 Research
 Open Access
Nonisothermal stability by linear heating: a fast method for preformulation stability screening of drugs at the discovery and development interface
 Agnes Kairer^{1},
 Shaoxin Feng^{1},
 Valentino J. Stella^{2} and
 Thomas K. Karami^{1}Email author
 Received: 12 January 2017
 Accepted: 23 March 2017
 Published: 26 April 2017
Abstract
The nonisothermal method for prediction of chemical stability of pharmaceuticals has been discussed in the literature for almost half a century but it has not yet been systematically evaluated. The purpose of this study was to carry out a comprehensive experimental evaluation of the nonisothermal method against the conventional isothermal method for a fast preformulation stability screening. The chemical stabilities of 20 pharmaceutical compounds in aqueous based solution were investigated. Degradation rate constants (k), activation energies (E _{a}), t _{90%} and t _{98%} (times for 10 and 2% loss of potency, respectively) were determined by applying the Arrhenius equation to stability data generated by both nonisothermal and isothermal methods. A comparison of the results indicated that the ‘1 week’ nonisothermal experiment is as accurate as the ‘8 weeks’ isothermal experiment for placing compounds (15 out of 16 cases) into the same binning categories based on t _{90%} and t_{98%} values. The absolute values of k, t _{90%} and t_{98%} at 25 °C determined by the nonisothermal method for compounds with first order (or pseudofirst order) degradation kinetics were within a factor of two compared to those determined by the isothermal method. The nonisothermal method proved to be not applicable for accurate prediction of the shelflives of pharmaceuticals, however, when used to bin discovery compounds based on likely issues related to chemical instability, the nonisothermal method can be carefully implemented as a cost effective, fast, and relatively ‘highthroughput’ method to support drug stability screening at the discovery and development interface.
Keywords
 Nonisothermal
 Chemical stability
 Degradation kinetics
 Arrhenius theory
 Simulations
 Linear regressions
 Stability screening
 Preformulation
Background
Nonisothermal stability by linear heating (LNISO) has been explored as an accelerated method for predicting the longterm stabilities and shelflives of pharmaceuticals for almost five decades (Yoshioka et al. 1987, 1988; Zoglio et al. 1968). However, this method has never been systematically evaluated across numerous compounds in a single study and compared directly to conventional isothermal stability method. LNISO can be a robust and cost effective method to rapidly (within a week) assess the chemical stabilities of drug candidates at the early stages of development. The experimental efforts and related costs of LNISO testing are minimal (e.g., 1 week experiment with 6 samples of each compound tested for chemical stability at different time points on an hourly timescale). The LNISO method allows for stability screening of a greater number of drug candidates in a short period of time during preformulation at the discovery and development interface.
Various theoretical models have been developed to apply the nonisothermal method by using linear, exponential, logarithmic, reciprocal, and step heating profiles (Zhan et al. 1997a, 1997b; Lin et al. 2009). Yoshioka, et al., evaluated nonisothermal methods by simulated linear heating of drug substances in solution to predict drug stability (Yoshioka et al. 1987, 1988). These studies used a Monte Carlo simulation method and not actual experimental data. A much earlier study by Zoglio, et al. highlighted the usefulness of the LNISO method in stability screening of drugs in different pharmaceutical formulations (Zoglio et al. 1968). However, no comprehensive studies have been conducted to show that stability parameters predicted by the LNISO method are reproducibly in good agreement with the same parameters obtained by the conventional Arrhenius stability method.
As the nonisothermal method may not accurately predict absolute rate constant (k) and activation energy (E _{a}) values (Yoshioka et al. 1987, 1988), the present study was designed to evaluate feasibility of the method for compound binning based on kinetic t_{90%} (time for 10% degradation) and t_{98%} (time for 2% loss of potency) values. Compound binning refers to the categorization of compounds into three groups: those which are highly stable and unlikely to present major challenges when it comes to drug stability (BIN 1), those which may be problematic with respect to chemical stability (BIN 2), or those which are chemically unstable and unlikely to have an adequate shelflife (BIN 3).
