Mean Kinetic Relative Humidity: A New Concept for Assessing the Impact of Variable Relative Humidity on Pharmaceuticals - Pharmaceutical Technology

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Mean Kinetic Relative Humidity: A New Concept for Assessing the Impact of Variable Relative Humidity on Pharmaceuticals
This article introduces the concept of "mean kinetic relative humidity" (MKRH) for evaluating the impact of humidity variability on the stability of solid-state pharmaceuticals analogously to the way mean kinetic temperature (MKT) is used for assessing the impact of temperature variability.


Pharmaceutical Technology
Volume 36, Issue 11, pp. 52-57

Systems with both variable temperature and variable relative humidity


Table I: Hypothetical scenarios for systems with both temperature and relative-humidity variability.
For systems that experience both temperature and relative-humidity variability, the calculations become more complex, but still can be dealt with by MKT and MKRH approaches. To illustrate one complicating factor, two similar, hypothetical scenarios are considered. In both scenarios, the same hypothetical solid-state pharmaceutical product is exposed to identical temperatures and relative humidity conditions, but in Scenario 1, the high temperature coincides with high relative humidity, and in Scenario 2, the high temperature coincides with low relative humidity, as shown in Table I.




As a consequence of the exponential nature of the humidity-corrected Arrhenius equation, Scenario 1 is more stressful to the product than Scenario 2. For instance, if the hypothetical product had an Ea of 120 KJ·mol-1 and a B term of 0.04 (see later for a discussion on average typical values for Ea and B), Scenario 1 would result in three-fold more degradation than in Scenario 2, and yet both scenarios have identical average temperature and humidity values (i.e., identical MKT, MKRH, arithmetic mean temperature, and arithmetic mean humidity). This illustrates how, in situations in which both temperature and humidity are varying, it can be misleading to calculate the MKT or MKRH in isolation of the other. In order to express situations with both varying temperature and humidity as a single, constant temperature and humidity condition, it is first important to recognize that there is a continuum of constant temperature and humidity conditions that would result in the same amount of degradation as the varying conditions, because any increase in the constant "average" temperature can be compensated by a decrease in the constant "average" relative humidity. Any temperature can be chosen, therefore, within the variable temperature range, and a corresponding MKRH can be calculated using Equation 6:

where MKRH = mean kinetic relative humidity (%) calculated for a given temperature, Tchoice, Tchoice = a chosen constant temperature (K), T 1 to T n = the variable temperature (K) measured at constant intervals, RH 1 to RH n = the variable relative humidity (%) measured at constant intervals, and n = the number of temperature and relative humidity measurements.




Alternatively, any relative humidity can be chosen (within the variable relative humidity range), and a corresponding MKT can be calculated using Equation 7:

where MKT = mean kinetic temperature (K) calculated for a given relative humidity, RHchoice, and RHchoice = a chosen constant relative humidity (%).


Figure 1: The solid lines represent the temperature-relative humidity combinations that are calculated to result in the same amount of degradation as the variable temperature and relative humidity in Scenarios 1 and 2. These lines were calculated for a product with an activation energy (Ea) of 120 KJ·mol-1 and a B term of 0.04, which represent average values for solid-state pharmaceutical products. (ALL FIGURES ARE COURTESY OF THE AUTHOR)
Despite their apparent complexity, these equations are relatively easy to apply using spreadsheet software. One potential problem with this approach is that there is a degree of arbitrariness when choosing Tchoice (or RHchoice). If this approach is used, then the use of the MKT calculated without consideration of the variable relative humidity (e.g., according to USP <1150>) should be a good choice for Tchoice in most situations, and the associated MKRH can be calculated using Equation 7 (4). Similarly, the use of the MKRH calculated without consideration of the variable temperature should be a good choice for RHchoice, and the associated MKT can be calculated using Equation 7. Figure 1 shows the MKT and MKRH combinations calculated for Scenario 1 and Scenario 2 using this 'combined' approach to temperature and relative humidity variations. As shown in Figure 1, the use of MKT and MKRH calculated in isolation of each other overestimates the degradation for Scenario 2 but underestimates the degradation for Scenario 1, and the use of arithmetic mean temperature and humidity significantly underestimates the degradation for Scenario 1 and even underestimates Scenario 2.


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