Data-Driven Neural Differential Equation Model and Stochastic Dynamics for Glioma Prediction

Abstract

Low-grade gliomas are infiltrative, incurable primary brain tumors that usually grow slowly and cause death. This study presents a unique low-grade glioma mathematical model and predicts the parameters of the model through real data using deep learning. We combine the advantages of mathematical models with deep learning features to provide results with precise solutions and high-performance prediction. The global stability of treatment success and failure equilibrium is effectively analysed using the Lyapunov method. Next, we estimate the parameters involved in the mathematical model by fitting them into a set of clinical data and employing a neural ordinary differential equations algorithm. Compared to baseline mechanistic tumor models, our approach reduces prediction root mean squared error to 3.37, demonstrating improved data alignment and forecasting accuracy. We also investigate the impact of stochastic perturbation in the model and the effect of time delay parameter on the rate of drug concentration. As an alternative to conducting clinical trials on patients, practitioners can make more informed decisions about patient treatment by studying the numerous models mentioned above that are appropriate for the patient's condition.