The use of accelerated stability studies is a well-established technique that has been widely used for more than 60 years to predict the shelf life and storage conditions of drugs and drug products (Baertschi 2007; Huynh-Ba 2008; Karstensen 1990; Waterman & Carella 2007). Whereas the experimental approaches may vary between studies, the general principles are the same and are based on the extrapolation of the rate of degradation at two or more temperatures above the intended condition, using the Arrhenius Relationship (Eq. 1).

$$ \ln k\kern0.5em =\kern0.5em \ln A-\frac{E_a}{RT} $$

where k is the rate constant for the reaction, T is the temperature, A is the collision frequency factor, Ea is the activation energy and R is the gas constant. Equation 1 is actually a variation of the empirical relationship developed by van’t Hoff in 1887 to describe the effect of temperature on chemical equilibria and used later by Arrhenius who found that the logarithm of the rate (or rate constant) for various reactions was proportional to the reciprocal of the absolute temperature. Predictions of stability based on the Arrhenius relationship (Eq. 1) work well for well-controlled homogenous systems (such as solutions) over relatively small temperature ranges (e.g. 50 °C). However, the Arrhenius relationship is less reliable over larger temperature ranges when the dependency of A and Ea on T described by Eyring (Stella, 2000) results in non-linear relationships between ln k and 1/T. Another important source of error arises from extrapolation of the data because the confidence interval of the predicted value increases as the difference between the measured and predicted values increases.

Deviations from ideal behavior (Eq. 1) in more complex, heterogenous systems, make the prediction of stability in solid dosage forms (SDF) more difficult. However, Waterman and co-workers (Waterman & Swanson 2014; MacDonald 2010; Colgan & Hofer 2015; Stella 2000; Timmerman 2003; Waterman 2011) have shown that the predominant factor that determines the rate of degradation in solid dosage forms, in addition to temperature, is the presence of water. That group has shown the rate of degradation of active pharmaceutical ingredients in tablets and other SDFs may be predicted using a modified Arrhenius equation (Eq. 2), which takes into account the water content as well as the temperature:

$$ \ln k= \ln A-\frac{E_a}{RT}+B(RH) $$

where B is the humidity sensitivity factor and RH is the relative humidity. Having demonstrated the applicability of various statistical approaches for the evaluation of data (Eq. 2) to predict the shelf life of SDFs, Waterman and co-workers (Waterman & Swanson 2014; MacDonald 2010; Colgan & Hofer 2015; Stella 2000; Timmerman 2003; Waterman 2011) have developed computer software (ASAPprime®) to facilitate the calculations. This approach relies on the measurement of the rates of degradation at various temperatures and relative humidities. Equation 2 contains two independent variables (T and RH); therefore, at least three combinations (a 3-point protocol) of T and RH are necessary to obtain values of A, Ea and B by regression analysis or other curve fitting techniques. The greater the number of points in the protocol the greater the reliability of the estimates of the regression coefficients, and the predicted shelf life.

If the stability of the drug product is significantly affected by the presence of moisture, sealing in a water-impermeable package (such as aluminum foil or blister) may be required to reduce the rate of degradation by eliminating any further ingress of water toward the product. Packaging in a semi-permeable container or blister may slow down the degradation by reducing the moisture vapor transmission rate (MTVR). However, if the product is particularly sensitive to the presence of water, packaging with a desiccant may be necessary. Accelerated stability studies of SDFs are frequently conducted in so called “open dish” studies in which the test article is exposed to the atmosphere and equilibrates with the ambient humidity. An alternative approach to understanding the effects of humidity on the rate of degradation is to first pre-equilibrate the SDF with an atmosphere of known RH and then seal it in a water-impermeable pouch made of aluminum foil. In addition to predicting the effects of temperature and relative humidity, ASAPprime® has the added advantage of allowing the effects of packaging in water-impermeable or partially impermeable containers or blisters on stability to be predicted.

