Pharmaceutics, Drug Delivery and Pharmaceutical Technology Degradation Rate Observations as a Function of Drug Load in Solid-State Drug Products Steven W. Baertschi 1 , Allison L. Dill 2, * , Timothy T. Kramer 3 , Garry Scrivens 4, * , Miroslav Suruzhon 4 1 Baertschi Consulting, LLC, Carmel, Indiana 46033 2 Eli Lilly and Company, Lilly Research Laboratories, Small Molecule Design and Development Indianapolis, Indiana 46285 3 Eli Lilly and Company, Lilly Research Laboratories, Global Statistical Sciences Indianapolis, Indiana 46285 4 Analytical Research and Development, Pfizer Inc., Sandwich, UK article info Article history: Received 22 November 2018 Accepted 4 December 2018 Available online 11 December 2018 Keywords: chemical stability drug-excipient interactions formulation hydrolysis in silico modeling kinetics mathematical models solid-state stability surface chemistry oxidation abstract Degradation rates of solid-state drug products generally increase as the drug load decreases. A model for quantifying this effect based on surface area ratios is proposed here. This model relates the degradation rate to an estimate of the proportion of drug substance in contact with the excipient, and that the drug substance in contact with excipients degrades more quickly. Degradation data from previously published case studies and from 5 new case studies were found to be consistent with our proposed model; our model performed better than similar previously published models. It was also found that the relationship between degradation rate and drug load is largely independent of the temperature and humidity con- ditions, suggesting that drug load solely affects the pre-exponential factor of the Arrhenius equation and does not significantly affect the activation energy of the degradation process. A second method for calculating the proportion of the drug substance surface in contact with the excipient surface is pre- sented in the Supplementary Material. Fundamentally, the 2 methods are very similar and provide almost identical fits to the experimental data. © 2019 American Pharmacists Association ® . Published by Elsevier Inc. All rights reserved. Introduction One of the areas critical to the development of pharmaceutical products is chemical stability sufficient to deliver an acceptable shelf life. Progress has been made in the rapid modeling of solid- state degradation kinetics via short-term accelerated stability studies using a humidity-modified Arrhenius equation. 1-3 Such models, while increasingly being recognized as effective tools for speeding development by reducing the time it takes to predict the shelf life of a product, are valid only for the specific solid dosage formulation and strength (i.e., drug load). There would be increased value if predictive models were available for relating degradation kinetics to drug load so that degradation rates associated with 1 or 2 drug loads could be used to predict degradation rates for a broad range of potential or actual drug loads. It is widely accepted that the stability of drug substances can be affected by excipient interactions 4 and that the rate of degradation of a drug product is dependent on the dosage strength, with the rate increasing significantly as the drug load decreases. Two ap- proaches for quantitatively modeling the rate of degradation of the drug substance as a function of drug load have recently been pro- posed. 5,6 Both models propose that the rate of degradation is faster at the interface between drug substance and excipient. The first of these approaches used a “quasi-liquid” model to calculate the proportion of drug substance at the interface; the quasi-liquid model assumes that the small drug substance particles randomly fill in the interstitial spaces between larger excipient particles and essentially act as one large fluid particle. From this, a power-law (allometric) relationship between the contact surface area (and hence the rate of degradation) and the volume fraction of the drug substance was derived (Eq. 1). LnðkÞ¼ a*Lnð%Drug SubstanceÞþ Lnðk 0 Þ (1) It was suggested that the slope, a, is expected to be between zero, when excipient interactions do not influence degradation, This article contains supplementary material available from the authors by request or via the Internet at https://doi.org/10.1016/j.xphs.2018.12.003. * Correspondence to: Garry Scrivens (Telephone: þ44 01304 649578) and Allison L. Dill (Telephone: þ1-317-476-1588). E-mail address: garry.scrivens@pfizer.com (G. Scrivens). Contents lists available at ScienceDirect Journal of Pharmaceutical Sciences journal homepage: www.jpharmsci.org https://doi.org/10.1016/j.xphs.2018.12.003 0022-3549/© 2019 American Pharmacists Association ® . Published by Elsevier Inc. All rights reserved. Journal of Pharmaceutical Sciences 108 (2019) 1746-1755