Page 241 - Computational Modeling in Biomedical Engineering and Medical Physics

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magnitude of AF in the depth of stimulated tissue and could concentrate the peak
values at the fiber depth level, rather than at the skin surface. It is possible that the
forms of the coils could be refined, considering quadruple coils with eccentric turns.
This geometry requires a slight modification of Eqs. (7.5) (7.7), for circular turns that
are not tangential to the coordinate axes.
The analytic solutions introduced in Section 7.2 provide valuable insights into the
MS aiming the activation of excitable tissues (nerve, muscle, or sensitive cells), pro-
duced by applying an electric stimulus near the cell membrane, which is produced
noninvasively, by electromagnetic induction. The main features of the electromagnetic
field and the electric current impulses released through a stimulation coil, which is
placed at the surface of the skin are the key results. However, numerical modeling
may be required to analyze the MS of the spinal cord, when computational domains
are to approach more realistic. Either CAD or image reconstruction of the lumbar
spine is needed to predict the distribution of the eddy current impulses. The sequel
provides a glimpse into such MS studies.

7.3 Magnetic stimulation of the spinal cord

Numerical modeling may be used as an assertive noninvasive evaluation of effects, pre-
operational stage in designing the LMS. To provide consequential insights, the assess-
ment has to be patient-related and to this aim customized computational domains are
valuable. This subsection concerns the numerical simulation of LMS when the
computational domain is patient-related, constructed using medical imaging techni-
ques. The magnetic field and the electric field are calculated to guide the optimal posi-
tioning and adjustment of the external excitation coils that are used to excite the
lower spinal cord. Attention is devoted to the numerical modeling of LMS using
patient-related anatomic information, to add predictive valences to the available ana-
lytic models presented before. The computational domain used for the lumbar spine is
obtained by imaging reconstruction of the spine, fused with CAD constructs for the
coils (Baerov et al., 2019). Different studies rely on CAD representations (e.g.,
Darabant et al., 2013; Soltoianu, 2018). Although producing results consistent with
known understanding and knowledge, CAD models are less relevant for patient-
related LMS evaluations.
Modeling the lumbar magnetic stimulation

Turning our attention to the computational domain, DICOM computed tomography
(CT) images in axial, coronal, and sagittal planes (e.g., WholeScan, 2017) are used as
input data. Fig. 7.6 presents the five vertebrae of interest and their associated interver-
tebral discs, the spinal cord, and the lumbar spinal nerves of concern, for one (Fig. 7.6,
left) and two (Fig. 7.6, middle) MS coils. When two coils are used (Fig. 7.6, middle)