Although the intended application of (ASAPprime®) is the prediction of the rates of chemical degradation in SDFs there is no reason that this approach cannot be applied to physical instability, because Eq. 2 is empirical and simply a way of correlating the rate of change of any measurable parameter of product performance as a function of time, temperature and relative humidity. Accordingly, the objective of this study was to test the hypothesis that ASAPprime® software can be used to predict the dissolution rate of change of the active ingredients in tablets at the intended storage condition, based on data obtained at elevated temperature and relative humidity. This approach is reasonable because the majority of changes in dissolution rate of SDFs can be attributed to changes in water content (Waterman & Swanson 2014; MacDonald 2010; Colgan & Hofer 2015; Stella 2000; Timmerman 2003; Waterman 2011). The SDF used to test the hypothesis was an investigational immediate release tablet containing two active pharmaceutical ingredients (API 1 and API 2) that had previously shown slowed dissolution at 40 °C/75 % RH in an open dish study and enabled better understanding of the risk to dissolution changes at room-temperature storage.

Results and discussion

Slowdown in dissolution of both APIs was observed for tablets stored at highly elevated temperature and relative humidity conditions, likely due to physical changes of the SDF, no chemical degradation of either API was observed under these conditions. Representative dissolution profiles are shown in Fig. 1a, which demonstrates that the dissolution of API 1 at 20 min decreased from an initial value of 90.9 to 82.9 % after three days storage in an open dish at 60 °C/60 % RH. The dissolution of API 1 decreased to 79.9 % after storage in an open dish for 7 days at 60 °C/65 % RH and 76.8 % after 3 days at 60 °C/75 % RH. A similar slowdown in the dissolution of API 2 was also observed (Fig. 1b).

Fig. 1
figure 1

a Dissolution Profiles of API 1 under Different Storage Conditions, in pH 1.5 Media. b Dissolution Profiles of API 2 under Different Storage Conditions, in pH 6.8 Media

The impact of temperature and RH (30–75 %) (T/RH) on dissolution at long term storage conditions was evaluated through a number of stressed and open dish studies. The dissolution changes at 20 min for both APIs over long term storage are of particular interest, as typical dissolution specifications for immediate release tablets are Q = 80 % at 20 min. (The quantity, Q, as defined per USP <711>, is the amount of dissolved active ingredient, in percent label claim). The data were analyzed by ASAPprime® to develop a model describing the effect of moisture and temperature on dissolution over the product shelf life at target storage conditions. The T/RH design space and target are shown in Fig. 2. Detailed experimental design and durations are shown in Table 1.Footnote 1 The predicated data from ASAPprime® modeling were compared against real-time stability data to validate the approach (Table 2). The experimental data used to construct the model relating the percent dissolved to values of T and RH were generated by pre-equilibrating the tablets at 25 °C and various values of RH (30–75 %) (Fig. 2). The mean values for the amounts of each API dissolved (n = 3) after 20 min are provided in Appendix 1. The data were fitted to Eq. 2 and the value for the regression coefficients (A, Ea, B and R2) are shown in Table 3. The values of 0.937 and 0.954 for R2 mean that 6.3 % (API 1) and 4.6 % (API 2) of the variance in the data for the two APIs are not explained by the model. Figure 3 shows the residuals obtained from the predicted values and those obtained by experiment were randomly distributed, indicating that there was no systematic error in the predictions.

Fig. 2
figure 2

Design Space showing the Conditions Studied (blue) and the Conditions for the Predictions (green)

Table 1 a Temperature (T) and relative humidity (RH) conditions used in ASAP modeling
Table 2 Stability studies/conditions used for external model validation
Table 3 Regression coefficients for data fitted to the modified Arrhenius equation (Eqs. 2 and 3) and the Dimensionless equation (Eq. 4) for the two active ingredients
Fig. 3
figure 3

Residuals for the Predicted Isoconversion Values for the Two Active Pharmaceutical Ingredients

