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Magnetic stimulation and therapy 231

Figure 7.6 Lumbar spine models, for one (left) and two (middle) LMS coils, and the FEM computa-
tional domain (Baerov et al., 2019). The FEM mesh is made of B3,000,000 tetrahedral quadratic ele-
ments for the geometry. FEM, Finite element method; LMS, lumbar magnetic stimulation.

these are oriented such that their axes focus on the nerve outline. The construction
process is detailed in Chapter 3, Computational Domains.
The complexity of the model created in the first place using a medical planning
model builder (e.g., 3D Slicer, 2020) was reduced using the “Quadric Edge Collapse
Decimation” and “Screened Poisson Surface Reconstruction” of MeshLab (2020) that
creates “watertight” surfaces and smoothes out the model. Then a CAD tool (e.g.,
Autocad, 2020) is used to convert these constructs to solid entities, assemble the entire
lumbar spine model, add the MS coil(s), and present it in FEM compatible format to
the FEM solver (e.g., Comsol, 2020).
The most frequently used stimulation coil is the circular one. It is used to stimulate
a larger area without the need for precise positioning but with a limited focus. The
“eccentric figure-eight coil,” which uses two (noncoplanar, “butterfly”) circular coils,
provides for more intense stimulation in the region where the axes of the two coils
come across (Maccabee et al., 1991; Sekino et al., 2020). Other MS methods are avail-
able or under investigation—for instance, implanted pulse generators used for spinal
cord stimulation (Lempka and Patil, 2018; Risson et al., 2018; Mayfield, 2020).
Thesizeand complexity of thespine constructmay exceed regular, availablecomputa-
tional resources therefore the containing torso segment is here replaced with an equivalent
cylindrical enclosure, as is the containing volume of the magnetic field, Fig. 7.6,right.
LMS may use pulsed, PWM (pulse width modulated), or harmonic stimuli. Here
the excitation is presented as harmonic (ac) at f 5 100 Hz—a sinusoidal signal per se
or the fundamental harmonic of a PWM pulses train.
The harmonic quasistationary EMF model (Chapter 1: Physical, Mathematical, and
Numerical Modeling) is described through the magnetic circuit law, r 3 H 5 J,