Graduate Program in Pharmaceutics, College of Pharmacy, University
of Minnesota
The deconvolution principle was used to evaluate the extent of
absorption and first-pass elimination of selected drugs. In the first
example, deconvolution of the portal blood profiles of etretinate (ET,
a synthetic retinoid) indicated that there was significant gut-wall
conversion of ET to acitretin (ETA, the primary metabolite of ET)
during a 60-min intestinal perfusion of ET. In the second example,
deconvolution was used to confirm that the extent of carbovir
disappearing from the gastrointestinal lumen was matched by the extent
of carbovir appearance in the portal blood. Thus, deconvolution has
several important applications in the study of absorption and
intestinal first-pass metabolism.
 |
Introduction |
One
approach to the determination of extraction by an
eliminating organ entails an area under the blood concentration-time curve (AUC)3 analysis. This may be achieved by
administration of drug by multiple routes followed by sampling at a
single site (the "multiple site input" approach). Alternatively,
administration of the drug at a single site followed by sampling from
multiple sites (the "multiple site sampling" approach) (1) may be
used. The extraction efficiency for the eliminating organ is then
estimated by the ratio of the appropriate AUCs (1).
An accurate determination of AUC necessitates the collection of samples
until the concentration-time profile is well within the terminal
elimination phase. This in turn requires extended blood sampling times
for drugs with long elimination half-lives. In smaller animals such as
rats, frequent sampling from multiple sites over a long period of
time is impractical. The use of other techniques such as the
Wagner-Nelson and the Loo-Riegelman analyses requires specific
compartmental restrictions to be placed on the disposition of the drug
(2).
The use of deconvolution theory to delineate the absorption and
gut-wall metabolism of drugs is presented here. This method of analysis
provides an advantage for those drugs for which multiple sites of
measurement are restrictive and for experimental protocols that do not
allow for extended blood sampling. In addition, no compartmental model
specification is required. Two examples are presented.
In the first example, deconvolution theory was used to generate an
estimate of the fraction of orally absorbed etretinate (ET) escaping
gut-wall metabolism (fg). ET, a synthetic
analog of the fat-soluble vitamin A, experiences variable absorption from the intestine as well as significant first-pass elimination. Acitretin (ETA) is the primary active metabolite of ET. Both retinoids (fig. 1) are currently on the market for
the treatment of psoriasis, and ET has been studied in clinical trials
for cancer chemoprevention and chemotherapy (3). The in situ
intestinal perfusion of ET in mixed micelles of sodium taurocholate and
egg phosphatidylcholine resulted in a steady-state loss of greater than
80% from the lumen (4). Very low levels of ET were observed in the
systemic circulation following intestinal perfusions, but ET and high
levels of ETA were detected in the portal blood. An estimate of the
extent of gut-wall metabolism of ET during its intestinal absorption
from mixed micelles was desired. However, because of the large volume of distribution and long terminal half-life for ET, blood sampling for
long periods post-perfusion were required for an AUC approach. Deconvolution of portal blood concentrations was explored to determine the extent of gut-wall metabolism of ET.
The second example involved carbovir [(
)-carbocyclic
2
,3-dideoxy-2,3-didehydroguanosine, CBV, fig. 1]. CBV is a
carbocyclic nucleoside with demonstrated in vitro activity
against the human immunodeficiency virus (5). In rats, the oral
bioavailability of CBV is only 20% (6), but CBV does not undergo
significant first-pass metabolism in either the liver or intestine (7). This suggested that poor intestinal absorption was responsible for the
poor oral availability of CBV in the rat.
In the present work, the fraction of intestinally perfused carbovir
that appeared in the portal vein during an in situ
intestinal perfusion was calculated with the use of deconvolution.
These estimates were compared with those obtained from the lumenal
disappearance of CBV during the intestinal perfusions.
| |
Theory |
The convolution principle may be expressed as follows:
|
(1)
|
The response function,
C(t), is obtained by the
convolution of the unit impulse function,
C(
), with the input function,
f(t). Mathematical convolution
has been functionally expressed here by the asterisk. The applications
of this theory are numerous (8-13).
