Data-driven prediction of blood glucose dynamics from vagus nerve recordings using neural controlled differential equations

Abstract Accurately predicting blood glucose dynamics is crucial for understanding metabolic regulation and advancing bioelectronic medicine. The vagus nerve (VN) plays a key role in glucose homeostasis, yet its real-time relationship with blood glucose fluctuations remains underexplored. We introduce neural controlled differential equations (NCDEs) as a novel data-driven approach for modelling the complex interaction between VN activity and blood glucose levels in rats. We utilise data collected from 12 rats including high-frequency neural recordings from single-channel microwire electrodes implanted around the left cervical VN, alongside capillary blood glucose measurements taken every 5 min. We compare the performance of the NCDE against traditional machine learning models–feed-forward neural networks (FFNNs), convolutional neural networks (CNNs) and gated recurrent units (GRUs)— for forecasting future blood glucose levels. The input features comprised the frequency and mean amplitude of detected VN spikes, combined with initial glucose concentration over the prediction window. Results demonstrate that NCDE significantly outperforms FFNNs, CNNs, and GRUs achieving a mean squared error (MSE) below 10%, compared to over 15% for the baseline models. Furthermore, replacing the real neural recordings with random noise led to a sharp increase in MSE (over 20%), confirming the ability of the NCDE in extracting meaningful neural signal information. These findings underscore the potential of NCDEs to enhance physiological time-series modelling, particularly for applications in bioelectronic medicine and precision neural signal decoding.