Download Predicting the Degradation Rate as a Function of Drug Load in Solid

Predicting the Degradation
Rate as a Function of Drug
Load in Solid-State Drug
Products
Allison Dill, Steve Baertschi, Tim Kramer
and David Sperry
Introduction
•  Background of Accelerated Stability
Assessment Program (ASAP) Approach
•  Relationship of Degradation Rates to
Dosage Strength
•  Case Studies
•  Implications – Is There a Conceptual
Model?
•  Future Directions
8/16/14
Company Confidential © 2014 Eli Lilly and Company
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What We Intend to Show
•  The log/log plots developed by Waterman are valid and
useful for predicting degradation rate as a function of
dosage strength
•  Challenge “Allometric” Model (quasi-liquid state
concept)
•  Proposal:
–  API-Excipient Surface Contact Area is Key
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Company Confidential © 2014 Eli Lilly and Company
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Accelerated Aging: Temperature •  Arrhenius equa5on (at a constant RH) ln k = ln A – Ea/(RT) •  k = specifica5on limit/isoconversion 5me •  ln A = collision frequency •  Ea = ac5va5on energy (T-­‐sensi5vity) •  Propor5on of reactants that can go over ac5va5on barrier depends on T 8/16/14
Company Confidential © 2014 Eli Lilly and Company
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What about Rela5ve Humidity? Slide courtesy of Ken Waterman, FreeThink™ 8/16/14
Copyright FreeThink Technologies, Inc. 2013
freethinktech.com
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Combining T and RH Effects Slide courtesy of Ken Waterman, FreeThink™ ln k = ln A – Ea/RT + B(RH) %RH ln k ln A B Ea/R 8/16/14
Company Confidential © 2014 Eli Lilly and Company
1/T 6 6
Drug Stability as Function of
Excipient Dilution
L1 L2 As weight percent of drug increases, surface area will increase at relaDvely slower rate 8/16/14
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The “log-log linear” relationship
•  If a plot of log(k) vs. log(100/API) is
linear
•  And the slope is between 0 and 1
•  Then the following general
relationships
also hold true.
80
60
k vs. API 2.5
log vs. log 2
log( k( API) ) 1.5
1
0.5
1
1.5
2
log
log(k) vs. API 2
20
100
API
( )
3
k( API) 40
2.5
1.5
log( k( API) )
0
0
2
4
6
8
10
log( k( API) ) 1
1
API (weight %)
0.5
0
0
2
4
6
8
10
API (weight %)
0
log(k) vs. 100/API 100
200
300
100
API
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Drug Stability as Function of
Dosage Strength: Low Strengths
8/16/14
File name/location
Company Confidential
Copyright © 2000 Eli Lilly and Company
Slide courtesy of Ken
Waterman, FreeThink™
9
A Case Study: Prasugrel Pediatric
• 
• 
• 
• 
• 
Prasugrel for pediatric indication
Adult marketed doses of 5 mg
and 10 mg
Pediatric dosage range 0.5 mg to
5 mg, based on body weight
Micronized API, main excipients
mannitol and starch
Pediatric dosing flexibility and
potential large dosage range
necessitates ability to assess
stability of various strengths
quickly
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Case Study: Prasugrel Pediatric
0.2% Drug Load 40°C
0.6% Drug Load 1.3% 1.5% 2% 1% 30°C
25°C
• 
• 
• 
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Fit using all markers Linear tread as func5on of drug load Parallel lines as func5on of storage temperature 11
Case Study: Prasugrel Pediatric
0.2% Drug Load Slope = 1.06 ± 0.03 0.6% Drug Load 1.5% 1.3% 1% 40°C
30°C
25°C
• 
2% • 
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Common slopes model using all data Slope is ≠ 2/3 12
Case Study: Model Compound A,
Common Slopes
10% Drug load Slope = 0.35 ± 0.02 5% Drug Load 70°C/45%RH
50°C/75%RH
70°C/30%RH
• 
• 
50°C/65%RH
• 
60°C/45%RH
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Higher drug loads Hydrolysis induced degrada5on Humidity factor in degrada5on rate 13
Case Study: Model Compound B,
Degradant 1
2.5% Drug Load 75°C/75%RH
Slope = 1.32 ± 0.09 70°C/75%RH
20% Drug Load 70°C/70%RH
65°C/75%RH
75°C/60%RH
• 
• 
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Large drug load span Slope > 1 Company Confidential © 2014 Eli Lilly and Company
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Case Study: Model Compound B,
Degradant 2
2.5% Drug Load Slope = 1.36 ± 0.04 20% Drug Load •  Both degrada5on products have ~ same slope but 2 different mechanisms of forma5on 75°C/75%RH
70°C/75%RH
70°C/70%RH
65°C/75%RH
75°C/60%RH
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Case Study: Model Compound
C
Slope = 0.96 ± 0.02 8% Drug Load 3% Drug Load 70°C/40%RH
60°C/75%RH
70°C/40%RH
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50°C/70%RH
• 
60°C/11%RH
• 
Company Confidential © 2014 Eli Lilly and Company
Linear tread as func5on of drug load Parallel lines as func5on of storage temperature 16
Summary Table of Model
Compounds
Compound/Degradant Prasugrel Pediatric Compound A Compound B, Degradant 1 Compound B, Degradant 2 Compound C 8/16/14
Slope 1.06 0.35 1.32 1.36 0.96 Company Confidential © 2014 Eli Lilly and Company
1 Std. Dev. 0.03 0.02 0.09 0.04 0.02 17
Conclusions
•  We see consistent linear relationships,
supporting the log/log approach (log / log
plots)
•  In our limited dataset, some slopes are less
than 0.67; most are higher.
•  These results call into question the proposed
“allometric” model (where slope of 0.67 is the
“limiting slope”)?
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Equivalent Views of Degradation by
Drug Load
Slopes: 1 2/3 0 Slope of 0 corresponds to proporDonal increase in degradant with drug load Slope of 1 corresponds to constant degradant amount with drug load Slope of 2/3 corresponds to increasing degradant amount with diminishing slope as drug load increases The Absolute DegradaDon Amount axis is representaDve but the scale is API dependent 8/16/14
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API to Excipient Size Relationship
Typical Excipient Par5cle Size Common API Par5cle Sizes 50 μm 5 μm 8/16/14
10 μm Company Confidential © 2014 Eli Lilly and Company
150 μm 20
Theoretical Construct
Big red spheres represent excipient parDcles 8/16/14
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Theoretical Construct
API (shown as blue circles) degrades only when in direct contact with excipient parDcles 8/16/14
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Theoretical Construct
As API load increases, more of the excipient surface gets covered 8/16/14
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Theoretical Construct
As API load increases, more of the excipient surface gets covered 8/16/14
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Theoretical Construct
In the limit, the excipient surface is completely covered and increasing drug load does not influence degradaDon 8/16/14
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Theoretical Construct
•  Assumptions:
–  API particles are small relative to the excipients
–  The API particles distribute randomly on the surface
of the excipients
–  Two particles cannot occupy the same space
–  Only API particles in direct contact with the
excipients degrade
•  The % of excipient surface that could be covered
by (in contact with) API particles is defined by an
area ratio:
–  Total Cross Sectional Area of API particles /
Total Surface Area of Excipient Particles
Area Ratio = API CSA/ Exc TSA
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Theoretical Construct
AR =API CSA/ Exc TSA
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Examples of Relative API Particle
Counts and Cross Sectional Areas
Maximum Excipient API Size Drug Load API Par5cles per Poten5al Excipient Size (microns) (by weight) Excipient Par5cle Surface Area (microns) Coverage 100 20 150 100 5 150 8/16/14
1% 10% 1% 10% 1% 10% 1% 10% 1 14 4 47 81 889 273 3000 Company Confidential © 2014 Eli Lilly and Company
1.3% 13.9% 1.9% 20.8% 5.1% 55.6% 7.6% 83.3% 28
Excipient Coverage as a Function of
Cross Sectional Area to Excipient Surface
Ratio
Only 63% of excipient surface is expected to be covered when the API could theoreDcally cover 100% of the surface 8/16/14
Company Confidential © 2014 Eli Lilly and Company
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Excipient Coverage as a Function of
Cross Sectional Area to Excipient Surface
Ratio
50%
17%
5%
8/16/14
DE = 150 μm DA = 5 μm Company Confidential © 2014 Eli Lilly and Company
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API-Excipient surface contact
•  As number-ratio of particle increases increases (DE = 100 µm, DA =
10 µm) , the interfacial contact area between API and excipients
decreases.
50 : 1
API : Excipient
5% Drug load
8/16/14
200 : 1
API : Excipient
17% Drug load
Company Confidential © 2014 Eli Lilly and Company
1000 : 1
API : Excipient
50% Drug load
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Resulting Drug Load Dependency
for Specific Case
Slope ~ 0 Slope = 2/3 1 Slopes: 2/3 DE = 150 μm DA = 5 μm 0 Slope ~1.5 Slope of 0 corresponds to proporDonal increase in degradant with drug load Slope of 1 corresponds to constant degradant amount with drug load Slope of 2/3 corresponds to increasing degradant amount with diminishing slope as drug load increases 8/16/14
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Drug Stability as Function of
Dosage Strength: Low Strengths
8/16/14
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Conceptual Model Summary
•  Theoretical construct suggests that one would
expect a slope greater than 0 (and potentially
bigger than 1) depending on relative ratios of
diameters and drug load
•  At very low drug loads slope is near 0 (doubling
drug load doubles amount of degradation
leaving %degradation essentially unchanged)
•  Slope could appear to be constant over narrow
range (5x change in drug load equates to ~1.6
unit change on log(100%/API%) scale)
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Model limitations
•  This simple model explains observed
dependence of degradation rate on drug load
qualitatively but not quantitatively
•  Quantitative prediction of degradation rate
may be possible if the fraction of API particles
that are in direct contact with excipient
particles can be determined / calculated (more
is needed to test this hypothesis)
•  Model does not consider catalytic or inhibiting
behavior (other than particle interference)
•  The mathematical problem of sphere packing
may be relevant to this quantification
8/16/14
Company Confidential © 2014 Eli Lilly and Company
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Conclusions & Future Direction
•  Explore impact of sphere packing on
conceptual model
•  Continue with conceptual model toward
quantitative predictability
•  Increase number of molecules studied
8/16/14
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Acknowledgements
-  Ken Waterman, FreeThink (slides)
-  Cherokee Hoaglund-Hyzer (slides)
8/16/14
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Backup Slides
8/16/14
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Sphere Packing
Spheres of one size packed in a cube 8/16/14
Cross-­‐secDon of spheres of many diameters packed in a cylinder Company Confidential © 2014 Eli Lilly and Company
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Effect of Dilution on Moisture
Sensitivity
•  RH sensitivity can be unchanged, increase
or decrease as a function of dilution
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