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22 QUA LITY CON TROL
Do the Math for
Shelf Life
Pharmaceutical Formulation & Quality >April/May 2011
P
harmaceutical scientists rou-
tinely
predict long-term chemi-
cal stability at a lower
temperature using data gener-
ated at a higher temperature over a shorter
time period.
The use of 40 degrees C chem-
ical data (e.g.,
assay and related sub-
stances) to predict levels over long-term 25
degrees C storage has become such com-
mon practice that
the underlying theory is
overlooked or was
never learned.
There is disagreement about whether
three months at 40 degrees C indicates ex-
pected 25 degrees C levels for 12 months
or for 24 months because of insufficient
understanding or information about the
kinetic model. More importantly, without
some theoretical understanding, the
practice is inappropriately applied to situ-
ations that do not fit the kinetic model
upon which it is based, resulting in erro-
neous predictions.
In addition to providing the back-
ground of how these kinetic predictions
work, this paper will provide the key to
understanding the temperature relation-
ships and the ability to more accu
rately
predict the expected long-term levels
for a
specific product.
Arrhenius Kinetics: Where
This All Began
Swedish scientist Svante Arrhenius pro-
vided the first kinetic model to interpret the
effect of temperature on reaction rate given
by Equation 1 (see info box).1-3 The Arrhe-
nius equation can be applied regardless
of the order (zero-order, first-order, etc.) of
the reaction kinetics.4Equation 2 presents
the linear form of the Arrhenius equation
for graphical presentation (y = mx + b).
For many reactions, a linear relationship
can be obtained between the inverse of
temperature (in degrees Kelvin) and the
natural log (Ln) of the measured rate con-
stant (k), as shown in Figure 1.
Equation 3 presents a simplified form
for use with two temperatures. Equation 4
expresses the relationship between the
reaction rates and the corresponding tem-
peratures when the activation energy (Ea)
of the reaction is known. Equation 4 allows
for the calculation of a reaction rate con-
stant at a lower temperature when the acti-
vation energy and the reaction rate at the
higher temperature are known.
As shown by Figure 1, the Arrhenius
model provides the ability to determine the
reaction rate and, hence, predict stability
at any temperature with knowledge of the
activation energy (Ea) and the reaction rate
at another temperature.
QUALITY CONTROL
© DREAMSTIME.COM
Do the Math for Shelf Life
Predict stability using data collected at higher
temperatures
>By Michelle Duncan, PhD, and Irene Zaretsky, MS
HIG H-TEM PER ATU RE S TAB ILI TY
Figure 1. Arrhenius plot of Ln K against
1/T. Slope = - Ea/R k = reaction
rate constant, T = temperature
in degrees Kelvin Ea = activation
energy, R = ideal gas constant.
THE ARRHENIUS EQUATION
K = A exp (-Ea/RT) (Equation 1)
k = reaction rate constant
A = Arrhenius factor (y-intercept constant)
Ea = the energy of activation for the reaction, cal/mole
(1000 cal = 1 kcal)
R = the ideal gas constant, 1.987 calories/deg mole
T = the absolute temperature (degrees Kelvin), for 25° C
T= 298° K and for 40°C T= 313° K)
THIS EQUATION CAN BE WRITTEN IN SEVERAL
EQUIVALENT FORMS AS FOLLOWS:
Ln k = -Ea/RT + Ln A (Equation 2, y = mx + b)
Ln k2/k1 = -Ea/R*(1/T2-1/T1) (Equation 3)
k2 = k1 * exp[-Ea/R*(1/T2-1/T1)] (Equation 4)
The constants k1 and k2 are the rate constants at tem-
perature T1 and T2 (for example 25 degrees C and 40
degrees C), respectively.
CAPSUL E
Swedish scientist Svante Arrhenius provided the first kinetic model to interpret the effect of temperature on reaction rate. Since then, pharma-
ceutical scientists have often attempted to predict long-term chemical stability with insufficient understanding about the kinetic model, applying
the practice in inappropriate situations. Understanding critical temperature relationships is the key to more accurately predicting long-term levels
for a specific product.