Under conditions of linearity and time invariance, the transport of
drug from a site i to a site j can be completely expressed by the three
functions in eq. 1. C(t) refers
to the concentration profile obtained when the drug is placed at site i
and the concentration measured at site j.
C() refers to the concentration profile at site j obtained after the drug is placed directly at site j, and
f(t) represents the transfer
function that governs the movement of mass from site i to j. The
knowledge of any two of these three functions allows a determination of
the third one.
Deconvolution is the mathematical inverse of convolution. This refers
to the situation where a knowledge of
C(t) and
C() is used to obtain the input
function, f(t).
| |
Materials and Methods |
Etretinate.
ET and ETA were obtained as gifts from Hoffmann-La Roche Inc. (Nutley,
NJ). Sodium taurocholate (NaTC) was purchased from Sigma Chemical Co.
(St. Louis, MO) and was recrystallized by a modification of the
procedure by Pope (14). Egg phosphatidylcholine (PC, lecithin) was
purchased from Avanti Polar Lipids (Alabaster, AL). PC was stored at
4°C under nitrogen and protected from light. Retinyl acetate and
HEPES (N-[2-hydroxyethyl]piperazine
-N-[2-ethanesulfonic acid]) were obtained from Sigma. All
other reagents were reagent grade or better. All procedures were
carried out under yellow light to prevent photodegradation of the
retinoids.
Mixed micelles containing ET (100 µg/ml) were prepared with 39 mM
NaTC and 30 mM egg PC by the simultaneous lyophilization of PC with ET,
followed by the addition of NaTC dissolved in buffer. Details for the
procedure are reported elsewhere (4).
Impulse response dosing.
Male Sprague Dawley rats, (N = 4) weighing 250-300 g
were fasted overnight before the intestinal perfusions. Water was
allowed ad libitum. Following an intraperitoneal injection
of sodium pentobarbital, a 15-cm segment of the jejunum was isolated.
The segment was gently flushed with 12 ml of normal saline warmed to
37°C, followed with 12 ml of air. The segment was cannulated with
inflow and outflow cannuli according to the procedure described
previously (4). A 22 G, 1 in., Jelco iv catheter (Criticon Inc.,
Johnson & Johnson Co., Tampa, FL) was directly inserted into the portal
vein. The needle was withdrawn, and once blood was seen emerging from
the catheter hub, the catheter was connected to a piece of Intramedic polyethylene (PE-20, Clay Adams, Parsipanny, NJ) tubing. This allowed
for sampling of portal blood. The PE-20 tubing and the catheter unit
were filled with pre-warmed (37°C) heparinized saline (10 units/ml of
heparin). The sheath of the catheter was secured to the portal vein
wall with two drops of cyanoacrylate adhesive.
The jejunal segment was perfused with the mixed micellar solution of ET
(100 µg/ml) at 0.35 ml/min with the aid of a compact infusion pump
(Harvard Apparatus, South Natick, MA). Outflow samples were collected
at 10-min intervals during the 60-min in situ intestinal perfusion. Blood samples of 200 µl were withdrawn from the portal vein at times during the perfusion that were generally at the midpoint
of the perfusion collection interval. The withdrawn blood was replaced
with 200 µl of heparinized saline. Two hundred microliters of the
withdrawn blood were pipetted into Vacutainer glass tubes containing
heparin. The tubes were gently vortexed and frozen until the time of
analysis. At the end of 60 min, the perfusion was stopped, and the
leftover perfusate in the jejunum was flushed with about 10 ml of blank
saline. The segment was then flushed with approximately 10 ml of air to
clear the segment of all fluids. At the end of the experiment, the
jejunal segment was separated from the surrounding vasculature. It was
cut open, and mucosal and intestinal cell scrapings were collected with
the aid of a glass slide. The scrapings were weighed and frozen until
analysis.
Unit impulse dosing.
