Measuremernt and recording of temperatures is vital to the storage of perishable goods such as pharmaceuticals, but there's more than one way to record an average

Good warehousing and distribution practice requires that warehouse temperatures are monitored and controlled and that appropriate actions are taken if temperatures exceed the specified storage conditions.

Those actions are the calculation of the mean kinetic temperature as a verification of exceeded storage conditions and if conditions are exceeded a second calculation to determine the reduction of shelf life with the help of the Arrhenius equation.

With the latest version of the data evaluation software from Elpro-Buchs, Elprolog, it is now possible to do both calculations, the mean kinetic temperature and ageing.

Mean kinetic temperature (MKT).

The ICH stability testing guidelines define mean kinetic temperature (MKT) as 'a single derived temperature which, if maintained over a defined period, would afford the same thermal challenge to a pharmaceutical product as would have been experienced over a range of both higher and lower temperatures for an equivalent defined period'.

In other words, MKT is a calculated, fixed temperature that simulates the effects of temperature variations over a period of time.

It expresses the cumulative thermal stress experienced by a product at varying temperatures during storage and distribution.

Mean kinetic temperature refers to a datum, which can be calculated from a series of temperatures.

It differs from other means (such as a simple numerical average or arithmetic mean) in that higher temperatures are given greater weight in computing the average.

This weighting is determined by a geometric transformation, the natural logarithm of the temperature number.

Disproportionate weighting of higher temperature in a temperature series according to the MKT recognises the accelerated rate of thermal degradation of materials at these higher temperatures.

MKT accommodates this non-linear effect of temperature.

The formula for MKT is: TK[K] = (-DH / R) / ln {(SUM (exp (-DH / (R * Tn)))) / n} where DH is the activation energy, R is the universal gas constant (0.0083144 kJ/molK), T is the temperature in degrees K, n is the total number of (equal) time periods over which data are collected, ln is the natural log and exp is the natural log base.

SUM is the mathematical function of building up a total over n periods, starting with period 1.

The practical application of this equation is less complex than it first appears.

For a huge range of pharmaceutics DH is within the range of 42 - 125 kJ/mol.

In cases where an exact knowledge of the activation energy is important, it is possible to determine this factor with the help of a differential scanning calorimetry (DSC) analysis.

T1 is the average temperature recorded over the first time period and Tn is the average temperature recorded over the nth time period.

Effect and calculation example from Elprolog for kinetic and arithmetic mean temperatures.

As an example of how the MKT calculation will affect an expressed mean for a calculation (important for the long term storage of critical drugs and chemicals), here is an illustration.

If the temperature is constant for a period of time, but is 'out of specs' for some moments of time, there will be a difference in the calculated arithmetic mean (the sum of all of the measurements divided by the number of measurements - a simple mean) and the kinetic mean.

Mean kinetic temperature: value = 9.4C Arithmetic mean temperature: value = 6.3C Conclusion.

Depending on temperature conditions the effect may be dramatic, it is clear that the MKT method weights the higher temperatures in a series more than the lower temperatures. This is a more appropriate way of calculating an overall thermal effect because of the acceleration of thermally driven processes of degradation at higher temperatures.

Ageing.

This calculation is used to determine the shelf life reduction due to incorrect storage conditions of a drug sub-stance or drug product.

The formula for this calculation is based on the Arrhenius2 life-stress model.

Example.

Due to the incorrect treatment during the unloading of a pharmaceutical product, its shelf life has been dramatically reduced from ten days down to 4.3 days.