Effects of temperature and relative humidity on dissolution

The computer software (ASAPprime®) uses the isoconversion method (Waterman (2011)), rather than regression analysis to calculate the values of A, Ea, B, where the isoconversion time, IC is the time to reach the pre-determined value for the acceptance criteria (not less 80 % dissolved after 20 min). Replacement of the rate constant, k with the reciprocal of IC gives:

$$ \ln \frac{1}{IC}= \ln A-\frac{E_a}{RT}+B(RH) $$

Equation 3 can be re-written in dimensionless terms by substitution of \( \frac{E_a}{R} \) by C,

$$ \ln \frac{1}{IC}= \ln A-\frac{\mathrm{C}}{T}+B(RH) $$

where C is the temperature sensitivity factor. Equation 4 allows the effects of changing T and RH to be assessed independently of each other. The effect of changing the atmospheric moisture from a value of RH1 to RH2 at a fixed value of T (ΔRH) may be determined as follows:

$$ \ln \frac{I{C}_{RH2}}{I{C}_{RH1}}=B\left(R{H}_1-R{H}_2\right) $$

Equation 5 can be re-written in non-logarithmic terms to give:

$$ \frac{I{C}_{RH2}}{I{C}_{RH1}}={F}_{\varDelta RH}={e}^{B\left(R{H}_1-R{H}_2\right)} $$

where F ΔRH is the factor by which the isoconversion time (the time to reach Q = 80 %) changes for a given change in RH (ΔRH). Equation 6 predicts that the value of F ΔRH is independent of the intital and final values of RH and depends only on the difference. Therefore, the values of F ΔRH , for 10 % change in absolute RH (ΔRH = 10 % RH) are 1.70 and 2.83 for API 1 and API 2, respectively. This means that the change in isoconversion time for the two APIs for a 10 % change in absolute RH is approximately 70 % for API 1 and approximately 183 % for API 2 at a fixed temperature.

The effect of changing T at a fixed value of RH (∆T) is slightly more complicated because the value of F ΔT , depends on the initial, (T1) and the final temperature (T2), as follows:

$$ \ln \frac{I{C}_{T2}}{I{C}_{T1}}=C\left(\frac{1}{T_2}-\frac{1}{T_1}\right) $$


$$ \ln \frac{I{C}_{T2}}{I{C}_{T1}}=C\left(\frac{T_{1-}{T}_2}{T_1{T}_2}\right) $$


$$ \frac{I{C}_{T2}}{I{C}_{T1}}={F}_{\varDelta T}={e}^{C\left(\frac{T_{1-}{T}_2}{T_1{T}_2}\right)} $$

That being said, the error in using a constant value of the product T1T2 is less than 10 % over relatively small temperature ranges (20 – 60 °C), in which case Eq. 9 simplifies to:

$$ \frac{I{C}_{T2}}{I{C}_{T1}}={F}_{\varDelta T}={e}^{C\varDelta \mathrm{T}\times {10}^{-4}} $$

Therefore, the values of F ΔT , for 10 °C change in temperature are 12.4 and 11.0 for API 1 and API 2, respectively. This means that the change in isoconversion time for a 10 °C change in temperature for API 1 and API 2 are approximately 1250 % and 1100 %, respectively, at a fixed value of RH.

It can be shown that the combined effect changing both T and RH (F ΔT,ΔRH ) can be estimated by:

$$ {F}_{\varDelta T,RH}={e}^{\left( B\varDelta RH+C\varDelta \mathrm{T}\times {10}^{-4}\right)} $$


$$ {F}_{\varDelta T,RH}={F}_{\varDelta T}\kern0.5em \times \kern0.5em {F}_{\varDelta RH}=\left({e}^{B\varDelta RH}\right)\kern0.5em \times \kern0.5em {e}^{\left(C\varDelta \mathrm{T}\times {10}^{-4}\right)} $$