The unit impulse dosing was carried out by giving a bolus dose of ET
into the portal vein with subsequent sampling of the same site. Rats
(N = 2) were given an intraportal bolus of 1 mg ET. A
separate group of rats (N = 3) received an intraportal
dose of 1 mg ETA. Because of the very poor water solubility of ET (15), the retinoids were each solubilized with 0.714 mg/ml
hydroxy-propyl-
-cyclodextran (Pharmatec, Inc. Alachua, FL). A 1-mg
dose was selected to ensure that the blood concentrations of ET and ETA
were comparable with those obtained following the intestinal perfusion
of ET in mixed micelles. The rats were anesthetized, and a Jelco iv
catheter was placed into the portal vein directed toward the liver and secured with two drops of cyanoacrylate adhesive. PE-10 tubing was
inserted through the catheter and into the portal vein lumen, and the
ET bolus dose was administered through this tubing. At the end of the
dosing (~1.5 min), the PE 10 tubing was flushed with heparinized
saline (10 units/ml heparin). The entire PE-10 tubing was then removed
and immediately replaced with PE-20 tubing that could be used later for
blood sampling. This ensured that there was no contamination from the
bolus dose during blood sampling. The first portal vein blood sample
was collected at least 3 min after injection of the bolus to ensure
that there was adequate time for the mixing and distribution of the
injected dose.
Analytical methods.
ET/ETA were extracted from the whole blood samples by modification of a
method previously reported (16, 17), with ether replacing
acetonitrile/1-butanol as the organic extracting solvent. The
recoveries of ET and ETA from rat whole blood were 99% and 91%,
respectively. The HPLC assay used for analysis of the samples was
reported earlier (4). A sensitivity of 0.005 absorbance unit full scale
and a typical injection volume of 45 µl was used on the
C18 column. The HPLC assay for the analysis of
ET/ETA extracted from whole blood was validated for precision and
accuracy (coefficient of variation 
16% at all concentrations) (18).
Data analysis.
The fraction of perfused drug that disappeared from the jejunum
(fa) was as follows:
|
(2)
|
where Xin = cumulative amount of
drug presented to the intestine and Xout = cumulative amount of drug that leaves the intestine unabsorbed.
The fraction of the drug escaping gut-wall metabolism
(fg) was given as follows:
|
(3)
|
where Eg = gut-wall extraction ratio
and Xp = cumulative amount of drug
appearing in the portal vein.
Based on metabolite concentration in the portal vein,
fg could also be determined by the
following method:
|
(4)
|
where Xp,m = cumulative amount of
metabolite appearing in the portal vein.
To use eq. 4, the following must be assumed: 1) all of the drug that
disappears from the gut lumen but does not appear in the portal vein is
metabolized and 2) there is no parallel or sequential metabolism
occurring in the gut wall.
The extraction ratio calculated according to eq. 3 or 4 is the
time-averaged value of the ratio over the period of drug sampling.
The cumulative amount of drug presented to the intestine
during the course of the intestinal perfusion
Xin is given as follows:
|
(5)
|
where Q (ml/min) refers to the perfusion flow rate,
Cin (µg/ml) refers to the total
concentration of ET within the mixed micelles, and 
refers to the
period of perfusion (60 min for these experiments). The value for
Q was obtained by plotting the volume of perfusate remaining
in the syringe as a function of time. The slope of the line of
regression for this plot provided the best estimate for the actual
perfusion flow rate.
From the analysis of the lumenal data, it was possible to determine the
total amount of drug that disappeared from the jejunum during each
10-min perfusion interval (Xdis
t) as follows:
|
(6)
|
Xout
t refers to the amount of ET
in the perfusion outflow from the intestine, gravimetrically corrected
for water flux during each 10-min interval.
Xdis, the cumulative amount of drug that
disappears from the jejunum (Xin Xout) during the perfusion, can be
determined by summing the individual
Xdist values over the total perfusion
period.
To determine Xp, the portal blood profiles
(the impulse response data) of rats receiving an intestinal lumen
perfusion of ET were deconvolved with the use of the unit impulse
profiles. PCDCON was used for the deconvolution (19). First, the
impulse response data were fit with the interpolating spline option
(19). The unit impulse data were then fit with a polyexponential
function in Kaleidograph (version 3.0). A biexponential fit was found
to be adequate. PCDCON directly provided the profile of the cumulative amount of drug metabolite appearing in the portal vein with time, Xp (or Xp,m).
