Bridging pharmacology and neural networks: A deep dive into neural ordinary differential equations

The advent of machine learning has led to innovative approaches in dealing with clinical data. Among these, Neural Ordinary Differential Equations (Neural ODEs), hybrid models merging mechanistic with deep learning models have shown promise in accurately modeling continuous dynamical systems. Although initial applications of Neural ODEs in the field of model-informed drug development and clinical pharmacology are becoming evident, applying these models to actual clinical trial datasets-characterized by sparse and irregularly timed measurements-poses several challenges. Traditional models often have limitations with sparse data, highlighting the urgent need to address this issue, potentially through the use of assumptions. This review examines the fundamentals of Neural ODEs, their ability to handle sparse and irregular data, and their applications in model-informed drug development.