The Influence of Averaging Procedure on the Accuracy of IVIVC
Predictions: Immediate Release Dosage Form Case Study
MICHAL OSTROWSKI,1 EWA WILKOWSKA,1 TOMASZ BACZEK2
1
R&D Departament, Polfa Tarchomin SA, Fleminga 2, 03-176 Warszawa, Poland
2
Department of Pharmaceutical Chemistry, Medical University of Gdańsk, Hallera 107, 80-416 Gdańsk, Poland
Received 4 September 2009; revised 11 March 2010; accepted 13 April 2010
Published online 25 May 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.22209
ABSTRACT: In vivo in vitro correlation (IVIVC) is an effective tool to predict absorption
behavior of active substances from pharmaceutical dosage forms. The model for immediate
release dosage form containing amoxicillin was used in the presented study to check if the
calculation method of absorption profiles can influence final results achieved. The comparison
showed that an averaging of individual absorption profiles performed by Wagner Nelson (WN)
conversion method can lead to lose the discrimination properties of the model. The approach
considering individual plasma concentration versus time profiles enabled to average absorption
profiles prior WN conversion. In turn, that enabled to find differences between dispersible
tablets and capsules. It was concluded that in the case of immediate release dosage form, the
decision to use averaging method should be based on an individual situation; however, it seems
that the influence of such a procedure on the discrimination properties of the model is then more
significant. ß 2010 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 99:5040 5045,
2010
Keywords: in vitro/in vivo correlations (IVIVC); formulation; mathematical model; anti-
infectives; bioavailability
INTRODUCTION appropriate discrimination properties for products
with lower bioavailability. In IVIVC studies for
In vivo in vitro correlation (IVIVC) has become an prolonged release oral dosage forms, the conditions
effective tool to predict absorption behavior of various of in vitro test are usually constant with three
pharmaceutical dosage forms. The most number of formulations having different extent of absorption.
described IVIVC s examples concerns prolonged On the other hand, a problem in IVIVC studies for
release oral forms1 3, but it is also possible to immediate release oral dosage forms is a large
establish IVIVC for immediate release oral dosage number of time points on the absorption part of
forms4,5 or even parenteral micospheres6,7 or bioavailability curve. Applying a time factor, period
implants.8 One of the most important issues of IVIVC between sampling during in vitro test becomes very
for immediate release oral dosage forms is require- short. On-line sampling systems may help to solve
ment to take into accounts time factor due to the technical problem, but from mathematical point of
relatively short dissolution time of immediate release view the results of dissolution test should be very
tablet or capsule. It enables to compare in vitro and close to real values of in vivo absorption profile. If
in vivo data. It is also quite difficult to achieve a good not, Tmax obtained from the in vitro data by back
fit and FDA level A correlation between in vivo calculation of Wagner Nelson (WN) method will be
absorption profile and in vitro dissolution profile displaced, which makes the model less reliable.9
(predicted absorption). To find the best conditions of Our recent work10 revealed that for certain group of
the dissolution test and best fit, it is possible to use active substances with known zero-order absorption
variable hydrodynamic conditions or pH change to process (e.g., amoxicillin)11 it is possible to simplify
simulate absorption in gastrointestinal tract, but the model for immediate release dosage form by
ideally a model should possess at the same time an removing points placed on linear part (positive slope)
of absorption profile and bioavailability curve, what
solves mathematical problems with Tmax and makes
Correspondence to: Tomasz Baczek (Telephone: þ48-583493135;
dissolution procedure easier. It was found that our
Fax: þ48-583493130; E-mail: [e-mail])
recent model established for dispersible tablets of
Journal of Pharmaceutical Sciences, Vol. 99, 5040 5045 (2010)
amoxicillin showed features of level A correlation and
ß 2010 Wiley-Liss, Inc. and the American Pharmacists Association
5040 JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010
IN VIVO IN VITRO CORRELATION 5041
possessed discrimination properties against forms of ples were withdrawn from each dissolution vessel at
lower bioavailability (in that case capsules).12 In 2 min 30 s, 8 min 46 s, 15 min, 25 min, 35 min, 60 min,
that work, WN method was used to calculate and filtered prior to spectrophotometric analysis on
absorption profiles. However, it has some obvious Unicam UV3 (Unicam Ltd, Cambridge, United King-
limitations. On the other side, it is very useful dom) spectrophotometer (wavelength 272 nm). The
because of no need to collect data from oral solution analytical method used was a validated procedure
or parenteral injection. It can be also properly used for routine dissolution control of production
used when the active substance is known to have batches. Each dissolution profile was taken from
complete (or almost complete) absorption. IVIVC can 12 units. The absolute coefficient of variation (CV)
be established on the basis of standard bioequivalence for all the points was less than 10%. In the case
clinical trial with the use of WN method. Subse- of capsules, two dosage units were used to achieve
quently, the model may be applied in order to justify 1000 mg dose in a dissolution vessel. To prevent
the lack of bioequivalence study in case of changes in floating, EP sinkers (Pharma Test Apparatebau
production scale or formulation. GmbH, Hainburg, Germany) were used. Variable
One of the latest article13 concerning IVIVC showed hydrodynamic conditions were implemented in the
that averaging procedure of in vivo data can possess study to imitate a minimal absorption of the drug in a
a certain influence on results. It is claimed that stomach. During the initial 2 min 30 s of the experi-
averaging of data should be done after deconvolution ment the paddles operated at 25 rpm. After that, the
performed on the individual subject level. Deconvolu- rotation increased to 95 rpm simulating rapid absorp-
tion on the averaged data can lead to lose information tion of amoxicillin in a duodenum and proximal part
connected with subject variability. It means that in of small intestine.
the case considered in the recent study10 it should be
In Vivo Study
done after calculations of absorption profiles from
each of a subject by WN method instead of WN Twenty-four adult volunteers (12 male and 12 female)
conversion made on averaged data. were taken into a count for this study. Details are
The aim of the current work was to evaluate if the described in Ref. 11.
procedure of data averaging can possess an influence
Pharmacokinetic Analysis
on the model prepared previously. As it was discussed
above the IVIVC of immediate release dosage form Details of the pharmacokinetics analysis are
has some differences in comparison to prolonged described in Ref. 11. The independent method to
release dosage form. Especially, the concern was done generate the suitable model was used. Cmax and Tmax
to evaluate the possible changes on the level of were the observed values. Elimination rate constant
discrimination properties of the model. Ke was calculated from the slope of the log-linear part
of the plasma concentration time curve using linear
regression. The area under the plasma concentra-
MATERIALS AND METHODS
tion time curve from time 0 to 12 h was calculated
using trapezoidal rule.
Batches Used in the Study
Absorption profile of amoxicillin was calculated by
Two batches of commercially available dispersible WN equation in the following ways:
tablets (Amotaks1 Dis produced by Polfa Tarchomin
At Ct þ Ke AUC0 t
ź (1)
SA, Warsaw, Poland) containing 1000 mg of amox-
A1 Ke AUC0 1
icillin (as trihydrate) were used in the study (batches
A and B). These batches came from the validated
In method 1 averaged bioavailability data (includ-
production process and are the same as bioavail-
ing averaged Ke) of all 24 subjects were converted into
ability batch described in Ref. 11. Additionally one
absorption profile as it was described in Ref. 11. In
batch of commercially available capsules (Amotaks1
method 2 individual Ke and bioavailability data were
produced by Polfa Tarchomin SA, Warsaw, Poland)
used, individual bioavailability data were converted
containing 500 mg amoxicillin (as trihydrate) was
into absorption profiles and afterwards individual
used to check the change in discrimination properties
profiles were averaged.
of the model (batch C).
The results were expressed as percentage of the
dose absorbed. In vitro averaged dissolution data
In Vitro Dissolution Testing
were converted into plasma concentration time curve
Dissolution testing was performed using Pharma
using back-calculation of WN equation:
test PTWS 3 (Pharma Test Apparatebau GmbH,
2 DF Ke AUC0 1 þ Ct ð2 Ke DtÞ
Hainburg, Germany) EP apparatus 2 (paddles)
Ctþ1 ź
2 þ Ke Dt
operating at 25 and 95 rpm. Water (37 0.58C) was
(2)
the dissolution medium. Approximately 10 mL sam-
DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010
5042 OSTROWSKI, WILKOWSKA, AND BACZEK
where Ct þ 1 is the plasma concentration at t þ 1,
DF ź Ft þ 1 Ft the difference of amount dissolved
between t þ 1 and t, Ct the calculated plasma
concentration at time t, Dt ź tt þ 1 tt. Ke and AUC0
were calculated as an average of individual
1
bioavailability data.
IVIVC Model
The concentration-time data from bioavailability
study were transformed into in vivo absorption profile
by WN equation applying method 2 described above.
