sub values are listed below the experimental results. The other
parameters used in this model prediction are listed in Table 1.
Table 3sMetabolite Recovery from a Local Infusion of
Acetaminophen for Three Separate Rats
[APAP],
[APAP], µM mean E , [APAP]
[AS]gain
µM(±SD)
,
d
a
µM(C
)
[S]lost (±SD)
(%) (±SD)
M
fraction
inlet
Rat 1
11.9 (A)
119 (B)
238 (C)
3.7 ± 0.5
35.6 ± 4.9
61.4 ± 6.0
31.1 ± 4.2
29.9 ± 4.1
25.8 ± 2.5
0.40 ± 0.026 10.82
c
2.34 ± 0.03
3.54 ± 0.14
6.59
5.77d
Rat 2
11.9 (A)
119 (B)
238 (C)
3.4 ± 0.1
27.4 ± 2.0
52.1 ± 5.2
28.6 ± 0.8
23.0 ± 1.7
21.9 ± 2.2
0.22 ± 0.12
1.56 ± 0.06
2.88 ± 0.2
6.25
c
5.69
5.54d,e
Rat 3
11.0 (A)
110 (B)
220 (C)
1.8 ± 0.2
18.9 ± 1.5
49.8 ± 4.4
16.3 ± 1.8
17.2 ± 1.4
22.6 ± 2.0
0.16 ± 0.02
1.03 ± 0.15
1.57 ± 0.55
9.53
c
5.44
3.17d,e
Modelf
23.6
25.1
100 (1)
100 (2)
23.6
25.1
5.08
2.80
21.5
11.2
a The Mfraction is found by multiplying the ratio of [AS]gain/[APAP]lost by100.
b Probes were perfused at 1.0 µL/min with acetaminophen in three different
rats starting with the lowest concentration (11−12 µM, group A). The solution
was changed to the higher acetaminophen concentrations (110−120 µM, group
B, and 220−240 µM, group C) by using a liquid switch. A 15 min wash−out
period was used between each concentration change. Data are expressed
as mean ± standard deviation (n ) 4 for each concentration in one rat).
c There is no statistical difference between the percentage recovered between
groups A and B using a paired t-test. d (P < 0.1) by using a paired t-test
between groups A and C. e There is no statistical difference in the percentage
recovered between groups B and C. f Models 1 and 2 included the parameters
listed in Table 1 with kep,met and kep,sub )2.0 and 5.0, km,apap ) 1.4 as estimated
using sulfate data from Table 4. Diffusion parameters are as listed in Table
1.
The Mfraction for acetaminophen sulfate when acetami-
nophen was perfused through the probe is lower than that
of phenacetin and is shown in Table 3 and Figure 3. This
is most likely due to differences in the in vivo transport
properties of acetaminophen as compared to acetami-
nophen sulfate. Despite the high capillary exchange rates
in liver, metabolites can be recovered after a local infusion
of phenacetin or acetaminophen. No acetaminophen glu-
curonide metabolite was detected during the infusion of
acetaminophen.
Figure 2sConcentration-time profile for the loss of phenacetin (9) and the
gain of acetaminophen (b) and acetaminophen sulfate (2) into the microdi-
alysis probe, which was perfused at 1.0 µL/min; 60 µM phenacetin was
included in the perfusion fluid. The graph on the bottom shows an enlarged
baseline for the graph on the top. Note that the concentration plotted is the
concentration exiting the probe at the collection time point and is not averaged
across the collection time as is usually the case for microdialysis pharmaco-
kinetic studies.45
model as presently formulated cannot predict concentra-
tions of multiple metabolite formation. Although possible
to do, the additional computer programming required was
not done because the experiments were not designed for
such an analysis. To model the formation of multiple
metabolites after a local microdialysis delivery of a sub-
strate would require inclusion of a metabolic model such
as that described by Morris and Pang to calculate multiple
metabolites generated from liver perfusion studies into the
microdialysis model.36
There are several explanations for the lack of acetami-
nophen glucuronide in the dialysate after infusion of
acetaminophen through the microdialysis probe. The
primary explanation is that glucuronides typically are
released into the bile duct after formation since the
glucuronyltransferases are membrane-bound. On the basis
of this argument, any acetaminophen glucuronide formed
will be excreted into the bile duct. Glucuronides of phenol
have been detected in vivo in the bile by Scott and Lunte37
and Davies and Lunte after iv injection of phenol.4 In
Journal of Pharmaceutical Sciences / 315
Vol. 87, No. 3, March 1998

Table 5sModeling Predictions of the Changes in Mfraction with
Changes in the Metabolite Diffusion Coefficient, DECF,met, and Capillary
a
Permeability, kep,met
D
Dmem,met
[S]
M
ECF,met
lost
ΦECF kep,met (µM)b (µgMain)
M
fraction
2
2
(cm /s)
(cm /s)
3.33 × 10-6 7.5 × 10-6
2.97 × 10-6 7.5 × 10-6
2.97 × 10-6 6.75 × 10-6
2.64 × 10-6 6.0 × 10-6
3.33 × 10-6 7.5 × 10-6
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.4
0.4
0.4
2.0
1.0
0.5
2.0
1.0
0.5
2.0
1.0
0.5
2.0
1.0
0.5
2.0
1.0
0.5
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
2.8
0.852
1.035
1.202
0.861
1.046
1.216
0.840
1.025
1.195
0.823
1.001
1.183
0.714
0.932
1.153
30.4
37.0
42.9
30.8
37.4
43.4
30.0
36.6
42.7
29.4
35.8
42.3
25.5
33.3
41.2
Figure 3sConcentration time profile for the gain of acetaminophen sulfate
(APAP−SO ) (2) and the loss of acetaminophen (APAP) (b) when APAP
4
a The model was performed using the acetaminophen parameters listed in
Table 1 with an initial concentration of 10 µM. The in vivo and membrane
diffusion coefficients listed in Table 1 were reduced 10% and 20% to achieve
was perfused through the probe (1.0 µL/min) at concentrations of 11, 110,
and 220 µM. The perfusion fluid concentration was changed at 75 and 150
min.
