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screw, the threaded insertion depth, and the properties (typically characterized by
speci
c gravity) of the material in which the screw is inserted. By transposing this
theory to the pedicle screw implantation procedure, the holding power (i.e., fastening
strength) of a pedicle screw is directly proportional to the screw diameter, the length
of the threaded portion of the screw inserted within the bone, and the speci
c gravity
of the pedicle body, typically characterized by its bone mineral density (BMD).
Based on this relationship, we de
ne Fastening Strength as a surrogate measure for
the screw holding power that combines both implant dimension and trajectory
estimated based on the virtually-templated images using the relationship below:
D = 2
Z
L
Z
2 p
Z
Fastening Strength
¼
r
Ir
ð
; h;
z
Þ
dr d h dz
;
0
0
0
where L is the length of the in-bone threaded portion of the screw, D is the screw
diameter, and I(r;
;z) is the image intensity at each voxel within bone volume
displaced by the virtual screw. The above relationship represents the intensity
θ
area product evaluated in transverse slices (de
ned by the in-plane cylindrical
coordinates radial distance r and angular increment d θ ) throughout the extent of
the insertion depth.
Studies [ 15 ] have revealed a linear correlation between the image intensity and
BMD measurements, based on calibrations of known BMD CaHA (calcium
hydroxyapatite) phantoms against the dynamic intensity range: BMD =
α ·
Inten-
sity, where
0.03. Moreover, the typical BMD of spinal cortical bone (hard
shell coating the pedicle surface) was reported as 192
α
= 0.8
±
10 mg/cm 3 [ 16 ], and the
BMD of the cancellous bone (spongy bone near the pedicle core) was reported
as
±
140 mg/cm 3 .
We refer to the Fastening Strength as a surrogate measure for the screw holding
power primarily because the voxel intensity is used to characterize the bone mineral
density (BMD) of the pedicle body segment displaced by the screw. Moreover, the
Fastening Strength is not intended to be interpreted or employed as an absolute
metric, but rather a relative measure to compare the expected holding power pro-
vided by implants of different dimensions and inserted along different trajectories
within the bone.
*
3.2.4 Physical 3D Model Generation
After the pre-surgical plan is completed, the original CT data and the SSP results
are imported into Analyze [ 17
20 ] for additional processing prior to 3D model
printing. The spine is segmented in the CT images using basic thresholding. If the
quality of the scans is low, additional manual techniques are required to correctly
delineate the spine. Following the detailed spine segmentation step, the pedicle
screw placement data generated by the SSP are incorporated by inserting
-
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