# Shelf Life Calculation of Drug Product

As per FDA,

ICH Q1E principles will help in the calculation of shelf life. Data from the three ANDA submission batches (i.e., 6 months), accelerated data meeting all criteria (without significant change per ICH Q1A(R2)), and 12 months long term data without variability will not need statistical evaluation, and with appropriate post approval stability commitments, can be used to support extrapolation to a 24 months shelf life.

If there is a significant change in the accelerated data, ICH Q1E, Appendix A, provides more details regarding when intermediate condition stability data are recommended.

The concept of accelerated stability testing is based upon the Arrhenius equation:

Where,

k = the reaction rate constant of any order,

R = the gas constant (1.987 calories degree^-1 mole^-1),

A = the frequency factor,

Ea = the activation energy and

T = the absolute temperature.

This equation describe the relationship between storage temperatures and degradation rate. Using Arrhenius equation, projection of stability from the degradation rates observed at high temperatures for some degradation processes can be determined.

• When the activation energy is known, the degradation rate at low temperatures may be projected from those observed at “stress” temperatures
• The stress tests used in the current International Conference on Harmonization (ICH) guideline (e.g., 40% for products to be stored at controlled room temperature) were developed from a model that assumes energy of activation of about 83 kJ per mole.

According to Arrhenius, for every 10°C rise in temperature, the speed of reaction increases about 2-3 times.

Estimation of k value

• The reaction is conducted at several temperatures.
• Concentration of reactants is determined (log (a-x).
• Appropriate graphs are drawn for the kinetic data.
• Data is processed for all the orders.
• The order of the reaction is identified.
• From the slopes of the lines, k values are calculated for all temperatures.

By using Arrhenius relationship, Log k values are plotted against reciprocal of absolute temperature. Extrapolate the straight line to room temperature (k25) and read the log k value on y-axis.

With substitution of the k26 value in the equation, the shelf life of the product is calculated:

t90=2.303/𝑘 log100/90

Shelf life is defined as the time necessary for the drug to decay to 90% of its original concentration.

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