Practical Applications of QbD for a Parenteral Drug Product

This presentation addresses the application of Quality by Design principles to two common unit operations encountered in the manufacture of parenteral products. Examples will be described for 1) the application of mixing models to facilitate the scale-up of the API dissolution step, and 2) an approach for establishing a sterilization design space based on chemical kinetics and sterilization theory.

API Dissolution During Solution Compounding

In this example, mixing conditions to achieve complete dissolution of an API are dependent on several process variables, including API particle size, temperature, agitation rate, agitation time, and tank/agitator configuration.  The fluid dynamics of the mixing vessel are scale-dependent, but can be modeled to enable predicted mixing conditions on scale-up. The approach taken in this example was to develop a lab-scale mixing vessel that was geometrically similar to the production vessel.  The key aspect ratios of the production equipment (impeller diameter/tank diameter, liquid height/tank diameter, distance between impeller/tank diameter) were reproduced in a lab-scale mixer.  Based on fluid dynamic principles, maintaining a similar power per unit volume (P/V) during mixing at either scale will result in similar solid-liquid mass transfer coefficient and therefore similar mixing times to achieve dissolution. Determinations of P/V were made using computational fluid dynamic (CFD) modeling of the mixing systems.  Dissolution studies were performed in the lab-scale mixer to evaluate the combined influences of agitation rate and batch temperature on dissolution time, using worst-case API (a batch with particle size parameters near the maximum control limits).  Using CFD modeling to determine agitation rates that will achieve the same P/V in the commercial tank, along with a constant scaling factor statistically determined during development of the model for this tank geometry, predicted agitation rates were determined that would achieve complete dissolution within the same time interval as observed in lab-scale. The suitability of the predicted agitation rates was determined for one full-scale batch, intentionally manufactured at the lower limit of the temperature range, representing worst-case conditions for dissolution.  Successful dissolution within the target time interval served to confirm the model predictions and verify the minimum agitation rate and time for commercial production.

Terminal Sterilization

The molecule for this example is heat sensitive, and when exposed to the pharmacopoeial (overkill) sterilization conditions (15 minutes at 121 °C), the extent of degradation exceeds an acceptable impurity level. Therefore a temperature below 121°C was evaluated for the sterilization cycle. Both microbiological lethality and degradant formation are directly dependent on cumulative thermal exposure, and therefore sterilization conditions are well suited for the development of a design space. To establish the design space, sterilization temperature and exposure time were explored in terms of conditions that simultaneously provide 1) a minimum log₁₀ reduction of 8 (assuring sterility), and 2) maximum degradant formation according to the specified limit (assuring appropriate purity).

This approach to the establishment of a design space is unique in that it allows the use of first principles (chemical kinetics and sterilization theory) to define acceptable boundaries for process parameters.  While some experimentation is required (i.e., determination of degradation rate constants and sterilization D-value), these studies are scale-independent and can be conducted at the lab bench.  The experimentally determined constants are incorporated into theoretical equations that are used to define the boundaries of the design space.

The degradation rate constants were determined in development studies by traditional chemical kinetic experimentation utilizing drug product exposed to elevated temperatures in the range of sterilization conditions (above 100°C).  Rate constants were determined at worst-case conditions of pH and headspace oxygen content based on targeted in-process control limits, thus representing worst-case stability conditions within the formulation design space. The Arrhenius equation was then used to define a time/temperature profile that results in a pre-defined maximum limit of degradation.  For sterilization requirements, the D-value of a thermally resistant spore-former (Geobacillus stearothermophilus) was determined in the drug product solution. Based on sterilization theory, a time/temperature profile was derived that would result in an 8 log reduction of microorganisms.  Superposition of these two time/temperature profiles then defines the design space, shown in Figure 1. 

The design space definition includes the 95% confidence limits for degradation. Statistical considerations for the lethality input (log-reduction) were not applied since the lethality experiments (D value generation) were performed with highly heat-resistance spores (Geobacillus stearothermophilus) to reflect exaggerated conditions.

Figure 1.  Moist Heat Sterilization Design Space and Normal Operating Ranges