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An approach to small-model generation and calibrating small-scale models to reliably predict performance at scale is presented.
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:
Problems with small-scale models include:
Regulatory guidance documents provide the following comments on process development requirements:
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.
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.
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.
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.
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).
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.
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.
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, firstname.lastname@example.org, www.qualitybydesginconsulting.com.
Vol. 28, No. 10
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.