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Background and Objective: This study aims to evaluate the dynamic effect ofnon-Newtonian cerebral arterial circulation on electrical conductivitydistribution (ECD) in a realistic multi-compartment head model. It addressesthe importance and challenges associated with electrophysiological modalities,such as transcranial electrical stimulation, electro-magnetoencephalography,and electrical impedance tomography. Factors such as electrical conductivity'simpact on forward modeling accuracy, complex vessel networks, data acquisitionlimitations (especially in MRI), and blood flow phenomena are considered.Methods: The Navier-Stokes equations (NSEs) govern the non-Newtonian flow modelused in this study. The solver comprises two stages: the first solves thepressure field using a dynamical pressure-Poisson equation derived from NSEs,and the second updates the velocity field using Leray regularization and thepressure distribution from the first stage. The Carreau-Yasuda modelestablishes the connection between blood velocity and viscosity. Bloodconcentration in microvessels is approximated using Fick's law of diffusion,and conductivity mapping is obtained via Archie's law. The head model usedcorresponds to an open 7 Tesla MRI dataset, differentiating arterial vesselsfrom other structures. Results: The results suggest the establishment of adynamic model of cerebral blood flow for arterial and microcirculation. Bloodpressure and conductivity distributions are obtained through numericallysimulated pulse sequences, enabling approximation of blood concentration andconductivity within the brain. Conclusions: This model provides anapproximation of dynamic blood flow and corresponding ECD in different brainregions. The advantage lies in its applicability with limited a prioriinformation about blood flow and compatibility with arbitrary head models thatdistinguish arteries.

Navier-Stokes Modelling of Non-Newtonian Blood Flow in Cerebral Arterial  Circulation and its Dynamic Impact on Electrical Conductivity in a Realistic  Multi-Compartment Head Model