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approximate a glenoid shape is
c
2
p
e
k
¼
(27
:
12)
where c is the height of glenoid fossa measured along the Y-axis and e is the tolerance of measurement.
Both terms are expressed in millimeters. For example, if the height of glenoid fossa c was 39.1 mm and
the humerus magnetic resonance imaging (MRI) slices were 2 mm in thickness, then the number of
tangents was seven (Figure 27.3). For thinner MRI slices, the minimum number of tangents needed to
fit the glenoid fossa geometric surface would be larger.
27.3 Data Collection
The method of geometrical description of the glenoid fossa concavity in a frontal plane, for a cross
section through the acromion, has been applied for 12 subjects participating in an experiment to deter-
mine their glenoid geometries. The participants' mean age (and standard deviation) was 40.5
+
8yr,
with an average height of 178
15.60 kg. Proper informed
consent forms were obtained from the participants, as approved by the Institutional Review Committee
(IRC) at the Liberty Mutual Research Institute for Safety. The geometric data of the glenoid concavity
means the tangents' inclination f
i
at the seven nodes (i
+
7.09 cm and body weight of 81.54
+
7) on the curve of the glenoid and the distances
z
i
between the middle deltoid attachment and a point at which each tangent to the glenoid fossa crosses
the Z-axis (Figure 27.3) were collected. Magnetic resonance images were taken at the same arm positions
¼
Y
z
1
z
7
z
2
z
6
z
3
z
5
z
4
Z
Z
f
7
f
1
f
6
f
5
f
2
f
3
f
4
FIGURE 27.3 The group of seven tangents approximated the bone surface data that fit to the glenoid fossa
geometric surface from MRI slice of 2 mm thickness.
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