The complementary guideline ICH Q1E⁽²⁾ recommends 12 months long-term data from stability testing to carry out a statistical analysis in order to extrapolate, in the packaging studied and for a given temperature and humidity level, the retest date or shelf life of 12 months maximum. Predictive approaches, which have been emerging for several years, prove very useful during development phases as they allow a better understanding of product behavior while being quicker and more economical with resources.

The Arrhenius law, which expresses the effect of temperature on the speed of a chemical reaction,⁽³⁾ is applicable to chemical reactions in a homogeneous medium, therefore in gases and liquids. The Arrhenius law can be written in two ways (equations 1 and 2). It is recognized that it can be used for liquid pharmaceutical formulations and that it allows modelling of the speed of a chemical degradation reaction according to temperature. Using an experimental plan based on the accelerated aging of a product at high temperatures, it is possible to deduce the kinetics of the reaction at a lower temperature and consequently shelf life.⁽⁴⁾

With:

k: reaction rate constant

A: pre-exponential factor (very little dependent on temperature)

Ea: activation energy of the reaction (in J.mol-1)

R: universal gas constant (8.314 J.mol-1.K-1)

T: temperature in Kelvin

Care must be taken, however, not to induce additional degradation factors. So it should be ensured that the degradation product formed does not generate a variation in pH and it is advised that samples be protected from light. Finally, as the Arrhenius reaction relates to a given degradation reaction, if several degradation products are formed, the behavior of each of them should be modelled.

Solid pharmaceutical forms are essentially inhomogeneous and the solid state drastically reduces the molecular mobility of reactive entities. Because of this, it has long been accepted that they could not follow the Arrhenius law. In addition, the modes of degradation of solids can be complex because of possible changes in the solid state structure of the active principle or interactions between the active principle and the reactive impurities of excipients. The main degradation factors are temperature, humidity, oxidation, light and pH.⁽⁵⁾

A solid pharmaceutical form is subject to the temperature external to the packaging and is more or less protected from relative humidity depending on the nature of its packaging. It may be more or less protected from oxidation by its packaging in the case of reaction with oxygen in the air, or by its formulation in the case of interaction with an oxidizing substance in the matrix. It is easy to protect the product from light if it is light-sensitive. Finally the pH, which plays a direct role in liquid formulations, also intervenes in the solid phase according to the acidic or basic nature of certain excipients, but as in the case of an oxidizing substance, it is possible to adjust the composition of the formulation to attenuate its effect. It is therefore temperature and relative humidity that principally act, in a systematic fashion, on the stability of the majority of solid pharmaceutical forms.

The joint action of temperature and of a factor representing the influence of water was demonstrated in 1977 by the tracking, in thin layer chromatography, of the decomposition of Nitrazepam diluted in microcrystalline cellulose.⁽⁶⁾ The inclusion of an exponential variation in the speed of degradation with relative humidity was taken up again by Waterman in 2007,⁽⁷⁾ with the addition of a term to the Arrhenius law (equations 3 and 4). The ASAPprime® software of the company FreeThink Technologies⁽⁸⁾ was constructed from this model. It is to be noted that the effect of humidity can be modelled by expressing the humidity factor differently.⁽⁹⁾

With:

k: reaction rate constant

A: pre-exponential factor (very little dependent on temperature)

Ea: activation energy of the reaction (in J.mol-1)

R: universal gas constant (8.314 J.mol-1.K-1)

T: temperature in Kelvin

B: humidity sensitivity constant

RH: relative humidity (%)

In order to subject the products studied to the desired relative humidity, the experimental plan was executed with unpackaged samples. The temperatures and relative humidities implemented may range from 40 °C to 90 °C and from 10 % to 90 %. Figure 1 represents graphically the conditions applied in an accelerated predictive stability study and the usual ICH conditions. Because of the diversity of the conditions to be implemented, relative humidity is generated by supersaturated saline solutions placed in watertight containers which also contain product samples and possibly a sensor that records temperature and relative humidity.

As in the case of liquids, conditions should be implemented in which the same reactions are observed for both temperature and relative humidity conditions (T/RH). To do this it is necessary:

• To target the same degradation rates for all T/RH conditions in order to observe the same reaction and to avoid chain reactions for the most severe conditions. Target degradation rates limited to 2 or 3 times the specification provide optimal conditions.

• To avoid any change in the solid form of the active principle studied as such or within a formulation. In effect, a change in polymorphic form or the formation of a hydrate modifies the physical structure of the active principle which no longer degrades according to the same kinetics because of a different activation energy or similarly if other degradation products are formed. In the presence of this type of phenomenon, the conditions in question must be eliminated whenexploiting the results, but if there is prior knowledge regarding the limits that should not be exceeded it is enough to reduce the range of the T/RH conditions applied when implementing the experimental plan.

3. From “open dish” studies to modelling a packaged formulation

The modified Arrhenius law allows simulation of the behavior of the active principle in the presence of constant relative humidity. Once formulated, this is exposed to an additional source of humidity associated with the water content of matrix excipients and with water possibly contributed by the manufacturing process. Under constant relative humidity an equilibrium is rapidly reached, but overly hjgh relative humidity can cause deliquescence as a result of one of the components starting to dissolve. As fortransformations of the solid state of the active principle, this critical relative humidity represents a limit that should not be exceeded in the experimental plan. The hygroscopicity of the product in relation to relative humidity can be determined by vapor sorption/desorption measurements which allow construction of a sorption isotherm as illustrated in Figure 2.