the reduced diffusion coefficients in columns 1 and 2. b The E for the substrate
d
2
in all cases was 28.3% assuming a DECF,Sub of 3.3 × 10-6 cm /s.
Table 4sEstimates of Michaelis−Menten Parameters for Phenolic
Conjugation in a Perfused Liver Modela
for a perfused liver model (model A) that assumes homo-
geneous distribution of these two enzymes. The numbers
do not sum to 100% because the extraction efficiency of the
liver removal is also included in Pang’s models. For the
model phenolic compound, approximately 43% is predicted
to be converted into a sulfate metabolite, while 25% is
predicted to become a glucuronide. The results for ac-
etaminophen show that approximately 5% of the dose
would become a glucuronide metabolite in a system with
an assumption of homogeneous distribution of enzymes. It
is known that in the hepatocytes homogeneous distribution
does not occur and so a more appropriate model would be
that of model B, which assumes the drug first passes
through a zone containing sulfotransferases only and then
passes through a zone that only contains glucuronyltrans-
ferases. For this model simulation, which is closer to the
in vivo reality, the conversion of acetaminophen to its
glucuronide ranges between 2.2% and 4.4%. With such low
conversion rates, it is unlikely that a detectable amount
of acetaminophen glucuronide could have entered the
dialysate.
Table 5 shows the affect on Ed of a lower metabolite in
vivo diffusion coefficient, membrane diffusion coefficient,
and kep,met. Diffusion coefficients were lowered by 10% and
20% as an estimate in the change in diffusion coefficient
due to changes in molecular weight differences of the
metabolite. Using a Stokes-Einstein relationship as an
approximation to calculate the differences between sub-
strate and metabolite in vivo and membrane diffusion
coefficient because of molecular weight change, the ex-
pected change in diffusion coefficients would be based on
the cubed root of the molecular weight.39 The difference
between the parent compound acetaminophen (MW 151)
and the metabolites acetaminophen sulfate (MW 231) and
acetaminophen glucuronide (MW 326) would be an ap-
proximate 15% and 30% reduction in the diffusion coef-
ficient based on the approximate Stokes-Einstein rela-
tionship. The lowering of the metabolite in vivo diffusion
coefficient by 10% of the parent in vivo diffusion coefficient
while keeping Dmem,met and kep,met the same as the parent
compound increases the Mfraction slightly. A 10% decrease
in both the in vivo and membrane diffusion coefficient
decreases Mfraction. A 20% decrease in both the in vivo and
membrane diffusion coefficient only makes about a 1%
change in the Mfraction. Table 5 clearly shows that Mfraction
is more highly dependent upon the metabolite capillary
Km
Vmax
Km
Vmax
(sulfate) (sulfate) (glucuronide) (glucuronide)
solute
(µM)
(nmol/min)
(µM)
(nmol/min)
Phenolic Model Drug
Acetaminophen
10
109
500
1476
200
915
1000
828
model A
model B
input liver
%
%
%
%
solute
concn (µM) sulfate glucuronide sulfate glucuronide
phenolic model
1
10
90.1
86.4
66.6
42.8
71.5
69.9
63.1
55.1
42.3
9.4
12.6
21.4
24.0
4.8
4.9
5.3
99.3
98.2
73.5
44.2
72.4
65.2
56.6
43.1
28.0
0.29
0.71
10.0
18.7
2.4
3.0
3.6
4.4
4.8
50
100b
1
acetaminophen
10
50
100
200
5.6
5.8
a Based on the liver perfusion modeling work of Morris and Pang.36 Model
A assumes homogeneous distribution of enzymes. Model B assumes that
sulfotransferases are encountered along the sinusoid before glucuronyltrans-
ferases. Note that these acetaminophen data were not found in the literature
until after most of the simulations in this paper were performed. Therefore, all
the simulations use the estimate for sulfation and glucuronidation based on
Pang’s model phenolic substrate data. b 200 µM was not calculated for the
phenolic model substrate in the paper by Morris and Pang.
