Parameter Sensitivity and Experimental Validation for Fractional-Order Dynamical Modeling of Neurovascular Coupling

Goal: Neurovascular coupling is a fundamental mechanism linking neural activity to cerebral blood flow (CBF) response. Modeling this coupling is very important to understand brain functions, yet challenging due to the complexity of the involved phenomena. One key feature that different studies have reported is the time delay that is inherently present between the neural activity and cerebral blood flow, which has been described by adding a delay parameter in standard models. An alternative approach was recently proposed where the framework of fractional-order modeling is employed to characterize the complex phenomena underlying the neurovascular. Thanks to its nonlocal property, a fractional derivative is suitable for modeling delayed and power-law phenomena. Methods: In this study, we analyzed and validated an effective fractional-order for the effective modeling and characterization of the neurovascular coupling mechanism. To show the added value of the fractional order parameters of the proposed model, we perform a parameter sensitivity analysis of the fractional model compared to its integer counterpart. Moreover, the model was validated using neural activity-CBF data related to both event and block design experiments that were acquired using electrophysiology and laser Doppler flowmetry recordings, respectively. Results: The validation results show the aptitude and flexibility of the fractional-order paradigm in fitting a more comprehensive range of well-shaped CBF response behaviors while maintaining a low model complexity. Comparison with the standard integer-order models shows the added value of the fractional-order parameters in capturing various key determinants of the cerebral hemodynamic response, e.g., post-stimulus undershoot. Conclusions: This investigation authenticates the ability and adaptability of the fractional-order framework to characterize a wider range of wellshaped cerebral blood flow responses while preserving low model complexity through a series of unconstrained and constrained optimizations.