**4. Determination of gait events**

*Assistive and Rehabilitation Engineering*

*Correlation (a) and Bland-Altman plot (b).*

From the results of the comparison (**Table 1**), **Figures 6** and **7**, the largest RMSE and the smallest CC are observed for the joint angles of the ankles. Three sources may induce these errors: percussion during walking, centripetal acceleration, and the cross-talk effect [28]. During the walk, the main percussions occur when the foot contacts the ground. Percussions influence the measurements of accelerometers and gyrometers; the filtering process used to reduce these influences does not fully eliminate them. Measurement errors can also be introduced by the cross-talk effect. During a straight walk, the ankles have more degrees of freedom than other joints. When positioning a sensor, there can be misalignments between the sensor and the segment of the human body. The consequence is that the movements in the planes other than the sagittal plane are combined in the measure. This problem can be solved by adding a calibration phase to align the sensor and human body [29]. This problem will be considered in a future study.

**148**

**Figure 7.**

*IMU signals and gait events of a healthy subject.*

**Figure 6.**

Detection of gait events is a fundamental problem. All captured gait signals should be normalized in gait cycles so that they could be compared between each other. Calculations of spatiotemporal parameters are also based on the timing of gait events. So, the determination of the IC and FC event occurrences is compulsory.

In everyday life conditions, the gait event can be captured whether by measuring the ground reaction force (GRF) or by processing of the signals from IMU.

GRF-based methods use foot switches (force sensitive resistor or mechanical switch) placed under toe and heel to determine IC and FC events. Gait event detection is quite easy with these methods. Due to the GRF, the foot switch state toggles both when the foot contacts the ground (Heel-Strike, IC event) and when the foot leaves the ground (Toe-Off, FC event). These systems are considered as the Gold Standard for normal gait due to their high accuracy.

But in pathological gait, the IC event could not correspond to heel-strike and the FC event not often corresponds to toe-off as in normal gait. For example, with foot drop gait, the IC event may be the moment when the toe starts to contact the ground and FC event is the moment of toe-off. Therefore, it is difficult to place the force sensor for the pathological gait, and this limits its use [30].

Several studies propose real-time or delayed real-time motion detection systems based on the use of acceleration and angular velocity signals of human body segments provided by IMU [30–36]. All the algorithms proposed in these studies consist of a set of rules that make it possible to identify several characteristics in the different gait signals. Currently, in everyday life gait event determination systems, the accelerometer seems to be the most used sensor [37]. The data it provides are often coupled with data from the gyrometer to get more reliable results.

**Figure 7** illustrates the acceleration, sagittal angular velocity, and inclination signals of both feet on a healthy subject during normal walking. The signals observed on both feet have almost the same characteristics and shapes. The local extrema of acceleration and angular velocity signals are the most commonly used characteristics for determining gait events (IC and FC) [37]. The accuracy of methods presented in different studies may achieve between 11 and 165 ms [35, 36]. Between 86 and 98% of events are correctly detected for normal gait [37].

**Figure 8** shows the acceleration, angular velocity, and inclination signals of the two feet of a hemiparetic patient during a straight walk. Due to the asymmetry of the gait, the acceleration and angular velocity signals are significantly distinct between the healthy side and the paretic side. The amplitudes of the acceleration and angular velocity signals are much lower than those of a healthy person. Local maximum is strongly attenuated, especially the local maximum corresponding to the IC event in the angular velocity signal. In addition, the style of pathological walking varies greatly between stroke persons and there is a significant variability in the shape of the recordings. Given this specificity, it is difficult to use existing

**Figure 8.** *IMU signals and gait events of a stroke subject.*

methods to treat different types of pathological walking. An alternative method is therefore necessary to determine the gait events.

#### **4.1 Proposed method**

During walk, the distance between the two feet varies periodically. Assume, at moment *t*0, the following situation: both feet are on the ground, right foot forward and left foot back. The beginning of the gait cycle of the right foot is the moment when it touches the ground. The distance between the two feet is maximum, which leads to a local maximum in the feet distance signal. During the single support phase of the right foot, the left foot being in swing phase, the distance between feet decreases until the first local minimum is reached when the left foot passes beside the right foot. This distance then increases to another local maximum when the left foot is on the ground. During the swing phase of the right foot, the second minimum appears when the right foot passes near the left foot. The gait cycle of the right foot ends with increasing distance to the third maximum when the right foot is on the ground. **Figure 9** illustrates the variation in the distance between the two feet during walking of a healthy subject and a stroke subject. Asymmetry in the length of the stroke patients justifies the larger differences in amplitude between adjacent local maximum.