addition to the majority of glucuronide products being
excreted into the bile duct, the efflux of acetaminophen
glucuronide out of hepatocytes is lower than for acetami-
nophen sulfate. Iida et al. report that in incubations of
hepatocytes with 5 mM acetaminophen in the media, efflux
of acetaminophen glucuronide is approximately 4 nmol/106
cells, whereas acetaminophen sulfate efflux is 10 nmol/106
cells, indicating a 2.5-fold preference for the sulfate con-
jugate.38
Another explanation for the lack of acetaminophen
glucuronide collection into the dialysate after acetami-
nophen perfusion may be related to the enzyme kinetics
for the production of these metabolites. Table 4 shows data
obtained from perfused rat liver models performed by
Morris and Pang.36 The kinetic parameters for a model
phenolic sulfotransferase and glucuronyltransferase are
compared to that of estimates for acetaminophen metabo-
lism. The data shown are for different concentration inputs
316 / Journal of Pharmaceutical Sciences
Vol. 87, No. 3, March 1998

Table 6sModeled Metabolite Concentration Differences between
c
Linear and Michaelis−Menten Metabolism
modeled
recovery
(%)
lost across
membrane/ [M]gain
,
Cinlet [S] (µM)
Coutlet [S]
(pmol/min)
outlet
M
fraction
1.0 (linear)a
28.7
28.7
28.7
28.7
28.7
28.7
28.7
28.7
0.71770
0.71770
7.1770
7.1770
71.770
71.770
143.54
143.54
0.287
0.287
2.87
2.87
28.7
28.7
57.4
57.4
0.085
0.084
0.85
0.75
8.5
3.9
17.1
5.3
29.7
29.3
29.7
26.0
29.7
13.5
29.7
9.3
1.0 (MM)b
10.0 (linear)
10.0 (MM)
100.0 (linear)
100.0 (MM)
200.0 (linear)
200.0 (MM)
a Indicates that the amount of metabolite predicted to enter into the probe
was calculated by using the model which assumes linear metabolism and
that CECF is lower than Km for the substrate compound. b MM indicates that
Michaelis−Menten kinetics were included in the generation term of the
metabolite model. c Model parameters are as follows: kep,sub ) 2.0 min-1,
km,sub,icf ) 5.0 min-1, km,met ) 0.0 min-1, kep,met ) 2.0 min-1, Vmax ) 50 µM/
Figure 4sModel prediction of the concentration profile in the tissue space
for the substrate (solid line pointing to the left axis) and the metabolite (dashed
line pointing to the right axis).
permeability, kep,met, rather than in vivo and membrane
diffusion coefficients.
min, Km ) 10 µM. Q ) 1.0 µL/min. [S] and [M] stand for the concentrations
d
To quickly determine the diffusion coefficient differences
between acetaminophen and its metabolites an in vitro
recovery (stirred) of acetaminophen, acetaminophen sul-
fate, and acetaminophen glucuronide was performed. The
recoveries found using a perfusion rate of 1.0 µL/min at
23 °C were 49%, 42%, and 28% for acetaminophen, ac-
etaminophen sulfate, and acetaminophen glucuronide,
which clearly indicates that acetaminophen glucuronide
has a lower aqueous diffusion coefficient than acetami-
nophen or acetaminophen sulfate. Using the resistance
equations derived by Bungay et al.,10 the reduction in
solution diffusion coefficient between acetaminophen and
its metabolites is 19% (sulfate) and 51% (glucuronide)
based on these in vitro Ed values. With a lower effective
diffusivity through the dialysis membrane, it is expected
that acetaminophen glucuronide would also have a lower
tissue diffusivity and possibly a lower in vivo extraction
efficiency than acetaminophen sulfate. The in vivo recov-
ery of acetaminophen was approximately 25%, as shown
in Table 3. The in vivo recoveries of acetaminophen sulfate
and acetaminophen glucuronide would be expected to be
lower than acetaminophen because they have lower diffu-
sion coefficients and because they do not undergo further
metabolism, thus reducing the contribution of kinetic
processes to kL in eq 2, which would have the effect of
decreasing the recovery.
of the substrate and metabolite.
for any metabolite will be dependent upon metabolite
kinetic and diffusive properties in the tissue.
