Developing an understanding of the stability of drug substances and drug products is a key activity carried out during the development life cycle of pharmaceutical products. These are carried out in order to obtain information on how the properties and quality of drug products and substances will behave over time, under specified environmental conditions. As performing stability studies is a key activity in a pharmaceutical laboratory, this article is the first of an ongoing series on the topic of drug and chemical stability.
It is well known that changes in temperature influence the rate of chemical reactions in an exponential fashion according to the Arrhenius equation:
Rate constant (k) = Ae-E/Rt
Where:
A = Arrhenius Factor
E = Activation Energy
R = Universal Gas Constant (8.314 J/°K mol)
t = Temperature
Mean Kinetic Temperature (MKT) is a concept that takes into account the exponential effect of temperature on the rates of chemical reactions when evaluating the effect of changes in temperature on the stability of pharmaceutical products. Alternatively, MKT can be considered as a single calculated temperature that simulates the thermal effects of temperature fluctuations over time.
The Mean Kinetic Temperature can be expressed in the following equation which is derived from the Arrhenius equation.
Where n = total number temperature sampling points. This assumes that the time intervals between each sampling point are equal, otherwise n should be replaced by T1 +T2 + Tn. Where T1,T2, Tn are the individuals time intervals.
At first sight calculating the mean kinetic temperature may seem a complex process. However, an average activation energy of 83.144 KJ/mol can be used unless compound specific data is available (this value comes from USP general chapter <1150>).
The ratio E/R is therefore 10000.09622 °K-1 (or 10000 °K-1, as the tolerance in the temperature specification is less than 0.1%). This result can then be divided by the temperature tn to yield a factor fn for each sampling time point n, thus,
After which the arithmetic mean of the individual factors for all of the time points is calculated (Fn =Σfn/n). The MKT in °K can then be calculated
The MKT can then be converted into °C by subtracting 273.1.
As an example that’s look at a typical country in climatic zone II where it is recommended that long term stability testing is carried out at 25 °C and 60 %RH, whereas, the storage conditions may vary between 15 and 30 °C. The following table shows the mean kinetic temperature for these two different temperature time distributions.
This shows that a MKT of 25.1 °C is equivalent to long term stability testing at 25 ± 2 °C, which is a good model for storing products in a warehouse or pharmacy between 15 and 30 °C which is equal to a MKT of 25.2 °C.
The use of mean kinetic temperature provides a method of calculating a single temperature which is representative of the effects on chemical reactions of varying temperature over a period of time. In addition to providing a model for stability studies on chemical products can also be used for other scientific and regulatory purposes, such as estimating the effects of temperature excursions on the quality and integrity of products.
