(68a) 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