Solid State Degradation Mechanisms:
Impact on Drug Product Design and
Stability Test Design
William R. Porter
33rd ANNUAL MIDWEST BIOPHARMACEUTICAL
STATISTICS WORKSHOP
Muncie, IN, May 25, 2010
Stability by Design (SbD):
Instability Assessment—
A Tool for Product Development
…in order to design stable products, you must
first understand how your product degrades!
Solid State Degradation Mechanisms
May 25, 2010
© 2010 Abbott
2
Why “instability” assessment?
“Good” bulk storage conditions, formulations and packaging are
really those that are “least bad.”
In order to develop “good” processes and procedures, you must
first...
Solid State Degradation Mechanisms
May 25, 2010
© 2010 Abbott
3
Find an elephant…
…to step on your product to make it fail!
Elephant tests are…
• Designed to induce product failure.
• Used to learn how the product fails under a
particular stress so that it can be
redesigned to avert this particular failure
mode.
• Useful in early phases of development to
select between alternate strategies.
References:
Nelson W. Accelerated Testing: Statistical Models, Test Plans,
and Data Analysis. New York: John Wiley & Sons (1990).
Meeker WO, Escobar LA Statistical Methods for Reliability
Data, New York: John Wiley & Sons (1998).
Solid State Degradation Mechanisms
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© 2010 Abbott
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What is a good elephant test?
One that produces the same failures and in the same
proportions that will occur in actual use, but in shorter time.
Elephant tests use stress conditions that exceed normal
environmental conditions to degrade product performance.
Solid State Degradation Mechanisms
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Elephant tests should...
Be done as soon as possible during formulation development.
Involve the whole team in design and implementation.
Use laboratory (NOT production support) facilities (meet good
scientific quality standards, not GMP).
Use best available methods for analysis.
Have adequate controls to minimize method validation
requirements .
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Prerequisites for instability assessment
“Stability-indicating” assay…
• “chicken & egg problem” —Need to understand how material degrades to
validate assay, need assay to understand how material degrades.
Controlled environment storage facilities…
• Need controlled temperature, controlled humidity, controlled light stress.
– Control does NOT mean constant, but nonisofactorial conditions complicate data analysis
Bulk material typical of future production lots…
• Atypical bulk material may have atypical failure modes.
Planning is the most crucial element of a successful program…
…Timing isn’t everything; it’s the only thing!
Solid State Degradation Mechanisms
May 25, 2010
© 2010 Abbott
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How do drugs degrade?
Reaction with solvent (solvolysis)*
• Hydrolysis, when the solvent is water
Reaction with oxygen (oxidation)*
Reaction with radiant energy (photolysis)
Reaction with manufacturing impurities*
Arrhenius kinetics (effect of
heat on reaction rate)
Rate
Frequency Activation
Factor
Energy
 Ea RT
kT  Ae
Reaction with added excipients*
T (Kelvin) =
Reaction with degradation products*
absolute
temperature
*Most, if not all of these processes are accelerated by heat!
…and the Arrhenius model usually can be applied to any process
that is accelerated by heat.
Solid State Degradation Mechanisms
May 25, 2010
© 2010 Abbott
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Thermal stress tests for solids
Arrhenius assumption often invalid, because…
• Phase changes, adsorbed moisture invalidate assumptions
True, but “reasonable” stress still practical…
That depends…
Use lowest temperature that produces measurable failure within
allocated time to avoid these complications.
• Using higher temperatures to save time can lead to changes in failure
mechanism, so always have a Plan B (additional samples stored at a
lower temperature for a longer time; assay these if higher
temperature samples show excessive degradation).
Good news is good news; bad news is no news.*
*You need to execute Plan B…and that takes extra time and money!
Solid State Degradation Mechanisms
May 25, 2010
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9
Chemical Degradation
for People Who Forgot
Physical Organic Chemistry
CH3
O
CH3
O
H2O
O
O
H
O
O
R-(+)-warfarin
HO
-
H
Lactone hydrolysis
OH
pH control
Pseudo-Zero-Order Kinetics
O
O
Pseudo-Zero-Order Arrhenius Plot
120.0
-
2
E a = 80.8 kJ/mol
1
(chromandione tautomer)
Decarboxylation
0
100.0
CO2
-1
OH
O
H3C
O
-
Tautomerization
OH
OH
Concentration
O
-2
80.0
ln(k)
-
HC
-3
-4
60.0
-5
-6
40.0
-7
Aldol
cyclization
-8
0.0027
O
O
0.0028
0.0029
0.0030
0.0031
20.0
0.0032
H2O
ln(k)
O
0.0
-
0
1
2
3
+
OH
H
Dehydration
pH control
4
5
6
7
8
All three temperatures used
Time. days
OH
25 °C
(5S)-3-(2-hydroxyphenyl)5-phenylcyclohex-2-en-1-one
("Alice's ketone")
Solid State Degradation Mechanisms
May 25, 2010
0.0033
0.0034
0.0035
0.0036
–1
1/T, K
Control
60 °C
75 °C
90 °C
© 2010 Abbott
60 °C fit
75 °C fit
90 °C fit
5 °C
10
Temperature
5 °C
25 °C
60 °C
75 °C
90 °C
Time for 2% Change in Potency, days
From Fitted Rate From Arrhenius Model
3513
337
9
11
3
3
1
1
Only data from three temperatures were used.
Some books to read in your copious spare time…
If (heaven forbid!) you have never taken a course in organic chemistry…
• Winter A. Organic Chemistry 1 for Dummies. John Wiley & Sons (2005).
If you have forgotten organic chemistry…
• Smith MB, March J. March's Advanced Organic Chemistry : Reactions,
Mechanisms, and Structure. John Wiley & Sons (2007).
If you have forgotten chemical kinetics and physical chemistry…
Moore JW, Pearson RG. Kinetics and Mechanism. John Wiley & Sons (1981).
If you want to focus on stress testing of pharmaceuticals…
Baertschi SW. Pharmaceutical Stress Testing: Predicting Drug Degradation. Taylor &
Francis (2005).
Yoshioka S, Stella VJ. Stability of Drugs and Dosage Forms. Kluwer Academic/Plenum
Publishers (2000)
Carstensen JT. Drug Stability Principles and Practices (2nd Ed). Marcel Dekker (1995)
Solid State Degradation Mechanisms
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…not to mention self-promotion…
Book chapters I’ve written on the subject:
• Zhou D, Porter WR, Zhang GZZ. “Drug Stability and Degradation
Studies.” Chapter 5 in: Qiu Y, Chen Y, Zhang GGZ, Liu L, Porter WR.
Developing Solid Oral Dosage Forms: Pharmaceutical Theory and
Practice. Elsevier/Academic Press (2009).
• Porter WR. “Residues and Cleaning Chemistry,” Chapter 9 in Pluta P.
Cleaning and Cleaning Validation, Vol 1. PDA/Davis Healthcare
International Publishing LLC (2009).
Solid State Degradation Mechanisms
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Hydrolysis
Hydrolysis is by far the most commonly encountered drug
degradation reaction both in solution and in the solid state.
Examples:
• Carboxylic acid derivatives.
O
R1
O
X
+
H2O
R1
OH
+
HX
• Acetals and ketals.
R2C(OR')2
H+
+ H2O
R2C=O
+ 2R'OH
• Nitrogen derivatives of carbonyl compounds.
R2C=NR'
Solid State Degradation Mechanisms
May 25, 2010
+ H2O
R2C=O
© 2010 Abbott
+ R'NH2
13
Oxidation
Oxidation is a major drug degradation pathway, second only to
hydrolysis.
Examples:
R1
H
• Amines
HO
N
N
R1
H
OH
• Sulfur moieties
R1
R2
H
R2
O O
R3
SH
R1
R3
S
R1
O O
O
OH
HO
H
R1
S
R2
O O
R3
R2
-
O
R2
R1
O
R2
+
N
R2
R1
O O
R1
O O
N
R2
R2
• Alcohols
R1
R1
O O
R1
R2
O
R3
S
R1
O O
R2
O
OH
H
R1
O O
H
H
Solid State Degradation Mechanisms
May 25, 2010
R2
R2
H
R1
O
© 2010 Abbott
H
H2O
H
OH
OH R2
14
S
O
• Alkenes & alkynes
R1
R3
OH
Photolysis
To undergo photodegradation, compound must absorb light in the
same spectral region as the radiant energy to which it is exposed.
• No absoption  no reaction
R1
Examples
• Radical induced oxidation
R1
R2
h
H
R3
• Radical formation and polymerization
O
R1
O
© 2010 Abbott
O
R3
OH
R2 C
R3
R1
R1
R2 C
R3
Solid State Degradation Mechanisms
May 25, 2010
R2
15
R1
R2
R2
R3
R3
Solid State Chemical Kinetics
One score and thirteen years ago, physical chemists brought
forth upon this planet a new paradigm, conceived in
simplicity, and dedicated to the principle that all solid state
kinetics problems can be solved by replacing kinetic models
and rates with time-to-failure.
Based on:
Vyazovkin A & Wight CA. Kinetics in Solids
Annu Rev Phys Chem. 48:125-149 (1977)
Look at the date!
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Chemical Kinetics
In solution:
In solids:
• Traditionally based on kinetic models
in which concentration (C) is
monitored as a function of time.
• Based on models in which fraction
degraded (α) is monitored as a
function of time.
• Reaction order concept dominates
model choices.
• Reaction order models less common.
– In stability experiments, most kinetic models
can be replaced by a zero-order model with
little loss of accuracy.
– Stress experiments are usually run under
conditions such that either zero- or first-order
kinetic models can be fitted to the data.
– Diffusion models
– Geometric contraction models
– Reaction order models
– Induction models
• Power law growth…
– You see nothing,
nothing,
nothing,
nothing,
– then WHAM! you get explosive growth,
and your product fails catastrophically.
Because your analytical method
is too insensitive!
Solid State Degradation Mechanisms
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The traditional unreadable slide…
Derivative form
Integral form
From: Vyazovkin A & Wight CA. Kinetics in Solids Annu Rev Phys Chem. 48:127-1128 (1977)
Solid State Degradation Mechanisms
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…and another
Example is
based on a
nonisothermal
kinetics
experiment.
From: Vyazovkin A & Wight CA. Kinetics in Solids Annu Rev Phys Chem. 48:132-133 (1977)
Their point: You can fit all 13 models to the same set of data, and they all fit equally well…
Solid State Degradation Mechanisms
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So, what does this mean?
Vyazovkin & Wight demonstrated that
isoconversional methods gave
consistent results and were model-free.
 1  t ,T


kT 



f
 t



g t ,T
kT 
t

 t ,T ,h
E 

 f  t ,T ,h A exp Bh  a 
RT 

E 

g  t ,T ,h   A exp Bh  a t
RT 

lnkT ,%RH   ln A 
Ea
 Bh
RT
E 

 A exp Bh  a 
RT 

Ken Waterman at Pfizer is popularizing
this model …
*Effect of temperature and relative humidity on nitrazepam
stability in solid state. J Pharm Sci 66: 676–680 (1977)
Solid State Degradation Mechanisms
May 25, 2010
humidity h:
t
Genton & Kesselring* proposed this
modified Arrhenius model:
kT ,%RH
Time-course of the reaction at any
particular temperature T and relative
© 2010 Abbott
Vyazovkin and Wight pointed out that the
use of the Arrhenius equation in solid state
kinetics is supported by a sound
theoretical foundation. But experimental
difficulties in actually studying solid state
reactions make it difficult, if not
impossible, to isolate an elementary
reaction (e.g., nucleation, crystal growth)
whose molecularity can be determined that
is uncomplicated by diffusion, adsorption,
desorption and other physical processes.
20
All things cometh to they who waiteth…
…but isn’t 33 years of waiting a little bit too long?
Everything we needed to know to design thermal stress degradation
experiments for solids was known in 1977.
The key, as pointed out by Vyazovkin & Wight, was to use “model-free”
methods. All you need to do is replace rates (which depend on kinetic
models) with time-to-failure:
t 0.005 ,T 
g   0.005
E 

Ag exp Bh  a 
RT 

The Arrhenius frequency factor A is a function of g, but g itself is
independent of the temperature T.
Solid State Degradation Mechanisms
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Using time-to-failure data at stress conditions…
It’s possible to make measurements at three separate conditions of
temperature and relative humidity and then solve the modified Arrhenius
equation to calculate the time-to-failure at any other temperature and
relative humidity:



ln t constant ,Tl ,hl  ln t constant ,Th ,hh

Ea

R
 1
1


 Th,
Tl , constant
constant


  B hh,
 hl , constant
constant




A plot of the logarithm of the time ti to obtain a specific fraction degraded
α versus the reciprocal absolute temperature Ti and relative humidity hi at
which α was determined is a plane in three-dimensional space:


ln t constant ,Ti ,hi 
Ea
 Bhi  C g , constant
RTi
Parameters estimated by fitting Arrhenius model to time-to-failure data
Solid State Degradation Mechanisms
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…we can calculate the shelf-life!

ln t constant ,Tnew ,hnew

Ea

 Bhnew  C g , constant
RTnew
Yes, C is kinetic model-dependent, but
we can use data from other
temperature and relative humidity
experiments to eliminate this nuisance
parameter. It’s just one of the
Arrhenius-humidity model-fitting
parameters that is obtained when you
fit the Arrhenius-humidity plane to
the temperature × relative humidity
time-to-failure data. It has no
meaning unless, of course, you decide
to select a particular kinetic model.
Solid State Degradation Mechanisms
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© 2010 Abbott
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…or, we can calculate how long to expose samples
to thermal stress to support a desired shelf-life
Time Required to Achieve Constant Fractional Degradation as a Function of
Temperature at B×h = 0 for tlow = 2 Years at 25 °C
Temperature
t(1 – α) (days) for Ea, kJoules/mole
T to cut t in half @ Ea = 71.74 kJmol–1

°C
K
25
298.15
32
305.15
459.91
392.96
40
313.15
277.99
48
321.15
56
50b
67b
71.74a,b
84b
100b
117b
376.10
335.76
289.55
247.40
200.15
182.63
144.11
105.79
76.17
172.29
105.43
91.93
64.52
40.64
24.87
329.15
109.30
57.29
47.85
30.03
16.35
8.57
65
338.15
67.21
29.86
23.82
13.27
6.18
2.75
75
348.15
40.32
15.06
11.44
5.62
2.23
0.83
85
358.15
24.90
7.89
5.73
2.50
0.85
0.27
730.50 days
a. “Rule of thumb” assumed value for ICH accelerated stability extrapolation.
b. Note that 50 kJ/mol ≈ 12 kcal/mol, 67 kJ/mol ≈ 16 kcal/mol, 84 kJ/mol ≈ 20 kcal/mol, 100 kJ/mol ≈ 24 kcal/mol, and 117
kJ/mol ≈ 28 kcal/mol.
Solid State Degradation Mechanisms
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What temperature and humidity conditions must our
products survive?
ICH Guideline Q1A(R2) recommends storage conditions of 25 °C
at 60% RH and 40 °C at 75% RH as a general case for use in
“long term” and “accelerated” stability trials. An “intermediate”
storage condition of 30 °C at 65% RH is used to provide backup
data in the event that product failure is detected under
“accelerated” stress conditions.
Can we predict whether or not a drug substance or drug product is
likely to meet specifications as recommended in ICH Guidelines
Q3A(R2) and Q3B(R2) using the Genton and Kesselring
expanded Arrhenius model and data obtained under higher
temperature and higher humidity?
Solid State Degradation Mechanisms
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© 2010 Abbott
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The Waterman plan…
Ken Waterman and colleagues at Pfizer recently proposed timeto-failure stress degradation studies using a range of accelerated
temperature and a range of relative humidity storage conditions to
be used routinely for preformulation and early formulation
development studies.
• Waterman KC, Carella AJ, Gumkowski MJ, Lukulay P, MacDonald
BC, Roy MC, Shamblin SL. Improved protocol and data analysis for
accelerated shelf-life estimation. Pharm Res 24(4):780–790 (2007).
• Waterman K. “Accelerated Stability Assessment Program (ASAP):
Using Science to Set Shelf Life,” presented at 5th Annual Forced
Degradation Strategies for Small Molecules, Baltimore, MD, February
26, 2008.
Solid State Degradation Mechanisms
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© 2010 Abbott
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Waterman’s “improved” 2008 design…
T, °C
h,% RH
50
60
60
70
70
80
75
5
40
5
75
40
Sampling
Time, days
4, 14
14, 21
4, 21
4, 21
⅓, 2
⅓, 4
The time at 70 °C is probably
long enough, but at 60 °C it
should be doubled…
Solid State Degradation Mechanisms
May 25, 2010
For moisture-sensitive materials,
the low humidity samples will
degrade very slowly, so much so
that no degradation will be seen in
the short exposure times used.
Unless the humidity used in the
“accelerated” test is greater than or
equal to the humidity used in the
“real time” test, which under ICH
guidance is typically 60% RH at 25
°C, then the “accelerated” test will
actually take much longer than the
“real time” test to produce the same
fractional degradation!
© 2010 Abbott
27
How does B (sensitivity to humidity) affect time-to
failure at different temperatures for different Ea?
Time Required to Achieve Constant Fractional Degradation as a Function of
Temperature at 75% Relative Humidity
B=
0.01
0.01
0.01
0.01
0.03
0.03
0.03
0.03
0.05
0.05
0.05
0.05
0.07
0.07
0.07
0.07
0.09
0.09
0.09
0.09
Temperature
T, °C
T, K
25
298.15
40
313.15
50
323.15
60
333.15
75
348.15
40
313.15
50
323.15
60
333.15
75
348.15
40
313.15
50
323.15
60
333.15
75
348.15
40
313.15
50
323.15
60
333.15
75
348.15
40
313.15
50
323.15
60
333.15
75
348.15
Solid State Degradation Mechanisms
May 25, 2010
50
67
239.26
132.07
75.54
34.71
177.25
97.84
55.96
25.71
131.31
72.48
41.46
19.05
97.28
53.69
30.71
14.11
72.07
39.78
22.75
10.45
Ea, kJ/mole
84
730.50 days
172.27
124.04
77.69
45.70
36.75
17.88
12.96
4.84
