Pharmaceutical products have an expiration date based on stability studies conducted under controlled temperature and humidity conditions which establishes the product’s recommended transport and storage environmental conditions [1, 2]. Pharmaceutical products are to be stored as per the manufacturer’s recommended storage conditions described in the label so that products are of acceptable quality throughout its established shelf-life.
However for public health programs through donor agencies (excluding cold-chain products), pharmaceutical products labeled with the usual storage temperatures of 25 °C or 30 °C [3] are often transported in non-refrigerated containers, potentially passing through different climate zones ranging from very cold to very hot temperatures (commonly found in Africa, portions of Asia and South America). Once in country, the products are purportedly stored under good storage conditions at temperatures at or below the required storage temperature. The product may be transferred thorough distribution channels and supplied in non-temperature regulated vehicles to health centers and hospitals where it may be stored for varying periods before eventually being supplied to the patient. Although guidance is available on good distribution practices [4, 5], the temperature and humidity values reached during storage and transportation routes can vary depending on the route, weather conditions and transport vehicles [6, 7] due to limited ability to monitor and control in limited resource settings. For example, an evaluation of pharmaceutical shipments sent by ocean from UNICEF in Copenhagen, Denmark to (a) Lagos, Nigeria, to (b) Mombasa, Kenya and then by land to Kampala, Uganda, and (c) to Bangkok, Thailand of various medicines stored in multiple locations in transport showed temperatures from − 3.5 °C to 42.4 °C and relative humidity ranges from 20 to 88% [8].
Devices are available to accompany shipments in order to monitor for temperature excursions (period of exposure to temperatures exceeding the designated range for the product [9]) during transport and storage [10, 11]. Although the data from these monitors indicate whether an excursion has occurred, the severity of the excursion and the risk to the product are likely to be less understood and may need to be assessed. Furthermore, the true temperature experienced by the product may be difficult to accurately determine (potentially complicating assessments) depending on the exact placement of the data logger, type of packaging, and the equilibration rate of the product’s temperature relative to its surroundings over brief periods of time (i.e., hours). Loss of product integrity (i.e., loss of potency, increase of degradation products) due to temperature excursions could increase risk or decrease benefit to the patient if used [12]; in contrast subsequent removal of product from the supply chain may lead to stock outs and wastage that present their own risks. Also, significant financial loss is incurred when lots are not recommended for distribution after experiencing a temperature excursion. From a regulatory perspective, the manufacturer is responsible for addressing temperature excursions when these occur. However, the information on the effects of temporary excursions are not always addressed in the labeling information and retrieving information from each manufacturer is complicated by prolonged response times, lack of available data, and the inability of some manufacturers to release the information.
To help procurers address these complications, modeling results for various temperature excursion scenarios that estimate the loss of shelf-life to pharmaceuticals and the potential impact to the supply chain are presented based on a key product quality attribute as assessed by mean kinetic temperature evaluations based on the Arrhenius equation for reaction kinetics. This assessment provides some guidance to public health programs that are required to manage the transport and storage logistics of various life-saving commodities, and that often are required to make risk-based decisions on product usage or removal for large inventories that may have experienced adverse environmental conditions.
Assessment of product quality attributes to establish the model framework
Important product quality attributes that can be influenced by temperature excursions during transport and storage are potency (loss of assay), dissolution (change in API release profile), impurities (increase in impurities or degradation products), and microbial contamination (discoloration due to microbial growth) [2, 12]. The overall consequence of the occurrence is that changes to these attributes may impact product degradation and microbial growth, which in turn may impact overall product therapeutic effectiveness and shelf-life.