Therefore, the combined effect of changing the storage conditions from the accelerated conditions 40 °C/75 % RH to the intended storage condition of 25 °C/60 % RH (ΔT = 15 °C ΔRH = 15 % RH) predicted by the model (F ΔT  × F RH ) is 96.5 and 181.3, for API 1 and API 2, respectively. The individual contributions from temperature and relative humidity are as follows


$$ {F}_{\varDelta T} = 43.6 $$
$$ {F}_{RH} = 2.21 $$


$$ {F}_{\varDelta T} = 38.9 $$
$$ {F}_{RH} = 4.66 $$

It is clear from Eqs. 1316 that the contribution to a reduction in dissolution at 20 min for both drugs from elevating the temperature is significantly greater than the contribution from increasing the relative humidity and that the effects of temperature on the dissolution of both drugs is about the same. Interestingly, although the effects of humidity change were relatively small, the effect of RH on the dissolution of API 1 (F RH  = 2.21) was much less than the effect on API 2 (F RH  = 4.66). The reason for the difference in the effect of water on the dissolution of the two APIs is not clear; however, it does have important implications for the stability of the tablets at room temperature, which are discussed in the next sections.

Effects of initial water content

The weak dependency of drug dissolution on RH (Eq. 4) was investigated further to determine if it was necessary to control the water content of the tablets in the drug-product specification. The amount of water taken up by the tablets at specific values of RH was entered into ASAPprime® to determine the water sorption isotherm over the entire range of RH (Fig. 4a).Footnote 2 Fig. 4a shows a sigmoidal relationship between the water content of the tablets in which the water content increases slowly up to 50 % RH to a value of 4 % and then increases exponentially to approximately 13 % at 100 % RH. Tablet water content change on stability can also be predicted based on the GAB parameters and given packaging configurations. Figure 4b and c are examples of predicted tablet water contents under 25 °C/60%RH and 30 °C/75%RH storage conditions over 2 years at different initial values. The software uses this information to predict the effect of the water content on the dissolution of the tablets. Figure 5 shows the anticipated effect that the amount of drug dissolved at 20 mins after two years’ storage decreases and the effect is more pronounced for API 1 than for API 2, which is expected from the previous discussions described above. Although the effect of humidity is much less for API 1 than API 2, the dissolution rate drop for both APIs are primarily driven by effect of temperature, which is more significant for API 1 than API 2; therefore, more changes are observed in API 1 than API 2 at the end of the two-year storage and the differences are more pronounced at 30 °C than at 25 °C. Despite the differences in the effects of initial moisture on the dissolution of the two APIs, ASAPprime® predicts that the dissolution of both drugs will remain within specification after storage (Q = 80 %) for two years at either 25 °C/60 % RH, or 30 °C/75 % RH independent of the initial water content up to 6.3 % water, which is the equilibrium water content of the tablets at 75 % RH. The equilibrium water content at 60 % RH was found to be 4.1 %.

Fig. 4
figure 4

a Predicted Water Isotherm (left) and the Predicted Water Content in the Tablets after Open-Dish Storage at 25 °C/60%RH (initial water content 4.0 %). b Predicted Water Contents in Tablets Packaged in Aclar Blisters Over 2 Years at 25 °C/60%RH with Different Initial Water Contents. c Predicted Water Contents in Tablets Packaged in Aclar Blisters Over 2 Years at 30 °C/75%RH with Different Initial Water Contents

Fig. 5
figure 5

Relationship between the Predicted Percent Dissolved at 20 min of Both Active Pharmaceutical Ingredients after Two Years and the Initial Water Content at 25 °C/60%RH and 30 °C/75%RH

Stability in Aclar® blisters

Although the ASAPprime® analysis predicted some differences in the sensitivity of the dissolution of the two APIs to moisture, the results also indicated the effect of RH was insufficient to warrant the need for special packaging. This is supported by the results of two studies summarized in Table 4, which show very little, if any, increase in moisture content of the tablets packaged in Aclar® blisters for three to six months at various storage conditions. Table 4 also shows very good agreement between the observed values of water content and the values predicted by ASAPprime®. Finally, Table 5 shows no difference in the amounts of the two APIs dissolved from tablets, packaged in Aclar® blisters, following storage for 12 months at 25 °C/60 % RH, 30 °C/65 % RH and 40 °C/75 % RH. Similar results were observed on a different batch of tablets stored at the same conditions in an open dish (Table 5). Notably, the ASAPprime® software predicted very accurately that the change in dissolution after storage of the tablets packaged in Aclar® blisters would be insignificant after storage for 12 months at the intended storage condition (25 °C/60 % RH). We will continue to the monitor the stability of these formulations with a view to establishing a two-year shelf life, a period over which predictions made by the ASAPprime® software indicated that the dissolution of the two drugs would be well within typical specifications (Q = 80 % at 20 min) for an immediate release product.

