Biomedical Engineering Reference
In-Depth Information
Solution
These three anatomical markers form a plane. The line between the right ASIS and left ASIS
represents one coordinate system axis. Another coordinate axis is perpendicular to the pelvic
plane. The third coordinate axis is computed to be orthogonal to the first two:
1.
Subtract vector
RASIS
from vector
LASIS
,
LASIS
RASIS
¼ð
0
:
831
ð
0
:
850
ÞÞ
i
þð
0
:
651
ð
0
:
802
ÞÞ
j
þð
0
:
652
0
:
652
Þ
k
to find
r
1
¼
0
:
0190
i
þ
0
:
1510
j
þ
0
:
0000
k
and its associated unit vector:
0
:
000
k
0
019
i
þ
0
:
151
j
þ
0
:
e
r
1
¼
p
019
2
151
2
000
2
:
þ
0
:
þ
0
:
e
r
1
¼
0
:
125
i
þ
0
:
992
j
þ
0
:
000
k
Unit vector
e
r1
represents the medial-lateral direction or
y
-axis for the pelvic anatomical coor-
dinate system
e
pay
(Figure 4.29).
2.
A second vector in the pelvic plane is required to compute the coordinate axis that is
perpendicular to the plane. Consequently, subtract vector
RASIS
from vector
PSIS
to find
r
2
¼
0
:
165
i
þ
0
:
098
j
þ
0
:
034
k
3.
Take the vector cross product
e
pay
r
2
to yield
i
j
k
r
3
¼
0
:
125
0
:
992
0
:
000
0
:
165
0
:
098
0
:
034
¼½ð
0
:
992
Þð
0
:
034
Þð
0
:
000
Þð
0
:
098
Þ
i
þ½ð
0
:
000
Þð
0
:
165
Þð
0
:
125
Þð
0
:
034
Þ
j
þ½ð
0
:
125
Þð
0
:
098
Þð
0
:
992
Þð
0
:
165
Þ
k
¼
0
:
034
i
0
:
004
j
þ
0
:
176
k
and its associated unit vector:
e
r
3
¼
e
paz
¼
0
:
188
i
0
:
024
j
þ
0
:
982
k
Unit vector
e
r3
represents the anterior-superior direction or
z
-axis of the pelvic anatomical
coordinate system
e
paz
(Figure 4.29).
4.
The third coordinate axis is computed to be orthogonal to the first two. Take the vector cross
product
e
pay
e
paz
to compute the fore-aft direction, or
x
-axis, of the pelvic anatomical
coordinate system:
e
pax
¼
0
:
974
i
0
:
123
j
0
:
190
k