At the discovery and development interface, the use of t_{90%} values to establish binning classifications for stability screening is considered adequate, since it most often represents the outer limit of the stability. However, t_{98%} is more relevant when evaluating degradation in terms of impurity limitations imposed by the ICH guidelines (ICH Guideline Q1A, R2 2003; ICH Guideline Q3A, R2 2006; ICH Guideline Q3B, R2 2006), and can therefore be more applicable for stability screening at later stages of the development.
The LNISO method used in this study was conducted with a focus only on chemical stability of drugs in solution. For chemical stability assessment of drugs in the solid state, an Accelerated Stability Assessment Program or ASAP can be used, which is discussed in detail elsewhere in the literature (Waterman 2011). The ASAP method is based on an isoconversion concept that compensates for the complexity of solidstate degradation reaction kinetics and applies a moisturecorrected Arrhenius equation that explicitly takes into account the effect of relative humidity (RH) on the degradation rates in solid state (Waterman 2011).
Another accelerated stability method presented in literature is single (high) temperature point stability testing (Yoshioka et al. 1990). While very useful, using the ‘single temperature stability’ approach to rank order drug candidates requires an assumption that the activation energies are similar across the comparing group. That is, it assumes that what is seen at a high temperature predicts the relative stability at, for example, controlled room temperature. This method also does not provide any insight into the relative temperature sensitivity of the degradation and thus a possible controlled temperature shelflife, however defined.

To assess feasibility of the LNISO method for binning drug compounds by comparing the predicted kinetic t_{90%} values at 25 °C with those determined by the conventional isothermal method. Herein, the anticipated binning categories were chosen as BIN 1: t_{90%} > 24 months, BIN 2: t_{90%} = 12 to 24 months and BIN 3: t_{90%} < 12 months, based on early development criteria. One could envision application of tighter criteria (e.g., t_{98%}) in later stage of the drug development.

To evaluate the effect of sampling frequency on precision of the stability parameters determined utilizing the LNISO method, as described by Yoshioka et al. in 1987.
To achieve these aims, the current study was conducted in two parts. The first, comprised a short term accelerated nonisothermal stability experiment (1 week in a LNISO oven by linear heating) on two compendial drugs and 18 discovery compounds with different pharmacophores. The second, was a longterm conventional Arrhenius stability experiment (8 weeks in five separate isothermal ovens), conducted in parallel on the same 18 discovery compounds. A subset of the conventional stability data (time 0 to week 4) was selected for evaluation as an abbreviated isothermal method that could be an alternative method for accelerated stability. Stability data from LNISO experiments were compared to those from the conventional isothermal and the abbreviated isothermal experiments. For the compendial compounds (acetaminophen and sulfacetamide), the nonisothermal data were compared to the isothermal stability data for these drugs reported in the literature (Koshy and Lach 1961; Meakin et al. 1971).
Methods
Materials
The two model compounds, acetaminophen (Lot# 10142144, purity 98%) and sulfacetamide (Lot# A05U023, purity 98%), were both manufactured by Johnson Matthey company and obtained from VWR (USA). Buffers used to maintain the pH in the drug solutions were obtained from VWR. The 18 drug substances (Compounds A1, A2, A3, …, and A18) used in this study all were research grade compounds (purity ≥ 98%) provided by Allergan R&D. All of the drug substances and reagents were used as received.
Experimental methods
Sample preparation
A sidebyside comparison of the experimental conditions for the three stability methods used herein
NonIsothermal (LNISO) Stability  Abbreviated Isothermal Stability  Conventional Isothermal Stability  

Drug Substance Concentration  40 ppm  40 ppm  40 ppm 
Vehicle  80:20 (~30 mM Phosphate Buffer/Ethanol)  80:20 (~30 mM Phosphate Buffer/Ethanol)  80:20 (~30 mM Phosphate Buffer/Ethanol) 
Target pH  Starting pH: 7.0, End pH: shifted by ≤ 0.2 pHunit due to the temp. increase  7.0  7.0 
Heating Type/Storage Temperatures  Linear Heating (50 – 95 °C)  Isothermal (50, 60, and 80 °C)  Isothermal (40, 50, 60, and 80 °C) 
Target Time Points  0, 8, 32, 56, 80, 104, 120, 128, 144, 152, 168 h  0, 3, 7, 14 and 28 days  0, 3, 7, 14, 28, 42 and 56 days 
Sample Storage Time  7 days  4 weeks  8 weeks 
Total Number of Samples  11  13  25 
To monitor any possible pH shifts as a result of increased temperature during the nonisothermal studies, the pH was measured at the end of the stability experiment at 95 °C and the pH shift (decrease in pH) was found to be less than 0.2 pH units.
Sample analysis
Before HPLC analysis, stability samples (including the t_{0} samples) were removed from the freezer and stored at 40 °C for 1–2 h to help redissolve any precipitate which may have formed during the storage at −20 °C. The ampules were vortexed, opened, and their contents were transferred to HPLC vials for analysis.
Experimental conditions for the universal HPLC method
HPLC System  Waters E2695 Module  

Detector  Waters 2489 UV detector and 2998 PDA detector  
Software  Waters Empower 2  
Column  Agilent Zorbax SBC18 3.5μm 4.6x150mm  
Mobile Phase  A: 0.05% TFA in DI Water  
B: Acetonitrile  
Gradient  Time (min)  A (%)  B (%) 
0  80  20  
2  80  20  
20  10  90  
25  10  90  
26  80  20  
28  80  20  
Flow Rate  1 mL/min  
Injection Volume  20 μL  
Running Time  28 min  
Column Temperature  30 °C  
Wavelength  Selected based on each compound’s λ_{max} 
Nonisothermal stability method
To perform the nonisothermal stability experiments, an advanced nonisothermal stability oven was developed, which maintained exposure of samples to heat by applying a linear heating profile with an accuracy of ±0.1 °C from the target temperatures. A heating block (compatible with ampules or HPLC vials) integrated with a PID (proportional integral derivative) controller was used to accurately control the temperature. A computer software program was developed to control sample heating by a linear temperature increase over the time (e.g., 1 week stability).
Samples were heated in the oven with the linear increase in temperature from 50 to 95 °C for 7 days (30 to 100 °C for 7 days for the model compounds). Stability samples were pulled out of the oven at different time points (time scale in hours) and placed in a freezer at −20 °C to prohibit any further degradation before HPLC analysis.
Theoretical model for the Nonisothermal stability
where k is the rate constant for the chemical degradation, t is the time, and f(C) is the function for remaining concentration of the parent over the time, which depends on the order of the reaction. For zero, first, and secondorder reactions, f(C) is C, ln C and −1/C, respectively. C _{o} is the initial concentration of parent compound at time zero (t_{0}).
where k ’ = apparent degradation rate constant at T ’, e.g., k ’ = k _{25} for the temperature at 25 °C
R = the universal gas constant (R = 1.987 cal mol^{−1} K^{−1}), which is equivalent to the Boltzmann constant but expressed in units of energy per temperature increment per mole
C _{t} = concentration of drug at time (t),
C _{o} = initial drug concentration,
dt = time points (variable),
E _{a} = activation energy (in cal mol^{−1}),
T ’ = temperature (in K) for which the rate constant (k ’) is estimated (e.g., 298 K for k _{25}),
T (t) = temperature (in K) at the time (t).
The experimental data was fit to the theoretical model in Eq. (5) to solve the rate constant for decay of the drug at 25 °C (k _{25}) plus the activation energy (E _{a}) by using the analytical concentrations of the drugs at different stability time points (C _{t}), the sampling times (t) and the temperature values, T(t), measured at each sampling time point.
Nonisothermal heating program
where α is the heating rate, T(t) is temperature at time (t) and T _{0} is the starting temperature at time 0.
Isothermal stability method
Samples were stored for 8 weeks in separate isothermal ovens with temperatures set to 40, 50, 60, and 80 °C. The stability samples were pulled out at different time points (time scale in days) and placed in a −20 °C freezer until the HPLC analysis.
Abbreviated isothermal stability method
The abbreviated isothermal stability was a subset of the conventional isothermal stability method described above. Samples were held separately in the same isothermal ovens at 40, 50, 60, and 80 °C for 4 weeks. The stability parameters predicted by the abbreviated method were compared to the same parameters predicted using the 8 weeks isothermal stability.
Data analysis and curvefittings
All HPLC chromatograms were processed using the Waters Empower software. Kinetic analysis of the majority of the compounds was performed by using the peak areas of the parent peak. For two compounds (A8 and A17) the peak areas of the degradation products were used.
