Biomedical Engineering Reference
In-Depth Information
from the knee center to the hip center represents the longitudinal axis of the coordinate system.
A second coordinate axis is perpendicular to the thigh plane. The third coordinate axis is computed
to be orthogonal to the first two.
The location of the knee center of rotation may be approximated as the midpoint between the
medial and lateral femoral condyle markers,
LK
þ
MK
¼
ð
0
:
881
Þþð
0
:
855
Þ
þ
ð
0
:
858
Þþð
0
:
767
Þ
þ
ð
0
:
325
Þþð
0
:
318
Þ
i
j
k
2
2
2
2
yielding
321
k
The location of the center of the head of the femur, referred to as the hip center, is approxi-
mated based either on patient anthropometry and a statistical model of pelvic geometry [6]or
from data collected while the subject executes a specific hip movement [8]. In this example, the
hip center can be located at approximately
knee center location
K
¼
0
:
868
i
0
:
812
j
þ
0
:
hip center location
H
¼
0
:
906
i
0
:
763
j
þ
0
:
593
k
Now the anatomical coordinate system for the thigh may be computed as follows:
1.
Subtract the vector
K
from
H
, giving
r
4
¼
0
:
038
i
þ
0
:
049
j
þ
0
:
272
k
and its associated unit vector
e
r
4
¼
e
taz
¼
0
:
137
i
þ
0
:
175
j
þ
0
:
975
k
Unit vector
e
r4
represents the longitudinal direction, or
z
-axis, of the thigh anatomical coor-
dinate system
e
taz
.
2.
As with the pelvis, a second vector in the thigh plane is required to compute the coordinate
axis that is perpendicular to the plane. Consequently, subtract vector
LK
from
MK
:
r
5
¼
0
:
026
i
þ
0
:
091
j
0
:
007
k
3.
Form the vector cross product
r
5
e
taz
to yield
r
6
¼
0
:
090
i
0
:
024
j
þ
0
:
017
k
and its associated unit vector
e
r
6
¼
e
tax
¼
0
:
949
i
0
:
258
j
þ
0
:
180
k
Unit vector
e
r6
represents the fore-aft direction, or
-axis, of the thigh anatomical coordinate
x
system
e
tax
.
4.
Again, the third coordinate axis is computed to be orthogonal to the first two. Determine the
medial-lateral or
y
-axis of the thigh anatomical coordinate system,
e
tay
, from the cross product
e
taz
e
tax
:
e
tay
¼
0
:
284
i
þ
0
:
950
j
0
:
131
k