April/May >Pharmaceutical Formulation & Quality
Limitations to Arrhenius’ Model
The first requirement is a reaction (ongo-
ing) where the reaction rate constant at
a given temperature can be determined.
When monitoring the generation of a pri-
mary degradation product, the presence
of a secondary degradation reaction can
introduce error to the calculation of the pri-
mary rate constant and any attempted Ar-
rhenius model predicted rates. Likewise,
if a component is consumed to the
extent
that the reaction equilibrium changes, the
reaction rate will not remain constant. The
Arrhenius kinetic model requires a reac-
tion rate constant (k).
The Arrhenius kinetic model can be uti-
lized across the temperature range where a
constant relationship between the effect of
temperature on the reaction rate is main-
tained, where the graph is linear. The reac-
tion mechanism should not change over the
temperature range studied. Conformance
to the model (linearity)
is often lost when
crossing a phase change, such as freezing
and the glass-phase transition of proteins
and peptides. Reactions where the rate is
dependent upon oxygen, light (photochem-
ical), diffusion, or microorganism-based
decomposition may not demonstrate Arrhe-
nius kinetics over any temperature range.
Finding Ea for the Reaction
The activation energy (Ea) for a reaction
can be determined by conducting stability
studies at several different temperatures
and applying the Arrhenius kinetic model.
The slope of the line formed with Equation
2 contains Ea, as demonstrated in Figure 1.
Higher temperatures (e.g., 55 degrees C,
70 degrees C) and corresponding shorter
times (e.g., weeks, days) can be employed
for this determination provided the Arrhe-
nius kinetic model remains valid (see Lim-
itations to Using Arrhenius Kinetic Model).
The Ea for drug decomposition will usually
fall in the range of 12 to 24 kcal/mole, with
a typical value of 19 to 20 kcal/mole.5The
activation energy can be approximated
based upon prior knowledge of the drug
decomposition kinetics. Once the Ea is
known, it usually remains valid for use
through small concentration changes or
slight formulation changes.
Importance of Ea: Theoretical
Model for Drug Loss
The following discussion demonstrates the
re-
lationship of drug degradation kinetics at 40
degrees C and 25 degrees C, where drug loss
is the shelf life-determining parameter. For
this illustration, acceptable product stability
is based upon a lower limit of 90% label claim
and the expiration date set at exactly 90% la-
bel claim. For this exercise, a zero-order
degradation kinetics model (Δdrug/Δtime =
—k) is applied to determine the rate for 10%
of drug loss occurrence over 24 months at 25
degrees C (Figure 2). The slope was calcu-
lated and is equal to —0.4167 drug %label
claim/ month, which is the reaction rate con-
stant at 25 degrees C (k25). Hence, for the drug
to remain within acceptance criteria for 24
months at 25 degrees C, the rate of degrada-
tion at 25 degrees C must be less than 0.4167
drug %label claim/month.
In a similar manner, drug loss can be
modeled at 40 degrees C accelerated temper-
ature for the two scenarios of 10% drug loss
occurring at three months and at six months
(Figure 3). The slopes, which represent the
reaction rate constant at 40 degrees C (k40),
were calculated to be —1.6667 drug %label
claim/month for the six months limit scenario
and —3.3333 drug %label claim/month for the
three months limit scenario.
Using the Arrhenius equation (Equation
3) and the reaction rates at 25 degrees
C
and
40 degrees C, the Ea can be calculated as
shown in Table
1.
The Arrhenius equation
PHARMAQUALITY.COM
Table 1. Relationship of reaction rates at 40 degrees C and activation
energy (Ea) for drug loss
Months at 40
degrees C to reach
10% drug loss
6
3
k40 (drug %label
claim per month)
-1.6667
-3.3333
k25 (drug %label
claim per month)
-0.4167
-0.4167
Ea (kcal/mole)
activation energy
17
26
Table 2. Relationship of reaction rates at 40 degrees C and activation
energy (Ea) for impurity generation
Months at 40
degrees C for impu-
rity to reach 1%
6
3
k40 (%w/w
impurity per month)
0.1667
0.3333
k25 (%w/w
impurity per month)
0.0417
0.0417
Ea (kcal/mole)
activation energy
17
26
Figure 2.
The zero-order kinetic model for 10% drug loss
over 24 months at 25 degrees C shown as the
percent of drug remaining as a function of time
at 25 degrees C.
Figure 3.
Zero-order kinetic models for 10% drug loss
over three months and over six months at 40
degrees C.
can be applied regardless of the order of the
reaction kinetics. For the kinetic model that
assumes 10% drug loss at 24 months at 25
degrees C (k25 = —0.4167 drug %label
claim/month) and 10% drug loss at three
months at 40 degrees C (k40 = —3.3333 drug
%label claim/month), the calculated Ea is
26 kcal/mole. For the model that assumes
10% drug loss at 24 months at 25 degrees C
(k25 = —0.4167 drug %label claim/month)
and 10% drug loss at six months at 40 de-
grees C (k40 = —1.6667 drug %label
claim/month), the calculated Ea is 17
kcal/mole.
Knowledge of the Ea is key to the in-
terpretation of accelerated data for pre-
dictions at lower temperatures. If the Ea
is low
(less than or equal to 17 kcal/mole),
the accelerated 40 degrees C drug con-
centration
must remain greater than
90% label claim for six months to achieve
at least 90% label claim for a shelf life of
24 month at 25 degrees C. If the Ea is high
(more than or equal to 26 kcal/mole), the
accelerated 40 degrees C drug concentra-
tion must remain greater than 90% la-
bel claim for only three months (and be
80 %label claim at six months), and yet
the product will remain at or above 90%
label claim for a shelf life of 24 month at
25 degrees C. This application of Ea and
Arrhenius kinetics to predict shelf life
can be applied to any drug level (limit)
specified.
Theoretical Model for
Impurity/Degradant Generation
The same approach can be used to under-
stand and predict the generation of im-
purities/degradants. For this exercise, a
zero-order degradation kinetics model
(ΔImpurity/Δtime = —k) is applied to de-
termine the rates for an arbitrary 1% im-
purity growth at 25 degrees C and at 40
degrees C. The calculated slope for growth
from 0 to 1.0% w/w over 24 months at 25
degrees C is equal to 0.0417% w/w per
month, which is the impurity generation
rate constant at 25 degrees C (k25). In the
same manner, the impurity generation
rate at 40 degrees C can be calculated for
reaching 1.0% w/w after three months
(0.3333% w/w per month) and for reaching
1.0% w/w after six months storage (0.1667%
w/w per month). Table 2 summarizes the
corresponding rates and Eas:
Example calculation
Where:
Ln k2/k1= -Ea/R*(1/T2-1/T1) (Equation 3)
Ln (k40/k25) = - [Ea/1.987*(1/313-1/298)]/1000cal/kcal
k40 = 0.1667%w/w degradant/month
k25 = 0.0417%w/w degradant/month
Solving for Ea:
Ea = - [Ln (0.1667/0.0417)*1.987]/[(1/313-1/298)*1000]
Ea = 17 kcal/mole
As the Ea increases, the reaction rate
at 40 degrees C increases. The degradant
level at six months at 40 degrees C is pre-
dictive of the degradant level to be reached
after 24 months at 25 degrees C when the Ea
is 17 kcal/mole. Degradants with reaction
mechanisms with high activation energies
(greater than 17 kcal/mole) can exhibit
levels exceeding 1.0% w/w by six months
at 40 degrees C, yet have 25 degrees C val-
ues below the 1.0% w/w limit.
Shelf Life, Rates, and
Activation Energy
To demonstrate the importance of Ea in
predicting long-term shelf life at 25 degrees
C from 40 degrees C rates, the Arrhenius
kinetic equation was used to demonstrate
the relationship of reaction rates and Ea. The
relationships are demonstrated in Table
3
for the scenario where the degradant
reaches the 1.0% w/w limit at six months
at 40 degrees C and the zero-order rate
constant (k40) is equal to 0.1667% w/w
degradant/month.
Pharmaceutical Formulation & Quality >April/May 2011
QUALITY CONTROL |HIGH-TEMPERATURE STABILITY
Table 3. Relationship of rates and activation energy (Ea) for shelf-life
stability when limit is reached after six months at 40 degrees C.
Months at 25
degrees C to
reach 1.0% w/w
degradant limit
(kinetic shelf life)
24
18
12
0.0417
0.0556
0.0834
0.1667
0.1667
0.1667
17
14
9
k25 (%w/w per
month) Rate of
degradant growth at
25 degrees C
through shelf life
k40 (%w/w per
month) Rate of
degradant growth at
40 degrees C when
1.0% w/w limit is
reached at six
months
Ea (kcal/mole)
activation energy
Table 4. Relationship of rates and activation energy (Ea) for shelf-life
stability when limit is reached after three months at 40 degrees C.
24
18
12
9
0.0417
0.0556
0.0834
0.1111
0.3333
0.3333
0.3333
0.3333
26
22
17
14
Months at 25
degrees C to
reach 1.0% w/w
degradant limit
(kinetic shelf life)
k25 (%w/w per
month) Rate of
degradant growth at
25 degrees C
through shelf life
k40 (%w/w per
month) Rate of
degradant growth at
40 degrees C when
1.0% w/w limit is
reached at three
months
Ea (kcal/mole)
activation energy
April/May >Pharmaceutical Formulation & Quality
PHARMAQUALITY.COM
CA SE STU DY
Predict Dextrose Degradation
t is widely reported that dextrose in solution degrades to form 5-hydrox-
ymethylfurfural (5-HMF) during heating (terminal sterilization) and over
time.6-8 According to the dextrose injection monograph in the USP, the
limit for 5-HMF and related substances is not more than 0.25 absorbance
units at 284 nm wavelength.9
The multiple pathway formation of 5-HMF by dehydration of dextrose is
depicted in Figure A.10The overall kinetic scheme, involving an intermediate,
with definable rate constants for formation and
reaction, has been published by at least three
groups.11The Eas for k1and k2of the reaction
scheme shown in Figure B, as determined by
Sturgeon and colleagues, are 32.6 kcal/mole and
12.3 kcal/mole, respectively. Previously, Heimlich
and Martin determined the Ea for 5-HMF formation
from dextrose to be 31.2 kcal/mole and 31.8
kcal/mole, dependent upon the method used to
determine the first-order rate constant.11
Before appreciable formation of 5-HMF can
occur, a reasonably high steady state level of the
intermediate must first be established. Thus, the
overall generation of 5-HMF will be dependent upon
the k1with an activation energy of 32.6 kcal/mole.
Using Table 5 and the Ea of 31 kcal/mole listing, the
last column indicates that 5-HMF levels measured
after two months at 40 degrees C will be predictive
of 24 months at 25 degrees C. The production of
5-HMF is proceeding at least 12 times faster at 40
degrees C than at 25 degrees C. The level of 5-HMF
after six months at 40 degrees C will be three times
higher than the level reached at 24 months at
25 degrees C.
