# A Hybrid Model to Predict Formulation Dependent Granule Growth in a Bi-Component Wet Granulation Process

^{*}

## Abstract

**:**

## 1. Introduction

- 1.
- Incorporate the nuclei particle characteristics in the population balance model based on the classification model result from Muthancheri et al. [30].
- 2.
- Develop a composition-dependent PBM framework for bi-component wet granulation process with a large binder droplet for predicting the granule quality attributes with change in percentage formulation.

## 2. Model Development

#### 2.1. Population Balance Model

#### 2.2. Mechanisms Involved in the Model

- 1.
- Immersion nucleation
- 2.
- Solid-spread nucleation of hydrophobic API
- 3.
- Granule surface wetting during liquid addition
- 4.
- Granule surface growth due to solid-spread nuclei
- 5.
- Hydrophilic excipient layering
- 6.
- Particle aggregation
- 7.
- Particle breakage
- 8.
- Compaction

#### 2.2.1. Immersion Nucleation

#### 2.2.2. Solid-Spread Nucleation

#### 2.2.3. Granule Surface Wetting during Liquid Addition

#### 2.2.4. Granule Surface Growth Due to Solid-Spread Nuclei

#### 2.2.5. Hydrophilic Excipient Layering

#### 2.2.6. Particle Aggregation

**A**(${s}_{1},{s}_{2},p$) and

**B**(${s}_{1}^{{}^{\prime}},{s}_{2}^{{}^{\prime}},{p}^{{}^{\prime}}$) (as shown in Figure 3). $\beta (\mathbf{A},\mathbf{B})={\beta}_{0}{\beta}^{*}\mathbf{A},\mathbf{B}$. ${\beta}_{0}$ is independent of the colliding particle properties and is an optimized parameter in this work. ${\beta}^{*}$ is the efficiency of particle collision which can be determined based on the following model proposed by Balakin et al. [35]. The model accounts for both capillary and viscous forces during particle collision. The efficiency is determined as a ratio of the total work of forces within the liquid bridge to the kinetic energy of the particle.

#### 2.2.7. Compaction

#### 2.2.8. Particle Breakage

#### 2.3. Hybrid Modeling

#### 2.4. Numerical Solution

#### 2.5. Sensitivity Analysis

_{10}, d

_{50}, and d

_{90}simulation. It shows that growth parameters (${k}_{layer}$ and ${k}_{sg}$) are much less sensitive than the aggregation and consolidation parameters when the variables are perturbed $\pm 20\%$. The average diameter is found to be highly sensitivity toward the coefficient of restitution of API (${e}_{s1}$). The study shows a decrease in average diameter with an increase in ${e}_{s1}$. A decrease in ${e}_{s1}$ indicates that the API is very deformable, resulting in smaller average granule size. The aggregation rate constant, ${\beta}_{0}$, has a positive impact on the granule size, showing an increase in the rate constant increasing the average granule size. The consolidation rate equation has a negative term (Equations (39) and (40)), which means the increase in ${k}_{con}$ results in a decrease in consolidation rate. In Figure 6c, it can be seen that a decrease in consolidation rate to 20% results in larger granules.

## 3. Results and Discussions

#### 3.1. Optimization and Parameter Estimation

#### 3.2. Model Training and Validation

#### 3.3. Model Applications

#### 3.3.1. Effect of Change in Formulation on Dynamic Granule Formation

#### 3.3.2. Effect of Change in Formulation on Granule API Content

#### 3.3.3. Effect of Change in Formulation on Average Granule Porosity

#### 3.3.4. Effect of Change in Formulation on Average Liquid Fraction

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

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**Figure 4.**Change in capillary numbers with increase in API fraction. (

**a**) Ibuprofen and MCC101 formulation, (

**b**) Acetaminophen (APAP) and MCC101 formulation.

**Figure 6.**Effect of changes in adjustable parameter values on d

_{10}, d

_{50}, and d

_{90}. Sensitivity to (

**a**) d

_{10}, (

**b**) d

_{50}, (

**c**) d

_{90}.

**Figure 7.**Effect of changes in adjustable parameter values on porosity and API content. (

**a**) Sensitivity to average API content, (

**b**) Sensitivity to granule average porosity.

**Figure 12.**Cumulative volume fraction prediction with change in percentage composition of API and 0.6 liquid-to-solid ratio.

**Figure 13.**Granule size distribution with increase in granulation time at a varying degree of hydrophobic content (ibuprofen). (

**a**) Granule size distribution with increase in granulation time at 40% hydrophobic component (ibuprofen), (

**b**) granule size distribution with increase in granulation time at 50% hydrophobic component (ibuprofen), and (

**c**) granule size distribution with increase in granulation time at 60% hydrophobic component (ibuprofen).

**Figure 14.**Model predicted granule size distribution with an increase in wet massing time (50% API content).

**Figure 16.**Change in granule micro-structure with increase in API content. (

**a**) Model predicted average porosity, (

**b**) Experimental envelop density.

Description | Notation |
---|---|

Independent variables | |

API solid volume | ${s}_{1}$ |

Excipient solid volume | ${s}_{2}$ |

External liquid volume | ${l}_{e}$ |

Internal liquid volume | ${l}_{i}$ |

Pore volume | p |

Dependent variables | |

Total granule volume | v |

Surface area | a |

Porosity | $\u03f5$ |

Content uniformity | q |

Parameters | Notation | Value |
---|---|---|

Aggregation rate constant | ${\beta}_{0}$ | $4.34\times {10}^{-10}$ |

Ibuprofen coefficient of restitution | ${e}_{s1,ibu}$ | $0.162$ |

APAP coefficient of restitution | ${e}_{s1,apap}$ | $0.103$ |

MCC101 coefficient of restitution | ${e}_{s2}$ | $0.07$ |

Consolidation rate constant | ${k}_{con}$ | $1.67\times {10}^{-3}$ |

Excipient layering rate constant | ${k}_{layer}$ | $2.01\times {10}^{-8}$ |

Surface growth rate constant | ${k}_{sg}$ | $4.59\times {10}^{-11}$ |

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**MDPI and ACS Style**

Muthancheri, I.; Ramachandran, R.
A Hybrid Model to Predict Formulation Dependent Granule Growth in a Bi-Component Wet Granulation Process. *Pharmaceutics* **2021**, *13*, 2063.
https://doi.org/10.3390/pharmaceutics13122063

**AMA Style**

Muthancheri I, Ramachandran R.
A Hybrid Model to Predict Formulation Dependent Granule Growth in a Bi-Component Wet Granulation Process. *Pharmaceutics*. 2021; 13(12):2063.
https://doi.org/10.3390/pharmaceutics13122063

**Chicago/Turabian Style**

Muthancheri, Indu, and Rohit Ramachandran.
2021. "A Hybrid Model to Predict Formulation Dependent Granule Growth in a Bi-Component Wet Granulation Process" *Pharmaceutics* 13, no. 12: 2063.
https://doi.org/10.3390/pharmaceutics13122063