Eqs. 2-4 were then used to determine the fraction of perfused drug
disappearing from the lumen and the fraction of absorbed drug escaping
gut-wall metabolism.
Carbovir.
CBV was obtained as a gift from Glaxo, Inc. (Research Triangle Park,
NC). Male Sprague Dawley rats weighing 250-300 g, obtained from
Bio-Labs (St. Paul, MN), were used in the intestinal absorption studies.
Impulse response dosing.
The intestinal perfusion procedure was identical to that described for
ET experiments. CBV was perfused (N = 12) through
either a jejunal or ileal segment in Krebs-Henseleit buffer at a
concentration of 50 µg/ml and a perfusion flow rate of 0.05 ml/min.
In contrast to the portal vein sampling for the ET studies, the femoral
vein was cannulated with PE-50 tubing to obtain blood samples during the intestinal perfusion experiments (20). Since blood samples were not
collected after the perfusion had stopped, an AUC methodology was not
used.
Unit impulse dosing.
The surgical procedure for the unit impulse animals (N = 3) was the same as that for the impulse response dosing experiments except that the intestine was not incised nor was perfusion of the
lumen carried out (20). The femoral vein was cannulated for blood
sampling. The hepatic portal vein was accessed for CBV dosing by
cannulation of the pyloric vein with PE-50 tubing. A bolus dose of 150 µg of CBV in normal saline was administered into the portal vein
followed immediately by a 60-min infusion of approximately
13µg/kg/min. The blood samples were extracted by a solid phase
extraction procedure and analyzed by HPLC as described elsewhere (21,
22).
Data analysis.
As in the previous example, PCDCON was used for performing the
deconvolution (19). The unit impulse data were fit by a polyexponential function. A biexponential function was previously found to be adequate
to describe CBV disposition in rats after an iv dose (20). The
concentration time course for a drug administered as an intraportal
bolus followed immediately by an intraportal infusion is given by the
following equation:
|
(7)
|
where Div and
R0 refer to the intraportal bolus and the
intraportal infusion rate, respectively, Vc
is the volume in the central compartment, 
and are hybrid rate
constants, and T is the duration of infusion. The unit
impulse data were fitted to eq. 7 to retrieve parameter estimates for
Vc, k2, ,
and , which were used to calculate corrected values for A and B for a 150-µg bolus of CBV (20). The estimates for , , A, and B were
used as the unit impulse parameters.
The response function was characterized for CBV from the femoral blood
profiles obtained during the intestinal perfusion of the drug. The
impulse response data were fitted with the interpolating spline option.
The input function obtained by deconvolution then corresponded to the
transport rate for CBV from the intestinal lumen to the portal vein.
This rate of transport (estimated by the deconvolution process) was
integrated over the time period of the intestinal perfusion to obtain
the cumulative amount of CBV that reaches the portal vein,
Xp,CBV. The fa
was then calculated for CBV as follows:
|
(8)
|
where Xin,CBV refers to the
cumulative amount of CBV perfused through the intestinal lumen and was
calculated with eq. 5 as in the previous example. The estimate of
fa obtained by using deconvolution was
compared with the value obtained by using eq. 2, which requires only
lumenal data. If there is no first-pass removal of CBV by the
intestinal wall, the two estimates of fa should be similar.
| |
Results |
Etretinate.
Following the intestinal perfusion of ET from mixed micelles, both ET
and ETA were detected in the portal vein. It was possible to obtain
estimates for the gut-wall extraction using the portal profile for
either ET or ETA. However, if the ETA profile was to be used, then the
corresponding unit impulse function needed to be characterized with an
intraportal bolus of ETA. It was for this reason that 1 mg of ETA was
administered as a bolus in some rats.
Fig. 2A shows the portal vein
profile for a 1-mg intraportal bolus dose of ET in a rat. There seemed
to be a rapid distribution phase for ET. The unit impulse profiles were
fitted by a polyexponential function, and a biexponential equation was
adequate for this purpose. The parameters for the biexponential fit are
reported in table 1. The mean terminal
half-life for ET in the portal vein was approximately 30 min.