Generally, most pharmaceutical forms used in public health programs are solid dosage forms. These dosages are a mixture of active pharmaceutical ingredients and a variety of other excipients either in a compressed tablet or capsule. The modelling assessment for this work is therefore focused on solid dosages, where the amount of API (assay) is the key parameter used in the calculations. Assay has been focused on for these simulations because the minimum assay specification of 90% through the end of the shelf-life is very common across pharmaceutical products. For other pharmaceutical quality parameters previously mentioned, the range of product specifications was considered more difficult to generalize and was not pursued here. Any one of these parameters may be a key driving force behind a certain product’s shelf-life. Truly knowing this relies on the manufacturer’s expertise, which as stated before may be difficult to obtain under certain circumstances and motivated this assessment. Packaging is assumed not be significantly affected by humidity. Recommended storage conditions for the products is assumed to be either 25 °C or 30 °C (depending on the specific scenario), due to the prominence of these storage conditions in finished products [3] and that WHO prequalified products [13] are observed that adhere to either of these conditions to provide coverage across climatic zones II and IV (a and b) [1, 2].
Review of mean kinetic temperature and the Arrhenius equation
Temperature excursions can be defined as environmental temperatures to which a product may be exposed during transport or long-term storage that exceed the manufacturer’s label claim conditions for the product. A common storage condition for many pharmaceuticals is “controlled room temperature;” the USP describes “controlled room temperature” as a temperature that includes the typical environment of 20 °C to 25 °C (68 °F to 77 °F), where excursions are allowed between 15 °C and 30 °C (59 °F and 86 °F) provided that the mean kinetic temperature (Tk) remains at or below 25 °C [14]. Furthermore (provided the Tk does not surpass 25 °C), the USP recommends that excursions up to 40 °C occur for no more than 24 h without consultation with the manufacturer [14].
Mean kinetic temperature (Tk) is a calculated temperature where the level of degradation over a certain time period is the same as the total of separate degradations that could result from a series of different temperatures throughout the same total time period, respectively [15]. When measured temperatures experienced by a sample are available for a series of time periods (i.e., for example with a regular periodicity of hours or days), Tk can be calculated using Eq. 1 below [15,16,17], where Ea is the
$${T}_k=\frac{E_a/R}{-\mathit{\ln}\left(\frac{e^{\left(-{E}_a/R{T}_1\right)}+{e}^{\left(-{E}_a/R{T}_2\right)}+\dots +{e}^{\left(-{E}_a/R{T}_n\right)}}{n}\right)}$$
(1)
activation energy, R is the universal gas constant, n is the number of time points in the overall series, and Tn is the absolute temperature (K) for each of the time periods 1 through n, respectively.
The calculation of Tk is based on the application of the Arrhenius model for reaction kinetics. Focusing on the degradation of active pharmaceutical ingredient B, the degradation of B can be represented with the generic reaction shown in Eq. 2, and the rate of reaction with respect to reactant B is provided in Eq. 3, where [B] is the reactant concentration, k is the rate constant for the reaction, and
$$\mathrm{B}\to \mathrm{degradation}\ \mathrm{products}$$
$$\frac{-d\left[B\right]}{dt}=k{\left[B\right]}^{\beta }$$
(3)
β is the reaction order for reactant B [18].
The rate constant (k) is an important parameter to characterize and can be determined by measuring reactant concentrations as a function of time. The rate constant (k) can be modeled with the Arrhenius equation shown in Eq. 4, where A is the frequency factor. Key features of the Arrhenius
$$k={Ae}^{-{E}_a/ RT}$$
(4)
equation are that k increases exponentially with temperature, where Ea and A are modeled as constants [18]. For a given reaction, Ea and A can be determined from the slope and intercept, respectively, of the linearized form of the Arrhenius equation, Eq. (5), by plotting experimentally
$$\ln \left(\mathrm{k}\right)=\ln \left(\mathrm{A}\right)-\left({\mathrm{E}}_{\mathrm{a}}/\mathrm{RT}\right)$$
(5)
determined k’s as a function of absolute temperature. With Ea and A, the rate constant (k) can be calculated at a specific temperature and subsequently used to determine the rate of reaction [19]. Basically, the Arrhenius equation demonstrates that a rate of reaction will increase exponentially with temperature, rather than linearly. Correspondingly, the mean kinetic temperature is important to understand because it provides the effective isothermal temperature experienced by the product that accounts for the Arrhenius-based effect of temperature excursions during storage [15].