Small-Scale and At-Scale Model Development and Optimization

During development, there is a need to characterize and optimize processes. In vaccines and biologics development, there are often scale and system differences between shaker flasks, 0.5 L, 2 L, 5 L, 10 L, 200 L, and 2000 L environments. Often the difference in scale makes scale up and prediction uniquely challenging. This article presents an approach to small-model generation and how to calibrate the small-scale models to reliably predict performance at scale. This assumes that the small-scale model development has been scientifically and thoughtfully designed to represent as many of the functions and environments that will be present at scale. No amount of secondary model tuning and correction will make up for a failure to select and reasonably range the parameters and build a good model of the process at small scale. 

Small-scale development and strategy
For most product development, characterization, and control strategies, there is a need to develop small-scale and at-scale process models to aid in product knowledge and promote process understanding, prediction, and control. 

Advantages of developing small-scale models include:
 

• Materials use and availability

• Equipment availability

• Cost of development

• Time to development solution

• Ability to generate product and process models at both scales

• Facilities availability

• Efficiently explore control strategies

• Experimental strategy.

Problems with small-scale models include:

• They may not be representative of the product or process at scale.

• They may not accurately represent the mean response at scale.

• They may not accurately represent the variation at scale.

• They may not accurately represent out-of-specification (OOS) and failure rates/modes. 

Regulatory guidance documents provide the following comments on process development requirements:
 

• International Conference on Harmonization (ICH) Q8 Pharmaceutical Development (1) states, “an assessment of the ability of the process to reliably produce a product of the intended quality (e.g., the performance of the manufacturing process under different operating conditions, at different scales, or with different equipment) can be provided.”

• ICH Q11 Development and Manufacture of Drug Substance (2) states, “small-scale models can be developed and used to support process development studies. The development of a model should account for scale effects and be representative of the proposed commercial process. A scientifically justified model can enable a prediction of product quality, and can be used to support the extrapolation of operating conditions across multiple scales and equipment.”

• ICH Q9 Quality Risk Management (3) states the following regarding development and scale up: “To establish appropriate specifications, identify critical process parameters, and establish manufacturing controls (e.g., using information from pharmaceutical development studies regarding the clinical significance of quality attributes and the ability to control them during processing) … To assess the need for additional studies (e.g., bioequivalence, stability) relating to scale up and technology transfer.”

• FDA’s process validation guidance (4) states, “before any batch from the process is commercially distributed for use by consumers, a manufacturer should have gained a high degree of assurance in the performance of the manufacturing process such that it will consistently produce APIs and drug products meeting those attributes relating to identity, strength, quality, purity, and potency. The assurance should be obtained from objective information and data from laboratory-, pilot-, and/or commercial-scale studies. Information and data should demonstrate that the commercial manufacturing process is capable of consistently producing acceptable quality products within commercial manufacturing conditions.”

Small-scale model development and design of experiments
Small-scale experimental models must be first generated. Care needs to be made that operational ranges represent conditions that occur in the full-scale process. For example, fill times may be 20 minutes in a small-scale process; however, in the full-scale process, it may take two hours. Small-scale models should be generated to represent conditions at scale as much as is practicable.

A low-level risk assessment and experimental design should be generated and the process model generated and saved. The following purification process example is presented.

Two significant factors are influencing the step yield: protein load on the column and wash molarity. The model explains more than 94.4% of the variation (R²) in titer step yield. The following are the steps in generating the small-scale model:

1. Low level risk assessment
2. Design of experiment
3. Model refinement for significant factors (Figure 1 and Figure 2)
4. Save the formula (transfer function) (Figure 3)
5. Simulate the process set point at scale (model, variation at set point, noise) (Figure 4)
6. Determine the variation in X at scale
7. Add the root mean squared error (RMSE) into the noise for the simulation
8. Simulate process conditions to predict the mean and standard deviation at scale.

Figure 1: Whole model for the small-scale purification experiment. [Click to Enlarge]

Figure 2: Scaled estimates or half effect of the factors in the small-scale. [Click to Enlarge]

Figure 3: Small-scale model equation for step yield in titer. [Click to Enlarge]

Figure 4: Simulation of full-scale results using the small-scale model. [Click to Enlarge]

GMP or engineering production runs at scale
At some point in the development, full-scale GMP or engineering runs will be performed. Care needs to be taken to record all of the run conditions that were present in the small-scale model. Using the equation from the small-scale experiment, plug in the full-scale measures into the small-scale model and compare them to the full-scale results. Notice the means and standard deviations are not well matched (calibrated) to the full-scale results. The difference in means and standard deviations (Figure 5) indicates some scale effects, and the small-scale model needs to be calibrated to predict the step yield titer more reliably at scale.  

