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