# Integrated Process Modeling—A Process Validation Life Cycle Companion

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## Abstract

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## 1. Introduction

- Risk assessment using knowledge of process experts, which leads to a candidate set of potential critical PPs for each unit operation.
- Experimental investigation of the impact of potentially critical PPs onto CQAs. This is usually performed in DoE approaches and statistical regression modeling is used to describe the relationship between significantly impacting critical PPs and CQAs mathematically.
- Comparison of the output of statistical model predictions within normal operating ranges or a design space to pre-defined acceptance limits for each unit operation.
- The risk of not meeting acceptance limits is mitigated by applying an appropriate control strategy, such as a reduction of the normal operating range.

- Prove process robustness of an existing design space: Prove that under normal manufacturing conditions it is unlikely to miss drug substance specification for defined CQAs
- Test process robustness under accelerated variance of process parameters and increased impurity burden
- Establish a platform that leverages process knowledge from PV stage 1 for further usage within PPQ and CPV (Stage 2 and 3 of process validation)

## 2. Materials and Methods

- Description of the process, order of unit operations, and variance of PPs under normal operating conditions (see Section 2.1). It is assumed that estimation of variance of PPs is representative for routine manufacturing.
- Optional: If initial unit operation of the process is not modeled by the IPM the starting distribution of each CQA needs to be estimated at the starting unit operation of the IPM. It is assumed that the estimation of starting distribution is representative for the real CQA distribution under routine manufacturing (see Section 2.2).
- Statistical regression models that describe significant relationships between PPs and CQAs for each unit operation (see Section 2.3.1). It is assumed that scientifically sound analytical methods (high accuracy, precision, robustness, selectivity, etc.) have been used to record the data that led to formation of those regression models. Moreover, it is assumed that no critical effect has been overlooked, which can be tested using power analysis approaches [9]. This ensures that residual variance in the regression models can be attributed to normal analytical- and process variance.
- Optional: Statistical spiking models of each unit operation describing the dependency between varied impurity load and specific impurity clearance (see Section 2.3.2). Identical assumptions as for the regression models must be met.

#### 2.1. Description of Biopharmaceutical Manufacturing Process

#### 2.2. Scope of IPM and Sampling Distribution of PPs

#### 2.3. Impurity Clearance Models

#### 2.3.1. Clearance and Yield as a Function of Process Parameters (DoE Models)

#### 2.3.2. Increased Clearance Due to Varied Spiking of Impurities

^{−8}) increase in specific clearance of process-related impurity 2. Significant (p-value < 0.05 as well as R

^{2}(explained variance) − Q

^{2}(from leave one out cross validation) difference < 0.3) spiking models were selected for each response/unit operation and are summarized in Table 2 and Table S2 of the Supplementary Materials.

## 3. Results

#### 3.1. Monte Carlo Approach for Integrated Process Modeling

- 1000 simulations were performed, each having a different set of PPs (${\mathrm{PP}}^{(i)}$) for the three modeled unit operations (chromatography column 1/2/3) and different initial specific CQA concentrations (${\mathrm{c}}^{(i)}{}_{\mathrm{CQA},\mathrm{init}}$) at the load of chromatography column 1, sampled from distributions which were estimated from LS runs. Also the variance in PPs was estimated from LS runs and is indicated by a schematic distribution on the x-axis in Figure 2A,B. Additional increase in simulations did not increase model accuracy and 1000 simulations are a common standard for Monte Carlo simulations [7]. A more detailed description of this step and a list of used process parameters are provided in Section 2.2.
- For each unit operation, we modeled the specific clearance (SC) of each CQA as a function of the critical PPs and the ILD by multiple linear regression. Each model is associated with a prediction error, which is indicated by the blue shaded area around the found regression line Figure 2A,B. The ILD can be derived from ${\mathrm{c}}_{\mathrm{CQA},\mathrm{load}}$ of each unit operation, which equals ${\mathrm{c}}_{\mathrm{CQA},\mathrm{init}}$ for the first modeled unit operation and ${\mathrm{c}}_{\mathrm{CQA},\mathrm{pool},u-1}$ for all subsequent modeled unit operations (u).
- Since ${\mathrm{c}}_{\mathrm{CQA},\mathrm{pool},u}$ can be calculated from SC and ${\mathrm{c}}_{\mathrm{CQA},\mathrm{load},u}$, on the whole, ${\mathrm{c}}_{\mathrm{CQA},\mathrm{pool},u}$ can be seen as a function of ${\mathrm{PP}}_{u}$ as well as ${\mathrm{c}}_{\mathrm{CQA},\mathrm{init}}$ or ${\mathrm{c}}_{\mathrm{CQA},\mathrm{pool},u-1}$, as indicated in the formula of Figure 2A,B, respectively. Thereby the model outputs from multiple unit operations can be stacked together, which is indicated by black arrows in Figure 2A, more thorough description of which models could be found on which CQA and unit operation is depicted in Section 2.3.

