Biomedical Engineering Reference
In-Depth Information
For this example, the anatomical coordinate system for the pelvis can be expressed as follows:
2
4
3
5 ¼
2
4
3
5
2
4
3
5
e pax
e pay
e paz
0
:
974
0
:
123
0
:
190
i
j
k
f
e pa
0
:
125
0
:
992
0
:
000
0
:
188
0
:
024
0
:
982
Note that the coefficients associated with these three axes represent the direction cosines that
define the orientation of the pelvic coordinate system relative to the laboratory coordinate system.
In summary, by monitoring the motion of the three pelvic markers, the instantaneous orienta-
tion of an anatomical coordinate system for the pelvis,
, comprising axes e pax , e pay , and e paz ,
can be determined. The absolute angular displacement of this coordinate system can then be
computed via Euler angles as pelvic tilt, obliquity, and rotation using Eqs. (4.32)-(4.34).An
example of these angle computations is presented later in this section.
f
e pa g
Thigh Anatomical Coordinate System
The thigh presents a more significant challenge than the pelvis because three bony
anatomical landmarks are not readily available as reference points during gait. A model
based on markers placed over the medial and lateral femoral condyles and the greater
trochanter is appealing but ill-advised. A marker placed over the medial femoral condyle
is not always feasible during gait—for example, with patients whose knees make contact
while walking. A marker placed over the greater trochanter is often described in the litera-
ture but should not be used as a reference because of its significant movement relative to
the underlying greater trochanter during gait—that is, skin motion artifact [3].
In general, the approach used to quantify thigh motion, and the shank and foot, is to
place additional anatomical markers on the segments during a static subject calibration pro-
cess. Then the relationship between these static anatomical markers, which are removed
before gait data collection, and the motion markers that remain on the patient during gait
data collection may be calculated. It is assumed that this mathematical relationship remains
constant during gait—that is, the instrumented body segments are assumed to be rigid. This
process is illustrated in the Example Problem 4.11.
EXAMPLE PROBLEM 4.11
Given the following marker coordinate data that have been acquired while the patient stands
quietly, also in meters,
lateral femoral condyle marker LK
¼
0
:
881 i
0
:
858 j
þ
0
:
325 k
medial femoral condyle marker MK
¼
0
:
855 i
0
:
767 j
þ
0
:
318 k
compute an anatomical coordinate system for the thigh.
Solution
A thigh plane is formed based on three anatomical markers or points: the hip center, the lateral
femoral condyle marker LK , and the medial femoral condyle marker MK . The knee center
location can then be estimated as the midpoint between LK and MK . With these points, the vector
Continued
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