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Magnetic stimulation and therapy 235

of the induced electrical field, while simplified spherically symmetrical models of the
head concluded the absence of this. The same observation is highlighted by
Nummenmaa et al. (2013), who also contributes with more information on this topic
by specifying that the volume conductor models (Chapter 4: Electrical Activity of The
Heart) influence the numerical evaluations of the electric field produced by TMS.
BEM is a good compromise between numerical accuracy and computational cost and
the anatomically accurate geometries are better for TMS navigation, especially when
considering prefrontal regions of interest, usually targeted in medical therapies.
Further on, Yang et al. (2006, 2007, 2010) and Xu et al. (2005) developed numerical
models for the analysis and geometrical optimization of the magnetic field source used in
TMS. Three different coil configurations were studied, starting from a single circular coil
placed above the scalp, then moving on to coil arrays based on two and seven circular coils
placed above the head. The best behavior was achieved with the array made of seven coils,
which generated the most intense stimulation currents and the lowest magnetic field attenu-
ationin-depthwhencomparedwith other simulated coilsetups.
Other studies are focused on more detailed aspects of the TMS magnetic field source.
For example, Chen and Mogul (2009) embeds a highly detailed 3D geometry of the brain
in a FEM numerical study for TMS, created using image-based segmentation and optimized
meshing. The level of anatomical accuracy goes deep down to the cerebral gyri and sulci all
reached by a skillful combination between CT and MRI image sources. Regarding the
TMS magnetic source field, an in-depth study of the magnetic coil numerical modeling,
published by Petrov et al. (2017), presents the effects of idealized coil geometries upon the
generated stimulating magnetic field. Thus after analyzing three coil geometries (a simple cir-
cular coil, a coil with in-plane spiral winding turns, and one with stacked spiral windings)
the FEM results showed that notable differences occurred. The numerical results were
empirically validated.
There are different TMS protocols—applicator, position, duration, etc. For instance, in
rTMS the applicator is positioned above the left inferior frontal region and uses frequencies
in the range 8 25 Hz for 10 s (Hallet, 2000).The “continuous theta-burst stimulation”
consists of trains of uninterrupted TBS (e.g., 20 s) with bursts of three pulses at 50 Hz,
repeated every 200 ms (i.e., 5 Hz), for a total number of pulses (e.g., 300 pulses; Noh et al.,
2015). The numerical simulation presented next is about a continuous harmonic stimulation,
at 10 Hz, using a planar, circular coil applicator.

Modeling the transcranial magnetic stimulation
The computational domain presented next, a numerical phantom, was created using
imaging-based segmentation techniques applied on a high-resolution CT dataset, Fig. 7.9,
the upper row (Chapter 3: Computational Domains). Three types of tissue are targeted: the
brain, the cranium bones, and the surrounding tissue (a homogenous muscle, fat, and skin