Figure 1. The results of dissolution tests for 1000 mg
In vitro absorption model was built using variable
dispersible tablets and 2 500 mg capsules. Time scale
hydrodynamic conditions to imitate different absorp-
without applying time factor. Dashed line represents dis-
tion rates in the various parts of gastrointestinal
solution results of capsules from Ref.11
tract. A time-scale factor of 0.0833 was used to enable
comparing in vivo and in vitro data (1 h of dissolution
paddles after 2 min 30 s of experiment to 95 rpm in
test corresponds to 12 h of bioavailability study).
order to fit absorption profile calculated by method 2
Conversion of dispersible tablets dissolution pro-
resulted in faster dissolution of dispersible tablets
files to predicted time-plasma concentration curves
and capsules in comparison to model described in Ref.
was performed with the use of averaged data for all
11. It must be remembered at that moment that in
twelve dosage units. But Ke and AUC0 1 were
method 2 individual bioavailability data were used;
calculated from each individual bioavailability profile
however, each individual bioavailability profile was
and then averaged because the absorption profiles
first converted into absorption profile and afterwards
were calculated before by method 2 taking into
profiles were averaged. The mean dissolution rate of
account individual subject data.
tablets (two batches averaged) and capsules at 8 min
It must be finally mentioned that using individual
46 s, which corresponded to Tmax in bioavailability
subject elimination rate constant for single dosage
study increased by 11.6% and 14.5%, respectively.
units was physically impossible (the same tablet
11.6% result from the comparison of 79.8% versus
should be tested both during in vitro and in vivo
91.4% and relates to the mean dissolution rate of
study).
tablets obtained in the study in contrast to the Ref. 11
U.S. Food and Drug Administration (FDA) criteria
14.5% result from the comparison of 46.30% versus
of predicted error (PE) were used to determine level of
60.80% and relates to the mean dissolution rate of
IVIVC.14 PE value smaller than 10% was considered
capsules obtained in the study in contrast to the
as correct model fit. Correlation coefficient (expressed
Ref. 11. In the case of dispersible tablets, the model
as R2) between absorption profile in vivo and
fulfilled FDA criteria of PE for AUC and Cmax. For
dissolution profile in vitro was calculated with the
capsules PE criteria were fulfilled in the case of AUC.
use of Microsoft Excel (Microsoft Co., Redmond, WA).
PE for Cmax was still greater than 10%.
Secondly, in vivo studies were included in the
RESULTS considerations. Summary of pharmacokinetic para-
meters are presented in Table 2 and the individual
First, in vitro dissolution testing was performed. absorption profiles of 24 volunteers are presented in
Detailed results of the dissolution tests are presented Figure 2. In the next step, pharmacokinetic analysis
in Table 1 and Figure 1. Increased rotation speed of was summarized with the WN plots of the percent of
Table 1. Detailed Results of Dissolution Tests
Time [h] 0.5 1.75 3 5 7 12
Time factored [min:sec] 2:30 8:46 15 25 35 60
Dissolution batch A [%] 8.60 90.60 93.20 97.80 100.10 103.40
CV batch A [%] 8.9 2.5 1.9 1.1 0.8 0.7
Dissolution batch B [%] 9.80 92.20 95.70 98.60 100.50 102.60
CV batch B [%] 7.2 2.8 2.0 1.2 1.0 1.0
Dissolution batch C [%] 2.60 60.80 74.20 82.50 87.70 92.90
CV batch C [%] 6.1 4.4 3.2 2.1 1.5 1.2
Dissolution capsules, Ref. 11 [%] 1.10 46.30 59.30 72.90 77.00 87.70
CV capsules, Ref. 11 [%] 6.9 5.3 4.0 3.1 1.7 1.3
Batches A and B dispersible tablets; batch C capsules.
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010 DOI 10.1002/jps
IN VIVO IN VITRO CORRELATION 5043
Table 2. Summary of Pharmacokinetic Parameters in the Case of Studies for Dispersible Tablets
AUC0 12 [mgmLh 1] Cmax [mg/mL] (Tmax ź 1.75 h) Ke [h 1] The Extent of Absorption at Tmax [%]
Mean value 52.23 20.21 0.678a 91.40a
SD 2.53 1.03 0.216 16.11
CV [%] 4.90 5.10 31.50 19.20
Min 46.78 18.49 0.395 66.32
Max 56.70 21.92 1.091 113.67
a
Mean value calculated by method 2.
dose absorbed versus time calculated on the basis of suitable and showed PE smaller than 10%, the
individual subject data averaged before (method 1) dissolution of capsules increased at the same time.
and after (method 2) conversion (Fig. 3). Finally, to It appeared that PE for capsules in the case of AUC
discuss the results from in vivo study, absorption was smaller than 10%, what can provide lost of model
profile in vivo and predicted plasma concentration discriminatively against lower bioavailability form.
time curve (Table 3 and Fig. 4) were subsequently The PE for Cmax was still greater than 10%, but for
presented. Moreover, observed and predicted data antibiotics it is not so important, because of their
along with the PE and R2 calculations are collected in mechanism of action plasma concentration should be
Table 4. over minimal inhibitory concentration at least for 30
40% of dosing interval. Higher correlation (expressed
as R2) was noted for increased speed of rotation.
