(T1430-02-10) Development of a Modified Arrhenius Equation to Predict the Kinetics of N-nitrosation of Active Drug in Solid Dosage Form

Purpose: This study investigates the kinetics of drug N-nitrosation reactions to predict the formation of nitrosamine drug substance-related impurities (NDSRIs) in solid dosage forms. Nitrosamines are a class of organic compounds that have raised significant concern due to their mutagenic and carcinogenic potential¹. NDSRIs are readily formed during the manufacturing and storage of pharmaceutical products. Consequently, strict control measures must be implemented to ensure that NDSRI levels in pharmaceuticals remain below the acceptable daily intake limits². Approaches to inhibit drug N-nitrosation reactions in solid dosage forms include controlling temperature and humidity^3,4, as well as incorporating inhibitor excipients. Most notably, alkaline excipients (AE) increase the local pH to alkaline conditions, thereby inhibiting N-nitrosation^4,5. However, to the best of our knowledge, no model equations that quantify the effects of temperature, humidity, and AE content on the N-nitrosation reaction rates of drugs in solid dosage forms have been reported. This study aims to develop a modified Arrhenius equation that incorporates percent (%) relative humidity (RH) and AE content to predict drug N-nitrosation kinetics in solid dosage forms.

Methods: In order to develop an Arrhenius equation that incorporates the effects of temperature, RH, and AE content, desloratadine (DES) (Fig. 1A) was selected as the model compound due to the nitrosation potential of its secondary amine to form N-nitroso desloratadine (NDES) (Fig. 1B). Sodium carbonate monohydrate was selected as the AE. The experiment included preparation of physical mixtures (PMs) containing 15mg of DES with various amounts of AE (0.5% w/w, 1.0% w/w and 2.0% w/w). These PMs were stored under various combinations of temperature (40, 50, 60 and 70°C) and RH (about 11%, 30%, 50%, and 75%) and sampled periodically during a 14 day storage period. The PMs were also stored at 25°C/60%RH and sampled over a period of 150 days to simulate long term storage conditions. The amount of NDES in each PM sample was measured using UPLC-QTOF-MS. The N-nitrosation reaction rate (k) under each storage condition was determined by plotting the amount of NDES (ng) formed in the respective PM sample versus the sample storage time (days). Linear regression analysis was performed using the least-squares method, and the slope of the regression line was used as the N-nitrosation reaction rate assuming first order kinetics. A modified Arrhenius equation was developed by multiple regression with JMP software utilizing ln k as the dependent variable and -1/T, RH, and % w/w(AE) as the independent variables. The possibility of interaction between explanatory variables was evaluated by analysis of variance (ANOVA) using a full implementation factorial plan.

Results: Multiple regression analysis of 45 experimental conditions yielded the predictive equation: ln k = ln A - Ea / (RT) + B(RH) + C(% w/w (AE)), which is a modified Arrhenius equation where B and C represent the coefficients for RH and the AE, respectively. This equation showed a strong correlation with experimental data (R² = 0.9365, p < 0.05) (left panel of Figure 2A). Residual analysis showed no consistent trends (right panel of Figure 2A), supporting the model's adequacy. The absolute t-values indicated the following order of influence: Temperature showed the most significant impact, followed by RH and AE content, respectively. All p-values for these factors were < 0.05, further supporting the inclusion of these terms in the resulting predictive equation. We compared models using the original Arrhenius equation (R² = 0.6379) and a relative humidity-modified Arrhenius equation (R² = 0.9093) (left panels of Figure 2B and C). These values were lower than the R² values for the relative humidity and AE content-modified Arrhenius model (0.9365). Furthermore, the vertical alignment of the ln k residual plots suggests a lack of explanatory terms in the multiple regression analysis (right panels of Figure 2B and C). The assessment of the interaction between explanatory variables indicated no statistically significant interaction effects between the variables (p > 0.05 for all interaction terms). The practical utility of the developed model is further supported by comparing its predictions with experimentally measured NDES amounts in PMs stored under long-term stability testing conditions (25°C/60%RH) (Figure 3). The excellent agreement observed between the predicted and measured values for PMs with different AE concentrations confirmed the model's ability to accurately predict the N-nitrosation reaction rates under relevant storage conditions.

Conclusion: In this study, we successfully developed a modified Arrhenius equation to accurately predict the rate of N-nitrosation of DES in solid form when stored under varying temperature, RH and AE content. Both RH and AE factors linearly influenced the reaction rate and multiple regression analysis confirmed their suitability as explanatory variables. The comprehensive equation was further supported by correlating experimental long-term stability data to the predicted values. The modified Arrhenius equation is a valuable tool for analyzing and predicting drug N-nitrosation in solid dosage forms, aiding in the development of safer pharmaceuticals.

References: 1. Horne S, Vera MD, Nagavelli LR, et al. Regulatory experiences with root causes and risk factors for nitrosamine impurities in pharmaceuticals. J Pharm Sci. 2023;112(5):1166-1182. doi:10.1016/j.xphs.2022.12.022
2. Schlingemann J, Burns MJ, Ponting DJ, et al. The landscape of potential small and drug substance related nitrosamines in pharmaceuticals. J Pharm Sci. 2023;112(5):1287-1304. doi:10.1016/j.xphs.2022.11.013
3. Moser J, Ashworth IW, Harris L, Hillier MC, Nanda KK, Scrivens G. N-nitrosamine formation in pharmaceutical solid drug products: Experimental observations. J Pharm Sci. 2023;112(5):1255-1267. doi:10.1016/j.xphs.2023.01.027
4. Shakleya D, Alayoubi A, Brown D, et al. Nitrosamine mitigation: NDMA impurity formation and its inhibition in metformin hydrochloride tablets. Int J Pharm. 2024;666:124832. doi:10.1016/j.ijpharm.2024.124832
5. Shakleya D, Asmelash B, Alayoubi A, et al. Bumetanide as a model NDSRI substrate: N-nitrosobumetanide impurity formation and its inhibition in bumetanide tablets. J Pharm Sci. 2023;112(12):3075-3087. doi:10.1016/j.xphs.2023.06.013


Chemical structures of (A) Desloratadine (DES) and (B) N-nitroso desloratadine (NDES).


Results of multiple regression analysis on various models based on the Arrhenius equation: (A) based on temperature, relative humidity and alkaline excipients (AE) content, (B) based on temperature only (original Arrhenius equation), and (C) based on temperature and relative humidity. Left: plot of ln k against experimental measured values of ln k and predicted values of ln k. Right: residual plot of experimental measured values of ln k.


Amount of N-nitroso desloratadine (NDES) produced in physical mixtures (PMs) at 25°C/60% relative humidity (RH). Straight lines are predicted values calculated from developed model. Plotted data points are experimentally measured values.