127.62
91.89
57.56
33.86
27.23
13.25
9.60
3.59
94.55
68.07
42.64
25.08
20.17
9.81
7.11
2.66
70.04
50.43
31.59
18.58
14.94
7.27
5.27
1.97
51.89
37.36
23.40
13.77
11.07
5.39
3.90
1.46
© 2010 Abbott
100
117
91.05
27.74
9.08
1.92
67.45
20.55
6.72
1.42
49.97
15.22
4.98
1.05
37.02
11.28
3.69
0.78
27.42
8.36
2.73
0.58
28
65.56
16.32
4.42
0.72
48.57
12.09
3.27
0.53
35.98
8.96
2.42
0.39
26.65
6.63
1.80
0.29
19.75
4.92
1.33
0.22
h=
%RH
60
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
75
What is the effect of humidity h…
…for different moisture sensitivities (B)?
Storage Time in Days Required to Achieve Degradation Equivalent to Storage
for 2 Years at 25 °C, 60% RH
0.09
Ea
kJ/mole
50
T
°C
50
T
h = 10% h = 30% h = 50% h = 75% h = 80%
h = 5% RH
K
RH
RH
RH
RH
RH
323.15
21661.58 13812.03
2283.11
377.40
39.78
25.36
0.09
50
60
333.15
12390.63
7900.62
1305.96
215.87
22.75
14.51
0.09
50
65
338.15
9488.03
6049.83
1000.03
165.30
17.42
11.11
0.09
50
75
348.15
5692.84
3629.92
600.02
99.18
10.45
6.67
0.05
84
50
323.15
830.64
646.91
237.98
87.55
25.08
19.53
0.05
84
60
333.15
324.98
253.09
93.11
34.25
9.81
7.64
0.05
84
65
338.15
207.54
161.64
59.46
21.88
6.27
4.88
0.05
84
75
348.15
87.98
68.52
25.21
9.27
2.66
2.07
0.01
117
50
323.15
32.86
31.26
25.59
20.95
16.32
15.52
0.01
117
60
333.15
8.89
8.46
6.93
5.67
4.42
4.20
0.01
117
65
338.15
4.76
4.53
3.71
3.04
2.36
2.25
0.01
117
75
348.15
1.44
1.37
1.12
0.92
0.72
0.68
B
Solid State Degradation Mechanisms
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© 2010 Abbott
29
So, what does this mean?
When substances sensitive to moisture (large B) are subjected to
thermal stress under conditions of low humidity (small h), it can
take a very long time for substances having a low Arrhenius
activation energy (small Ea) to degrade, even at elevated
temperatures (high T) to the same extent that would be observed
in a real time stability trial conducted in accordance with ICH
Guidelines.
• For example, in the case where B = 0.09, h = 5% RH, Ea = 50 kJ/mole
and T = 75 °C, it would take 5693 days exposure to achieve the same
amount of degradation seen in 730 days at 25 °C and 60% RH
Conclusion: Experiments at low humidity are useless for
moisture sensitive compounds.
Solid State Degradation Mechanisms
May 25, 2010
© 2010 Abbott
30
A better design…
Skip the low humidity test conditions
• You really need to do initial experiments at only one humidity—the
highest the product must ever face.
• Per ICH guidelines, this is 75% RH for all climate zones.
Use the highest thermal stress that does not result in a change of
physical form.
• Desolvation/dehydration
• Polymorph conversion
If you have time, use two or more temperatures to estimate Ea.
Solid State Degradation Mechanisms
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© 2010 Abbott
31
But what about those thirteen kinetic models?
When only a small amount of degradation occurs, these can be
approximated by only FIVE kinetic models:
• Diffusion model (time-to-failure tα ≈ C×square root of time)
• Zero-order model (time-to-failure tα ≈ C×time)
• Power law models (time-to-failure tα ≈ C×timen, n = 2,3,4)
You only need a few different sampling times to establish the
shape of the curve.
Solid State Degradation Mechanisms
May 25, 2010
© 2010 Abbott
32
Hypothetical Stability Trial Results
Stability Trial Assay Results
Need to know shape of
plot in advance!
0.55%
Threshold for toxicological qualification
0.50%
– not detected…
– or not quantifiable,
…so you need to
modify the stability
sampling plan.
Solid State Degradation Mechanisms
May 25, 2010
0.45%
Critical Degradant, %
• Use data from high
temperature and high
humidity degradation
experiment.
• Note that for power law
(induction) kinetics,
early degradation is
either:
0.40%
0.35%
0.30%
0.25%
0.20%
0.15%
0.10%
Detected, Not Quantified
0.05%
Not Detected
0.00%
0
0.5
1
1.5
2
Time, Years
Diffusion
© 2010 Abbott
Zero Order
Quadratic
33
Cubic
Quartic