DISCUSSION In the case of capsules, two approaches were
applied. In the first approach, data for dispersible
Biopharmaceutical aspects of in vitro absorption tablets (Ke and AUC0 1) were taken into account
model for amoxicillin were described in detail in to calculate predicted time-plasma concentration
Ref. 11. The aim of the present study was to evaluate curves, what can allow to treat a capsule as a
if the way of absorption profile calculating by WN modified formulation of dispersible tablet with pre-
method can possess an impact on discrimination of viously established IVIVC. Then the presented
the in vitro model. research revealed how misleading may be a corre-
The in vitro model described in Ref. 11 was built on lation, which utilizes variability of subjects and
assumption that dissolution level of dispersible implements less discriminative conditions of dissolu-
tablets and absorption extent at Tmax should be as tion test. The PE was calculated against dispersible
small as possible. The rotation speed of 85 rpm tablets in vivo data. In the second approach,
enabled to achieve good correlation and discrimina- literature data15 for conventional 1000 mg dosage
tivity against capsules. But data averaged after WN form of amoxicillin (coated tablets, Ke ź 0.578 h 1)
conversion of each subject bioavailability profile, were taken into account. AUC0 1 was assumed as
what was performed in the present study, resulted 85% AUC0 1 of dispersible tablets.12 Usually con-
in higher absorption level at Tmax. The in vitro model ventional dosage forms of amoxicillin (coated tablets,
had to be changed to achieve higher dissolution level capsules) are claimed to have lower extent of
at Tmax. The rotation speed of 95 rpm enabled to absorption12,15 with no clinical significance and have
achieve dissolution level of dispersible tablets at Tmax lower value of Ke than fast dissolving formulation
similar to the absorption level calculated by method 2 (0.578 and 0.694 h 1, respectively15). The Ke value for
from averaged individual absorption profiles. fast dissolving formulation in Ref. 15 was found to be
Although the new model for dispersible tablets was very close to the results obtained in the current study.
Figure 3. Wagner Nelson plots of percent of dose
Figure 2. Individual absorption profiles of 24 volunteers. absorbed versus time calculated by method 1 and method 2.
DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010
5044 OSTROWSKI, WILKOWSKA, AND BACZEK
Table 3. Summary of Results from In Vivo Study, Absorption Profile In Vivo, and Predicted Plasma Concentration Time
Curve
Tmax
Time [h] 0.5 1.75 3 5 7 12
Time factored [min:sec] 2:30 8:46 15 25 35 60
Concentration in vivo study [mg/mL] 2.06 20.21 9.53 2.91 1.70 0.16
Absorption profile method 1 [%] 6.79 84.08 87.94 91.34 97.17 100.00
Absorption profile method 2 [%] 8.11 91.40 92.50 92.70 97.92 100.00
Predicted in vivo concentration batch A [mg/mL] 2.62 21.58 9.39 2.78 1.02 0.17
Predicted in vivo concentration batch B [mg/mL] 2.99 21.83 9.71 2.48 0.88 0.05
Predicted in vivo concentration batch C [mg/mL] 0.79 14.85 9.39 3.56 1.79 0.23
Predicted in vivo concentration capsules Ref.11 [mg/mL] 0.34 11.43 7.90 4.43 1.73 0.96
Predicted in vivo concentration batch C [mg/mL]a 0.58 11.28 7.85 3.46 1.78 0.23
Predicted in vivo concentration capsules, Ref.11 [mg/mL]a 0.25 8.68 6.54 3.98 1.74 0.80
a
Calculated with the use of literature data Refs., 13,15 batches A and B dispersible tablets; batch C capsules.
