Platform
Commercial equipment could be used for acquisition of human movement, which has a competitive advantage when applied to nonvideo monitoring environments. The method described in this paper uses MTx motion trackers (Xsens Technologies B.V., the Netherlands) to acquire the movements of human lower limbs. The MTx is a small and accurate 3DOF inertial orientation tracker which provides driftfree 3D orientation and kinematic data of human body segments: 3D acceleration, 3D rate gyro and 3D Earthmagnetic field. The Xbus Kit (Xsens Technologies B.V., the Netherlands) contains an Xbus Master with Bluetooth wireless link, a wireless receiver and a number of MTx sensor modules. The Xbus Master is a lightweight, portable device that controls multiple MTx modules on the Xbus. Xbus Master and MTx sensor modules are powered by batteries which allow continuous operation for at least 3 h.
Sensor location
Six sensor nodes were used for the experiment (as shown in Figure 1). Four sensors were attached to thigh and shank, on the lateral skin surface near the knee joint and ankle joint, respectively. The other two sensors were attached on the dorsum of feet.
The sensor axes were adjusted in the anteriorposterior plane to accurately measure the motion in the sagittal plane.
The sensors were attached using medical bands. The sensor attachment locations are optimized to reduce the skin movement artifacts based on the clinician’s knowledge and experience [20]. Acceleration, angular rate and magnetic vectors were obtained at sampling frequency of 100 Hz.
Coordinate system
The initial coordinate system X_{0}Y_{0}Z_{0} was difined as: we chose the Zaxis to be directed upwards, perpendicular to the horizontal plane and Xaxis to be directed forwards, in parallel with the subject’s sagittal plane. The Yaxis was a cross product of Xaxis and Zaxis.
The femoral coordinate systems X_{1}Y_{1}Z_{1} and X_{2}Y_{2}Z_{2} were defined using three anatomical feature points. The Zaxis was directed towards the lateral epicondyle, connecting it with the medial epicondyle. The Xaxis, being perpendicular to the Zaxis, was directed towards the great trochanter. The Yaxis was a cross product of Xaxis and Zaxis.
The tibial coordinate systems X_{3}Y_{3}Z_{3} and X_{4}Y_{4}Z_{4} were defined by four anatomical feature points. Zaxes were coincided with the Zaxis of the femoral coordinate system. The point To was the middle point between lateral epicondyle and medial epicondyle. The Xaxis was defined as the line directed towards the point To, that connects it with the middle point between the lateral malleolus and medial malleolus. Then, the Yaxis was a cross product of Xaxis and Yaxis.
The foot coordinate systems X_{5}Y_{5}Z_{5} and X_{6}Y_{6}Z_{6} were defined as follows: the Zaxis was perpendicular to each foot plate, with direction upwards; the Xaxis was in parallel with each foot plate, with direction forwards; the Yaxis was a cross product of Zaxis and Xaxis.
The initial coordinate system and body coordinate systems were defined as described above, using the measured anatomical feature points. All MT sensors’ orientation output values were set to zero when the sensors’ axes were exactly aligned with the axes of the initial system. The rotation transform parameters that are needed to align the coordinate systems of a sensor and a human body segment were employed. The data obtained from the sensors were corrected by the rotation transform parameters to acquire the acceleration and magnetic vectors of the bones.
Experimental design
Twenty subjects (ten hemiplegic patients, ten normal subjects) were recruited. There were five hemiplegic patients with abnormal left lower limb, and five patients with abnormal right lower limb. The experimental procedures were in accordance with the Declaration of Helsinki and were approved by the ethic committee of Shenzhen Institutes of Advanced Technology. Each subject signed informed consents prior to testing. The group included fifteen males and five females with average age of 58.3±12.85 years. The subjects were asked to stand still for 5 seconds for sensor calibration, then to walk straight for five meters at a selfselected comfortable speed towards a target line on the floor. Each subject performed this procedure three times. The actions of each subject were recorded in real time by a camera.
Acquisition of gesture data
The classical method to describe a gesture of an object is to use Euler angles, i.e. roll angle, yaw angle and pitch angle. Gestures of an object could be determined by only integration of angular rate data. However, this solution would be prone to drift over time due to the buildup of bias and drift errors. In order to avoid drift, additional complementary sensors must be used. These sensors usually include accelerometers and magnetometers. Measuring the gravity vector using accelerometers allows estimation of orientation relative to the horizontal plane which can be described by roll angle and pitch angle. However, when the object is rotated around the vertical axis, the gravity vector of each axis of the accelerometer will not change. Since accelerometer data could not be used to describe the rotation around the vertical axis, magnetometer is used to measure the local magnetic field vector to determine the orientation relative to the vertical by calculating the angle between object and geomagnetic North Pole. The data from the incorporated sensors is normally fused using Kalman or other complementary filtering algorithm [21].