The Scientist® software by Micromath (Manual for Scientist 3.0 Program 2006) was used for all data analysis, curve fittings, and determination of the 95% confidence intervals and R^{2} (coefficient of determination) values. The mathematical model of Eq. (5) was programmed in Scientist®. The program uses a least square fit (regression) for the curve fittings to calculate the k _{25} and E _{a} values. The R^{2} values, which indicate goodnessoffit for fitting experimental data to the theoretical model in Eq. (5), were calculated by the software. In addition, the Scientist® program was used to calculate confidence interval values (95%) for each estimated stability parameter, i.e., k _{25} and E _{a}, where the best regression fit was achieved.
Results and discussions
Model Compound  Conventional Isothermal Method (Literature)^{a}  Nonisothermal Method^{b} 

Acetaminophen (pH 3.0)  k _{25} = 3.27 · 10^{−4} day^{−1} E _{a} = 18.0 kcal/mol  k _{25} = 7.92 · 10^{−5} (±1.54 · 10^{−6}) day^{−1} E _{a} = 19.5 (±0.7) kcal/mol 
Sulfacetamide (pH 7.4)  k _{25} = 6.83 · 10^{−5} day^{−1} E _{a} = 22.9 kcal/mol  k _{25} = 2.38 · 10^{−5} (±3.12 · 10^{−7}) day^{−1} E _{a} = 25.0 (±0.4) kcal/mol 
Table 3 is a summary of the k _{25} and E _{a} values predicted for the model compounds, acetaminophen and sulfacetamide, by LNISO method vs. the same stability parameters determined by conventional isothermal stability in the literature (Koshy and Lach 1961; Meakin et al. 1971). These results verified that the nonisothermal method might not reproduce exactly the same stability parameters obtained by the isothermal method in the literature but the values for E _{a} are comparable while rate constant values differ by a factor of 2–3. Similar disparities were predicted by the Yoshioka MonteCarlo simulation study (Yoshioka et al. 1987, 1988). Other possible explanations for the discrepancy between the literature values and those predicted by the LNISO method might be: 1) differences in experimental conditions such as pH shift upon increase of temperature by the nonisothermal, buffer concentration, temperature control, etc. 2) differences in sensitivity of the analytical tools (Koshy and Lach 1961; Meakin et al. 1971). It is unfortunate that we did not perform our own isothermal study to address any differences but we were unable for logistical reasons to go to perform such a study but as will be seen with the Allergan compounds, similar differences were seen between the two stability testing methods.
In an initial analysis of the LNISO data for the 18 Allergan compounds, three of these compounds (A3, A9 and A18) were quickly excluded from the more complete study. The first of the excluded compounds, A3, was so unstable that even the timezero sample (stored in the freezer) showed a large degradation peak in the HPLC chromatograms (>20% by peak area). Two other compounds, A9 and A18, were excluded due to significant and persistent precipitation that was discovered after the removal of the stability samples from the freezer. Lower solubility and recrystallization upon storage at −20 °C may possibly explain the precipitation. The presence of precipitated materials in stability samples for these two compounds caused large variations in the measured drug concentrations that made the data analysis difficult. Another set of three compounds (A8, A16, and A17), showed no statistically significant decrease in parent peak, but fortunately, there was only one major degradation product for each compound as indicated by the HPLC chromatograms. The degradation rate constants for these compounds could be determined with a high precision by monitoring growth of the single degradant of each compound. Since the response factors of the degradants were unknown, an assumption was made that the degradants have the same response factors as the parent drugs. The degradants by both methods were identical (same retention time by HPLC). In summary, there were only three (out of the 18) compounds for which the degradation kinetics could not be accurately determined (i.e., A3, A9 and A18).
Summary of degradation rate constants and activation energies determined using the three stability methods
Compound #  LNISO^{a} Method (1 week)  Conventional Isothermal (8 weeks)  Abbreviated Isothermal (4 weeks)  

11 time points  6 time points  
E_{a} (kcal/mol)  k_{25} (1/day)  E_{a} (kcal/mol)  k_{25} (1/day)  E_{a} (kcal/mol)  k_{25} (1/day)  E_{a} (kcal/mol)  k_{25} (1/day)  
A1^{b}  Stable, no degradation observed.  
A2^{b}  Stable, no degradation observed.  