#### 3.2. Validation of the IPM Using Observed CQA Distribution in Drug Substance

#### 3.3. Impact of Accelerated Variation in Process Parameters on Drug Substance

## 4. Conclusions

## Supplementary Materials

**top**) product-related impurity 1 distribution and observed (

**bottom**) product-related impurity 1 from LS after each column step, Figure S2: Comparison of simulated (

**top**) product-related impurity 2 distribution and observed (

**bottom**) product-related impurity 2 from LS after each column step, Figure S3: Comparison of simulated (

**top**) process-related impurity 2 distribution and observed (

**bottom**) process-related impurity 2 from LS after each column step, Figure S4: Comparison of simulated (

**top**) process-related impurity 1 distribution and observed (

**bottom**) process-related impurity 1 from LS after each column step, Table S1: Overview of found models based on DoE data, Table S2: Overview of models showing a correlation between specific CQA clearances and CQA load density.

## Author Contributions

## Conflicts of Interest

## References

- Process Validation: General Principles and Practices; U.S. Department of Health and Human Services: Washington, DC, USA, 2011.
- Guideline, I.H.T. Pharmaceutical Development Q8 (R2). Curr. Step
**2009**, 4, 1–24. [Google Scholar] - Guideline, I.H.T. Quality risk management, Q9. Curr. Step
**2005**, 4, 408. [Google Scholar] - Katz, P.; Campbell, C. FDA 2011 process validation guidance: Process validation revisited. J. GXP Compliance
**2012**, 16, 18. [Google Scholar] - Peterson, J.J.; Lief, K. The ICH Q8 definition of design space: A comparison of the overlapping means and the bayesian predictive approaches. Stat. Biopharm. Res.
**2010**, 2, 249–259. [Google Scholar] [CrossRef] - Herwig, C.; Wölbeling, C.; Zimmer, T. A holistic approach to production control. Pharm. Eng.
**2017**, 37, 44–46. [Google Scholar] - Bonate, P.L. A brief introduction to Monte Carlo simulation. Clin. Pharmacokinet.
**2001**, 40, 15–22. [Google Scholar] [CrossRef] [PubMed] - Goudar, C.T.; Biener, R.; Konstantinov, K.B.; Piret, J.M. Error propagation from prime variables into specific rates and metabolic fluxes for mammalian cells in perfusion culture. Biotechnol. Prog.
**2009**, 25, 986–998. [Google Scholar] [CrossRef] [PubMed] - Iman, R.L. Latin hypercube sampling. Encycl. Quant. Risk Anal. Assess.
**2008**. [Google Scholar] [CrossRef] - Singhee, A.; Rutenbar, R.A. Why quasi-monte carlo is better than monte carlo or latin hypercube sampling for statistical circuit analysis. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst.
**2010**, 29, 1763–1776. [Google Scholar] [CrossRef] - Zahel, T.; Marschall, L.; Abad, S.; Vasilieva, E.; Maurer, D.; Mueller, E.M.; Murphy, P.; Natschläger, T.; Brocard, C.; Reinisch, D.; et al. Workflow for Criticality Assessment Applied in Biopharmaceutical Process Validation Stage 1. Bioengineering
**2017**, 4, 85. [Google Scholar] [CrossRef] [PubMed]

**Figure 1.**Exemplary plot for dependency of specific clearance (here of process-related impurity 2) against impurity loading density of process-related impurity 2 of DoE runs (blue) and large scale (LS) runs (red). Yellow error bars indicate the mean model prediction error. Normalization has been performed by division of the maximal value for each axis.

**Figure 2.**Schematic description of the integrated process model using a Monte Carlo approach: 1000 simulations are performed, each having a different set of process parameters (indicated as distribution on the x-axis of (

**A**,

**B**)) and initial specific CQA concentration $({\mathrm{c}}_{\mathrm{CQA},\mathrm{init}})$. Multiple linear regression models describe the relationship between the ${\mathrm{c}}_{\mathrm{CQA}}$ of the pool of unit operation u (

**B**) and the PP of this unit operation as well as the pool concentration of the previous unit operation u − 1 (

**A**). Thereby, models from multiple unit operations (

**A**,

**B**) are connected to predict the CQA distribution in the drug substance (

**C**). Since 1000 simulations are performed, the CQA values form a distribution after each unit operation. The higher the model uncertainty, indicated by blue shaded area around the regression line, the wider the resulting CQA distribution. This ultimately propagates until drug substance, where the chance of out of specification events can be assessed.

**Figure 3.**Comparison of simulated (

**top**) product-related impurity 1 distribution and observed (

**bottom**) product-related impurity 1 from LS after each column step. Normalization was performed by dividing by the maximum observed ${\mathrm{c}}_{\mathrm{CQA}}$.

**Figure 4.**Comparison of simulated (

**top**) product-related impurity 2 distribution and observed (

**bottom**) product-related impurity 2 from LS after each column step. Normalization was performed by dividing by the maximum observed ${\mathrm{c}}_{\mathrm{CQA}}$.

