Estimation of the Focality of Coils and Quality of Stimulation of Biological Tissues During Transcranial Magnetic Stimulation

Transcranial magnetic stimulation (TMS) is a well-established neurostimulation technique that regulates the synaptic activity of neurons in the treatment of several neurological conditions and psychiatric disorders. During TMS, electric fields (
$E$
-fields) are induced within the brain through the application of time-varying magnetic fields, using coils located outside the head. Various definitions in the literature calculate the focality of the
$E$
-field by estimating the stimulated area during TMS. Most of these definitions differ in measurement methodologies, showing a lack of homogeneity and diverse criteria toward a unique conception, without evaluating possible scenarios of
under-stimulation
of the target and
overstimulation
of the adjacent biological tissues. Another common fact in the field is the use of “
focality
” definitions regardless of the
target area
or
focal distance
, parameters intrinsically related and required for comparison between coils. Furthermore, to evaluate the degree and quality of stimulation, a criterion indicating how well the
stimulated area
covers the
target area
is required. This work proposes a generalized function and methodology for the focality quantification in TMS coils, considering the target area, focal distance, maximum magnitude of the
$E$
-field, and stimulation threshold. New definitions such as
specific focality (sf)
and
focality form factor ( $d_{n}$ )
have been introduced to describe the suitability of coils for specific stimulation applications. The proposed definitions also offer a general framework to compare coils using homogeneous methodology, parameters, and nomenclature, with potential impact on the standardization of measurement methods in the industry of TMS devices. Using a finite-element simulation tool ANSYS Maxwell 3D, we calculated the
sf
over a magnetic resonance imaging (MRI)-based realistic head model of an adult healthy human subject. The proposed definition assigned dimensionless values to three coils under study, compared to results in surface units of pre-existing definitions. The coils studied are as follows: a figure-of-eight (Fo8) coil, a quadruple butterfly coil (QBC), and a quintuple AISI 1010 carbon steel core coil (QCC). The results confirm the suitability of the method to evaluate contexts of specific target area and focal distance and identify scenarios of focal stimulation, under-stimulation, or overstimulation with respect to the target size.