The packaging used is rarely totally impermeable to humidity except for glass bottles and double layer aluminum packaging. Once the active principle or the finished product is packaged, the relative humidity inside the packaging progresses to an equilibrium value depending on the hygroscopicity of components and the possible presence of a dehydrating agent. Moreover, the permeability of the packaging material causes an exchange of relative humidity between the outside and inside of the container as shown schematically in Figure 3. This permeability to water vapor (MVTR) is also dependent on the exchange surface area and the temperature.

The combination of kinetic calculations derived from the experimental plan in an open dish and thermodynamic calculations associated with changes in relative humidity in the packaging allows calculation of a degradation kinetics for a given condition of temperature and relative humidity according to the characteristics of the packaging. The use of statistical enhancement based on the Monte Carlo method allows construction of a prediction interval around the degradation kinetics calculated. The ASAPprime® software, whose operational principle is illustrated in Figure 4, includes the hygroscopicity data of the usual excipients and the permeability data of the main packaging materials, but it is also possible to enter your own values.⁽⁸⁾

ASAPprime® software has the benefit, in addition to access to validated calculations, of offering tools that assist modelling (design of the experimental plan, graphs of residues, graphs showing the influence of conditions or Ea and B parameters on modelling).

4. Specific features of predictive stability studies

4.1 Isoconversional principle

As not all chemical reactions are zero order, degradation kinetics are not necessarily linear. The use of an isoconversional method avoids taking account of kinetic equations by targeting the time necessary to obtain a reasonable level of degradation for each of the T/RH conditions (hence the term isooconversional).Targeting a degradation rate around the specification for all T/RH conditions allows consistent degradation kinetics to be obtained, that is to say without risk of initiating secondary reactions.^(7,10) Ideally the storage periods applied to each T/RH condition are distributed between the limit of quantification of the analytical procedure and 2 to 3 times the specification. This isoconversional principle is illustrated in Figure 5.

The model constructed with the data in Table 1 gives the following parameters for the Arrhenius equation:

• LnA: 30.01 ± 6.4
• Ea: 99.42 ± 18.7 kJ.mol-1
• B: 0.03 ± 0.1

with model adjustment coefficients of 0.997 for R2 and 0.987 for Q2.

The degradation rate as a function of time for a given condition of temperature and relative humidity was determined using the parameters of the modified Arrhenius equation (Figure 6). The prediction interval constructed from statistical enhancement is wide but it should be kept in mind that it represents an extrapolation to 1 year of values obtained over 14 days of aging. The expiration period to be selected corresponds to the intercept of the upper limit of prediction (green line) with the degradation rate represented by the specification (yellow line).

Using the model established in an open dish, and once the data relating to the composition of the formulation and to the initial tablet water content were integrated, the impact of different types of packaging was simulated in-silico. Table 2 presents the estimated shelf lives for different packaging.

In the event that several degradation products are present, a model should be constructed for each degradation product, and it is the degradation product that is least stable in terms of its specification, therefore with the shortest shelf life, that represents the shelf life to be taken into account for the product studied.

6. Fields of application of APS and regulatory admissibility

Accelerated predictive stabilitycan be used to address different specific cases and to support different points during the product life cycle. Thus they can be used for:

• Determining the retest dates of active principles and the shelf lives of pharmaceutical forms intended for clinical studies. It is recommended not to exceed a shelf life of 12 months, which generally proves sufficient to initiate a Phase I or Phase II clinical study. The monitoring of the clinical batch under ICH stability testing conditions and a match between the results obtained and the predicted values then allow the retest date or shelf life to be extended,
• Comparing the batches of active principle in order to evaluate the impact of a change in the synthesis process or of the amorphous phase level for a crystallized product,
• Comparing different formulations in order to rapidly select the most chemically stable,
• Evaluating the impact of a change of excipient supplier or a process change on the stability of the pharmaceutical form,
• Evaluating numerous types of packaging in-silico in order to select the most appropriate for product preservation and to justify, when a dehydrating agent is necessary, its type and the
• quantity necessary,
• Strengthening the scientific argument provided in MA dossiers, with regard to the previous points,
• Evaluating the impact of temperature excursions on product conformity.

These examples of applications show that accelerated predictive stability studies fall completely within the ‘Quality by Design’ approach described in the ICH Q8(R2) guideline on pharmaceutical development by providing a better understanding of product behavior and of its manufacturing process.⁽¹³⁾They also allow, with regard to the chemical stability of active principles and pharmaceutical forms, a risk assessment based on scientific knowledge as recommended by the guideline ICH Q9 on quality risk management.⁽¹⁴⁾ Because of this, these predictive studies represent an effective tool that can be used or mobilized throughout the product life cycle as described by ICH Q10.⁽¹⁵⁾

A survey published in 2020,⁽¹⁶⁾ conducted among manufacturers using accelerated predictivemethodologies, presents around twenty cases of studies that were incorporated in registration dossiers. While the proportion of studies accepted to support an initial shelf life is very large, the survey observes that the direct acceptability of accelerated predictive stability studies without requests for additional data is very dependent on the countries in which the dossiers were filed.

Conclusion

Accelerated predictive stability studies allow modelling of the chemical degradation of active principles and pharmaceutical forms which represents the main risk to patients. Although they do not allow the modelling of all the tests and trials in a monograph, studies have reported their use in modelling changes in tablet color and to a lesser extent dissolution testing. They can be used to rapidly obtain useful information to guide product development while requiring fewer material and human resources.

The use of predictive stability studies during pharmaceutical development therefore falls fully within the concepts of ‘Quality by Design’ and ‘Life Cycle Management’. Let us hope that the ICH guidelines on stability testing will soon change in order to suggest the inclusion of this type of study and to take full advantage of the qualitative benefits that they generate.