Effect of skull thickness and conductivity on current propagation for noninvasively injected currents

Objective.When currents are injected into the scalp, e.g. during transcranial current stimulation, the resulting currents generated in the brain are substantially affected by the changes in conductivity and geometry of intermediate tissue. In this work, we introduce the concept of 'skull-transparent' currents, for which the changing conductivity does not significantly alter the field while propagating through the head.Approach.We establish transfer functions relating scalp currents to head potentials in accepted simplified models of the head, and find approximations for which skull-transparency holds. The current fields resulting from specified current patterns are calculated in multiple head models, including MRI heads and compared with homogeneous heads to characterize the transparency. Experimental validation is performed by measuring the current field in head phantoms.Main results.The main theoretical result is derived from observing that at high spatial frequencies, in the transfer function relating currents injected into the scalp to potential generated inside the head, the conductivity terms form a multiplicative factor and do not otherwise influence the transfer function. This observation is utilized to design injected current waveforms that maintain nearly identical focusing patterns independently of the changes in skull conductivity and thickness for a wide range of conductivity and thickness values in an idealized spherical head model as well as in a realistic MRI-based head model. Experimental measurements of the current field in an agar-based head phantom confirm the transparency of these patterns.Significance.Our results suggest the possibility that well-chosen patterns of current injection result in precise focusing inside the brain even withouta prioriknowledge of exact conductivities of intermediate layers.