Information Technology Reference
In-Depth Information
where matrix R
z
ðuð
i
Þþ/
p
Þ
(Eq.
54
) represents the axial vertebral rotation for angle
uð
Þþ/
p
about axis z of the image-based coordinate system. In this case, the axial
vertebral rotation
uð
i
ned in transverse planes that are orthogonal to
axis z of the image-based coordinate system (i.e.
uð
i
Þ
has to be de
i
Þ
¼
u
z
ð
i
Þ
, Eq.
13
). As a result,
the resulting cross-sections are no longer de
ned on the basis of the spine-based
coordinate system, and therefore the spine curve is no longer represented by a
straight line.
Axial Oblique Curved-Planar Cross-Sections
Axial oblique curved-planar cross-sections are obtained by rotating the axial
orthogonal curved-planar cross-section for angles
#
¼
#
p
about axis u and/or for
angle
w
¼
w
p
about axis v of the spine-based coordinate system. However, the
resulting cross-sections are similar to axial oblique multi-planar cross-sections
(section
Axial Oblique Multi-planar Cross-Sections
), with the difference that they
are centered at the selected point p
c
¼
ð
u
c
;
v
c
;
w
c
Þ
in the spine-based coordinate
system, and that rotation angles
ned against the axes of the spine-
based and not against the axes of the image-based coordinate system.
#
p
and
w
p
are de
3.3 Cross-Sectional Visualization
The ef
ciency of the spine-based coordinate system for cross-sectional visualization
of 3D spine images can be observed in cross-sections that result from
flattening
different types of reformations (i.e. MPR and CPR) onto a 2D plane. The examples
are presented for a 3D MR image of a normal spine (Figs.
26
,
28
and
30
) and for a
3D CT image of a scoliotic spine (Figs.
27
,
29
and
31
).
By applying MPR, sagittal orthogonal and oblique multi-planar cross-sections of
the normal spine (Fig.
26
a, b) simultaneously display the anatomy of all vertebrae
along the whole length of the spine, although in the sagittal oblique multi-planar
cross-section, cervical vertebrae go out of the sampling plane because the center of
rotation was at a selected point on the thoracic spine curve. On the other hand, in
the case of the scoliotic spine (Fig.
27
a, b), the anatomy of all vertebrae cannot be
simultaneously displayed in sagittal orthogonal or oblique multi-planar cross-sec-
tions, because the vertebrae come in and out of the sampling plane due to the
curvature of the spine in the coronal plane. The situation is reversed in the case of
coronal orthogonal and oblique multi-planar cross-sections. In the case of the nor-
mal spine (Fig.
28
a, b), vertebrae go out of the sampling plane due to the curvature
of the spine in the sagittal plane, while in the case of the scoliotic spine (Fig.
29
a,
b), all vertebrae can be simultaneously observed along the whole length of the spine
in coronal orthogonal or oblique multi-planar cross-sections. Axial orthogonal
multi-planar cross-sections (Figs.
30
a and
31
a) in general do not display the
fl