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|
Fig. 2.
A) ET unit impulse dosing (1 mg
of ET given as intraportal bolus followed by sampling from portal
vein). B) ETA unit impulse dosing (1 mg of ETA given as intraportal
bolus followed by sampling from portal vein).
|
|
Portal blood profiles from rats that had undergone unit impulse dosing
with ETA were also fit to a biexponential function (fig.
2B). These estimated parameters are given in table
2. The mean values of the individually
fitted parameter estimates of the unit impulse rats were used for
deconvolution of the impulse response profiles.
In the impulse response experiments, blood samples were collected from
the portal vein, and these concentration profiles were used for
deconvolution. The appearance of ET and ETA in the portal vein during
the intestinal perfusion of 100 µg/ml ET is shown in fig.
3. The metabolite levels were much higher
than those of the parent. PCDCON directly generated the time profile
for the cumulative amount of drug and metabolite appearing in the
portal vein, as shown in fig. 4. The
curve was continuously rising, indicating that absorption was occurring
throughout the 60-min perfusion. The amount of metabolite that appeared
in the portal vein exceeded the amount of the parent, indicating
substantial gut-wall metabolism.
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|
Fig. 3.
ET ( ) and ETA
( ) concentration in the portal vein during the 60-min
intestinal perfusion of 100 µg/ml ET in mixed micelles.
|
|
The deconvolution of the profile in fig. 4 allowed the determination of
Xp and Xp,m.
The values for Xp,m were corrected for molecular weight to make the amounts equimolar with respect to the
parent (ET). For deconvolution based on the parent (ET) profile, the
value for the extraction ratio was found to be 0.65 ± 0.19 (mean ± SD; table 3). This
indicated that there was loss of 65% of the ET molecules between their
uptake from the jejunum and their appearance in the portal vein. The ET
and ETA in the mucosal cell scrapings at the end of the ET perfusion
studies constituted less than 0.5% of the total perfused ET dose. This
indicated that there was no accumulation of ET or its metabolite in the
gut tissue during the infusion.
When deconvolution was performed based on the metabolite profile in the
portal vein, a mean value of 0.51 ± 0.275 was obtained for
Eg (table 3). There was significant
inter-animal variability associated with this value. There was no
statistical difference in the value of Eg calculated using the
parent or the metabolite profiles (t test, p
value < 0.05).
Carbovir.
Data from the in situ vascularly perfused rat intestine
suggested that CBV was not metabolized in the intestinal wall (7). The
fraction of the CBV dose that appeared in the hepatic portal vein was
determined with the use of deconvolution. This value was compared with
the estimate of fa obtained from analysis
of the lumenal disappearance of CBV (eq. 2). A good correlation between the two estimates would confirm that there was indeed no gut-wall metabolism of CBV. In one of the rats in which the ileum was perfused, several lumenal samples were lost, and eq. 2 could not be used. This
rat was excluded from further analysis.
Fig. 5 shows the femoral profile for the
intraportal dosing (150 µg of bolus followed immediately by a 13 µg/kg-min infusion) of CBV in a representative rat. These profiles
were fit to a biexponential disposition function (eq. 7) to retrieve
the estimates of A, B, , and (table
4). These estimates were then used as the
unit impulse parameters.
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|
Fig. 5.
CBV unit impulse dosing (150 µg of bolus
followed immediately by a 13 µg/kg-min infusion) into the portal
vein; sampling from femoral vein.
|
|
The CBV concentration in the femoral vein following jejunal perfusion
was used as the impulse response function. Lumenal data from these CBV
intestinal perfusions have been reported elsewhere (23). PCDCON was
employed to deconvolve the impulse response function with the unit
impulse parameters from table 4. This provided the profile of the
cumulative amount of CBV appearing in the portal vein during the
jejunal perfusion (fig. 6), which was
used to determine Xp,CBV. The estimated
values of fa (using eq. 8) are reported in
table 5. Table 5 also provides the
estimates of fa obtained with the use of
lumenal data (eq. 2) alone. There was no statistical difference between
the fa values obtained from the two
methods. However, there was a difference in the fraction of CBV
absorbed as a function of intestinal site (two-way analysis of
variance, p < 0.05).
| |
Discussion |
Deconvolution has been used for evaluating the transit of drugs
over most biologic barriers. Most studies have concentrated on studying
the extent and rate of drug absorption (8-10). Deconvolution has also
been used to study drug transport across the blood-brain barrier (12).
There are several advantages to the deconvolution technique. No
functional form or compartmental model needs to be specified for the
disposition of the drug. Second, the technique can be used for
protocols in which an organ extraction ratio is desired but multiple
sites of sampling are not attainable. Deconvolution can also be an
advantage for situations where computation of AUCs over long periods of
time is impractical, such as for drugs with long half-lives.
On the other hand, use of the data from time 0 to t gives
information about the drug transit only during that specific interval of time. For example, in the studies reported here, the value of the
extraction ratio is a time-averaged value over the period of sampling
only. There may be a danger in extending interpretation of the value
over longer periods of time or in situations where the disposition of
the drug may change, e.g. in case of enterohepatic recirculation at late times after an oral dose.
The present work has extended the use of deconvolution to the
evaluation of the intestinal first-pass effect. Deconvolution of portal
drug or metabolite profiles during lumenal dosing of the drug allows an
estimate of intestinal extraction ratio. However, the high inter-animal
variability observed with the use of the metabolite profile is a
concern and may be due to violation of one of the assumptions for the
use of eq. 4. The assumption is that there is no parallel or sequential
metabolism occurring in the gut wall. If the parent molecule is not
exclusively converted to the measured metabolite or if the measured
metabolite is sequentially converted to another chemical species, then
the use of the metabolite profile will underestimate the gut-wall
extraction of the drug. Although the metabolic profile for ET
metabolism in the gut wall has not been studied, the possibility of the
sequential metabolism of ETA cannot be eliminated. The glucuronidation
of ETA has been reported to occur in the liver (16).
The conversion of ET to ETA is probably mediated by retinyl esterases
present in the intestinal brush border. The activity of one of the
major classes of intestinal retinyl esterases is bile salt dependent
(24). In studies carried out with rat brush border membrane vesicles,
the rate of hydrolysis of shorter-chained retinyl esters was
particularly accentuated in the presence of the trihydroxy bile salt,
NaTC (24). ET is a short-chain retinoid ester, and the NaTC used for
the micellar preparation may be stimulating the metabolism of the
compound. This may explain the high level of gut-wall metabolism for ET
that was observed during its jejunal uptake from mixed micelles.
Although the gut-wall metabolism of ET is significant, it may not have
serious pharmacological implications since ETA is the active metabolite
of ET.
The deconvolution of CBV profiles from intestinal perfusions provides
another application for the technique. When carrying out intestinal
perfusion studies and sampling perfusate alone, the question arises as
to whether lumenal loss of drug correlates with entry into the portal
or systemic circulation. In the present study, the unit impulse dose
was placed into the portal vein, with sampling in the systemic
circulation. The impulse response function was also measured in the
systemic circulation. The input function indicated the input into the
portal circulation from a lumenal dose. Comparison of the drug
disappearance from the lumen and its appearance in the systemic
circulation indicated that the intestinal wall did not participate in
the metabolism of absorbed drug. In the absence of gut-wall metabolism
as is the case with CBV, deconvolution provided another check on the extent of absorption of drug from the lumen.
| |
Conclusions |
The technique of deconvolution has been successfully applied to
the determination of intestinal first-pass extraction. In addition, the
technique can be used to verify the estimates of the extent of
absorption obtained from the lumenal disappearance of the drug.
The authors thank Hoffmann-La Roche and Glaxo Wellcome for the gifts of
the retinoids and carbovir, respectively. The authors also acknowledge
the technical assistance of Enas Soud and Shaomei Han.
This work was supported in part by Glaxo Inc., PHS Grants
RO1-AI28236 and RO1-CA55493, and the University of Minnesota
International Student Work Opportunity Program.
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Abstract
Introduction
