  Volume conductor problems in cerebral electrophysiology and bioimpedance do
not have analytical solutions for nontrivial geometries and require a 3D model
of the head and its electrical properties for solving the associated PDEs
numerically. Ideally, the model should be made with patient-specific
information. In clinical practice, this is not always the case and an average
head model is often used. Also, the electrical properties of the tissues might
not be completely known due to natural variability. The objective of this work
is to develop a 4D (3D+T) statistical anatomical atlas of the electrical
properties of the upper part of the human head for cerebral electrophysiology
and bioimpedance applications. The atlas is an important tool for in silico
studies on cerebral circulation and electrophysiology that require
statistically consistent data, e.g., machine learning, sensitivity analyses,
and as a benchmark to test inverse problem solvers. The atlas was constructed
based on MRI images of human individuals and comprises the electrical
properties of the main internal structures and can be adjusted for specific
electrical frequencies. The proposed atlas also comprises a time-varying model
of arterial brain circulation, based on the solution of the Navier-Stokes
equation in the main arteries and their vascular territories. The atlas was
successfully used to simulate electrical impedance tomography measurements
indicating the necessity of signal-to-noise between 100 and 125dB to identify
vascular changes due to the cardiac cycle, corroborating previous studies.
