Modeling of Biopharmaceutical Processes. Part 2: Process Chromatography Unit Operation - How to apply the latest thinking in process modeling to your process using a Quality by Design approach. - BioP

MODELING TO IDENTIFY OPTIMAL CONDITIONS FOR PROCESS CHROMATOGRAPHY

Figure 7. Exemplary representation of a matrix of a 729 data point virtual three-level full factorial and response surface
model. Profiles of normalized single factor response for all other factors held constant.

Kaltenbrunner, et al., recently compared the use of a chromatographic model to rank operational parameters to the traditional
statistical experimental design approach.^{2} They performed both the typical screening of parameters in a fractional factorial experimental design and, independently,
developed a theoretical model as described by Yamamoto, et al., for a particular ion-exchange chromatography operation.^{13 }
While the original model is based primarily on the response of protein elution to ionic strength, flow rate, and gradient
slope; extensions for resin ligand density and pH were included.^{14} With a series of small-scale linear gradient experiments, a model for the ion-exchange operation based on established response
relations was constructed. As interactions and curvature are inherent to the model assumptions, once the right model was chosen,
fewer experiments were necessary to define system behavior than with a traditional statistical factorial approach, where no
prior information about parameter relations was available. The model was then used to predict a matrix of potential experimental
conditions similar to statistical experimental design. In this case though, there were no material restrictions and cost considerations
and a full factorial matrix with several factor levels could be modeled easily and rapidly.

Figure 8. Exemplary representation of a matrix of a 729 data point virtual three-level full factorial and response surface
model. Surface plots of all two-factor interactions and pH with respect to purity and recovery.(A)Flow Rate; (B)Initial ionic
strength; (c)Bed hight; (D)Gradient Slope; (E) Ligand density

Parameter screening by chromatographic modeling and by fractional factorial experimental design both rank three parameters—the
ionic strength at the beginning of the elution gradient, pH, and resin ligand density—as the parameters that have the highest
effect on separation behavior (Figure 6). Similarly, both methods identify gradient slope and flow rate—within the range considered
in this study—as parameters that have a lesser effect on separation behavior. This comparison indicates that the modeling
approach outlined by Yamamoto, et al., can be applied for the initial screening of operational parameters during process characterization.
In this case of six model input factors, to obtain a traditional multiple regression model that could describe all possible
two-factor interactions and simple quadratic curvature, fewer than 50 factor combinations have to be predicted by the model.
To predict all factor combinations for 3 levels, 3 x 3 x 3 x 3 x 3 x 3 = 729 combinations must be calculated. This can easily
be done when using computational analysis. As a result, normally neglected higher order interaction could be included in the
analysis. Figure 7 represents a virtual full factorial experiment with all combinations of factor inputs at three levels.
The panels show changes in predicted recovery and resolution to single factor changes within normalized input ranges from
–1 to +1. All other factors were held at center point condition, and therefore, factor interactions were not detectable in
this representation. As seen in Figure 8, interactions with pH are demonstrated with respect to two model outputs. The red
areas represent factor combinations where the expected product purity is undesirable, and blue areas represent factor combinations
where the expected product recovery is undesirable. The model can help inscribe the process design space in which the process
performance is acceptable. In practice, the selection of a design space is much more complex than implied in these plots.
In these plots, all other parameters were held constant at their target. Although two- or three-dimensional visualization
is difficult because of the multidimensional nature of the model, chosen parameter ranges can be tested in all their combinations
by stochastic modeling.

Figure 9. A comparison of the simulation shown in figure 4 and the corresponding experimental chromatogram. Details shown
in Table 3

Mollerup, et al., also demonstrated the usefulness of such simulations for process optimization and scale-up.^{4} As seen in Figure 5, the process model was shown to be in good agreement with the experimental data. This model was then
used as a simulation tool to optimize the process. The column size and the properties of the loading solution were fixed and
the independent variables that were examined included load volume, flow rate, and gradients. The concentration in the collected
pool volume was stipulated to be within specified limits. Figure 9 compares the experimental and the simulated separation.
The agreement between the experimental and the simulated chromatogram is satisfactory and sufficient to optimize the current
separation. The experimental chromatogram is broader than the simulated one, which indicates that the collected fraction containing
the product must be increased compared to that used in the simulation. The results in Table 3 further demonstrate the use
of the simulation in optimization and increasing the overall productivity.

Anurag S. Rathore, PhD, is a consultant, Biotech CMC Issues, and a member of the faculty in the department of chemical engineering at the Indian Institute of Technology. Rathore is also a member of BioPharm International's Editorial Advisory Board.
Articles by Anurag S. Rathore, PhD

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