Electric field depth-focality tradeoff in transcranial magnetic stimulation: simulation comparison of 50 coil designs

Various transcranial magnetic stimulation (TMS) coil designs are available or have been proposed. However, key coil characteristics such as electric field focality and attenuation in depth have not been adequately compared. Knowledge of the coil focality and depth characteristics can help TMS researchers and clinicians with coil selection and interpretation of TMS studies.

To quantify the electric field focality and depth of penetration of various TMS coils.

The electric field distributions induced by 50 TMS coils were simulated in a spherical human head model using the finite element method. For each coil design, we quantified the electric field penetration by the half-value depth, d(1/2), and focality by the tangential spread, S(1/2), defined as the half-value volume (V(1/2)) divided by the half-value depth, S(1/2) = V(1/2)/d(1/2).

The 50 TMS coils exhibit a wide range of electric field focality and depth, but all followed a depth-focality tradeoff: coils with larger half-value depth cannot be as focal as more superficial coils. The ranges of achievable d(1/2) are similar between coils producing circular and figure-8 electric field patterns, ranging 1.0-3.5 cm and 0.9-3.4 cm, respectively. However, figure-8 field coils are more focal, having S(1/2) as low as 5 cm(2) compared to 34 cm(2) for circular field coils.

For any coil design, the ability to directly stimulate deeper brain structures is obtained at the expense of inducing wider electrical field spread. Novel coil designs should be benchmarked against comparison coils with consistent metrics such as d(1/2) and S(1/2).