Fractional dynamical model for neurovascular coupling.

Area of Science:

• Neuroscience
• Biophysics
• Mathematical Modeling

Background:

• Neurovascular coupling links neural activity to hemodynamic responses, crucial for understanding brain function.
• Existing models often simplify time delays, limiting their accuracy in complex brain dynamics.
• Functional Magnetic Resonance Imaging (fMRI) relies on Blood Oxygen Level Dependent (BOLD) signals, which are influenced by neurovascular coupling.

Purpose of the Study:

• To propose a novel fractional system model for neurovascular coupling.
• To incorporate the nonlocal properties of fractional derivatives for modeling time-delayed phenomena.
• To couple the fractional model with the balloon model for BOLD signal analysis in fMRI.

Main Methods:

• Development of a fractional calculus-based model for neurovascular coupling.
• Integration of the fractional model with the established balloon model.
• Numerical simulations to analyze the fractional model's properties.
• Preliminary validation against real fMRI BOLD data.

Main Results:

• The fractional model effectively captures time-delayed neurovascular coupling dynamics.
• Numerical simulations demonstrate the model's behavior and parameter influence.
• Preliminary comparisons show potential for improved BOLD signal modeling.

Conclusions:

• Fractional calculus offers a suitable framework for modeling time-delayed neurovascular coupling.
• The proposed fractional balloon model provides a more nuanced approach to fMRI data analysis.
• Further research can refine this model for enhanced brain function understanding.