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Computational domains 85

A one-time use of the Gaussian smoothing algorithm (Taubin, 1995) along with
the flood-filling filters upon the initial mask (Fig. 3.14A and B) is enough to remove
the small imperfections, to guarantee spatial continuity and to obtain the desired post-
processed final solid model presented in Fig. 3.14C and D. Once FEM discretized, this
geometry becomes the computational domain for action potential propagation numer-
ical studies, presented in Chapter 4, Electrical Activity of The Heart.

A vertebral column segment
Although CAD-built computational domains may offer the needed, accurate support
for numerical simulations that are aimed to unveil the outlining physics that govern a
certain application, however, when patient-related specificities are at a prime, then,
provided they are available, image-based computational domains have to be utilized.
For instance, in the analysis of the magnetic stimulation of the spinal cord [e.g., in the
treatment of the spasticity (Korzhova et al., 2018)], starting with a set of images pre-
senting CT scans in sagittal, axial, and coronal planes, CT scans (Whole Spine
(Cervical Dorsal Lumbar Sacral) CT image data set, 2018) a 3D model is built for
the L1 L5 lumbar segment, as presented next (Baerov, 2019). Fig. 3.15 shows the
data set as presented by Slicer (2018) and the (re)construction produced for medical
purposes—the three main views.
The path to build a solid model usable in an FEM modeler, as part of the computa-
tional domain, for each of the L1 L5 lumbar vertebrae, is as follows. First, the whole col-
umn is visualized, and the ROI containing each of the vertebrae is defined. Next a crop
function is used to visualize singled out vertebrae. Manual segmentation is performed using
the following: (1) threshold tools (to select bone); (2) save island effect (to separate the vertebra
from other entities); (3) paint effect (the parts that do not belong to the vertebra are erased,
and the vertebra is colored to identify its tissue); and (4) split, merge,and build (to create the
1
desired 3D volume of the vertebra). Each model is saved in the STL format introduced
by 3D Systems (1988, 1989, 1994). Fig. 3.16 presents the stages of construction.
Using the same path, the intervertebral discs and the spinal marrow volumes are
constructed (Fig. 3.17).
Next the STL objects are discretized using the following sequence and tools
(MeshLab, 2018): (1) filtering using RSR (remeshing, simplification, and reconstruction);
(2) reduction in the complexity of the 3D model using QECD (quadric edge collapse decima-
tion); (3) filtering using RSR; and (4) “polyface” mesh boundaries closure and smoothing
using SPSR (screened poisson surface reconstruction). The resulting models (Fig. 3.18) are
saved in 3DS format.

1
The STL acronym is related to “standard triangle language,”“stereolithography language,” and “stereo-
lithography tesselation language,” introduced by 3D Solutions (3D Systems, Inc., 1988, 1989, 1994;
Grimm, 2004).