A3  Unstable  
A4  24.22  6.58E4  24.25  6.49E4  25.14  4.76E4  24.66  5.42E4 
A5^{b}  Stable, no degradation observed.  
A6^{b}  Stable, no degradation observed.  
A7  27.68  3.78E4  27.80  3.70E4  28.18  2.88E4  28.49  2.67E4 
A8  25.47  1.32E5  25.62  1.26E5  24.45  1.67E5  23.14  2.15E5 
A9  Precipitations, data could not be processed.  
A10^{b}  Stable, no degradation observed.  
A11 ^{c}  14.14  4.14E4  12.69  6.39E4  18.71  6.67E5  15.58  1.61E4 
A12  17.54  3.02E3  17.72  2.86E3  18.66  1.63E3  16.85  2.04E3 
A13  25.26  2.76E4  25.20  2.80E4  24.93  2.31E4  24.54  2.51E4 
A14  31.78  4.33E5  31.70  4.40E5  32.98  2.60E5  32.81  2.70E5 
A15  31.91  1.80E5  31.87  1.82E5  31.68  1.40E5  30.35  1.90E5 
A16 ^{c}  9.59  3.94E4  10.36  3.27E4  10.32  8.40E5  12.11  8.50E5 
A17  27.05  3.09E6  26.91  3.20E6  25.57  2.94E6  28.64  1.82E6 
A18  Precipitations, data could not be processed. 
There were five compounds (A1, A2, A5, A6 and A10) that had no significant degradation in both nonisothermal experiments and isothermal experiments at 40, 50 and 60 °C (four of the five compounds showed only minor degradation at 80 °C but even this onetemperature point could not be used to estimate a k _{25} value). These five compounds were considered stable and classified as BIN 1 (t_{90%} > 24 months).
In summary, there were 10 compounds (out of 15 compounds with usable kinetic stability data) for which k _{25} and E _{a} values were determined by all three methods for further binning classifications, out of which two compounds (A11 and A16) did not follow first order kinetics.
Examining the stability data in Table 4 and ignoring the two compounds that did not follow the firstorder degradation kinetics (A11 and A16), the k _{25} values determined by the LNISO method (11 data points) had an average difference of ±43% compared to those determined by the isothermal method. The E _{a} values predicted by the LNISO method had an average difference of ±3.9% compared to those determined by the isothermal method. These results were better than the previous data on the model compounds, acetaminophen and sulfacetamide, possibly because there was better consistency in experimental conditions, such as pH and buffer concentration, analytical methods and extrapolations.
Stability parameters and R^{2} values determined by LNISO (11 data points) vs. LNISO (6 data points)
Compound #  LNISO^{a} (11 data points)  LNISO^{a} (6 data points)  

Ea (kcal/mol)  k(25) (1/day)  R^{2}  Ea (kcal/mol)  k25 (1/day)  R^{2}  
A4  24.22 ± 0.88  6.58 ± 1.45E4  0.99977  24.25 ± 1.94  6.49 ± 3.34E4  0.99972 
A7  27.68 ± 1.70  3.78 ± 1.61E4  0.99966  27.80 ± 1.13  3.70 ± 1.04E4  0.99994 
A8  25.47 ± 1.18  1.32 ± 0.46E5  0.99966  25.62 ± 2.61  1.26 ± 1.05E5  0.99961 
A11 ^{b}  14.14 ± 4.42  4.14 ± 6.05E4  0.98775  12.69 ± 6.18  6.39 ± 16.17E4  0.99341 
A12  17.54 ± 1.43  3.02 ± 1.10E3  0.99913  17.72 ± 2.64  2.86 ± 2.04E3  0.99912 
A13  25.26 ± 0.22  2.76 ± 0.17E4  0.99998  25.20 ± 0.35  2.80 ± 0.27E4  0.99999 
A14  31.78 ± 0.42  4.33 ± 0.50E5  0.99996  31.70 ± 0.96  4.40 ± 1.20E5  0.99996 
A15  31.91 ± 0.38  1.80 ± 0.20E5  0.99996  31.87 ± 0.72  1.82 ± 0.38E5  0.99998 
A16 ^{b}  9.59 ± 2.82  3.94 ± 3.11E4  0.99395  10.36 ± 3.79  3.27 ± 3.86E4  0.99712 
A17  27.05 ± 0.96  3.10 ± 0.90E6  0.99969  26.91 ± 1.80  3.20 ± 1.80E6  0.99982 
Regarding accuracy of the key stability parameters, since the conventional isothermal method follows compendial conditions (i.e., pharmacopeia) and requires long time incubations (e.g., 2 months) at constant temperatures, this method is considered as the most accurate method among those studied. By comparing the k _{25} values determined by the three methods, the 4 weeks abbreviated isothermal values are the closest to the k _{ 25} values obtained by the 8 weeks conventional isothermal stability with an average deviation of ± 24%. However, the k _{25} values determined by the LNISO methods (six data points vs. 11 data points) demonstrated similar deviations from the results by the conventional isothermal method. The average deviations were ± 44% by the LNISO method (6 data points) versus ±43% by the LNISO method (11 data points). For the above analysis, the two outlier compounds (A11 and A16) were excluded.
