Mean Kinetic Temperature: What the Calculation Weights and What It Hides

MKT summarizes a product’s temperature-exposure history as a single effective or virtual temperature.

A mean kinetic temperature calculation gives higher temperatures greater weight than an arithmetic mean does.

Use this guide to work through the equation, choose the calculation window and prepare an excursion review. Start with the shipment temperature chart review, or explore the wider temperature monitoring section.

What the calculation weights

MKT integrates the time–temperature history using assumptions about chemical-degradation kinetics.

Disproportionate weighting of higher temperatures recognizes accelerated thermal degradation at those temperatures.

Long excursions at slightly elevated temperatures can be as impactful as, or more impactful than, short excursions at elevated temperatures.

Mean kinetic temperature calculation: equation and inputs

For equally spaced observations, use the following equation:

Tk = (ΔH/R) / {−ln[(exp(−ΔH/RT1) + exp(−ΔH/RT2) + … + exp(−ΔH/RTn))/n]}.

Read the inputs as follows:

In the USP public revision, the heat of activation is 83.144 kilojoules · mole−1 unless more accurate experimental information is available.

The universal gas constant is 8.3144 × 10−3 kj · mole−1 · K−1.

n is the total number of storage temperatures recorded during the observation period.

T1 is the temperature recorded during the first time period.

All temperatures in the equation are absolute temperatures in degrees Kelvin (K).

The logarithm is base e.

Work through the equation

Convert Celsius to kelvin using °C + 273.15.

Evaluate the exponential term for each temperature, average the terms, take the negative natural logarithm, and divide ΔH/R by that result.

Convert kelvin to Celsius using K - 273.15.

MKT can be calculated using all temperature data available during the observation period.

Every 15 min is an example of a frequent temperature measurement interval in the USP public revision.

Published calculation example

LogTag Analyzer uses a default activation energy of 83.144 KJ/mol.

For the example readings 12.3, 15.9, 16.2, 14.7 and 14.9 °C, LogTag’s guide calculates MKT as 14.9 °C using the default ΔH.

Use the published example as a calculation cross-check. Record the activation-energy setting beside the output in your own worksheet.

Equal intervals and unequal timestamps

When all time intervals are equal, the duration-weighted equation reduces to the usual equally spaced MKT equation.

Commercial data loggers record time points rather than time intervals.

Tong and Lock present a trapezoidal approximation for unequally spaced timepoint-temperature pairs.

Their derivation assumes Arrhenius degradation behavior and negligible temperature dependence of the prefactor.

Before applying the equal-interval equation, inspect the timestamps. For unequal timestamps, document the elapsed-time method used.

A refrigerator record with irregular sampling

The published refrigerator example in Tong and Lock has estimated MKT of 3.93 degrees Celsius.

The published refrigerator example has a naively calculated arithmetic mean of 3.37 degrees Celsius.

Reading intervals in the refrigerator example can be as short as 3 minutes.

Reading intervals in the refrigerator example can be as long as an hour.

Read these reported results together with their sampling context. Keep the timestamp series alongside the summary.

Choose the observation window deliberately

The time frame used to calculate MKT is information needed for excursion review.

For CCT excursions, USP recommends using 24 h to calculate MKT.

Using 52 weeks of data can skew an excursion evaluation when that period does not reflect the product’s storage time.

For a controlled cold temperature excursion, identify the event and record the start and end of the selected calculation window before calculating.

What the summary leaves for excursion review

MKT alone is not enough to assess a temperature excursion’s impact.

Excursion duration is information needed alongside MKT.

The excursion temperatures are information needed alongside MKT.

Each product excursion outside USP excursion limits must be evaluated for its effect on the final product.

Justifying MKT for distribution excursions requires confirming that the product’s stability-limiting characteristic follows zero-order or first-order kinetics over the encountered temperature range.

Degradation due to higher temperature is not reversible.

MKT may be inappropriate for products subject to phase change.

Biologics are a category for which MKT may not be suitable.

The label storage statement should be directly linked to demonstrated drug-product stability.

Where applicable, specific labeling instruction should be provided for drug products that cannot tolerate freezing.

Keep the product stability evidence and labeling beside the excursion record. For investigation planning, continue to packout failure investigation.

Temperature monitoring procedure and review sheet

The application of MKT should be described in a written procedure.

For controlled cold temperature review, each excursion should be considered a separate event.

A storage or transportation system that has repeated excursions should be considered a system out of control that needs to be corrected.

For CCT, excursion ranges, time, and MKT within allowances should be documented and can be reviewed for compliance and trending.

MKT must never substitute for proper temperature control or excursion investigation.

Use this temperature monitoring sheet as a review aid. Copy the field labels into your procedure and complete them for the record under review.

Table: scroll horizontally if needed to see every column.

Record	Complete for this review
Temperature file and identity	File reference; logger or record identifier; product and lot
Observation window	Start; end; storage or transport context; selection rationale
Sampling	Timestamps; interval consistency; gaps to resolve
Calculation inputs	Temperature unit; activation energy and its source; gas constant; method or software
Calculation output	MKT; output unit; calculation window
Excursion detail	Event temperatures; duration; event reference
Product evaluation	Label storage statement; stability evidence; evaluation reference
Review handoff	Reviewer; disposition reference; corrective action reference

Before closing the review, compare the completed sheet with the original temperature chart and the documented evaluation. Keep the calculation and the event review together.

Sources

• United States Pharmacopeia — public chapter revision on the use of mean kinetic temperature to evaluate temperature excursions.
• United States Pharmacopeia — APEC training on mean kinetic temperature.
• Tong and Lock — Mean Kinetic Temperature for Unequally Spaced Data, ASA proceedings.
• NIST — SI Units: Temperature.
• LogTag — Analyzer user guide, Mean Kinetic Temperature.
• Tecnosoft — TS Manager manual, Mean Kinetic Temperature.
• EMA / ICH — Stability Testing of New Drug Substances and Products.
• ABB — Mean Kinetic Temperature best-practice guide.
• Vaisala — Mean Kinetic Temperature application note.