Design Space Development for Lyophilization Using DOE and Process Modeling

ABSTRACT

In the Quality by Design framework, there is a significant emphasis on the robust characterization of manufacturing processes and prospectively identifying manufacturing design space that ensures product quality. In this article, we discuss an approach that leverages risk assessments, design of experiments, and mechanistic modeling of unit operations to establish a design space that is relevant for manufacturing. We present an overview of our methodology and its application to lyophilization process characterization for a monoclonal antibody formulation.

Lyophilization is a drying process in which a formulation containing the active pharmaceutical ingredient of interest is frozen at low temperatures (well below 0 °C) and water is then sublimed by subjecting it to low pressure. Removal of water in this manner preserves the physical and biochemical attributes of the product, thus resulting in good long-term stability. In a typical lyophilization process, the drying consists of a primary drying step, in which low pressure provides the driving force for frozen water in the product to start subliming; and a secondary drying step to remove any residual adsorbed water by desorption. Figure 1 shows a schematic of a lyophilizer with three main components—the drying chamber in which vials are heated or cooled; the vacuum pump, which provides low pressure in the chamber; and a condenser, which traps water vapor leaving the vials.

Genentech, Inc.

The Quality by Design (QbD) philosophy is increasingly being adopted in the pharmaceutical and biopharmaceutical industries.^1,2 From a manufacturing perspective, this translates into leveraging a sound, scientific understanding of unit operations to design a manufacturing process with prospectively defined multivariate parameter ranges that produce acceptable product quality attributes. In the QbD framework, the multidimensional combination and interaction of input variables that have been demonstrated to provide assurance of quality is termed the design space. Approaches for identifying the design space in the pharmaceutical industry that are discussed in the scientific literature or at conferences generally rely on statistical design of experiments (DOE), which can be resource intensive.^3–5 In cases where the number of input variables is large, performing a full-blown statistical DOE may simply be impractical.

Figure 1. Schematic of a lyophilization unit operation

In this article, we present a methodology in which a combination of a statistical DOE and a mechanistic mathematical model was used to arrive at larger and practically relevant design space with fewer experiments than a full factorial DOE. Figure 2 presents a flowchart illustrating our approach to developing a design space for lyophilization.

Figure 2. Methodology for developing a design and excursion space for lyophilization. Details of the use of the model to expand the design space are shown in Figure 7.

In the subsequent sections, we will further illustrate some of the steps in this methodology using a case study for lyophilization of a monoclonal antibody (MAb).

Figure 3. Freeze-drying microscopy of a model antibody formulation

DESIGN SPACE DEVELOPMENT: A CASE STUDY

Thermal Characterization and Initial Lyophilization Development

The MAb discussed in this case study was formulated in a solution containing a buffer, a sugar lyoprotectant, and a surfactant. To understand the thermal characteristics of this formulation, we performed freeze-drying microscopy experiments.⁶ The collapse temperature was determined to be –14 °C (Figure 3), suggesting that product temperature during primary drying must be maintained well below –14 °C.

Table 1. Initial/target lyophilization cycle for monoclonal antibody X

During the early process development phase for this molecule, an initial lyophilization cycle (Table 1) was implemented based on prior lyophilization experience with similar products and literature knowledge.^7–9 Briefly, the approach consisted of experiments to accomplish primary drying in a reasonable duration while maintaining product temperature well below the collapse temperature.

Figure 4. Process inputs and outputs for lyophilization design space development

Risk Assessments for the Lyophilization Unit Operation

The process inputs and outputs for lyophilization generally are well known and are shown in Figure 4.^7–9 To identify the parameters that must be characterized, we used the risk ranking tool depicted in Figure 5.¹⁰ The main and interaction effect scores for each parameter were assigned based on a mechanistic understanding of the lyophilization process and experience with products and equipment. The overall severity score was then used to decide the nature of characterization for the parameter.

Figure 5. Risk ranking and filtering tool (CQA = critical quality attribute)

Pilot-Scale Lyophilization Characterization

This section addresses the development of a design space at the pilot scale for lyophilization using a DOE approach.^11,12 All pilot-scale lyophilization runs were performed using a mixed load of active and placebo material in a BOC Edwards (IMA, Tonawanda, NY) lyophilizer with 2 m² shelf area. Thermocouples were used to monitor the temperature profile of the material during the cycle. For selected runs, the sublimation rate was determined by sealing selected vials with stoppers during the course of primary drying and measuring the weight loss as a function of time.

Table 2. Design of experiments strategy for lyophilization process characterization

Based on the outcome of the risk assessment discussed in the previous section, it was determined that the following parameters must be characterized: primary drying temperature, secondary drying temperature and time, chamber pressure, and freeze ramp rate. The approach to the DOE (Table 2) was as follows: 1) Evaluate the main effect of the freeze ramp rate. The first two experiments examined the effect of varying the freeze ramp rate on product temperature, sublimation rates, and moisture content. As shown in Table 3, no significant difference in product attributes was found among the different freezing rates. 2) Because freeze ramp rate did not impact product attributes, this parameter was excluded from subsequent characterization studies and multivariate characterization was performed on the primary drying temperature, the secondary drying temperature and time, and the chamber pressure. It should be noted that if a main effect of the freeze ramp rate was seen, this would have been included as a factor in the multivariate studies. In all runs, primary and secondary drying times were kept the same as the initial target cycle (Table 1).