Summary of the t _{90%} values and binning classifications predicted by the three methods described herein
Compound #  Description  LNISO^{a} t_{90%} (month)  CONV.^{b} t_{90%} (month)  Abbrev. t_{90%} (month)  LNISO^{a} Binning  CONV.^{b} Binning  Abbrev.^{c} Binning 

A1  Stable No Degradation  >24 months  >24 months  >24 months  BIN 1  BIN 1  BIN 1 
A2  Stable No Degradation  >24 months  >24 months  >24 months  BIN 1  BIN 1  BIN 1 
A3  Precipitation, Unstable: Not Processed             
A4  First Order Degradation  5.3  7.4  6.5  BIN 3  BIN 3  BIN 3 
A5  Stable No Degradation  >24 months  >24 months  >24 months  BIN 1  BIN 1  BIN 1 
A6  Stable No Degradation  >24 months  >24 months  >24 months  BIN 1  BIN 1  BIN 1 
A7  First Order Degradation  9.3  12.2  13.1  BIN 3  BIN 2  BIN 2 
A8  Processed using degradant peak.  >24 months (266)  >24 months (210)  >24 months (163)  BIN 1  BIN 1  BIN 1 
A9  Precipitation: Not Processed             
A10  Stable No Degradation  >24 months  >24 months  >24 months  BIN 1  BIN 1  BIN 1 
A11  Non First Order Kinetics  8.5  53.0  21.8  BIN 3  BIN 1  BIN 2 
A12  First Order Degradation  1.2  2.2  1.7  BIN 3  BIN 3  BIN 3 
A13  First Order Degradation  12.7  15.2  14  BIN 2  BIN 2  BIN 2 
A14  First Order Degradation  >24 months (81)  >24 months (135)  >24 months (130)  BIN 1  BIN 1  BIN 1 
A15  First Order Degradation  >24 months (195)  >24 months (251)  >24 months (185)  BIN 1  BIN 1  BIN 1 
A16  Non First Order Kinetics  8.9  41.8  41.3  BIN 3  BIN 1  BIN 1 
A17  Processed using degradant peak.  >24 months (1136)  >24 months (1194)  >24 months (1929)  BIN 1  BIN 1  BIN 1 
A18  Precipitation: Not Processed.             
Summary of t_{98%} values and binning classifications predicted by the three methods described herein
Compound #  Binning Classification  LNISO^{a} t_{98%} (month)  CONV.^{b} t_{98%} (month)  Abbrev.^{c} t_{98%} (month) 

A1  Stable  >24 months  >24 months  >24 months 
A2  Stable  >24 months  >24 months  >24 months 
A3  Precipitation, Not Processed       
A4  Unstable  1.0  1.4  1.2 
A5  Stable  >24 months  >24 months  >24 months 
A6  Stable  >24 months  >24 months  >24 months 
A7  Unstable  1.8  2.3  2.5 
A8  Stable  >24 months (51)  >24 months (40)  >24 months (31) 
A9  Precipitation: Not Processed       
A10  Stable  >24 months  >24 months  >24 months 
A11  Unstable (NonFirst Order Kinetics)  1.6  10.0  4.1 
A12  Unstable  0.22  0.41  0.33 
A13  Unstable  2.4  2.9  2.6 
A14  Unstable by LNISO  15.3  >24 months (25.6)  >24 months (24.6) 
A15  Stable  >24 months (37)  >24 months (47)  >24 months (35) 
A16  Unstable (NonFirst Order Kinetics)  1.7  7.9  7.8 
A17  Stable  >24 months (215)  >24 months (226)  >24 months (365) 
A18  Precipitation: Not Processed.       
