Biomedical Engineering Reference
In-Depth Information
a
3
x
2
Table 9.5
Clavicle linear and parabolic
(
+
a
2
x
+
a
1
)
fitting coefficients for rotational DoFs
]
ₒ
) and frontal (range
]
ₒ
)
versus thoracohumeral elevation in sagittal (range
[−
50
,
100
[−
100
,
0
planes and center of humeral head vertical translation (range
[
0
,
80
]
mm)
Linear
Parabolic
a
2
a
1
mean(SD)
a
3
a
2
a
1
mean(SD)
Three DoFs rotations versus thoracohumeral flexion/extension (ZXY convention)
X
−
0
.
11159
−
23
.
2327 3.2(2.2)
−
0
.
00098513
−
0
.
061326
−
21
.
4709 2.8(1.6)
Y 0.16736
−
7
.
0886 2.1(1.8) 0.0001033 0.16209
−
7
.
2734 2.1(1.8)
Z 0.23586 14.7331 1.7(1.4) 0.00052921 0.20886 13.7866 1.5(1.1)
Three DoFs rotations versus thoracohumeral flexion/extension (OVP convention)
X
−
.
−
.
−
.
−
.
−
.
0
1466
22
5823 3.5(2.4)
0
0013939
0
080827
20
5679 3.0(1.6)
Y
5563 2.2(1.8)
Z 0.20731 15.8171 1.6(1.1) 0.0005262 0.18248 15.0566 1.5(0.8)
Three DoFs rotations versus thoracohumeral abduction/adduction (ZXY convention)
X
0.095759
−
10
.
2201 2.4(1.8)
−
0
.
00045932
0.11743
−
9
.
0.41363
−
10
.
6629 2.6(2.0)
−
0
.
0034611
0.1206
−
14
.
5356 2.1(2.1)
Y
−
0
.
19048
−
14
.
1894 3.3(2.3)
0.0046046
0.19937
−
9
.
0372 2.5(2.4)
Z
21968 10.1708 4.0(2.4) 0.0059972 0.28807 16.8813 2.8(2.6)
Three DoFs rotations versus thoracohumeral abduction/adduction (OVP convention)
X
−
0
.
0.32993
−
11
.
4658 1.5(1.1)
−
0
.
00093541
0.24472
−
12
.
4539 1.4(1.1)
Y
−
0
.
01723
−
12
.
3698 1.3(1.0)
0.0010837
0.081494
−
11
.
2251 1.2(0.9)
Z
038051 13.8456 1.8(0.8)
Three DoFs rotations versus humeral head vertical translation (ZXY convention)
X
−
0
.
13985
12.6652 1.9(0.9)
0.0011174
−
0
.
−
0
.
32202
−
15
.
225
1.6(0.9)
−
0
.
00035388
−
0
.
29515
−
15
.
4762 1.5(1.0)
Y
0.19283
−
12
.
1147 3.7(3.2)
0.002303
0.017935
−
10
.
4796 3.5(3.2)
Z
10661 12.6846 4.3(3.6)
Three DoFs rotations versus humeral head vertical translation (OVP convention)
X
0.2721
9.144
4.7(4.3)
0.0049868
−
0
.
−
0
.
34035
−
13
.
8726 2.0(0.6)
−
0
.
00042286
−
0
.
30824
−
14
.
1729 1.1(0.9)
Y
0.062493
−
12
.
4087 2.8(2.3)
0.00039623
0.032402
−
12
.
1274 2.7(2.3)
Z
0.22085
11.304
3.9(3.3)
0.0037506
−
0
.
063977
13.9668 3.7(2.8)
data were fitted by polynomial regressions. These non-linear functional relationships
were then used to construct multiple regression functions for ShRm evaluations
covering the full humerus reach. A linear multiple regression approach is presented
in this section to estimate possible solutions.
This approach allows predicting 6 DoFs dependent motions (relative clavicle and
scapula displacements) from the combination of up to 6 DoFs that characterizes
humerus displacements relative to the thorax anatomical frame.
Let's define for the current frame of motion
Q
i
q
i
are predefined weight coefficient and value of humerus i-th DoF. A set of normalized
=
c
i
q
i
,
i
=
1
,...,
6, where
c
i
,
i
=
1
6
weight coefficients is defined as
w
i
=
c
i
|
q
i
|
/
S
,
i
=
1
,...,
6, where
S
=
c
i
|
q
i
|
.
Using these weights one can predict the current values of the dependent DoFs as:
