predicting the long-term stability of solid-state

Predicting the Long-Term Stability of Solid-State Pharmaceuticals

London, March 2015 Garry Scrivens, Ph.D.

Pfizer Global R&D, Sandwich, UK

[email protected]

ASAP (Accelerated Stability Assessment Program): Theory, Limitations and Applications

Garry Scrivens, Pfizer 2

Environmental Factors that Influence the rate of chemical degradation in the solid state

1.  Temperature

2.  Humidity

3.  Light –  Accepted rapid ICH accelerated conditions

exist –  Packaging used for most solid drug

products protect from light

4.  Oxygen level

(etc.?)

Not in scope of presentation

Garry Scrivens, Pfizer

Temperature and Humidity… n  Schumacher (1972) and Grimm (1986, 1998) proposed four long-term stability storage

conditions –  Zone 1: “Temperate” 21°C/45%RH –  Zone 2: “Subtropical and Mediterranean” 25°C/60%RH –  Zone 3: “Hot and Dry” 30°C/35%RH –  Zone 4: “Hot and Humid” 30°C/70%RH n  Temperature, Arrhenius equation (ca. 1889):

k = Ae-Ea/(RT)

Ln k = Ln A - Ea/(RT) Until recently only thought to apply ‘in general terms’ to solid-state pharmaceutical systems

Collision frequency “pre-exponential factor”

Activation energy

Gas constant

Temperature (in K)

Rate constant (e.g. %deg per day)


Arrhenius Plots

The rate of a chemical reaction at a particular temperature can be interpolated / extrapolated from the rates at other temperatures

Ln k = Ln A – (Ea/R).(1/T)

Ln k

(1/T)

x

x x

x x

Intercept of line = Ln A Slope of line = -Ea/R

Accelerated (high temperature) results

e.g. T = 25ºC

Predicted rate of degradation at

25ºC


Accurate application of Arrhenius to the solid state

Ken Waterman et.al.1 cites two main reasons that led to the historical misconception that Arrhenius does not apply accurately to solid-state pharmaceuticals:

a)  API is in multiple different micro-environments in solid state (This can lead degradation curves that cannot be defined as simply 0th, 1st or 2nd order curves - which can lead to errors in defining a reliable rate constant for chemical degradation)

b)  Effect of relative humidity is not factored into the Arrhenius equation2

1. Waterman, K.C.; Carella, A.J.; Gumkowski, M.J.; Lukulay, P.; MacDonald, B.C.; Roy, M.C.; Shamblin, S.L. Improved protocol and data analysis for accelerated shelf-life estimation of solid dosage forms. Pharmaceutical Research 24 (2007) 780-790.

2. Actually back in 1977, a paper by Genton and Kesselring covered some of the ground J.Pharm Sci 66: 676–680 (1977)


API Micro-Environments in Solid-State

n  Solution: –  Molecules are in same environment –  Reactivity shows homogeneous kinetics

n  Solid State: –  Molecules in different microenvironments:

•  crystal lattice •  surface •  amorphous •  solid-solution

–  Multiple k’s –  Heterogeneous kinetics – formation of product is a superposition of multiple

rates

–  Shape of degradation curve in solid state may not be well described by simple 0th, 1st or 2nd order kinetics

[Pt] = Σikit (different k for each API state)


Degradation Curves

7

Zero Order First Order Second Order

All curves appear linear over the first few % of degradation… …if all API molecules are in same environment

00.20.40.60.81

1.21.41.61.82

0 500 1000 1500 2000

% Degradation

Time (Days)

00.20.40.60.81

1.21.41.61.82

0 500 1000 1500 2000

% Degradation

Time (Days)

00.20.40.60.81

1.21.41.61.82

0 500 1000 1500 2000

% Degradation

Time (Days)


Real-world Solid-State Degradation Curves

n  ~50% (in our experience) appear to be essentially linear

n  ~50% exhibit a degree of curvature

8

00.20.40.60.81

1.21.41.61.82

0 500 1000 1500 2000

% Degradation

Time (Days)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 500 1000 1500 2000

% Degradation

Time (Days)

Overall degradation curve observed

Degradation curve from a small proportion of API in reactive environment

Degradation curve from a large proportion of API in a more stable environment

n  Other causes of curvature are discussed later….

This curve is not accurately described by a simple 0th ,1st or 2nd order rate equation


Dealing with real-world solid-state degradation curves

n  Objective: to calculate ‘k’ (rate constant for the degradation) over a range of temperatures so that an Arrhenius plot can be produced

n  Problem…in order to calculate k, we need to apply a model to account for the curvature of degradation

n  Plan A: acquire %deg results at multiple timepoints so that a empirical model can be applied to the data (à k) – Labour intensive – Prone to errors associated with fitting models to data

(>1 parameter is required to model the data)

n  Plan B: use a ‘Time to failure’ or ‘Isoconversion’ approach 9


Degradation Kinetics at Different Conditions

For a given system, the shape of the curve (i.e. degradation kinetics) is usually very similar across different stability conditions, just the timescale is different

(cases where this assumption is invalid are discussed later)

3.1x faster

3.1x faster

Etc.

11.7x faster


Traditional (Constant Time) Approach vs. Isoconversion Approach

Time

%Deg Prod

30ºC

60ºC

70ºC

Spec. Limit

kT = Slope of line

30 days

Constant Time

t1 t2

Isoconversion

kT = Slope of line

With an isoconversion approach, the shape of the degradation curve is unimportant


Isoconversion Principle - Summary

n  Select timepoints for each Temp / %RH condition to give approximately the level of degradation that you’re interested in (typically the specification limit) –  Shape of the degradation curve (order of reaction) is unimportant –  Degradation far removed from specification level may lead to an inaccurate

shelf life prediction –  Proportion of reaction from different API environments assumed to be

consistent across different conditions


Caution: Isoconversion Approaches

Time

%Deg Prod

Spec. Limit

Actual Degradation

Predicted Degradation

Accurate prediction at (e.g.) spec level


-8

-7

-6

-5

-4

-3

-2

-1

2.9 3 3.1 3.2 3.3 3.4

1/T (X1000)

ln k

10% RH

75% RH

Applying Arrhenius to the Solid State: 2. Effect of Relative Humidity

30°C 20°C 60°C 40°C 70°C

Degradation of Aspirin Tablets:

Garry Scrivens, Pfizer Garry Scrivens, Pfizer 15

Humidity Sensitivity

n  Observation: solid-state degradation rates increase exponentially with %RH

n  At constant temp, ln k = B(%RH)

Moisture dependence(Constant Temperature)

-9-8.5

-8-7.5

-7-6.5

-60 20 40 60 80 100

%RH

ln k


Humidity Corrected Arrhenius Equation

Ln k = Ln A - Ea/(RT) + B(%RH)

Measured (calculated from %degradation results)

Selected by user, at least 3 combinations required

3 parameters need to be determined (using multilinear regression) for each

degradation reaction


Accelerated Stability Protocol Design

n  Isoconversion: aim to degrade sample to the specification level for all conditions –  Initial trials: use average (typical) Ln A, Ea and B values – Subsequent trials on same drug product / API can use Ln A,

Ea and B values from previous studies to provide better isoconversion (an iterative process)

n  A minimum of 3 different temperature - %RH combinations are required (3 unknown parameters, Ln A, Ea and B to be determined) – More than 3 conditions are required in order to provide

greater confidence in prediction and to provide some measure of goodness of fit to ASAP model (an ‘over-determined’ system)


Standard (Default) ASAP Protocol*

Protocol T (°C) %RH Days

API Stability

70 5 14 70 75 14 80 5 14 80 40 14

Drug Product Stability

50 75 14 60 40 14 70 5 14 70 75 1 80 40 2

Conditions and durations chosen for their practicality and to provide about 0.5% degradation based on typical Ln A, Ea and B values

*Other temperature / humidity / duration combinations can be used to meet the needs of the particular application


Protocol Design: Practicalities

n  Humidity-controlled ovens

n  Saturated Salt Solutions, e.g.: – 30%RH: MgCl2

– 50%RH: NaBr – Etc.

n  Amebis

19


ASAP Drug Product Design Space (DOE)

0

1020

3040

50

6070

80

45 55 65 75 85

Temperature (C)

%R

H


ln k

1/T

%RH

x

x

x x

x o

o o o

ln k = ln A - Ea/R(1/T) + B(%RH)

40/75 30/75

30/65 25/60

70/75

80/40

70/ 5

50/75 60/40

Visualizing the ASAP Experiment

Ln A

B

Ea/R


22

Interpretation of Ea and B Values: Quantifying the effect of temperature and %RH

Ea Term: a measure of the temperature dependence of the degradation

Ea = 50 KJ.mol-1, degradation rate 1.9x between 30ºC and 40ºC Ea = 100 KJ.mol-1, degradation rate 3.6x between 30ºC and 40ºC Ea = 150 KJ.mol-1, degradation rate 6.7x between 30ºC and 40ºC

B Term: a measure of the moisture dependence of the degradation

B = 0.07, degradation rate doubles for every 10% RH increase B = 0.035, degradation rate doubles for every 20% RH increase


Using Ea and B to Quantify the effects of Temperature and %RH…Examples

23

Ea = 220 KJ/mol

Ea = 140 KJ/mol

Ea = 60 KJ/mol

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

25 30 35 40

%D

eg p

er m

onth

Temperature (ۥC)

B= 0.08 B= 0.04

B= 0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

10 15 20 25 30 35 40 45 50 55 60 65 70 75

%D

eg p

er m

onth

%RH


Typical Ea and B values (n=60)

Mean Ea ~124 KJ.mol-1

Mean B ~0.04

0

0.02

0.04

0.06

0.08

0.1

0.12

50 100 150 200

B

Activation Energy / KJ.mol-1


Checking the Goodness of Fit of data to the ASAP Model

n  Comparison of prediction against actual long-term stability is of course the ‘definitive-test’ of the ASAP approach – Many examples of excellent predictions on historical batches

(retrospective analysis)

n  How can we assure ourselves that the ASAP approach will work on new products in development (without waiting 2 years to find out)? –  Internal validation of model: ability to predict ‘itself’ – e.g. use 4 of the

ASAP conditions to predict the 5th; evaluating how well data fit the model % Degradation: Observed vs Predicted

-0.5

0

0.5

1

1.5

0 0.5 1 1.5

Observed % Deg

Pred

icte

d %

Deg

70C / 5% RH 70C / 75% RH

50C / 75% RH 60C / 40% RH

80C / 40% RH

Best Fit

Ideal

Garry Scrivens, Pfizer Garry Scrivens, Pfizer

Checking the Goodness of Fit of data to the ASAP Model

–  Examination of residuals:

–  Examination of Arrhenius Plots:

– R2prediction

20%RH

20%RH

40%RH

40%RH

60%RH

60%RH0%RH

0%RH

80%RH

80%RH

-9

-7

-5

-3

-1

1

3

50.0028 0.0029 0.0029 0.003 0.003 0.0031 0.0031 0.0032

1/T

ln k

75% RH

40% RH

5% RH


Estimation of Shelf-Life for Packaged Products

n  Ln A, Ea and B terms can be used to predict the rate of degradation: just need to know temperature and humidity

n  But the humidity inside the packaging needs to be known for accurate packaged product stability predictions – Humidity inside packaging changes over time, e.g.:

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

Days

%RH

2 tablets

15 tablets

15 tablets + desiccant

empty bottle


0

1

2

3

4

5

0 10 20 30 40 50 60 70

Days

%Degradant 2 tablets

15 tablets 15 tablets + desiccant

Predicted (lines) vs. Measured Degradation

open bottle

Drug Product ‘A’ in 60-cc HDPE Bottles (40°C/75%RH)


The humidity inside the packaging can be accurately predicted

n  In order to do this you need to know: 1. The ‘MVTR’ (moisture vapour transmission rate) of the packaging, and 2. The Moisture vapour sorption isotherm for your product (can be obtained by

combining the isotherms for the individual excipients of the product) and the desiccant (if using)

3. The ingoing water content / water activity of the tablets (& desiccants)

See Next Presentation


Product Degradant Real Time ASAP Prediction

Comments

Product A- MR Tablets 9 months, 25°C/60%RH

A1 4.1% 4.2% + 0.84 Hydrolysis A2 1.5% 1.2% + 0.24 Esterification

Product B- 5mg Tablets 12 months, 30°C/75%RH B1 0.02% 0.07% + 0.02 Oxidative degradation

Product B- 1mg Tablets 12 months, 30°C/75%RH B1 0.05% 0.29% + 0.1 Oxidative degradation

Product C- 100mg IR Tablets 3 months, 25°C/60%RH C1 5.3 ppm 6.2 ppm + 1 Low- level oxidative

degradant

Product A- Oral Solutions (5 Formulations) 7 months, 5°C

A1

1. 0.56% 2. 0.35% 3. 0.47% 4. 0.32% 5. 0.53%

1. 0.60% ± 0.03 2. 0.36% ± 0.01 3. 0.61% ± 0.03 4. 0.30% ± 0.02 5. 0.69% ± 0.03

Hydrolysis

Product D- Oral Solution 2 years, 30°C D1 0.31% 0.4% ± 0.08 Lactam formation

ASAP: How Well Does it Work?


Product Degradant Real Time ASAP Prediction

Comments

Product E- Patch 6 months, 40°C

E1 E2 E3

0.15% 1.72% 0.89%

0.12% ± 0.08 1.19% ± 0.24 0.88% ± 0.17

Prod D- formamide Acetyl- Prod D

Hyrdoxy- Prod D

Product F- Tablets 2 years, 25°C/60%RH

F1

0.70 0.98% + 0.08

Hydrolysis

API Qualifications, Root Cause

Investigative studies & Formulation Screenings

2 years , 30°C/75%RH 1.51 1.93%+ 0.16

6 months, 40°C/75 %RH 4.80 3.85% + 0.24

Product G - POS 6 months, 40°C/75%RH G1

(106.7 mg/g) 3% potency

loss

(103.4 mg/g ) 6% potency loss Hydrolysis Tech Transfer & API

Qualification

Product H- Tablets 4 years, 25°C/60%RH

H1 H2

0.22% 0.06%

0.22% + 0.06 0.07 %+ 0.02

Lactam formation

Ester (Lactone) formation

Oxidation

Lactam formation

Oxidation

Proposed Package Changes,

Shelf Life Extension & Replacement of Annual Stability Commitments

Product I- 100mg Tablets 2 years, 25°C/60%RH I1 0.01% 0.01% + 0.01

Product J- Capsules 2 years, 25°C/60%RH J1 0.08 0.08%+ 0.0

Product K- Capsules 3 years, 25°C/60%RH K1 0.03 0.03%+ 0.10



Product L (45 mg tablets) stored at 30°C/75%RH


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3

%D

egra

datio

n

Years

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 Years

Foil / foil blisters HDPE Bottles (30 count) + desiccant


Example Applications of ASAP (1)

n  Accurate prediction of shelf-life of API and drug products. ASAP can be used to set interim use-periods (e.g. for IMPDs and INDs). –  Unpackaged Study (no delay in starting the study), 14 day protocol

n  During Development: Helps to quantify stability risks and accelerates development: –  Quantifies the effects of temperature and humidity on stability performance (e.g.

“10% increase in RH or 10ºC increase in temperature increases rate by x-fold”) –  Allows the stability impact of any changes throughout development to be rapidly

assessed. •  Formulations/processes •  Synthetic routes •  Assessing batch-batch equivalence of API and drug products

–  Reduces or eliminates the need to wait for long-term stability readouts at key timepoints during development

n  Packaging Selection. This is a major benefit of the ASAP approach: the stability performance in any pack-type can be predicted and compared ‘at the touch of a button’ (all that is needed is the MVTR of the pack-type). The need to conduct expensive, lengthy packaging selection studies is reduced or eliminated.

n  Prediction of Stability in any Climatic Zone. The effect of changing storage conditions from (e.g.) 25ºC / 60% RH to (e.g.) 30ºC / 75% RH can be assessed and the risks quantified.


Example Applications of ASAP (2)

n  At Registration – Use ASAP as supportive data or as an alternative to traditional stability

to minimize stability commitments – Use diagnostic tools to demonstrate applicability of the ASAP model

applied for each drug product

n  QBD for Stability: –  ASAP / Packaging Tool is in-line with the QBD principle of

understanding and modelling the effects of parameters that may affect stability performance (e.g. temperature and humidity).

–  ASAP can also be used as a tool for rapidly quantifying the stability effects of changes to the product or process (e.g. ref. Kougoulos et. Al., AAPS PharmSci Tech, 2011) QBD for Stability.

n  Post-Approval – Use ASAP as part of post-approval change protocol –  Annual stability commitments: costs / overheads can be reduced


1g

2g

3g

4g

5g

85.0%

87.5%

90.0%

92.5%

95.0%

97.5%

100.0%

12 14 16 18 20 22 24 26 28 30 32 34 36Minim

um Probability of Reaching Shelf Life

Shelf Life

30°C60cc bottle, 30 count

65%RH75%RH25°C/60%RH, 1g desiccant

Case Study 1: Global Registration, Climatic Zone 4 and Package Selection


–  Tighter control of water activity at point of packaging reduces batch-batch variability

Tighter Control on Water Activity

Case Study 2: Using ASAP to understand and quantify the effect of different extents of drying of a wet-granulated product


Case Study 3: Simulation of In-Use Stability

Humidity inside unopened bottles

Humidity inside bottles during in-‐use period

Initiated at 45months

Initiated at 57 months

a a a a ab b b b bc

cc

c

cd

d

dd

d

a. Desiccant removed on Day 1 of in-‐use stability; patient regimen (1 tablet removed daily)

b. Desiccant removed on Day 1 of in-‐use stability; analytical testing regimenc. Desiccant kept inside bottle during in-‐use stability; patient regimen

(1 tablet removed daily)d. Desiccant kept inside bottle during in-‐use stability; analytical testing regimen

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6

Internal RH (%

)

Years

ab

cd





0

10

20

30

40

50

60

70

80

0 1 2 3

%RH

in P

acka

ging

Time (years)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3

% D

eg

Time (yrs)

0

10

20

30

40

50

60

70

80

0 1 2 3

%RH

in P

acka

ging

Time (years)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3

% D

eg

Time (yrs)


Case Study 4: Temperature Excursions

0

10

20

30

40

50

60

70

13/04/11 17/04/11 21/04/11 25/04/11

Date

Tem

pera

ture

(ºC

)

Temperature Excursion

00.0020.0040.0060.0080.01

0.0120.0140.0160.018

13/04/11 17/04/11 21/04/11 25/04/11

Date

Deg

rada

tion

Rat

e, k

(% p

er h

our)

Degradation Rate (Product D, % per hour)

Degradation Rate (Product E, % per hour)

00.10.20.30.40.50.60.70.80.9

13/04/11 17/04/11 21/04/11 25/04/11

Date

Cum

ulat

ive

Deg

rada

tion

(%).

Cumulative Degradation (Product D, %)

Cumulative Degradation (Product E, %)

Temperature Logger data

A, Ea

Degradation Rate

Cumulative

% Degradation (as measured by e.g. HPLC)

Thank you For Listening

Questions / Discussion

Garry Scrivens, Ph.D. Pfizer Global R&D, Sandwich, UK

[email protected]

http://www.linkedin.com/pub/garry-scrivens/17/8a0/4a1


Packaged-Product Stability

H2O H2O

H2O

Moisture transfer depends on MVTR, ΔRH and temperature

MVTR = P. ΔRH

H2O

Moisture inside packaging equilibrates between headspace (RH), tablets, desiccant (vapor sorption isotherms)


Moisture Vapour Sorption Isotherms

– The water content varies with water activity, Aw (≡ %relative humidity) according to the ‘water vapour sorption isotherm’ for the material, e.g.:

Aw

PVP

–  GAB parameters are used to describe water vapour sorption isotherm curves


Moisture Vapour Sorption Isotherms

0

100

200

300

400

500

600

700

800

900

1000

0 20 40 60%RH

Wat

er (m

g) Total

Desiccant

Drug Product

Head Space


Potential Pitfalls

1.  Non-isoconversion

2.  Form / Phase changes caused by temperature and/or humidity (e.g. melts, glass transitions, anhydrate / hydrate formation, deliquescence etc.)

3.  Secondary Degradation (consecutive reactions)

4.  Competitive Processes

5.  Significant contribution to overall degradation from multiple API environments that have significantly different Ea and B parameters

6.  Significant contribution to overall degradation from multiple degradation pathways that have significantly different Ea and B parameters

7.  Combinations of the above


Potential Causes of Poor Fit / Prediction

Form / Phase changes caused by temperature and/or humidity (e.g. melts, glass transitions, anhydrate / hydrate formation, deliquescence etc.)

ln k

1/T

%RHln k

1/T

%RH

B

Ea/R

x

x80/40 x

x

x ooo

o

40/7530/75

30/6525/60

70/75

50/7560/40

70/5


Potential Causes of Poor Fit / Prediction

ASAP %RH condition(s) exceed Critical Relative Humidity, CRH (e.g. of one of the excipients), which leads to deliquescence.

Excipient CRH @ 20ºC CRH @ 40ºC PEG 3350 94 85 Dextrose 100 88 Fructose 72 64 Sorbitol 80 69 Sucrose 86 83 Xylitol 91 73

Tartaric Acid 85 78 Potassium Chloride 84 82

Sodium Chloride 75 75 Sodium Citrate 61 78


Potential Sources of Inaccuracy: Degradation Kinetics at Different Conditions

Low Temperature

High Temperature

00.20.40.60.81

1.21.41.6

0 10 20 30 40 50 60

Time

%Degradant

0 100 200 300 400 500 600

For a given system, the shape of the curve (i.e. degradation kinetics) is usually very similar across different stability conditions, just the timescale is different …

…sometimes this is not the case


Potential Sources of Inaccuracy: Complex systems

Significant contribution to overall degradation from multiple API environments that have significantly different Ea and B parameters

APIForm A

APIForm B Deg Prod

kA f(Ea,A and BA)

kB f(Ea,B and BB)

-9

-8

-7

-6

-5

-4

-3

-2

-1

00.0028 0.003 0.0032 0.0034

Ln k

1/T

Contribution from Form A

Contribution from Form B

Overall Observed Arrhenius Plot

xx

x

Prediction error

This problem can manifest as a curved Arrhenius plot. This is rare because degradation usually derives predominantly from one form of API


Potential sources of Inaccuracy: Complex Systems

Significant contribution to overall degradation from multiple degradation pathways that have significantly different Ea and B parameters

API Deg Prod kA f(Ea,A and BA)

kB f(Ea,B and BB)

-9

-8

-7

-6

-5

-4

-3

-2

-1

00.0028 0.003 0.0032 0.0034

Ln k

1/T

Contribution from Path A

Contribution from Path B

Overall Observed Arrhenius Plot

xx

x

Prediction error

This problem can manifest as a curved Arrhenius plot. This is rare because degradation usually derives predominantly from a single pathway


O

OH

O

R

OH

OHR

O

O

O

R

O

OH

OR

Hydrolysis Oxidation

Oxidative Dimerisation

OH

RO

O

OR

k = f(T,RH)

k = f(T,RH)

k = f(T,RH)

“Deg C”

“Deg B” “Deg G”

“Deg D”

Complex Systems: Competitive and Consecutive Processes Kinetic Simulations


Complex Systems: Competitive and Consecutive Processes Kinetic Simulations

Form A (unstable form) à Form B (stable form) (nucleation-type kinetics)

Form A à 10-H (degradation product) (1° kinetics) Form A à 10-K (degradation product) (1° kinetics) 10-K à Other Degs (1° kinetics)

Form B ßà Dihydrate (nucleation-type kinetics)

Etc. 30°C/65%RH, 30-count 60cc HDPE bottle No Desiccant: 25°C/60%RH, 30-count 60cc HDPE bottle With Desiccant:

51

F'/G

10-‐H10-‐Kother

DihydrateGH0

0.5

1

1.5

2

2.5

3

0 200 400 600 800

% Degradation

Time (Days)

F'/G

Form B

10-‐H10-‐KotherDihydrateGH0

20

40

60

80

100

120

0 200 400 600 800

% Degradation

Time (Days)

10-‐H10-‐K

otherDihydrateGH0

0.5

1

1.5

2

2.5

3

0 200 400 600 800

% Degradation

Time (Days)

F'/G

Form B10-‐H10-‐KotherDihydrateGH0

20

40

60

80

100

120

0 200 400 600 800

% Degradation

Time (Days)

predicting the long-term stability of solid-state

Documents