Machine Learning Modeling of Wet Granulation Scale-up Using Particle Size Distribution Characterization Parameters

  • Nada MillenEmail author
  • Aleksandar Kovačević
  • Jelena Djuriš
  • Svetlana Ibrić
Original Article



Optimal particle size distribution (PSD) is an important factor in wet granulation in order to achieve appropriate powder flow, compactibility, and content uniformity. Parameters like D50 and surface area (SA) are used to define PSD but both are only able to compare separate fractions of a granulate. In this work, we made an attempt to characterize PSD of a final dry granulate blend and suggest novel parameters (determination coefficient R2 and trend line slope of a PSD model) to quantitatively describe PSD.


The significance of these parameters was tested using machine learning. Laboratory-scale samples were used for training and commercial-scale samples for testing a model. Several machine learning techniques were used to further examine the importance of these input variables using a large data set from wet granulation scale-up study.


The Gradient Boosted Regression Trees (GBRT) algorithm had the lowest root mean square error (RMSE) values for the several responses studied (tablet tensile strength, tablet diameter and thickness, compaction work, decompaction work, and net work). The GBRT model for tablet tensile strength had an R2 model value of 0.87 and was not overfitted. The importance of input variables R2 and a was proven by the stepwise regression model’s p value (0.0003) and GBRT importance score (0.37 and 0.44, respectively). The GBRT model was the most successful in predicting decompaction work (R2 model = 0.97) with the least regularization effect.


The proposed parameters can be used in PSD characterization and applied in critical quality attributes (CQA) prediction and wet granulation scale-up.


Particle size distribution Machine learning modeling Wet granulation Scale-up 



We thank Wesley Stringer, Con Psalios, Lalit Khera, Snehal Malani, Danijel Canji, and Emanuel Millen for their support. We thank operators from Probiotec Ltd., Ursula Basilio, and Charlie Cutajar, for their assistance in commercial scale runs.


Aleksandar Kovačević was partially supported by the Grant No. III-47003 provided by the Ministry of Education, Science and Technological Development of the Republic of Serbia.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Supplementary material

12247_2019_9398_MOESM1_ESM.docx (59 kb)
ESM 1 (DOCX 58 kb)


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Pharmaceutical Technology and Cosmetology, Faculty of PharmacyUniversity of BelgradeBeogradSerbia
  2. 2.Faculty of Technical SciencesUniversity of Novi SadNovi SadSerbia

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