A mathematical framework for modelling the dynamic nature of ADHD symptoms

Area of Science:

• Neuroscience
• Computational Psychiatry
• Mathematical Modeling

Background:

• Attention-Deficit/Hyperactivity Disorder (ADHD) symptoms (inattention, hyperactivity, impulsivity) are dynamic and context-dependent.
• Current diagnostic criteria are static and fail to capture symptom variability.
• Existing computational models for ADHD may lack interpretability or clinical applicability.

Purpose of the Study:

• To develop interpretable mathematical models for the dynamic, context-dependent nature of ADHD core symptoms.
• To ground these models in established neuropsychological principles.
• To provide a quantitative framework for ADHD symptom representation.

Main Methods:

• Formulated algebraic equations to model symptom dynamics.
• Modeled inattention using modulated exponential decay functions.
• Represented hyperactivity with a modulated sinusoidal function.
• Modeled impulsive choice using hyperbolic delay discounting and a probabilistic softmax rule.

Main Results:

• Developed specific mathematical equations quantifying temporal dynamics and contextual modulation for ADHD symptoms.
• Provided a formal representation of attention decay, hyperactivity fluctuation, and impulsive choice.
• Incorporated individual sensitivities and situational factors into the models.

Conclusions:

• Proposed mathematical models offer a novel, quantitative, and interpretable framework for understanding ADHD symptom dynamics.
• Models advance beyond static descriptions, potentially improving clinical assessment and personalized treatment.
• Further empirical validation is needed to establish clinical utility.