Figure 4 shows the predicted metabolite and substrate
concentration profiles to and from the microdialysis probe
as calculated by the model. The metabolite concentration
profile from the probe has a maximum value offset from
the phenacetin (subsrate) concentration profile. This oc-
curs because of the concentration gradient caused by
removal of material by the microdialysis probe and the sink
conditions in the tissue caused by removal processes such
as capillary uptake or bile duct removal. The metabolite
actually has two directions in which it can move to an area
of lower concentration: the probe and the far-field tissue
space. The probe acts as an artificial blood vessel that is
capable of removing the metabolite from the tissue. Since
the concentration of the parent compound is zero at the
far-field boundary, the metabolite concentration at that
space point would also be expected to be zero. Thus, the
far-field boundary is a sink for the metabolite that is
generated closer to the probe.
The Mfraction for acetaminophen sulfate is statistically
different (P < 0.1) between the 11 and 220 µM acetami-
nophen perfusions. This appearance of concentration
dependence can be attributed to two factors. The obvious
explanation is that the concentration in the ECF using
acetaminophen concentrations of greater than 100 µM in
the dialysis perfusion fluid may exceed the estimated Km
for the phenolsulfotransferase, which is 10 µM.21 After the
compilation of all the model data, the paper by Morris and
Pang was found which contains an estimated Km for
acetaminophen of 109 µM.36 Using this estimate, the
change in Mfraction between different concentrations can still
be explained by nonlinear Michaelis-Menten kinetics. The
second is that the protein that transports acetaminophen
sulfate from the intracellular space to the extracellular
space may be saturated.41 A shift would be expected for
the values between 10 and 50 µM for the acetaminophen
as modeled by Morris and Pang for the isolated perfused
liver36 and described experimentally for phenol and other
phenolic compounds by others.42 Table 6 shows the predic-
tion differences between the model that uses linear kinetics
for the production of metabolite versus Michaelis-Menten
kinetics. Changes in the Mfraction will occur with saturation
of enzymes due to the reduction of the enzymatic velocity
based on calculations using Michaelis-Menten kinetics.
Other authors have reported the formation and collection
of metabolites from microdialysis experiments in rat liver.
Van Belle et al. observed an Mfraction of 18% for oxidative
The model predicts a Mfraction of 21.5% for acetaminophen
with a kep,sub and kep,met ) 2.0 min-1 and a Mfraction of 11.2%
for kep,sub, kep,met ) 5.0 min-1 using the acetaminophen data
presented by Morris and Pang.40 These data are shown in
Table 3 for comparison with the experimental data for
acetaminophen. The model predicts a Mfraction of 23.6% for
phenacetin conversion to acetaminophen using kep,sub and
kep,met ) 2.0 min-1 and 12.8% for kep,sub, kep,met ) 5.0 min-1
.
The metabolite recovery obtained for the metabolites of
phenacetin and acetaminophen do not match the model
predictions using the kep flow limited estimate of 2.0
min-1 34
but they are not worse than a factor of 2-3, which
,
is not unexpected when a complex model is used to predict
events which occur in a complicated biological matrix.
Possible reasons for the discrepancy include incorrect
estimates of the diffusion and kinetic parameters and/or
possible convection around the microdialysis probe. The
diffusion coefficient used in the model prediction was the
same for the metabolite as for the parent compound.
Additionally it is possible that capillary permeation may
be different between the parent and metabolite. A decrease
in the kL that describes total metabolite kinetic processes
would allow more of the metabolite to enter the probe, as
shown in Table 5 for various changes in kep. Thus, Mfraction
Journal of Pharmaceutical Sciences / 317
Vol. 87, No. 3, March 1998

a
a
Table 7sMfraction Predictions for Different kep,met
Table 8sEffect of Q on M
d fraction
steady state
concn in
dialysate
Cmax
flow rate
(µL/min) C
E
E
Cmax
d
d
maximum
concn
E (est)a C /CMax position
d dial
radial
(substrate) Cmetab,outlet CMax (est) C /Cmax position
outlet
dial
kep,met
M
fraction
0.5
1.0
2.0
5.0
55.9
71.7
83.5
92.7
44.1
28.3
16.5
7.3
11.3
8.5
5.5
2.6
22.13 30.0
25.22 17.7
27.12 9.7
28.38 4.1
0.51
0.34
0.20
0.09
0.0275
0.0275
0.0280
0.0280
0.001
0.01
0.05
0.1
0.5
1.0
18.24
17.35
15.92
15.01
12.03
10.36
8.52
64.5
61.3
56.3
53.0
42.5
36.6
30.1
21.4
61.5
57.6
51.6
48.0
36.9
31.2
25.2
17.6
5.08
5.75
7.43
8.61
12.6
15.0
17.7
21.7
29.7
0.0317
0.0306
0.0301
0.0296
0.0286
0.0280
0.0275
0.0275
30.1
30.9
31.7
32.6
33.2
33.8
34.5
a The model was calculated using km ) 5.0 min-1 and kep ) 2.0 min-1.