Table 4 Predicted and observed water content of tablets packaged in Aclar® foil blisters at different storage conditions (Temperature (T) and Relative Humidity (RH))
Table 5 Predicted and observed dissolution of the two active pharmaceutical ingredients after 20 min at different storage conditions of temperature (T) and relative humidity (RH)


In this study, we have clearly demonstrated that the computer program, ASAPprime®, originally developed to predict the rates of degradation of SDFs arising from chemical reactions can also be used to predict changes in dissolution. Experiments conducted under various conditions of elevated temperature and relative humidity accurately predicted that the reduced rates of dissolution of two APIs in an SDF, IR tablet seen under accelerated conditions would not translate into any measurable changes in dissolution over the shelf life of the product (up to two years at 25 °C/60 % RH or 30 °C/75 % RH). Furthermore, the software predicted accurately that no special precautions are necessary to protect the product from moisture and that there is no need to control the water content of the tablets in the drug product specification. The methodology described here adds great value to the overall Quality by Design approach to tablet development.



Chemicals and reagents

All chemicals and reagents, obtained from various commercial sources, were reagent grade, except for the HPLC solvents, which were HPLC grade. Deionized water was prepared in-house.


The article used to test the hypothesis was an investigational, solid dosage form (SDF) tabletFootnote 3 containing two active pharmaceutical ingredients, API 1 and API 2: both drugs were small molecules with molecular weights of less than 1000.


Dissolution procedure

Tablet dissolution testing was performed on three tablets stored at each condition using USP Apparatus 2 in 900 mL of dissolution media at 37 °C. Due to their different aqueous solubilities, the dissolution profile of API 1 was obtained with pH 1.5 media, and the dissolution profile of API 2 was obtained with pH 6.8 media. Dissolution profiles were collected at 5, 10, 15, 20, 30, 45 and 60 min at 75 rpm and 65 rpm, respectively for API 1 and API 2, with an “infinity spin” from 60-75 min at 200 rpm.

Sample analysis

Samples (1.5 mL) were removed and filtered immediately through a polyvinylidene fluoride (PVDF, 10 μm,) filter at the sampling times listed above and analyzed for API content by HPLC. The HPLC procedure was validated for accuracy, precision and linearity and found to be suitable for the intended application. The system was calibrated using external standards containing concentrations of API 1 and API 2 equivalent to 100 % of the label claims (LC) of each API.

Stability studies

In one set of experiments the tablets were pre-equilibrated to constant water content at various relative humidity (RH) values ranging from 30 % to 75 % at 25 °C sealed in aluminum foil pouches and stored for various periods of time (Table 2) at 50 °C and 60 °C. In a second set of experiments tablets were stored in petri dishes (open dish) at 40 °C/75 % RH. Detailed experimental conditions and durations are listed in Table 1. The samples were stored in calibrated stability chambers.

Water content

The water content of the tablets was determined by automated Karl Fischer titration.

Water sorption isotherm

The water sorption isotherm of the tablets was determined using a dynamic water sorption analyzer.

Data analysis

The concentrations of the dissolved APIs at each sampling point (C1,t and C2,t) were expressed as a percentage of the label claim (LC%1,t) (Eq. 17) and plotted against time, t to generate the dissolution profiles (LC%1(or 2),t vs. t).

$$ LC{\%}_{\left(1 or2\right),\ t} = \frac{C_{1(or2),t}}{L{C}_{1(or2),t}}100\% $$

The relationships between the values of LC%1,20 and LC%2,20, temperature (T) and relative humidity (RH) were established by fitting the data Eq. 2 to calculate the regression coefficients, A, Ea, and B, using the ASAPprime® software (version 3, FreeThink Technologies, Inc. Montvale, NJ 06405).