How conductivity boundaries influence the electric field induced by transcranial magnetic stimulation in in vitro experiments

Background

Although transcranial magnetic stimulation (TMS) has become a valuable method for non-invasive brain stimulation, the cellular basis of TMS activation of neurons is still not fully understood. In vitro preparations have been used to understand the biophysical mechanisms of TMS, but in many cases these studies have encountered substantial difficulties in activating neurons.

Objective/hypothesis

The hypothesis of this work is that conductivity boundaries can have large effects on the electric field in commonly used in vitro preparations. Our goal was to analyze the resulting difficulties in in vitro TMS using a simulation study, using a charge-based boundary element model.

Methods

We decomposed the total electric field into the sum of the primary electric field, which only depends on coil geometry and current, and the secondary electric field arising from conductivity boundaries, which strongly depends on tissue and chamber geometry. We investigated the effect of the conductivity boundaries on the electric field strength for a variety of in vitro experimental settings to determine the sources of difficulty.

Results

We showed that conductivity boundaries can have large effects on the electric field in in vitro preparations. Depending on the geometry of the air-saline and the saline-tissue interfaces, the secondary electric field can significantly enhance, or attenuate the primary electric field, resulting in a much stronger or weaker total electric field inside the tissue; we showed this using a realistic preparation. Submerged chambers are generally much more efficient than interface chambers since the secondary field due to the thin film of saline covering the tissue in the interface chamber opposes the primary field and significantly reduces the total field in the tissue placed in the interface chamber. The relative dimensions of the chamber and the TMS coil critically determine the total field; the popular setup with a large coil and a small chamber is particularly sub-optimal because the secondary field due to the air-chamber boundary opposes the primary field, thereby attenuating the total field. The form factor (length vs width) of the tissue in the direction of the induced field can be important since a relatively narrow tissue enhances the total field at the saline-tissue boundary.

Conclusions

Overall, we found that the total electric field in the tissue is higher in submerged chambers, higher if the chamber size is larger than the coil and if the shorter tissue dimension is in the direction of the electric field. Decomposing the total field into the primary and secondary fields is useful for designing in vitro experiments and interpreting the results.