**Figure 5.**Comparison of simulated (

**top**) process-related impurity 1 distribution and observed (

**bottom**) process-related impurity 1 from LS after each column step. For chromatography column 3 pool, no process-related impurity 1 value was observed above LoQ, therefore, no histogram bar is plotted for the observed values at chromatography column 3 pool. Normalization was performed by dividing by the maximum observed ${\mathrm{c}}_{\mathrm{CQA}}$.

**Figure 6.**Comparison of simulated (

**top**) process-related impurity 2 distribution and observed (

**bottom**) process-related impurity 2 from LS after each column step. Normalization was performed by dividing by the maximum observed ${\mathrm{c}}_{\mathrm{CQA}}$.

**Figure 7.**Estimated OOS event for product-related impurity 2 at drug substance as a function of change in set-point (

**A**) and variance (

**B**) of all PPs as well as a function of increased specific impurity concentration after primary recovery (

**C**). Deviations in set-point of pH and salt concentration in wash of chromatography column 1 impact severely on OOS chance, which is not the case when variance in PPs increases by up to 50%. A change of specific product-related impurity 2 concentration at the primary recovery level will also increase OOS chances.

**Table 1.**Available data sets, process parameters, and monitored critical quality attributes (CQAs) for each unit operation included in the integrated process model (IPM). CC is abbreviation for chromatography column, PCI stands for process-related impurities and PRI product-related impurities.

UO | Available Data Sets | PPs Varied in DoEs | Rel. Std. of PPs between LS [%] ^{1} | Std/NOR [%] ^{2} | Monitored CQAs |
---|---|---|---|---|---|

CC 1 | pH [–] | 1.61 | 46 | PCI 1, PCI 2, PRI 1, PRI 2 | |

Column loading density [g/L] | 12.05 | 50 | |||

9 manufacturing runs | Wash Strength [mM] | 5.00 | 62 | ||

13 DoE runs with definitive screening design | Elution strength [mM] | 5.00 | 44 | ||

End pooling [CV] | 1.36 | 40 | |||

CC 2 | 9 manufacturing runs | pH [–] | 0.79 | 30 | |

11 DoE runs using full factorial design | Column loading density [g/L] | 4.84 | 20 | ||

1 spiking run with increased PRI 1 concentration in load | Gradient slope [% of Buffer] | 5.00 | - | ||

1 spiking run with increased PCI 1 concentration in load | |||||

CC 3 | pH [–] | 0.92 | 35 | ||

9 manufacturing runs | Column loading density [g/L] | 12.78 | 30 | ||

9 DoE runs using definitive screening design | Gradient slope [% of Buffer] | 5.00 | - | ||

Wash Strength [mM] | 5.00 | 50 |

^{1}Relative standard deviation to the set-point of the process parameters;

^{2}Ratio of one standard deviation to the normal operating range.

**Table 2.**Summary of the presence of models that describe the relationship of a CQA specific clearance factor as a function of PPs (indicated by “DoE”) or the impurity loading density of the respective CQA (“Spiking”) and the respective p-value of the regression. In cases where no significant function of PPs on a CQA clearance could be found, mean large scale clearance was assumed indicated by “LS clearance” in the table. CC is abbreviation for chromatography column, PCI stands for process-related impurities and PRI product-related impurities.

CQA/Unit Operation | CC 1 | CC 2 | CC 3 |
---|---|---|---|

PRI 1 | DoE | LS clearance + Spiking | DoE |

(linear, p = 0.09) | (p = 0.00) | (quadratic, p = 0.01) | |

PRI 2 | DoE | LS clearance | LS clearance |

(linear, p = 0.01) | |||

PCI 1 | DoE | LS clearance + Spiking | DoE |

(quadratic, p = 0.00) | (p = 0.04) | (quadratic, p = 0.00) | |

PCI 2 | LS clearance + Spiking | LS clearance | LS clearance + Spiking |

(linear, p = 0.00) | (linear, p = 0.00) | ||

Yield | DoE | LS clearance | DoE |

(linear, p = 0.00) | (quadratic, p = 0.00) |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Zahel, T.; Hauer, S.; Mueller, E.M.; Murphy, P.; Abad, S.; Vasilieva, E.; Maurer, D.; Brocard, C.; Reinisch, D.; Sagmeister, P.;
et al. Integrated Process Modeling—A Process Validation Life Cycle Companion. *Bioengineering* **2017**, *4*, 86.
https://doi.org/10.3390/bioengineering4040086

**AMA Style**

Zahel T, Hauer S, Mueller EM, Murphy P, Abad S, Vasilieva E, Maurer D, Brocard C, Reinisch D, Sagmeister P,
et al. Integrated Process Modeling—A Process Validation Life Cycle Companion. *Bioengineering*. 2017; 4(4):86.
https://doi.org/10.3390/bioengineering4040086

**Chicago/Turabian Style**

Zahel, Thomas, Stefan Hauer, Eric M. Mueller, Patrick Murphy, Sandra Abad, Elena Vasilieva, Daniel Maurer, Cécile Brocard, Daniela Reinisch, Patrick Sagmeister,
and et al. 2017. "Integrated Process Modeling—A Process Validation Life Cycle Companion" *Bioengineering* 4, no. 4: 86.
https://doi.org/10.3390/bioengineering4040086