The "quasi-uniform" assumption in animal and computational models of non-invasive electrical stimulation.

Transcranial stimulation encompasses all non-invasive brain stimulation techniques where electrical current is generated or induced in the brain for experimental or therapeutic purposes using scalp electrodes or magnetic coils. Each modality (e.g. transcranial current stimulation, cranial electrotherapy stimulation, transcranial magnetic stimulation, electroconvulsive therapy) produces a spatiotemporal pattern of electric current flow in the brain that then determines neurophysiological response. Due to the relatively large separation between electrode/coil and stimulated tissue, the target region is often in the “far-field” of the electric field. Thus, unlike stimulation with implanted electrodes, the gradient of the electric field is limited in the vicinity of the brain target. Computational models of transcranial stimulation predict brain current flow patterns for dose optimization. Translational animal models aim at elucidating the cellular mechanisms of neuromodulation. Here we identify and define a ubiquitous assumption underlying both computational and animal models, referred to herein as the “quasi-uniform assumption”. Though we attempt to rationalize the biophysical plausibility for the quasi-uniform assumption based on the limited electric field gradients generated during stimulation, our goal is neither to justify nor repudiate it, but rather emphasize its implicit use in a majority of modeling and animal studies. The quasi-uniform assumption states that local polarization in a target region is proportional to the local electric field magnitude (EF): Polarization (target)f EF (target). This assumption is not trivial becausemembranepolarizationhas longbeen linkedto the change in electric field, via the so-called “activating function”. However, it is well known that in a uniform electric field, where by definition the electricfieldgradient is zero,membrane compartmentsmaypolarize linearly with electric field (see below). The term “quasi-uniform” implies that the spatial gradient of electric field is locally negligible (withinabrain region) to bringabout changes inmembranepolarization, and thus local membrane polarization is determined by electric field. The electric field may vary globally across brain regions, thus determining which targets are preferentially polarized. The general quasi-uniform assumption is that polarization is linear with electric field magnitude for each target with comparable sensitivity: compartment polarization distribution across targets is comparable for a given electric field. The general assumption ignores regional differences in morphology, biophysics, and function, but may be a reasonable first approximationwhen considering cortex. Because any neuromodulation, and resulting cognitive/behavioral changes, are assumed to follow from membrane polarization, the extent of polarization indicates the probability of a region to be influencedby the stimulation. Certainly, “neuromodulation” encompasses a broad swath of potential acute and plastic changes, and is dependent not only on polarization but also endogenous factors such as ongoing (patho) physiological neuronal activity. Changes may even be non-monotonic with polarization level. Nonetheless, membrane polarization remains the only known biophysical mechanism of action for transcranial stimulation modalities. In this letter we establish the ubiquity of the quasi-uniform assumption rather than address the more complex issue of its justification and limitation; nevertheless, some explication is useful. During transcranial stimulation, the generated electric field changes incrementally over space (compared to the space constant of the neuronal membrane) such that the resulting membrane polarization of any given neuronal segment is approximated by the local electric field. For example, if we consider the electric field generation around the initial segment of a cortico-spinal axon, the same segment would respond similarly (e.g. trigger an action potential) to a uniform electric field of comparable magnitude. More generally, the electric field is assumed to change incrementally on the scale of a neuron or cortical column. Thus, on the scale of a neuron, any electric field gradients are not significant in the sense of contributing to neuronal polarization. This assumption of functionally negligible electric field gradient is reasonable for transcranial electrical/magnetic stimulation, which uses macro-scalp electrodes or coils at a distance from the brain [1,2]. To be clear, it is not assumed that the electric field is uniform across the entire brain. The two key implications of the quasi-uniform assumption are then: