AbstractWe utilize single neuron models to understand mechanisms behind Temporal Interference (TI) stimulation (also called “Interferential Stimulation”). We say that a neuron exhibits TI stimulation if it does not fire for a high-frequency sinusoidal input, but fires when the input is a low-frequency modulation of the high-frequency sinusoid (specifically that generated by addition of two high frequency sinusoids with a small difference in their frequencies), while the maximum amplitude is kept the same in both cases. Our key observation – that holds for both FitzHugh-Nagumo and Hodgkin-Huxley neuron models – is that for neuron models that do exhibit TI stimulation, a high frequency pure sinusoidal input results in a current balance between inward and outward currents. This current balance leads to a subthreshold periodic orbit that keeps the membrane potential from spiking for sinusoidal inputs. However, the balance is disturbed when the envelope of the sinusoids is modulated with a high slope: the fast-changing envelope activates fast depolarizing currents without giving slow outward currents time to respond. This imbalance causes the membrane potential to build up, causing the neuron to fire. This mechanistic understanding can help design current waveforms for neurons that exhibit TI stimulation, and also help classify which neuron-types may or may not exhibit TI stimulation.

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 without a priori knowledge of exact conductivities of intermediate layers.

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