Therefore, in that case a difference between two seems to be appropriately justified. In fact, the model
in vitro models is presented. AUC0 12 for PE for immediate release oral dosage form must be built
calculations was assumed as 85% AUC0 12 of dis- to suit absorption profile achieved from in vivo data
persible tablets. Nevertheless, the change in dis- and usually there is no immediate release formula-
criminativity was considered as similar to that tion with another extent of absorption to verify
observed with dispersible tablet data. discrimination properties of model. Moreover, elim-
It was also checked if the kind of averaging ination rate do not play such an important role in
procedure for in vitro dissolution data (prior or post absorption phase of immediate release oral dosage
conversion into predicted plasma concentration time forms with confirmed zero-order process.
curve) have an impact on the final results. No Prolonged release dosage form models are built on
influence was found due to the impossibility of the basis of three different formulations with variable
simultaneous in vivo and in vitro testing of single extent of absorption, what is obviously impossible for
dosage unit the same averaged Ke and AUC0 1 had immediate release dosage form. It enables to imple-
to be used for all dosage units (data not shown). ment constant hydrodynamic conditions, but at the
The higher level of absorption at Tmax resulted from same time PE for Cmax still should be less than 10%
a variability of elimination rate constant (Ke in and the model should present ability to show more
Tab. 2). Greater inter-subject variability led to higher than 10% difference between each of the formula-
positive difference between mean absorption extent tions. In this situation, the appearance of inter-
at Tmax. Considering IVIVC s suitability as a tool subject variability seems to be fully justified because
to predict absorption behavior of immediate release of higher influence of elimination rate constant on
dosage form it is a problem of smaller importance. absorption profile.
Although including inter-subject variability in IVIVC In the case studied previously it was found that two
immediate release dosage forms possess different
absorption of no clinical significance,12 but it is useful
for purposes of IVIVC.
In the current case, consequences of averaging
individual absorption profiles appeared to be very
significant because of the lost of discrimination
properties. From that point of view, averaging after
WN transformation (including inter-subject variabil-
ity) is not recommended.
CONCLUSIONS
The results confirm that method of averaging
significantly influence absorption profiles. The
method, which applies averaging of individual data
Figure 4. The results of dissolution data conversion into
seems to be more correct from the methodological
predicted plasma concentration time curve and result of
point of view, but the loss of model discriminativity
in vivo study. Dashed line represents predicted in vivo
results of capsules from Ref. 11. must be considered as its great disadvantage. In fact,
JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 99, NO. 12, DECEMBER 2010 DOI 10.1002/jps
IN VIVO IN VITRO CORRELATION 5045
Table 4. Observed and Predicted Data With Predicted Error (PE) and Correlation Coefficient (R2)
Cmax [mg/mL] AUC0 12
(Tmax ź 1.75 h) [mgmLh 1] PE AUC [%] PE Cmax [%] R2
Dispersible tablets in vivo data 20.21 52.28   
Dispersible tablets predicted in vivo data batch A 21.58 54.10 3.46 6.77 0.9992
Dispersible tablets predicted in vivo data batch B 21.83 53.85 3.00 8.00 0.9994
Capsules predicted in vivo data batch C 14.85 48.47 7.29 26.52 0.9782
Capsules predicted in vivo data Ref.11 11.43 44.74 14.44 43.44 0.9487
Capsules predicted in vivo data batch Ca 11.28 41.07 7.58  
Capsules predicted in vivo data Ref.11 a 8.68 37.75 15.07  
a
Calculated with the use of literature data Refs., 13,15 PE Cmax not calculated due to the lack of in vivo data.
it is a lack of possibility to establish IVIVC for 6. Da-Feng C, Xue-Qi F, Wan-Hui L, Ke L, You-Xin L. 2006.
Pharmacokinetics and in vitro and in vivo correlation of huper-
immediate release dosage form, which is verified by
zine. A loaded poly(lactic-co-glycolic acid) microspheres in dogs.
another immediate release dosage form with smaller
Int J Pharm 325:116 123.
extent of absorption. For immediate release dosage
7. Cheung RY, Kuba R, Rauth AM, Wu XY. 2004. A new approach
form, the decision what method of averaging should
to the in vivo and in vitro investigation of drug release from
be chosen must be made on the basis of individual locoregionally delivered microspheres. J Control Release 100:
121 133.
case. From practical point of view, it seems that
8. Schliecker G, Schmidt C, Fuchs S, Ehinger A, Sandow J, Kissel
discriminatively is more important than inter-subject
T. 2004. In vitro and in vivo correlation of buserelin release
variability included in a model.
from biodegradable implants using statistical moment analy-
sis. J Control Release 94:25 37.
9. Wagner JG, Nelson E. 1963. Percent absorbed time plots
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