Figure 5: Small-scale and full-scale results. [Click to Enlarge]

Small-scale model calibration
Generally, regression is used to determine how to calibrate the model. When calibrating the small-scale model to the full scale, the Y response is the full-scale measurements, and the X factor is the predicted small-scale model results (see Figure 6). An orthogonal principle components fit was used in fitting the line. The intercept corrects for the mean, and slope corrects for the standard deviation. Linear regression using a least-squares error method of line calculation is used when the correlation is high (70%+R2); however, when the correlation is poor, an orthogonal method of regression is typically more reliable. If a least-squares line were used in this example, it would not correctly calibrate the small-scale model. Other regression fits are possible to calibrate a small-scale model; however, it is beyond the scope of this paper.

Figure 6: Full-scale and small-scale model calibration using orthogonal regression. [Click to Enlarge]

To correct the small-scale model (Figure 7), an intercept of -261.926 and a slope of 3.688 must be applied to the small-scale model. Once this is complete, the results should match the at-scale model (Figure 8). In most cases, there is a small-scale to full-scale correction to make the models match both mean and standard deviation. 

Figure 7: Full-scale calibrated model. [Click to Enlarge]

• At scale mean and standard deviation MFG data 86.3, 5.9

• Pre-calibration small scale mean and standard deviation 94.4, 1.6

• Post-calibration full scale mean and standard deviation 86.3, 5.9

Figure 8: Calibrated full-scale model and actual measurement data. [Click to Enlarge]

Using the full-scale calibrated model
Using the current process settings of 137 and 16, simulations can be run to determine the failure rates and OOS and operational ranges (Figure 9). The power of generating a calibrated full-scale model is how the model can be used to reliably predict the influence of variation in the input parameters, set operational ranges, and evaluate the design space (Figure 10) and edge of failure (Figure 11).

Figure 9: Full-scale simulation. [Click to Enlarge]

Figure 10: Purification design space from full-scale model. [Click to Enlarge]

The full-scale simulation is used to determine design margin and to visualize and evaluate failure rates. The design space helps to visualize design margin and process centering. The edge of failure plot helps to predict design margin relative to specifications and acceptance criteria.

Full-Scale Model and Process Validation
Once predictions are made from the full-scale model, they can be compared to actual GMP production lots. Typically, a 99% interval is used to see if every batch is falling within the full-model predictions. If so, it indicates the validity of the full-scale model. Model simulation and scale-up results should be part of the development report and Stage I process validation reports.

Figure 11: Purification design space from full-scale model. [Click to Enlarge]

Conclusion
Model development at various scale and variation understanding and modeling is a core component of modern drug development. It is a required element of Stage I validation and increases product and process knowledge and reduces risk. Generating reliable small-scale models and calibrating the models to full-scale results are essential steps in generating process understanding and communicating that understanding to development and GMP team members. Using a valid and well-defined process model to simulate, predict, and control drug substance and drug product is core to every drug development team globally.

Learning how to reliably predict performance at multiple scales is an essential skill for all CMC team members. Failure to build reliable process models will likely generate higher variation and is likely to result in OOS measures and lot failures.

References
1. ICH, Q8(R2) Pharmaceutical Development (IHC, 2009).
2. ICH, Q11 Development and Manufacture of Drug Substance (ICH, 2011).
3. ICH, Q9 Quality Risk Management (ICH, 2006).
4. FDA, Guidance for Industry, Process Validation: General Principles and Practices (FDA, 2011).

About the Author
Thomas A. Little is president of Thomas A. Little Consulting, 12401 N Wildflower Lane, Highland, UT 84003,
tel. 1.925.285.1847, drlittle@dr-tom.com, www.qualitybydesginconsulting.com.

Article Details
BioPharm International
Vol. 28, No. 10
Pages: 54–59

Citation: When referring to this article, please cite it as T.A. Little, “Small-Scale and At-Scale Model Development and Optimization,” BioPharm International 28 (5) 2015.