Design Space Development for Lyophilization Using DOE and Process Modeling - Develop a relevant design space without full factorial DoE. - BioPharm International
Establishment of a Mechanistic Model and Expansion of Primary Drying Design Space
Figure 8. Comparison of the measured versus predicted product temperature profiles for the target cycle
Having established an initial design space for primary drying, the next step was to use a mechanistic process model to expand
the primary design space beyond the initially tested experimental conditions. The general methodology used for this purpose
is depicted in Figure 7. The model used in this study was developed by Sane, et al.13 The necessary inputs to the model are the vial-shelf heat-transfer coefficients, cake resistance as a function of dry layer,
vacuum pump throughput, condenser capacity, batch size, fill volume, shelf temperature profile, and chamber pressure profile.
The outputs that could be obtained are product temperature, condenser temperature, sublimation rate, and nitrogen bleed-valve
flowrate. Vial heat transfer coefficients were obtained by performing closed vial experiments, in which dynamic response of
product temperature to changes in shelf temperature was measured at different pressures.13 Cake resistance as a function of dry layer thickness was obtained by performing independent sublimation rate measurements.14,15
Figure 9. Comparison of the measured versus predicted product temperature profiles for the minimum sublimation rate case
The next step was to fit the model parameters to yield the product temperature profile for the target/initial lyophilization
cycles. This was done by further tuning the cake resistance parameters and fitting the model predictions to the experimental
data at target lyophilization cycle conditions. As seen in Figure 8, the predicted product temperature profile compared well
with the experimental thermocouple measurements during the sublimation phase. This was important because the product temperature
during primary drying is critical to ensure no meltback or collapse during the cycle. Toward the end of primary drying, experimental
product temperature profiles exceeded the shelf temperature while the model profile ramped up asymptomatically to the shelf
temperature setpoint. This difference is mainly because of radiative effects from the lyophilizer walls and door which contribute
to heating the vial beyond the temperature of the shelf. For practical purposes, based on model predictions it was assumed
that primary drying was complete if the product temperature was within ± 2 °C of the shelf temperature. Based on this criterion,
the primary drying duration predicted by the model was comparable to that for the slowest drying vial. After the cake resistance
parameters were tuned to fit the temperature profile for the target lyophilization cycle, they were kept constant during subsequent
simulations for different lyophilization cycle conditions.
Figure 10. Comparison of the measured versus predicted product temperature profile for the maximum product temperature case
The next step was to use the model to identify experimental conditions outside the initial primary drying design space that
would yield acceptable product quality. During this exercise, the primary drying duration was kept the same as the target
cycle while the shelf temperature and chamber pressure were allowed to vary. The idea was to find two extreme conditions:
1) a condition of low shelf temperature and low chamber pressure that would result in the lower extreme in sublimation rate
while ensuring that the primary drying is completed within the allotted time and 2) a condition of high shelf temperature
and high chamber pressure that would result in the upper extreme in sublimation rate and product temperature without causing
product collapse. Using the model, one can come up with a series of conditions that satisfy these two criteria in a matter
of minutes. Only a few of those are of practical relevance. In this particular case, we selected the primary drying parameters
of –18 °C and 70 mTorr for the lower extreme; the model predicted that under these conditions, the product temperature, would
barely reach the shelf temperature indicating that the primary drying duration was just adequate. For the upper extreme, we
selected –2 °C and 220 mTorr; the model predicted that the product temperature during sublimation phase would be –18 °C, which
is slightly below the collapse temperature for the product formulation. Based on our experience with manufacturing-scale equipment,
these lyophilization conditions bracketed a great majority of manufacturing situations that we anticipated with this type
of product configuration. We tested these two input conditions experimentally. The comparison between the predicted and experimental
product temperature profiles was good and is shown in Figure 9 and Figure 10. The product attributes for both these runs were
acceptable (Table 5).
Table 5. Results of experiments for expanded design space for primary drying
Thus, using a combination of process modeling and two targeted experiments, the design space could be significantly expanded
as illustrated in Figure 11 (entire blue and tan shaded region). Even though input condition A in Figure 11 was not determined
experimentally, we know from understanding the lyophilization process (and supported by a mechanistic model) that this condition
produces product temperatures lower than those in Experiment 8 because it has the same chamber pressure but a lower shelf
temperature, and it produces a higher sublimation rate than Experiment 9 because it has the same shelf temperature but higher
chamber pressure. As a result, the entire region bounded by points 8, A, 9, 6, and 5 in Figure 11 can be claimed as the final
primary drying design space.
