Mathematical and machine learning-assisted modelling of Raman spectroscopy for biomedical applications

Over the past few decades, Raman spectroscopy has emerged as a powerful biomedical tool. Its non-destructive nature and sensitivity to subtle biochemical changes, particularly when combined with machine learning, have enabled promising applications such as surgical assistance and cancer diagnosis. Nevertheless, there are still several challenges, including high data dimensionality, biological sample variability, and imbalanced datasets, which can limit its clinical potential. These challenges also complicate the design of reliable instrumentation and analytical software pipelines. In this critical review, we focus on mathematical and machine learning-assisted spectral generation methods that aim to enhance the applicability of Raman spectroscopy in biomedical research. We explore various spectral generation techniques, ranging from bottom-up approaches (like DFT and TD-DFT) that involve quantum mechanics simulations, to AI-assisted spectral generation techniques (such as GANs and Auto-encoders), while examining their advantages and limitations. Additionally, we discuss the challenges of transitioning Raman spectroscopy from controlled in vitro applications to comprehensive in vivo use. Instead of proposing new methodologies, we summarise and critically evaluate existing mathematical approaches that may assist with signal optimisation, safety analysis, and probe design. By making these methodologies more accessible, we outline open challenges and future directions to provide guidance with reduced costs, shorter development cycles, and improved safety profiles. Finally, we highlight open challenges and outline future research directions to inspire further progress in this field.