(84h) Size and Shape Characterization of Plate-like Particles

Particle size and shape are important in crystallization processes as they dictate downstream properties like the flowability and bioavailability of the crystallized product. Most pharmaceutical products crystallize as nonequant particles (i.e. needles, platelets), which are more difficult to process than equant particles.¹ To manipulate the crystal shape, a quantitative size and shape characterization device is needed. Dual projection imaging has been used in the past to successfully characterize and manipulate the particle size and shape distribution (PSSD) of an ensemble of needles. ^2,3 Despite the relevance of platelets in pharmaceutical industries, there is a severe scarcity of techniques to reliably characterize their size and shape. This serves as a motivation for this work. Initial simulation studies that mimic a single and dual projection imaging technique shows that platelets are more challenging to characterize, since they exhibit a high rotational variance, as illustrated in Figure 1. Using single projection onto two different planes, two PSSDs can be obtained. The two PSSDs thus obtained are significantly different from each other and neither of them is a good approximation of the true 3D PSSD. Dual projection mitigates to some extent the effects related to particle orientation, but preliminary studies indicate that it is also not sufficient for a quantitative characterization. Since platelet dimensions (with L₁ ≥ L₂ ≥ L₃) cannot be measured accurately with either mono or dual projection imaging, new techniques have to be developed. This work will systematically characterize the accuracy of the state-of-the-art dual projection imaging method and the newly proposed methods for platelets at different conditions.

A simulation tool, henceforth referred to as the “Virtual Test Bench” (VTB),² was used to quantify the accuracy of the different measurement methods. The VTB imitates the dual projection imaging device.³ The VTB samples 5000 particles from a given population, places them within a virtual flow channel, calculates their two projections, and processes them to obtain the characteristic dimensions of the imaged particles. The measured population can then be compared to the true population to identify weaknesses of the measurement technique. Additionally, a population balance solver is also coupled with the VTB to observe the evolution of the measured and the true populations of crystals in a crystallization process. Based on this, the effectiveness of the methods for estimating kinetic model parameters and for manipulating the crystal shape is evaluated.

A preliminary case study revealed that the average relative error on the particle thickness L₃ and on the particle volume reaches up to 200 %. Additionally, the errors heavily depend on the alignment of the particle with respect to the camera and their aspect ratios, both of which are impossible to control by a user.⁴ Therefore, two approaches are tested in silico in an effort to reduce the measurement error. One involves adding an additional projection to provide more shape information and the other involves building a mathematical model that maps the raw images to the particle dimensions. The former approach is successful in reducing the error on the platelet volume. However, the accuracy in characterizing the platelet thickness is only marginally improved. The latter approach trains a data-driven model using data generated using the VTB. Several regression techniques are optimized, including support vector machines, regression trees, and artificial neural networks.⁵ The model input features are extracted from the 2D contours and the 3D reconstructed volume of individual particles. The final model targets are the three characteristic dimensions of the platelet. The training data includes over 450 000 particles with varying size, shape, aspect ratios, and alignment with respect to the camera. Average relative errors of 2 %, 7 %, and 20 % on L₁, L₂, and L₃, respectively, are achieved on individual particles by utilizing an artificial neural network-based model. To evaluate the effectiveness of the proposed enhancements, populations obtained through a simulated crystal growth and dissolution process are virtually measured using the VTB. The true and measured time-resolved cross moments of the distributions are compared. The study highlights the superior performance of the dual projection imaging device coupled with the data-driven model when compared to the state-of-the art technique to characterize the average dimensions and distribution width.⁴

In conclusion, the state-of-the-art dual projection imaging method is inadequate for quantifying platelet dimensions, so two potential improvements are proposed and tested in a simulation framework. A mathematical approach using a data-driven model proves to be successful. This model significantly improves the measurement of platelet dimensions and paves way for developing processes aimed at manipulating the shape of such particles toward more desirable ones that eventually enhances their downstream processability.

References
[1] Megarry, A. J.; Swainson, S. M. E.; Roberts, R. J.; Reynolds, G. K. A big data approach to pharmaceutical flow properties. Int. J. Pharm. 2019, 555, 337–345.
[2] Schorsch, S.; Ochsenbein, D. R.; Vetter, T.; Morari, M.; Mazzotti, M. High accuracy online measurement of multidimensional particle size distributions during crystallization. Chem. Eng. Sci. 2014, 105, 155–168.
[3] Rajagopalan, A. K.; Schneeberger, J.; Salvatori, F.; Bötschi, S.; Ochsenbein, D. R.; Oswald, M. R.; Pollefeys, M.; Mazzotti, M. A comprehensive shape analysis pipeline for stereoscopic measurements of particulate populations in suspension. Powder Technol. 2017, 321, 479–493.
[4] Jaeggi, A.; Rajagopalan, A. K.; Mazzotti, M. How to Characterize Ensembles of Plate-like Crystals in Suspension? 2020 (In Preparation)
[5] Kuhn, M.; Johnson, K. Applied Predictive Modeling; Springer New York: New York, NY, 2013.