Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 2 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 8/16/14 Company Confidential © 2014 Eli Lilly and Company 3 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 4 What about Rela5ve Humidity? Slide courtesy of Ken Waterman, FreeThink™ 8/16/14 Copyright FreeThink Technologies, Inc. 2013 freethinktech.com 5 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 Company Confidential © 2014 Eli Lilly and Company 7 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 8/16/14 Company Confidential © 2014 Eli Lilly and Company 8 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 8/16/14 Company Confidential © 2014 Eli Lilly and Company 10 Case Study: Prasugrel Pediatric 0.2% Drug Load 40°C 0.6% Drug Load 1.3% 1.5% 2% 1% 30°C 25°C • • • 8/16/14 Company Confidential © 2014 Eli Lilly and Company 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% • 8/16/14 Company Confidential © 2014 Eli Lilly and Company 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 8/16/14 Company Confidential © 2014 Eli Lilly and Company 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 • • 8/16/14 Large drug load span Slope > 1 Company Confidential © 2014 Eli Lilly and Company 14 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 8/16/14 Company Confidential © 2014 Eli Lilly and Company 15 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 8/16/14 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”)? 8/16/14 Company Confidential © 2014 Eli Lilly and Company 18 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 Company Confidential © 2014 Eli Lilly and Company 19 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 Company Confidential © 2014 Eli Lilly and Company 21 Theoretical Construct API (shown as blue circles) degrades only when in direct contact with excipient parDcles 8/16/14 Company Confidential © 2014 Eli Lilly and Company 22 Theoretical Construct As API load increases, more of the excipient surface gets covered 8/16/14 Company Confidential © 2014 Eli Lilly and Company 23 Theoretical Construct As API load increases, more of the excipient surface gets covered 8/16/14 Company Confidential © 2014 Eli Lilly and Company 24 Theoretical Construct In the limit, the excipient surface is completely covered and increasing drug load does not influence degradaDon 8/16/14 Company Confidential © 2014 Eli Lilly and Company 25 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 8/16/14 Company Confidential © 2014 Eli Lilly and Company 26 Theoretical Construct AR =API CSA/ Exc TSA 8/16/14 Company Confidential © 2014 Eli Lilly and Company 27 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 29 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 30 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 31 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 Company Confidential © 2014 Eli Lilly and Company 32 Drug Stability as Function of Dosage Strength: Low Strengths 8/16/14 Company Confidential © 2014 Eli Lilly and Company 33 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) 8/16/14 Company Confidential © 2014 Eli Lilly and Company 34 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 35 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 Company Confidential © 2014 Eli Lilly and Company 36 Acknowledgements - Ken Waterman, FreeThink (slides) - Cherokee Hoaglund-Hyzer (slides) 8/16/14 Company Confidential © 2014 Eli Lilly and Company 37 Backup Slides 8/16/14 Company Confidential © 2014 Eli Lilly and Company 38 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 39 8/16/14 Company Confidential © 2014 Eli Lilly and Company 40 Effect of Dilution on Moisture Sensitivity • RH sensitivity can be unchanged, increase or decrease as a function of dilution 8/16/14 Company Confidential © 2014 Eli Lilly and Company 41 8/16/14 Company Confidential © 2014 Eli Lilly and Company 42 8/16/14 Company Confidential © 2014 Eli Lilly and Company 43 8/16/14 Company Confidential © 2014 Eli Lilly and Company 44 8/16/14 Company Confidential © 2014 Eli Lilly and Company 45 8/16/14 Company Confidential © 2014 Eli Lilly and Company 46 8/16/14 Company Confidential © 2014 Eli Lilly and Company 47