Considering mechanism of degradation for the compounds tested in this study, the model compounds (acetaminophen and sulfacetamide) both degrade by hydrolysis of an acetamide group as described in the literature (Koshy and Lach 1961; Meakin et al. 1971). The amine in the aniline group of sulfacetamide is reported to be also subject to oxidation in the presence of heat and light (Meakin et al. 1971).
 1)
Five compounds (A1, A2, A5, A6, and A10) that didn’t show significant degradations at conditions examined in this study contained functional groups that may be susceptible to hydrolysis, oxidation, or epimerization at different test conditions.
 2)
Six compounds (A7, A8, A12, A13, A14, and A15) contained amide, sulfonamide, or urea groups, which were prone to hydrolysis, and all degraded by following the first order kinetics. Compounds (A9 and A18) which precipitated during storage and resulted in unusable stability data could possibly be subject to hydrolysis.
 3)
Two compounds (A3 and A17) contained benzylic carbon bridges sensitive to oxidation.
 4)
One compound (A11) contained functional groups susceptible to hydrolysis or sulfaoxidation and demonstrated biphasic, nonfirst order degradation.
 5)
One compound (A4) contained chemical groups susceptible to halide displacement, or possible oxidation of hydroxyl group.
 6)
One compound (A16) with unknown degradation path that didn’t follow first order kinetics.
In summary, there are a few experimental considerations that need to be highlighted regarding use of the nonisothermal methodology for preformulation stability screening at the early stages of drug development. As described here, the theoretical model used for the nonisothermal stability is derived assuming first order kinetics. For this reason, the LNISO predictions are most valid for compounds whose degradation follows such kinetics. When applied to compounds with known, or unknown, degradation pathways, the R^{2} (Coefficient of Determination) values can be utilized to determine the reliability of the predicted stability parameters obtained by fitting experimental data to the theoretical model for nonisothermal stability. In this study, the results with R^{2} values higher than 0.999 were considered reliable. In addition, other factors to consider for the experimental design of LNISO stability studies include pH and catalytic buffer effects, both of which could significantly affect the degradation rate constants. For example, compounds that are predicted to be unstable at pH 7, could have significantly greater stability at, for example, pH 5. The results of this study also suggest that the LNISO stability method can be utilized for liquid formulation screenings, where the relative stability of a lead drug candidate can be tested in different solution media for liquid formulations.
Conclusions
The LNISO method is found to be a powerful highthroughput technique for rapid preformulation stability screening of pharmaceutical compounds by binning the compounds into categories based on the predicted t_{90%} or t_{98%} values to discern the most stable compound at the tested condition(s). The LNISO method may not yield k _{25} and E _{a} values that exactly match the isothermal values, however, the results of this study shows that these stability parameters correlate very well by the two methods when the same experimental conditions are applied. The good correlations between k _{25} (Fig. 8) and E _{a} (Fig. 11) determined by nonisothermal vs. isothermal and the comparable binning classification results by the two methods (Tables 6 and 7) indicate that the LNISO method is feasible for compound binning. The LNISO method should be used judiciously, keeping in mind that the method cannot predict the absolute stability parameters as accurately as the conventional isothermal stability, and it is most effective for compounds whose degradation pathways follow first order (or pseudo first order) kinetics.
Declarations
Acknowledgement
The authors would like to acknowledge Dr. Scott Smith for his valuable input, scientific discussions and technical guidance regarding use of the nonisothermal method for stability screening of drug substances. The authors wish to thank fellow peers at Allergan, Dr. Patrick Hughes, Dr. Richard Graham and Dr. James Cunningham, for their valuable feedback on this work. Technical support by Mr. Prem Mohanty in preparation of the stability samples, and technical discussions with Dr. Ke Wu are acknowledged. The authors also wish to thank Dr. Sesha Neervannan, Head of the Allergan Pharmaceutical Development, Mr. Lorenz Siddiqi and Allergan Medical Affairs Publications Team for review and approval of this manuscript for publication at AAPS Open.
