Biomedical Engineering Reference
In-Depth Information
For this example, the anatomical coordinate system for the thigh can be expressed as
2
4
3
5 ¼
2
4
3
5
2
4
3
5
e tax
e tay
e taz
0
:
949
0
:
258
0
:
180
i
j
k
f
e ta
0
:
284
0
:
950
0
:
131
0
:
137
0
:
175
0
:
975
, comprising axes e tax,
e tay , and e taz . Its basis, however, includes an external marker (medial femoral condyle MK ) that
must be removed before the walking trials. Consequently, the location of the knee center cannot
be computed as described in the preceding example. This dilemma is resolved by placing another
marker on the surface of the thigh such that it also forms a plane with the hip center and lateral
knee marker. These three reference points can then be used to compute a “technical” coordinate
system for the thigh to which the knee center location may be mathematically referenced.
This defines an anatomical coordinate system fixed to the thigh,
f
e ta g
EXAMPLE PROBLEM 4.12
Continuing Example Problem 4.11, and given the coordinates of another marker placed on
the thigh but not anatomically aligned,
thigh wand marker TW
¼
0
:
890 i
0
:
937 j
þ
0
:
478 k
compute a technical coordinate system for the thigh.
Solution
A technical coordinate system for the thigh can be computed as follows:
1. Compute the longitudinal direction, or
-axis, of the technical thigh coordinate system e tt .
Start by subtracting vector LK from the hip center H to form
z
r 7 ¼
0
:
025 i
þ
0
:
094 j
þ
0
:
268 k
and its associated unit vector
e r 7 ¼
e ttz ¼
0
:
088 i
þ
0
:
330 j
þ
0
:
940 k
-axis of the thigh technical coordinate system, e ttz .
2. To compute the axis that is perpendicular to the plane formed by LK , H , and TW , subtract
vector LK from TW to compute
Unit vector e r7 represents the
z
r 8 ¼
0
:
009 i
0
:
079 j
þ
0
:
153 k
3. Calculate the vector cross product r 7
r 8 to yield
r 9 ¼
0
:
036 i þ
0
:
001 j þ
0
:
003 k
with its associated unit vector
e r 9 ¼
e ttx ¼
0
:
996 i
þ
0
:
040 j
þ
0
:
079 k
Unit vector e r9 represents the fore-aft direction, or
x
-axis, of the thigh technical coordinate
system e ttx .
Continued
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