2.0
5.0
6.07
a Initial substrate concentration was found by using the values listed in
Table 1. The modeled substrate recovery was 28.3% using an inlet
concentration of 100 µM. In the calculation of the metabolite outflow
concentration, km,met is set to zero. kep in these simulations was varied and
thus not set at 2.0 min-1 as shown in the table. b E (est) is the modeled in
d
vivo E for the metabolite based on the parameters in Table 1 and kep,met
d
given in this table.
conversion of carbamazipine when it was included in the
microdialysis perfusion fluid using a 2 µL/min perfusion
flow rate.5 The 18% Mfraction of this oxidative metabolite
was reported to agree with isolated perfused liver data.
They also suggested that microdialysis can be used as an
alternative to isolated perfused liver studies to determine
the metabolic formation of compounds. In our work ac-
etaminophen produced an Mfraction of 4-10% at a perfusion
flow rate of 1 µL/min. The acetaminophen data presented
here do not match that of isolated perfused liver data,
which has reported a 75% conversion of acetaminophen to
acetaminophen sulfate at concentrations entering the
perfused rat liver of less than 40 µM.43 There may be
several reasons for this discrepancy. First, these animals
were anesthetized with ketamine which may interfere with
local metabolism. A second reason, which is more likely,
is that Mfraction is a function of physiological parameters for
the metabolite and probe parameters such as membrane
length and flow rate.
Figure 5sModel predicted concentration profiles with varying values of capillary
permeation, kep. kep ) 0.001 (9), 0.01 (b), 0.05 (2), 0.1 (1), 0.5 ([), 1.0
(+), and 5.0 (*). The dashed line indicates the position of the membrane.
Table 7 and Figure 5 exhibit the model predictions and
concentration profiles for variations in kep,met
. Table 7
shows that Cdialysate,met and Mfraction will increase as kep,met
decreases for a substrate with model parameters listed in
Table 1 for acetaminophen. This table also shows the
metabolite maximum concentration and its corresponding
radial point in the ECF. The position of the maximum
concentration does not change more than 50 µm between
a kep,met of 0.001 min-1, which would be poor capillary
permeability, and a kep,met of 5.0 min-1, which would be high
capillary permeability. This small change in the maximum
concentration radial position shows that the probe is
sampling from a limited area.
Figure 6sModel predicted concentration profiles with different values of the
volumetric flow rate, Q : (9) 0.5 µL/min, (b) 1.0 µL/min (2), 2.0 µL/min
d
(1), 5.0 µL/min. The dashed line indicates the position of the membrane.
A ratio of Cdial divided by this maximum concentration
is shown in Table 7 for each kep,met value. This ratio can
be compared to a model-predicted Ed for the metabolite
based on the kep,met values given. These model predictions
show that an in vivo Ed for the metabolite cannot be used
to predict the maximum concentration in the tissue. The
concept of Ed is based on knowing Csample and Cdial for an
unknown. For a recovery experiment, Csample is the far-
field concentration and Cdial is zero, whereas for a delivery
experiment Csample is set to zero and Cdial is known. In these
metabolism experiments, Csample varies across the ECF and
is zero at the far field but reaches a maximum at distances
that vary from the probe center based on the metabolite
physiological parameters. The probe is sampling a space
very close to it and is removing very little material. This
removal does not appear to affect the maximum concentra-
tion distance significantly, which means that little is being
removed. The lack of change in Csample for a recovery
experiment of dopamine has been reported with flow rates
varying between 0.3 and 1.6 µL/min, where no change in
Csample was observed.44 Table 7 shows that with decreasing
Ed, Mfraction will increase.
Table 8 and Figure 6 shows the affect of using different
Qd in the calculation of Mfraction
. Mfraction increases with
decreasing Qd. This may be due to more mass being
collected at the higher flow rates. More mass is released
per minute at the higher flow rates and more mass is
gained back. Additionally, probe residence time may affect
Mfraction since a metabolite in the perfusate could diffuse
back into the tissue space if time and concentration
gradients conditions exist to permit back-diffusion into the
ECF to occur. This indicates that comparing microdialysis
results for the conversion of a metabolite to liver perfusion
data is highly dependent upon the conditions of the
experiment such as flow rate and membrane length plus
318 / Journal of Pharmaceutical Sciences
Vol. 87, No. 3, March 1998

Table 9sEffect of Membrane Length on Modeled Resultsa
Gi
Generation term of the metabolite in the tissue
space (M/min)
length (mm)
E (substrate)
d
[M]dial
M
fraction
E (metabolite)
d
kep,met
kep,sub
Capillary permeability rate constant (metabolite)
(min-1
)
1
2
4
9.0
16.5
28.3
49.6
3.1
5.4
8.5
34.4
32.7
30.0
23.8
5.1
9.7
17.7
35.0
Capillary permeability rate constant (substrate)
(min-1
Metabolism rate constant (metabolite) (min-1
Metabolism rate constant (substrate) (min-1
Lumped kinetic term (min-1
Michaelis constant (mol/L; M)
)
10
11.8
km,met
km,sub
kL
)
a The model parameters are listed in Table 1. km,sub ) 5.0 min-1.
