3 MATERIALS AND METHODS
3.3 D ATA ANALYSIS
3.3.1 Definition and calculation of variables
Link-segment model assumes that human body is linked by many rigid body segments. In our study, the lower part of human body is constructed by seven segments including pelvic, left thigh, right thigh, left calf, right calf, left foot and right foot. The upper part is constructed by eight segments including head, trunk, left upper arm, right upper arm, left forearm, right forearm, left hand and right hand. We use a simple yet rigorous enough marker system with thirty-three reflect markers to define these body segment and obtain the relative motion of the rigid body segments in three dimensions. The relationship between marker set and the segment is as following depictions:
A. Head is defined by markers at T, L.AC, and R.AC.
B. Trunk is defined by markers at C7, L.AC, and R.AC.
C. Upper arm is defined by markers at AC, LE, and OP.
D. Forearm is defined by markers at LE, OP, RS and, US.
E. Hand is defined by markers at RS, US, and MI.
F. Pelvic is defined by markers at L.ASIS, R.ASIS, and sacrum.
G. Thigh is defined by markers at ASIS, THI, and LFE.
H. Shank is defined by markers at LFE, ME, SK, LM, and MM.
I. Foot is defined by markers at L.TO, HL, LM, and MM.
3.3.1.2 Joint center and local coordinate system
We use the concept of local axes and Euler rotation angles to define the three-dimensional joint angle motion based on the set of body surface markers.
In order to calculate the relative Euler angles, we need to define a set of orthogonal local axes both in the moving segment as well as in the reference segment. The sections that follow describe the details associated with the determination of the local coordinate systems, the joint center locations, and the joint angles.
A The global coordinate system
Before participants enter the laboratory, we finish the procedure of calibration and setup a global coordinate system. The calibration is divided into two parts: one is static calibration another is dynamic calibration. Static calibration is used to establish the origin and direction of global orthogonal coordinate. We accomplish it by using reference frame to acquire position and fixing the hinged axis in the correct corner of the force-platform. After build up the coordinate system, we need dynamic calibration to calculate the relative position and orientation of the eight cameras. By doing this, we reconstruct 2-Dimension data from each camera and obtain the 3-Dimension data. The global coordinate system(X, Y, and Z), defined here, the Z axis is along the walkway, the Y axis is the vertical pointing upwards, and the X axis is
perpendicular to both X and Z directions, forming a right-handed Cartesian coordinate system.
B Define joint center
We first use thirty-three reflective markers to define the orientation and direction of seven segments of lower body parts and eight segments of upper body parts in the global coordinate system. And then combine it with anthropometric data to calculate joint center of rotation, which is assumed as a fixed point on the proximal segment during the rotation. These joint centers of rotation and reflective markers are not only orientated by global coordinate system, also construct the embedded coordinate system and each corresponding segment.
i Hip joint center
An empirical relation developed by NCH in 1981 which is based on a pelvic radiograph study is used to estimate the location of the hip joint center relative to the ASIS location and pelvic orientations. In this method, the X, Y, Z coordinate distances of the hop center from the ASIS marker are calculated as a function of the leg length. The location of the hip joint center can also be computed using the distance between the two ASISs as the independent variable (Bell, Brand and Pedersen 1989; Davis, Ounpuu, Tyburski and Gage 1991). Particular mean values, e.g.,
θ
,β
, and C were produced for theWith n R-square correlation coefficient is 0.90. the location (in meters) of the hip joint center in pelvic coordinates relative to the origin of the pelvic embedded coordinate system is defined as
[
ker]
cos cos sinxLdis is the anterior/posterior component of the left ASIS/hip center distance(in meters) in the saggital plane of the pelvic. xRdis is the component of right side.
LLleg = Left leg length, distance between L.ASIS and L.LM; LRleg is right leg length (in meters).
L = average of left and right leg length.
C = distance between L.ASIS and left hip joint center on frontal plane, a function of L (in meters).
ker
rmar = radius of reflective marker (in meters)
dASIS = distance between R.ASIS and L.ASIS (in meters).
θ
= sinθ
=0.467, cosθ
=0.880.β
=sin β = 0.309
,cos β = 0.951
.S = -1 for left side; and +1 for right side.
Same process is repeated for right hip joint center
ii Knee joint center
The knee joint center is assumed to lie in the plane defined by the knee marker, thigh-wand marker, and the hip joint center, halfway between the femoral condyles (Kadaba, Ramakrishnan and Wootten 1990). The location is calculated based on the coronal plane knee width measurement, wknee(in meters), that is, the location of the knee joint center in thigh coordinates and relative to the lateral knee marker is
k
0
The location of it employs the same strategy that is used for the knee center location. The ankle center is assumed to fall in the plane defined by the ankle markers, the knee center, and the shank-wand marker and located halfway between the malleoli (Kadaba, Ramakrishnan and Wootten 1990).
iv Wrist joint center
The joint center of the wrist is the middle between the ulnar and radial wrist marker (Schmidt, Disselhorst-Klug, Silny and Rau 1999):
( )
1 ker ker
wrist
2
rs usC
=
Mar+
Mar (Eq.9) v Elbow joint centerThe elbow joint center is the middle between the medial and lateral elbow markers (Schmidt, Disselhorst-Klug, Silny and Rau 1999):
( )
1 ker ker
elbow
2
me elC
=
Mar+
Mar (Eq.10)vi Shoulder joint center
The shoulder joint center is assumed to fall in the beeline between the acromion marker and the elbow joint center (De Leva 1996):
( )
shoulder kerAC 0.095 elbow kerAC
C =Mar + C −Mar (Eq.11) C Establish a local coordinate system
The three-dimensional coordinates of following points in the absolute reference system are used to calculate the local coordinates systems: sacrum, R.ASIS, L.ASIS, hip center, knee center, ankle center The local coordinates are represented by three orthogonal unit vectors I, J, and K along the embedded X, Y, and Z axes, respectively. The third unit vector K is perpendicular to both I and J, defining a right-handed Cartesian coordinate system.
3.3.1.3 Kinematic and kinetic data
The limb rotation algorithm is based on the determination of Euler angles with a y-x-z axis rotation sequence. Since the orthopedic angles specify the relative orientation of the distal moving segment with respect to the proximal reference frames, the corresponding rotational matrix can be derived in terms of these angles. Let the unit vectors of the proximal reference frame in the absolute reference system be represented by I, J, and K, and the unit vectors in the distal local system of the moving segment be Iz, Jz, and Kz. Then the following relationship can be easily derived based on orthopedic angels
θ
x ,θ
y, andθ
zdefined previously for the pelvic, hip and knee:cos cos sin sin sin cos sin sin cos cos sin sin cos cos sin sin sin cos cos sin sin cos sin sin
sin cos sin
From this, the rotation angles can be calculated as shown below:
sin 1 These joint angles correspond to flexion/extension, adduction/abduction, and internal /external rotation, respectively. Note that the trunk and pelvic angles are absolute angels, i.e., referenced to the initially fixed laboratory coordinate system. The hip, knee, and angle angels are all relative angles,