The U.S. Food and Drug Administration/Inter-
national Conference on Harmonisation Guidance for
Industry, Q1A(R2), Stability Testing of New Drug
Substances and Products, requires long-term testing over 12 months at
room temperature (25 degrees C or 30 degrees C) and over six months at
accelerated conditions of 40 degrees C at the time of submission. The docu-
ment’s Objections of the Guidance section states: “The guidance exempli-
fies the core stability data package for new drug substances and products,
but leaves sufficient flexibility to encompass the variety of different practical
situations that may be encountered due to specific scientific considerations
and characteristics of the materials being evaluated. Alternative approaches
can be used when there are scientifically justifiable reasons.”12
The known chemistry of dextrose degradation to 5-HMF as presented
here represents a justifiable reason for submitting a shorter time period of
accelerated data. The kinetic model with known activation energy indicates
that submission of two months at 40 degrees C data is sufficient and more
appropriate than six months at 40 degrees C data to estimate the level of
5-HMF at 25 degrees C and to support a requested 24 months at 25 degrees
C expiration dating period. n
I
Figure A.
Figure B.
Possible mechanism of 5-HMF formation in dextrose solutions
(reference 10).
Simplified reaction scheme for 5-HMF formation.
Table 5. Stability predictions based upon the ratio of rates (Ea) at 40
degrees C and 25 degrees C.
Ea
(kcal/mole)
activation
energy
9
14
17
20
22
26
31
Ratio (R)
k40 to k25
(k40 =
R*k25)
2
3
4
5
6
8
12
Required
months at 40
degrees C
to reach level
equivalent to
12 months at
25 degrees C
6
4
3
2.5
2
1.5
1
Required
months at 40
degrees C
to reach level
equivalent to
18 months at
25 degrees C
9
6
4.5
3.6
3
2.25
1.5
12
8
6
5
4
3
2
Required
months at 40
degrees C
to reach level
equivalent to
24 months at
25 degrees C
Pharmaceutical Formulation & Quality >April/May 2011
Table 4 demonstrates these relation-
ships for the scenario where the degradant
reaches the 1.0% w/w limit at three months
at 40 degrees C and the zero-order rate
constant (k40) is equal to 0.3333% w/w
degradant/month. The zero-order degradant
generation rates at 25 degrees C (k25) are
calculated for reaching 1.0% w/w at dif-
ferent expiry time intervals: 12, 18, and 24
months (Tables 3 and 4). For these exam-
ples, the initial time zero starting level is set
to 0% w/w. As shown in Tables 3 and 4, each
of these different shelf-life scenarios has a
reaction mechanism with a different Ea
.
As the Ea decreases, the reaction rate at
25 degrees C increases relative to the rate at
40 degrees C. The temperature sensitivity
of the reaction decreases with decreased
activation energy, as indicated by the de-
creased proportionality between the rates
(k40 αk25). When the activation energy is
9 kcal/mole (very low), even when remain-
ing within the limit of 1.0% w/w degrada-
tion through six months at 40 degrees C,
a maximum of 12 months at 25 degrees C
shelf life can be projected.
In comparison, when activation en-
ergy is 17 kcal/mole with 1.0% w/w degra-
dation through six months at 40 degrees
C, 24 months elapses before the same
1.0% w/w degradant level is reached at
25 degrees C. If the Ea is known to be 17
kcal/mole or greater, then 40 degrees C
values at six months of 1.0% w/w (or less)
can kinetically support a shelf life, for this
degradant limit, of 24 months at 25 degrees
QUALITY CONTROL |HIGH-TEMPERATURE STABILITY
Editor’s Choice
1. Weiss WF IV, Young TM, Roberts CJ. Principles, approaches, and challenges for predicting protein aggregation rates and shelf life.
J Pharm Sci. 2009;98(4):1246-1277.
2. Zahn M, Kållberg PW, Slappendel GM, et al. A risk-based approach to establish stability testing conditions for tropical countries.
J Pharm Sci. 2006;95(5):946-965.
3. Waterman KC, Adami RC. Accelerated aging: Prediction of chemical stability of pharmaceuticals. Inter J Pharm. 2005;
293:101-125.
4. Beaman J, Whitlock M, Wallace R, et al. The scientific basis for the duration of stability data required at the time of submission.