)
E (metabolite) is calculated using the parameters in Table 1 with km,met ) 0.0
d
)
min-1.
Km
[M]dial
Absolute metabolite concentration exiting the
dialysate (mol/L; M)
the physiological parameters of metabolism rate constant
and capillary permeability.
Our proportion of Mfraction results also differ from those
of Davies and Lunte.4 They report hydroquinone concen-
trations between 0.62 and 5.8 µM after a 100% Ed loss of
phenol to the liver. These results give Mfraction of less than
1%, which is lower than what we observe for acetami-
nophen and phenacetin. With such a high Ed, it is possible
that any metabolite that diffused into the probe at one
point along the probe axis may then diffuse out again
further down the probe axis. Table 9 shows that with
increasing length, and thus increasing Ed, the Mfraction
decreases. This is likely due to back-diffusion of the
metabolite into the ECF space. Thus, the variation in Ed
due to physiological parameters, volumetric flow rate, and
membrane length will greatly affect the results obtained
when using microdialysis to study in situ metabolism.
Mfraction [M]dial/[S]lost (dimensionless)
ΦECF
Φmem
Volume fraction in the ECF (dimensionless)
Volume fraction in the membrane (dimension-
less)
Dialysate volumetric flow rate (cm3/min)
Qd
r
Radial position (cm)
[S]lost
t
C(substrate)inlet - C(substrate)outlet (mol/L; M)
Time (min)
Vmax
Maximum velocity of an enzyme (mol/min)
References and Notes
1. Robinson, T. E.; J ustice, J . B., J r., Eds. Microdialysis in the
Neurosciences; Elsevier: Amsterdam, 1991.
2. Ungerstedt, U. MicrodialysissPrinciples and applications for
studies in animals and man. J . Internal. Med. 1991, 230,
365-373.
Summary
In the present study it has been demonstrated that
microdialysis can be used to study local metabolism in the
liver when a substrate compound is included in the
perfusion fluid. Substrates metabolized through cyto-
chrome P450 processes and conjugation processes can be
subject to such studies. However, not all possible metabo-
lites may enter the microdialysis probe because of physi-
cochemical, physiological, and/or mass transport reasons
such as was shown with the lack of acetaminophen glucu-
ronide after acetaminophen perfusion. The mathematical
model was used to predict the concentrations of metabolites
produced after one-step metabolism of a substrate delivered
from a microdialysis probe. Predictions of Mfraction are
dependent upon metabolite physiological and microdialysis
probe parameters. Further work is necessary to develop
the model to be able to predict concentrations from
processes which occur via multistep metabolic pathways.
3. Lunte, S. M.; Lunte, C. E. Microdialysis sampling for
pharmacological studies: HPLC and CE analysis. In Ad-
vances in Chromatography; Brown P. R., Grushka, E., Eds.;
Marcel Dekker Inc.: New York, 1996; Vol. 36, pp 383-432.
4. Davies, M. I.; Lunte, C. E. Simultaneous microdialysis
sampling from multiple sites in the liver for the study of
phenol metabolism. Life Sci. 1996, 59, 1001-1013.
5. Van Belle, K.; Sarre, S.; Ebinger, G.; Michotte, Y. Brain, liver,
and blood distribution kinetics of carbamazepine and its
metabolic interaction with clomipramine in rats: A quantita-
tive microdialysis study. J . Pharmacol. Exp. Ther. 1995, 272,
1217-1222.
6. Scott, D. O.; Lunte, C. E. In vivo microdialysis sampling in
the bile, blood, and liver of rats to study the disposition of
phenol. Pharm. Res. 1993, 10, 335-342.
7. Ståhle, L.; Segersva¨rd, S.; Ungerstedt, U. Drug distribution
studies with microdialysis. II. Caffeine and theophylline in
blood, brain, and other tissues in rats. Life Sci. 1991, 49,
1843-1852.
8. Ungerstedt, U; Herrera-Marschitz M; J ungnelius, U; Ståhle,
L; Tossman, U.; Zetterstro¨m, T. Dopamine synaptic mecha-
nisms reflected in studies combining behavioral recordings
and brain dialysis. In Advances in Dopamine Research;
Kohsaka, M., Ed.; Pergamon Press: New York, 1982; pp
219-231.
9. Ault, J . M.; Riley, C. M.; Meltzer, N. M.; Lunte, C. E. Dermal
microdialysis sampling in vivo. Pharm. Res. 1994, 11, 1631-
1639.
10. Bungay P. M.; Morrison P. F.; Dedrick R. L. Steady-state
theory for quantitative microdialysis of solutes and water in
vivo and in vitro. Life Sci. 1990, 46, 105-119.
11. Morrison, P. F.; Bungay, P. M.; Hsiao, J . K.; Mefford, I. V.;
Dykstra, K. H.; Dedrick, R. L. Quantitative microdialysis.
In Microdialysis in the Neurosciences, Robinson, T. E.,
J ustice, J . B., J r., Eds.; Elsevier: Amsterdam, 1991; pp 47-
80.
