The concept of a shelf life for a product is now quite widely accepted in modern life. They can be found on a huge number of consumables, from foods and cosmetics to slightly more surprising items like batteries and sterile products. For some items, there can be obvious cues as to when a product is no longer suitable for use, irrespective of their shelf life, such as when foods have spoiled. For other products their continued suitability for use may not be immediately apparent to human senses and we rely more on a stated date until which they are considered safe to use. Most pharmaceutical products fall into this latter category, where it can be hard to determine if they are suitable for use by sight or smell. The construction of shelf lives is an involved process that relies on the chemical analysis of products and statistical modelling (Capen et al, 2012) but ultimately relates to how fast a product degrades under expected conditions. The following calculations will run through a highly simplified scenario to demonstrate how a product changes over time and how this relates to its shelf life.
For simplicity, the following calculations will not consider variations of drug concentrations within a batch, or statistical variations in assay results.
Consider a batch of tablets where each contain 10 mg of their active drug X. X undergoes zero order decay over time at constant temperature, ie a constant rate of loss of the active drug.
QUESTION 1
What is the rate (in micrograms per day) that a tablet will lose active ingredient, as it degrades?
By general convention the shelf life is usually set as what is known as T90, which is to say the time it takes for the amount of active drug in a product to fall to 90% of its original value (Aulton and Taylor, 2013).
QUESTION 2
Using the data in Table 1, calculate the shelf life of these drug X tablets.
Table 1. Assay of drug X per tablet (mg)
| Time after manufacture (days) | Amount of drug X per tablet (mg) |
|---|---|
| 0 | 10 |
| 30 | 9.973 |
| 90 | 9.919 |
| 200 | 9.820 |
The shelf life also depends upon the storage conditions. The full equations used in practice contain allowances for temperature, which is governed by the temperature coefficient rate constant value (Q10). This is the change in decomposition produced by a 10 degree temperature change (either centigrade or Kelvin) (Aulton and Taylor, 2013). In pharmaceutical terms, the Q10 is usually in the range of a 2–3 fold change in the rate of decomposition for a 10 degree temperature change: a 10 degree increase in temperature doubles to triples the rate of drug loss, a 10 degree reduction in temperature reduces it to 1/2 or 1/3.
QUESTION 3
If the drug X tablets have a Q10 value of 3 and they are stored in a hot room 10 degrees above the manufacturer rated storage temperature, how long will they last before they reach T90 and are unsuitable for use?
While it is not considered to be good practice (or covered by the licensing) to use medicines that have passed their expiration date, it can be seen from above that expired medications do still contain significant amounts of active ingredients, so it should be expected that they are able to produce effects right up until the expiration date, provided that they are stored appropriately.
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