J Pharm Sci. 2010;99(6):2538-2543.
5. Bauer M. Stability of drug substances and drug products: Considerations on the stability of drug substances and formulation in
the pharmaceutical industry domain. STP Pharma Pratiques 2005;15(3):232-246.
Figure 5.
Kinetic model for
1% w/w degradant
formation after
three months at
40 degrees C.
Figure 4.
Predicted
degradant forma-
tion at 25 degrees
C when 1% w/w
degradation is
reached after
three months at
40 degrees C for
different activation
energies (Ea).
April/May >Pharmaceutical Formulation & Quality
C. (This article does not address data accu-
racy—variability of the analytical method-
ology and/or the product samples—or the
use of confidence intervals, which should
also be incorporated when establishing
product shelf life.)
Because many drugs demonstrate Eas
of 19-20 kcal/mole, this is the basis for the
practice of comparing six month 40 de-
grees C values against the specification
limit as a predictor of meeting that speci-
fication through a shelf life of 24 months
at 25 degrees C. The proportionality of six
months storage at 40 degrees C as predic-
tive of 24 months at 25 degrees C is predi-
cated upon an activation energy of at least
17 kcal/mole.
Some reactions proceed relatively fast
at higher temperatures, as demonstrated
in Table 4 and Figure 4. In this example,
the degradant growth at 40 degrees C
reaches the product limit (assigned here as
1.0% w/w) after three months storage (k40
= 0.3333%w/w degradant per month). The
usual response is to assume that only a
12-month shelf life at 25 degrees C can be
achieved. In reality, the levels of degradant
reached at 25 degrees C are dependent
upon the Ea of the reaction as shown in
Figure 5.
The proportionality of the level meas-
ured after three months at 40 degrees C as
predictive of the level for 12 months at 25
degrees C is valid only for an Ea of 17
kcal/mole. If the activation energy isknown
to be 22 kcal/mole or greater, then 40 de-
grees C values at three months up to 1.0%
w/w can kinetically support a shelf life,
for this degradant limit, of 18 months at
25 degrees C. This application of Ea and
Arrhenius kinetics to the prediction of
shelf life can be applied to any degradant
level specified.
Stability Prediction Made Easy
Now that the relationship of reaction rates
to Ea is understood, it becomes easier to
predict values over longer time periods at
lower storage temperatures, like 25 de-
grees C, from values obtained at higher
(accelerated degradation) temperatures,
such as 40 degrees C.
The Ea is the proportionality factor be-
tween reaction rates at different tempera-
tures (k40 αk25). The Arrhenius equation
(Equation 4) can be solved for the exact
relationship between reaction rates at 40
degrees C and 25 degrees C for any activa-
tion energy Ea. This proportionality can
be used to predict levels and shelf life, as
presented in Table 5. When the activation
energy is 17 kcal/mole, the same degradant
limit is reached at six months at 40 degrees
C and at 24 months at 25 degrees C.
Table 5 can be used as a guide to inter-
pret 40 degrees C kinetic prediction of 25
degrees C shelf life. As data is collected
over time at 40 degrees C, the results at
each test interval can be used to predict the
level and, hence, the shelf life at 25 degrees
C. When the activation energy is greater
than 17 kcal/mole, samples stored at 40 de-
grees C and tested at six months will exhibit
levels greater than what will be actually
reached over 24 months at 25 degrees C. If
the activation energy is 26 kcal/mole, the
level measured at three months at 40 de-
grees C represents the expected level for
24 months at 25 degrees C, and the level
measured at six months at 40 degrees C
will actually represent twice the expected
level for 24 months at 25 degrees C.
The concept presented in Table 5 is
shown in Figures 6 and 7. Figure 6 shows
three different rate scenarios for the months
at 40 degrees C to reach 1% w/w degradant.
