Modeling of blood flow in cerebral arterial circulation and its dynamic impact on electrical conductivity in a realistic multi-compartment head model

This study aims to assess the dynamic impact of non-Newtonian cerebral arterial circulation on electrical conductivity within a realistic multi-compartment head model. Evaluating this research question is crucial and challenging due to its relevance to electrophysiological modalities like transcranial electrical stimulation (tES), electro-/magnetoencephalography (EEG/MEG), and electrical impedance tomography (EIT). In these modalities, accurate forward modeling depends on the electrical conductivity, which is affected by complex tortuous vessel networks, limited data acquisition in Magnetic Resonance Imaging (MRI), and non-linear blood flow phenomena, including shear rate and viscosity in non-Newtonian fluid. To obtain an approximation for the blood concentration, we first use Navier-Stokes equations (NSEs) to solve for the pressure and velocity of the blood in the major vessels. Then Fick's law is used to solve for the blood concentration in the tissues. Finally, Archie's law is used to estimate the electrical conductivity distribution based on the blood concentration. The results, obtained with an open 7 Tesla MRI dataset, suggest that a dynamic model of cerebral blood flow (CBF) for both arterial and microcirculation can be established; we find blood pressure and electrical conductivity distributions given a numerically simulated pulse sequence and approximate the blood concentration and electrical conductivity inside the brain based on those. Our model provides an approximation of the dynamical blood flow and the corresponding electrical conductivity distribution in the different parts of the brain. The advantage of our approach is that it is applicable with limited a priori information about the blood flow and with an arbitrary head model distinguishing the arteries.