Glossary
Coutlet
Cinlet
Outlet concentration from the microdialysis probe
(mol/L; M)
Inlet concentration into the dialysis probe (mol/
L; M)
C∞ECF
Far-field concentration (mol/L; M)
C
ECF(r,t) Concentration of any species in the ECF at
position r and time t (mol/L; M)
Dmem,sub Membrane diffusion coefficient for the substrate
(cm2/s)
Dmem,met Membrane diffusion coefficient for the metabolite
12. Dykstra, K. H.; Arya, A.; Arriola, D. M.; Bungay, P. M.;
Morrison, P. F.; Dedrick, R. L. Microdialysis study of zidovu-
dine (AZT) transport in rat brain. J . Pharmacol. Exp. Ther.
1993, 267, 1227-1236.
13. Wallgren, F.; Amberg, G.; Hickner, R. C.; Ekelund, U.;
J orfeldt, L.; Henriksson, J . A mathematical model for
measuring blood flow in skeletal muscle with the microdi-
alysis ethanol technique. J . Appl. Physiol. 1995, 72, 648-
659.
(cm2/s)
DECF,sub ECF diffusion coefficient for the substrate
(cm2/s)
DECF,met ECF diffusion coefficient for the metabolite
(cm2/s)
Ed
Recovery (extraction fraction) (dimensionless)
Journal of Pharmaceutical Sciences / 319
Vol. 87, No. 3, March 1998

14. Hickner, R. C.; Ekelund, U.; Mellander, S.; Ungerstedt, U.;
Henriksson, J . Muscle blood flow in the cat: comparison of
the microdialysis ethanol technique to direct measurement.
J Appl. Physiol. 1995, 79, 638-647.
32. Houston, J . B. Utility of in vitro drug metabolism data in
predicting in vivo metabolic clearance. Biochem. Pharmacol.
1994, 47, 1469-1479.
33. Hayes, K. A.; Brennan, B.; Chenery, R.; Houston, J . B. In
vivo disposition of caffeine predicted from hepatic microsomal
and hepatocyte data. Drug Metab. Disp. 1995, 23, 349-353.
34. Ichikawa, M.; Tsao, S. C.; Lin, Tsu-H.; Miyauchi, S.; Sawada,
Y.; Iga, T.; Hanano, M.; Sugiyama, Y. ‘Albumin-mediated
transport phenomenon’ observed for ligands with high
membrane permeability: Effect of the unstrirred water layer
in the Disse’s space of rat liver. J . Hepatol. 1992, 16, 38-
49.
15. Stenken, J . A.; Lunte, C. E.; Southard, M. Z.; Ståhle, L.
Factors that influence microdialysis recovery. Comparison
of experimental and theoretical microdialysis recoveries in
rat liver. J . Pharm. Sci. 1997, 86, 958-966.
16. Rappaport, A. M. The structural and functional unit in the
human liver (liver acinus). Anat. Rec. 1958, 130, 673-689.
17. Arias, I. M.; J akoby, W. B.; Popper, H.; Schachter, D., Eds.
The Liver: Biology and Pathobiology, 2nd ed.; Raven Press
Ltd.: New York, 1988.
18. Pang, K. S.; St-Pierre, M. V. Hepatic modeling of drugs and
metabolites. In Biliary Excretion of Drugs and Other Chemi-
cals; Progress in Pharmacology and Clinical Pharmacology;
Siegers, C-P, Watkins, J . B., Eds.; Gustav Fischer Verlag:
Stuttgart, 1991; Vol. 8, pp 89-126.
19. Pang, K. S. Kinetics of conjugation reactions in eliminating
organs. In Conjugation Reactions in Drug Metabolism; Mul-
der, G. J ., Ed.; Taylor and Francis: London, 1990; pp 5-39.
20. Gillette, J . R. Kinetic aspects of metabolism and elimination
of foreign compounds in animals. In Enzymatic Basis of
Detoxication; J akoby, W. B., Ed.; Academic Press, Inc.:
Orlando, 1980; Vol. 1, pp 9-24.
21. Gores, G. J .; Kost, L. J .; LaRusso, N. F. The isolated perfused
rat liver: Conceptual and practical considerations. Hepatol-
ogy 1986, 6, 511-517.
22. Bass L; Keiding S. Physiologically based models and strategic
experiments in hepatic pharmacology. Biochem. Pharmacol.
1988, 37, 1425-1431.
23. Smith, R. L.; Timbrell, J . A. Factors affecting the metabolism
of phenacetin I. Influence of dose, chronic dosage, route of
administration and species on the metabolism of (1-c14-
acetyl)phenacetin. Xenobiotica 1974, 4, 489-501.
24. Miner, D. J .; Kissinger, P. T. Evidence for the involvement
of N-acetyl-p-quinoneimine in acetaminophen metabolism.