When the Ea for the reaction is 26 kcal/mole
or greater, although the 1% w/w level is
reached by three months at 40 degrees C
(k40 = 0.3333% w/w degradant/month), the
degradant growth at 25 degrees C will not
reach 1%w/w until 24 months or beyond,
as represented in Figure 7.
When the Ea for the reaction is 22 kcal/
mole and at four months at 40 degrees C
the 1% w/w level is reached (k40 = 0.2500%
w/w degradant/month), the degradant
growth at 25 degrees C will again not reach
1%w/w until 24 months, as represented in
Figure 7. An Ea of 17 kcal/mole and a six
months 40 degrees C degradant level of
1% w/w (k40 = 0.1667% w/w degradant/
month) likewise
corresponds to a projec-
tion of 24 months at 25 degrees C to reach
1% w/w. Thus, as demonstrated, different
rates at 40 degrees C can project to the
same or similar stability at 25 degrees C.
Additionally, as indicated in Table 5, for
the same activation energy of 17 kcal/mole,
when the degradation rate at 40 degrees C
is faster, reaching 1% w/w by three months
(k40 = 0.3333% w/w degradant/month),
PHARMAQUALITY.COM
Figure 6.
Degradant reached 1%w/w at 40 degrees C; each model predicts the
same level at 25 degrees C.
Figure 7.
Degradant level at 25 degrees C for the three activation energy
models in Figure 6.
the 1%w/w level is projected to be reached
by 12 months at 25 degrees C (Figures 4
and 5). A shelf life of 12 months is kineti-
cally supported. Consequently, if the acti-
vation energy is lower than 17 kcal/mole
for this same k40 rate of reaching 1% w/w
by three months (k40 = 0.3333% w/w
degradant/ month), levels at 25 degrees C
will reach 1% w/w before 12 months, and a
shelf life of 12 months is not kinetically
supported. The information in Table 5 can
be used to estimate shelf life based upon
the Ea and stability at 40 degrees C.
The practice of predicting long-term
chemical stability at a lower temperature
using data generated at a higher tempera-
ture over a shorter time period is based
upon application of the Arrhenius kinetic
model. The Arrhenius equation can be ap-
plied regardless of the order of the reaction
kinetics. By using the Ea with the experi-
mental level of drug or degradant ob-
tained at a higher temperature (40
degrees C), the expected level of drug or
degradant over long-term storage at a
lower temperature (25 degrees C) can be
more accurately predicted and the kinetic
shelf life estimated. The proportionality of
six months storage at 40 degrees C as pre-
dictive of 12 months at 25 degrees C is
predicated upon an activation energy of
9 kcal/mole. The proportionality of six
months storage at 40 degrees C as pre-
dictive of 24 months at 25 degrees C is
predicated upon an activation energy of
17 kcal/mole. As the activation energy
increases, the temperature sensitivity of
the reaction increases, resulting in a
greater difference in the rates at different
temperatures. The information in Table 5
can also be used to estimate shelf life at
25 degrees C based upon the activation
energy and the stability at 40 degrees C.
As presented, the Arrhenius kinetic
model can be applied to specific drug
chemistry to scientifically justify appro-
priate months at accelerated 40 degrees C
condition for submission. n
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QUALITY CONTROL |HIGH-TEMPERATURE STABILITY
Michelle Duncanis an associate director in global research and development with
Baxter Healthcare. She holds a bachelor’s in biochemistry and molecular biology from
Northwestern University and earned her PhD in pharmaceutics from the University of
Texas at Austin. She specializes in the formulation development of parenteral products and has
led numerous injectables through FDA approval (NDA and ANDA routes)and to successful com-
mercialization. Irene Zaretsky is a research associate with Baxter, supporting analytical and
formulation development. She earned her master’s in chemistry from the Institute of Technol-
ogy in Minsk, Belarus, and has worked more than 13 years in the U.S. pharmaceutical industry.
Reprinted with permission from PFQ Magazine April/May 2011.
Baxterbiopharmasolutions.com
Contact us at biopharmasolutions@baxter.com