Funding
The research resources and materials used for the studies presented in this manuscript were funded by Allergan R&D. The manuscript was approved by Allergan Medical Affairs Publications for submission to the AAPS Open journal on January 3, 2017.
Authors’ contributions
The authors are AK, (Scientist, former employee of Allergan), SF. (Sr. Scientist at Allergan Early Development), TK. (Associate Director at Allergan Early Development) and VS. (Distinguished Professor Emeritus at Pharmaceutical Chemistry, The University of Kansas and Academic Consultant of Allergan). The authors’ contributions are the following: AK, SF and TK contributed to the experimental design, laboratory work, data analysis, theoretical interpretation of the results, literature search, review and presentation of Arrhenius theory applied to the nonisothermal stability. Prof. VS had valuable intellectual contributions to the design of the studies, interpretation of the results, literature review and review of the experimental and theoretical sections presented in the manuscript. All authors have equally contributed to the writing of the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 ICH Guideline Q1A, R2 (2003) Stability Testing of New Drug Substances and ProductsGoogle Scholar
 ICH Guideline Q3A, R2 (2006) Impurities in New Drug SubstancesGoogle Scholar
 ICH Guideline Q3B, R2 (2006) Impurities in New Drug ProductsGoogle Scholar
 Koshy KT, Lach JL (1961) Stability of Aqueous Solutions of NAcetylpaminophenol. J Pharm Sci 50:113–8View ArticlePubMedGoogle Scholar
 Lin B, Zhan XC, Tao JL, Li LL, Qi HJ (2009) Step Nonisothermal Method to Study Stability of Drugs. Drug Dev Ind Pharm 35(2):154–64View ArticlePubMedGoogle Scholar
 Manual for Scientist 3.0 Program (2006) Micromath Scientific Software V1., pp 51–8Google Scholar
 Meakin BJ, Tansey IP, Davies DJG (1971) The effect of Heat, pH and some Buffer Materials on the Hydrolytic Degradation of Sulfacetamide in Aqueous Solution. J Pharm Pharmacol 23:252–61View ArticlePubMedGoogle Scholar
 Official US Pharmacopoeia (2011) Monograph for Acetaminophen. USP 34:1720–1Google Scholar
 Rao RM, Rao YM, Shah AH (1999) A reverse phase ionpairing HPLC method for the stability monitoring of sulfacetamide ophthalmic preparations. J Pharm Biomedical Analysis 20:717–22View ArticleGoogle Scholar
 Waterman KC (2011) The Application of the Accelerated Stability Assessment Program (ASAP) to Quality by Design (QbD) for Drug Product Stability. AAPS Pharm Sci Tech 12(3):932–7View ArticleGoogle Scholar
 Yoshioka S, Aso Y, Uchiyama M (1987) Statistical Evaluation of Nonisothermal Prediction of Drug Stability I. J Pharm Sci 76(10):794–8View ArticlePubMedGoogle Scholar
 Yoshioka S, Aso Y, Uchiyama M (1988) Statistical Evaluation of Nonisothermal Prediction of Drug Stability II: Experimental Design for Practical Drug Products. Int J Pharm 46:121–32View ArticleGoogle Scholar
 Yoshioka S, Aso Y, Takeda Y (1990) Statistical evaluation of accelerated stability data obtained at a single temperature. I. Effect of experimental errors in evaluation of stability data obtained. Chem. Pharm. Bull (Tokyo) 38(6):1760–2View ArticleGoogle Scholar
 Zhan X, Yin G, Wang L, Ma B (1997a) Exponential Heating in Drug Stability Experiment and Statistical Evaluation of Nonisothermal and Isothermal Prediction. J Pharm Sci 86(6):709–15View ArticlePubMedGoogle Scholar
 Zhan X, Yin G, Ma B (1997b) Determination of Rate Order for Degradation of Drugs with Nonisothermal Stability Experiment. J Pharm Sci 86(10):1099–104View ArticlePubMedGoogle Scholar
 Zoglio M, Windheuser J, Vatti R, Maulding H, Kornblum S, Jacobs A, Hamot H (1968) Linear Nonisothermal Stability Studies. J Pharm Sci 57(12):2080–5View ArticlePubMedGoogle Scholar