The rotation angles, which resulted from the object’s rotation from one gesture to another, could be expressed by Euler angles, i.e. the rotation angle of Xaxis corresponds to the yaw angle in Euler angles, which could be derived from quaternion (the other classic method to describe a gesture). In this study, the quaternion was directly acquired from the output of Xsens MTx motion trackers.
Flexion/extension angle
The Zaxis of sensors on the thigh and shank (at the same limb side) were adjusted to be in the same directions. In this way, the rotation angle of thigh and shank in sagittal plane could be regarded as the angle between two sensors in XY plane. Thus, a virtual point was used as a knee joint center, with two virtual lines in parallel with the Xaxis of each sensor, respectively. It could be regarded that the sensors on the thigh and shank are moved along the virtual lines towards the knee joint until the both sensor centers coincide. Then the knee joint flexion/extension angle could be described by the angle between two virtual lines.
We defined that the coordinate system of the shank sensor will be used as a reference. Then rotations of the thigh could be described in relation to the shank. Let q_{
thigh
} and q_{
shank
} represent the quaternion that describes the gesture of sensors on the thigh and shank relative to the initial coordinate system, q_{
st
} represent the quaternion that describes the gesture of sensor on the thigh relative to the relative coordinate system. The rotation could be described as follows:
{q}_{st}={q}_{\mathit{shank}}^{1}\otimes {q}_{\mathit{thigh}}
The angle amplitude of knee flexion/extension (AK) was defined as the maximum knee flexion/extension throughout one gait cycle.
Gait cycle
The gait cycle is defined as the time interval between two successive occurrences of one of the repetitive events of walking. There were many researches on gait parameter identification that used inertial sensors. Katia Turcot et al. [22] used maximal and minimal values of acceleration in gait cycle to identify the events ‘initial contact’ and ‘toe off’. Arash et al. [23] used the positive and negative peak angular velocities from sensor on the shank to detect gait cycles and estimate temporal parameters of gait. In our work, the event ‘heel off’ of the gait cycle starts from the zero value of the pitch angle that follows the negative value. The event ‘toe off’ was identified by the negative peak value in one gait cycle (Figure 2).
Although any event could be chosen to define the gait cycle, in this work, it starts from one heel off the ground. If it is decided to start with heel off of the right foot, then the cycle continues until the next heel off of the same leg. The left foot goes through exactly the same series of events as the right one, but shifted in time by half a cycle.
The duration of a complete gait cycle is known as a gait cycle time, which is divided into stance time and swing time. The following terms are used to identify major events during the gait cycle:

1.
Initial contact

2.
Toe off
These two events divide the gait cycle into two periods, stance phase, when the foot is on the ground, and swing phase, when the foot is moving forward. The stance phase, which is also called contact phase, lasts from the initial contact to the toe off. The swing phase lasts from the toe off to the next initial contact. The angle amplitudes of initial contact (AIC) and toe off (ATO) were defined as the both limbs’ angles of initial contact and toe off, respectively.
The gait parameters were acquired from the sensors tied on feet, using the method mentioned above. Let q_{
foot
} represent the gesture of the foot at the very beginning of the first gait cycle after the subject was standing still on a horizontal plane, q_{
gait
} represent the gesture of the foot when walking, and let both be relative to the initial coordinate system. q_{
fg
} represent the quaternion of q_{
gait
} rotated from q_{
foot
}. Then q_{
fg
} could be acquired by:
{q}_{fg}={q}_{\mathit{foot}}^{1}\otimes {q}_{\mathit{gait}}
The angle between foot and the horizontal plane could be considered as the rotation angle of yaxis which corresponds to the pitch angle in Euler angles. It could be derived from q_{
fg
}.
Balance level definition
Each subject performed many gait cycles in the experiment, thus the AK, AIC, and ATO of left and right limbs of all gait cycles were added respectively, to denote the angle values of each parameter (AK, AIC, and ATO). In order to quantitatively analyze the balance level of the subject, the balance levels of each parameter were defined as:
\mathit{Balanc}{e}_{H}=\left\frac{\mathit{mea}{n}_{\mathit{AN}}\u2012\mathit{mea}{n}_{N}}{\mathit{mea}{n}_{\mathit{AN}}+\mathit{mea}{n}_{N}}\right
\mathit{Balanc}{e}_{N}=\left\frac{\mathit{mea}{n}_{L}\u2012\mathit{mea}{n}_{R}}{\mathit{mea}{n}_{L}+\mathit{mea}{n}_{R}}\right
where Balance_{
H
}, Balance_{
N
} represent the balance level of hemiplegic gait and normal gait, respectively, mean_{
AN
} and mean_{
N
} represent the mean values of the parameter for the abnormal and the normal limb of hemiplegic patients, respectively, mean_{
L
} and mean_{
R
} represent the mean values of left lower limb and right side of normal subjects, respectively.