Biochem. Pharmacol. 1979, 3285-3290.
35. Davies, M. I.; Lunte, C. E. Microdialysis sampling for hepatic
metabolism studies: Impact of microdialysis probe design
and implantation technique on liver tissue. Drug Metab.
Disp. 1995, 23, 1072-1079.
36. Morris, M. E.; Pang, K. S. Competition between two enzymes
for substrate removal in liver: Modulating effects due to
substrate recruitment of hepatocyte activity. J . Pharmacokin.
Biopharm. 1987, 15, 473-496.
37. Scott, D. O.; Lunte, C. E. In vivo microdialysis sampling in
the bile, blood, and liver of rats to study the disposition of
phenol. Pharm. Res. 1993, 10, 335-342.
38. Iida, S.; Mizuma, T.; Sakuma, N.; Hayashi, M.; Awazu, S.
Transport of acetaminophen conjugates in isolated rat hepa-
tocytes. Drug Metab. Disp. 1989, 17, 341-344.
39. Barrow, G. N. Physical Chemistry, 5th ed.; McGraw Hill Book
Co.: New York, 1988; p 803.
40. The estimated Vmax and Km for acetaminophen were found
in the paper by Morris and Pang36 after most of the
simulations for the tables were performed using the model
phenol metabolism estimates given by Pang.18
41. Goresky, C. A.; Pang, K. S.; Schwab, A. J .; Barker, F. I.,
Cherry, W. F.; Bach, G. G. Uptake of a protein-bound polar
compound, acetaminophen sulfate by perfused rat liver.
Hepatology 1992, 16, 173-190.
42. Koster, H.; Halsema, I.; Scholtens, E.; Knippers, M.; Mulder,
G. J . Dose-dependent shifts in the sulfation and glucuronida-
tion of phenolic compounds in the rat in vivo and in isolated
hepatocytes: The role of saturation of phenolsulfotransferase.
Biochem. Pharmacol. 1981, 30, 2569-2575.
25. Van Belle K.; Sarre S.; Ebinger G.; Michotte Y. Quantitative
microdialysis for the in vivo measurement of carbamazepine,
oxcarbazepine and their major metabolites in rat brain and
liver tissue and in blood using the internal standard tech-
nique. Eur. J . Pharm. Sci. 1995, 3, 273-280.
26. Stenken, J . A. Identification and Modeling of Parameters that
Influence Microdialysis Sampling in vitro and in vivo. Ph.D.
Dissertation, University of Kansas, 1995.
43. Pang K. S.; Terrell J . A. Conjugation kinetics of acetami-
nophen by the perfused rat liver preparation. Biochem.
Pharmacol. 1981, 30, 1959-1965.
44. Sam, P. M.; J ustice, J . B., J r. Effect of general microdialysis-
induced depletion on extracellular dopamine. Anal. Chem.
1996, 68, 724-728.
27. Carnahan, B.; Luther, H. A.; Wilkes, J . O. Applied Numerical
Methods. Robert E. Krieger Publishing: Malabar, FL, 1990.
28. Press, W. H.; Flanner, B. P.; Teukolsky, S. A.; Vetterling,
W. T. Numerical Recipes in FORTRAN: The Art of Scientific
Computing, 2nd ed.; Cambridge University Press: Cam-
bridge, 1986.
45. Ståhle, L. Microdialysis in pharmacokinetics. Eur. J . Drug
Metab. Pharmacokinet. 1993, 18, 89-96.
29. Laidler, K. J . Chemical Kinetics, 3rd ed.; Harper Collins
Publishers: New York, 1987; p 401.
Acknowledgments
30. Rice, M. E.; Gerhardt, G. A.; Hierl, P. M.; Nagy, G.; Adams,
R. N. Diffusion coefficients of neurotransmitters and their
metabolites in brain extracellular fluid space. Neuroscience
1985, 15, 891-902.
31. Rice, M. E.; Nicholson, C. Diffusion and ion shifts in the brain
extracellular microenvironment and their relevance for vol-
tammetric measurements. The brain is not a beaker: In vivo
vs In vitro voltammetry. In Neuromethods, Vol. 27: Volta-
mmetric Methods in Brain Systems; Boulton, A., Baker, G.;
Adams, R. N., Eds.; Humana Press Inc. New York, 1995; pp
27-79.
This work was supported by NIH (R01 GM45566) and the
Swedish Medical Council (09069). A Procter & Gamble Bioana-
lytical Chemistry Fellowship and a J . William Fulbright Fellow-
ship to Sweden supported J .A.S. Conversations with Dr. Paul
Morrison and discussions, faxes, and e-mail with Dr. Peter
Bungay, who both work at the Drug Delivery and Kinetics
Resource, Biomedical Engineering & Instrumentation Program,
Office of Research Services, National Institutes of Health, are
greatly appreciated.
J S970288Z
320 / Journal of Pharmaceutical Sciences
Vol. 87, No. 3, March 1998