Statistical data analysis methods in Brillouin spectroscopy: Tutorial

The non-contact and label-free nature of Brillouin microscopy, a type of optical elastography, is contributing to the growing popularity of this technology worldwide for applications in fundamental mechanobiology and biomedical diagnostics. The resolution of Brillouin microscopy, however, is not as high as super-resolution imaging and is limited by phonon properties to approximately a micrometer. Since the majority of subcellular and extracellular matrix components are significantly smaller than 1 μm, many cell and tissue components become averaged in a single imaging voxel. This, in turn, presents a challenge for data analysis of Brillouin microscopy measurements collected from heterogeneous samples, especially since the cellular components often have similar and closely positioned spectral features. In this tutorial, we discuss in detail the application of the two unsupervised machine learning methods, principal component analysis and vertex component analysis, which can be used to retrieve information from the Brillouin microscopy data of heterogeneous samples. The main advantage of both methods is their unsupervised nature, thus no preliminary knowledge of structure and composition is needed to isolate the components of interest. We describe the underlying theory for each method and their practical application to Brillouin microscopy. We review their unique advantages and limitations and propose novel ways of applying these methods separately and together for better identification and separation of components. We demonstrate this methodology on a Brillouin dataset collected from a two-phase biological system formed by liquid–liquid phase separation of proteins in a buffer solution, but the method can be universally applied to Brillouin microscopy measurements of any biological object.