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Unsupervised pharmaceutical polymorph identification and multicomponent particle mapping of ToF-SIMS data by non-negative matrix factorization



Thomas P. Forbes, J Greg Gillen, Amanda Souna, Jeffrey Lawrence


Crystal polymorphism of pharmaceutical compounds directly impacts resulting physicochemical characteristics, a critical aspect in active pharmaceutical ingredient (API) production. Tools to characterize and chemically map these polymorphs at the single particle scale remain important to advancing directed manufacture of targeted polymorphs. Here, time-of-flight secondary ion mass spectrometry (ToF-SIMS) was employed for chemically imaging inkjet printed acetaminophen samples. ToF-SIMS generates large datasets of high spatial resolution images. Extracting relevant data and peaks of interest can be laborious for, and biased by, users. Advances in machine learning approaches have introduced many supervised and unsupervised methods for data analysis. In this study, we apply non-negative matrix factorization (NMF) for the unsupervised analysis of ToF-SIMS chemical image data. More specifically, an expanded variant of NMF, NMFk, was employed to determine the dataset's latent dimensionality. NMFk combines the spectral unmixing of traditional NMF with k-means clustering of the resulting factors and an optimization of the reconstruction and clustering. The method was used to identify the number of polymorph phases – and their representative mass spectra – generated from inkjet printed acetaminophen samples. Amorphous, crystalline form I, and crystalline form II polymorphs were observed. The learned polymorph mass spectra were then used to map the learned polymorphs onto subsequent particle samples of acetaminophen. Finally, NMFk also enabled the decomposition of mixed particle samples (i.e., migraine medicine), learning the number of compounds and their composition. The extracted constituent phase mass spectra – representing single compounds – were searched against mass spectral libraries for identification.
Analytical Chemistry


Unsupervised machine learning, Non-negative matrix factorization, ToF-SIMS, Polymorph, Pharmaceuticals, Chemical mapping


Forbes, T. , Gillen, J. , Souna, A. and Lawrence, J. (2022), Unsupervised pharmaceutical polymorph identification and multicomponent particle mapping of ToF-SIMS data by non-negative matrix factorization, Analytical Chemistry, [online],, (Accessed May 19, 2024)


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Created November 15, 2022, Updated November 29, 2022