Mean Kinetic Temperature Background
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 based on the calculation
of the mean kinetic temperature as a verification of exceeded storage conditions.
The International Conference on Harmonisation of Technical Requirements
for Registration of Pharmaceuticals for Human Use (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 time periods, starting with time period
1.
The practical application of the equation is less
complex than it first appears. For a huge range of pharmaceuticals 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.
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 spec' 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 = 9.4°C
Arithmetic mean temperature: value = 6.3°C
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. For ageing a secondary calculation is used
to determine the shelf life reduction due to incorrect storage conditions of
a drug substance or drug product. The formula for this calculation is based
on the Arrhenius2 life-stress model. This is not included on RF500. 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.
Lethality
Lethality equivalent time is calculated using the formula:
LET
= (SUM(10^((Tn-Tref)/Z)))*Tinc
Tn is a temperature
reading in Celcius
Tref is the reference temperature
in Celsius
Z is a constant just known as the 'Z value'
Tinc is the reading time increment in seconds
Tref and Z are entered on task setup form.
Standard lethality (Fo) uses Tref = 121.1°C and Z =
10
If the channel does not read in temperature then the result will
be shown as ‘N/A’.
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