A discrete-continuous-time stochastic framework for attention-deficit/hyperactivity disorder-related symptom modeling and pharmacological intervention via methylphenidate

Oana-Maria-Catalina Crisan

This paper presents an original mathematical and computational framework for modeling the efficacy of methylphenidate as an optimal control policy acting on the nonlinear dynamics of attention deficit hyperactivity disorder. Neural processes in ADHD are conceptualized as stochastic processes with trajectories that inherently converge towards stable, yet dysfunctional patterns associated with clinical symptoms. The pharmacological intervention is mathematically formalized as an external control signal that reassesses the system's drift and redirects these trajectories towards neurotypical regimes. To bridge these theoretical stochastic models with empirical clinical data, latent representations are inferred using a novel deterministic hybrid deep learning architecture, combining a one-dimensional convolutional neural network and a Vision Transformer, trained on preprocessed functional magnetic resonance imaging data.