Table 3. Freeze ramp rate study and results

Experiments 3–7 provided a half factorial experimental design around primary drying temperature, secondary drying temperature, and chamber pressure. The results of this multivariate DOE are shown in Table 4. The low and high extremes tested for primary drying temperature, secondary drying temperature, and chamber pressure were –11 °C to 1 °C, 15 °C to 25 °C, and 70 to 140 mTorr, respectively.

Table 4. Results of DOE with primary and secondary drying parameters

Run #5, with elevated temperature and pressure, saw an increase in sublimation rate (+34%) and average product temperature (+15%) relative to the target cycle. In contrast, Run #4, with both primary drying parameters lowered, saw a decrease in sublimation rate (–25%) and average product temperature (–16%), compared with the target cycle. Both Run #3 (–, +, +) and Run #6 (+, –, +) exhibited similar average product temperatures and comparable drying rates. All cycles produced a solid off-white-colored cake with no collapse or meltback. Based on these experiments, an initial design space can be constructed for primary drying (blue region in Figure 6). The process outputs and product attributes from the DOE were quantitatively assessed using the statistical analysis program JMP (Version 8, SAS, Cary, NC) and yielded the statistical model shown in Equation 1 (eq 1) below.

The dependence of product temperature during primary drying on shelf temperature and chamber pressure (a largely linear additive effect with some interaction) is described by eq 1, in which Tp is the product temperature, PDT is the primary drying temperature, and CP is the chamber pressure. For the parameter space outside the initial primary drying design space region shown in Figure 6, eq 1 can be used to obtain extrapolated values for product temperature and sublimation rates. The red curve in Figure 6 was obtained by identifying the primary drying temperature and chamber pressure values from eq 1 that yield a product temperature of –15 to –16 °C (slightly below the collapse temperature for this formulation). The relevant output for secondary drying is residual moisture, and thus based on results from Table 4. The experimentally demonstrated design space for secondary drying was a shelf-temperature range of 15–25 °C and a chamber pressure of 70–140 mTorr.

Figure 6. Experimental initial design space for primary drying and schematic of hypothetical process limits

Because the primary drying step is where the product is at greatest risk of impact relative to the process control capability of the equipment, the subsequent sections will focus on developing the primary drying design space further.

Figure 7. Steps involved in the use of the mechanistic process model to expand the primary design space for lyophilization

Establishment of a Mechanistic Model and Expansion of Primary Drying Design Space

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 8. Comparison of the measured versus predicted product temperature profiles for the target cycle

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 9. Comparison of the measured versus predicted product temperature profiles for the minimum sublimation rate 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).

Figure 10. Comparison of the measured versus predicted product temperature profile for the maximum product temperature case

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.

Table 5. Results of experiments for expanded design space for primary drying

ESTABLISHMENT OF PRIMARY DRYING EXCURSION SPACE

Occasionally, during routine production, a process may undergo a short-term deviation outside the established design space (e.g., because of a mechanical failure). Here, we present an example of a manufacturing deviation to illustrate how a mathematical model could be a powerful guiding tool in such situations. One of the more frequent lyophilization cycle deviations occurs when, in response to a spike in chamber pressure, the lyophilizer goes into a safety shelf freeze to protect the product. We performed a planned deviation experiment at the pilot scale to mimic the above scenario. A pressure deviation to 200 mTorr was modeled at two points of interest in the cycle: at the beginning of the primary drying hold when the shelf temperature first reaches the primary drying set point, and toward the end of sublimation when the product temperature starts to ramp up to the shelf temperature. After the experiment was complete, we simulated the same planned deviation recipe using the mathematical model, and we compared the product temperature profiles predicted by the model with the experimentally obtained data (Figure 12). Based on both the model and the experiment, the product temperature stayed well below the collapse temperature, even during the pressure deviation. However, as the shelf temperature returned to the setpoint after each safety freeze event, the product temperatures needed an additional 0.75 h to reach the temperature value just before the pressure deviation. Thus, for a pressure excursion of this type in manufacturing, the recommendation would be to extend primary drying by 0.75 h for each safety freeze. During routine production at full scale, product temperature data typically are not available. This study demonstrates that the model can be used to predict what the product temperature profile would be under a deviation scenario, thus enabling in-line cycle modifications and batch release decisions based on a sound scientific rationale.

Figure 11. Final experimentally verified primary drying design space

CONCLUSIONS

One of the key elements of QbD is to prospectively develop in-depth process and product understanding, and to apply that knowledge to establish robust manufacturing processes. From industry perspective, although the QbD approach is expected to bring about significant long-term benefits, concerns remain around the increased amount of characterization work that is needed upfront. In this article, we presented an approach in which a combination of risk assessments and mathematical modeling of lyophilization was used to guide characterization studies. With this approach, we were able to obtain a lyophilization design space that is relevant for manufacturing through relatively fewer experiments compared to a purely empirical approach. We also discussed how mathematical modeling can be used to simulate the impact of process deviations on process attributes, thereby enabling a more informed response to process deviations. This article shows that mathematical models based on a good mechanistic understanding of unit operations are excellent tools for more efficient implementation of QbD elements during manufacturing process development.

Figure 12. Comparison of measured product temperature profiles and the predicted profile (blue curve) for the pressure excursion case

Jagannathan Sundaram is engineer II, Chung C. Hsu is an engineer, and Samir U. Sane is an associate director, all in process research and development at Genentech Inc., South San Francisco, CA, 650.467.4798, jagannas@gene.comYun-Hua Max Shay was a co-op at Genentech Inc. when this work was done.

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