**Figure 10** illustrates the variation in the normalized foot distances in the gait cycle of a healthy and of a stroke person during straight walking. The two signals have similar shapes close to the letter 'w'. The signals are composed of three local maxima and two local minima. This phenomenon seeable during the gait of the healthy person is also encountered in pathological walking. The two local maxima located at the beginning and at the end of the gait cycle correspond to the IC event of the same side. The third local maximum located at around 50% of the walking cycle identifies the IC event of the opposite side. The two local minima occur as the feet pass closest to each other. It is observed that the median local maximum on the signal of the healthy people is very close to the point corresponding to 50% of walking cycle. Opposite, because of the gait asymmetry of the hemiparetic patient, the median local maximum is slightly offset from the middle point of the gait cycle.

**151**

**Figure 10.**

*An Embedded Gait Analysis System for CNS Injury Patients*

Compared to the acceleration and angular velocity signals, the foot distance signal is simpler to use for the recognition of gait events as the extrema are more significant. The IC event can be highlighted by searching for the local maximum of

**Figure 11** shows the relationship binding the distance between the two feet and the IC event. In this figure, the blue curve is the relative distance between feet during the walk of the hemiparetic patient. This distance is captured by the 3D-GA system. The red dots correspond to the IC events determined manually by visual inspection. Green triangles are the local maximums of the distance. Local maxima are very close to the IC events determined manually. Feet distance can then be an

However, local maxima only allow determining that an IC event is produced by a foot. To distinguish, the foot that produces the IC event is the one that has just finished its swing phase, because the opposite foot is in its **support** phase. The acceleration experienced by the foot that produces the IC event must be significantly greater than that of the opposite foot before the IC event. Comparing the accelerations of both feet for a time just before the IC event occurs is the way to

After the IC events have been correctly determined, it is then possible to partition and normalize the recording in gait cycles. Between two IC events on the same foot, there must be a FC produced by this foot. Even if the local maxima that correspond to the IC events are attenuated and become undetectable, the local maxima

alternative, simpler, and more robust method than existing ones.

identify the foot that produces this event.

*Distance between feet normalized in gait cycle.*

*DOI: http://dx.doi.org/10.5772/intechopen.83826*

the foot distance signal.

*Distance between feet during walk.*

**Figure 9.**

**Figure 9.**

*Assistive and Rehabilitation Engineering*

methods to treat different types of pathological walking. An alternative method is

During walk, the distance between the two feet varies periodically. Assume, at moment *t*0, the following situation: both feet are on the ground, right foot forward and left foot back. The beginning of the gait cycle of the right foot is the moment when it touches the ground. The distance between the two feet is maximum, which leads to a local maximum in the feet distance signal. During the single support phase of the right foot, the left foot being in swing phase, the distance between feet decreases until the first local minimum is reached when the left foot passes beside the right foot. This distance then increases to another local maximum when the left foot is on the ground. During the swing phase of the right foot, the second minimum appears when the right foot passes near the left foot. The gait cycle of the right foot ends with increasing distance to the third maximum when the right foot is on the ground. **Figure 9** illustrates the variation in the distance between the two feet during walking of a healthy subject and a stroke subject. Asymmetry in the length of the stroke patients justifies the larger differences in amplitude between adjacent

**Figure 10** illustrates the variation in the normalized foot distances in the gait cycle of a healthy and of a stroke person during straight walking. The two signals have similar shapes close to the letter 'w'. The signals are composed of three local maxima and two local minima. This phenomenon seeable during the gait of the healthy person is also encountered in pathological walking. The two local maxima located at the beginning and at the end of the gait cycle correspond to the IC event of the same side. The third local maximum located at around 50% of the walking cycle identifies the IC event of the opposite side. The two local minima occur as the feet pass closest to each other. It is observed that the median local maximum on the signal of the healthy people is very close to the point corresponding to 50% of walking cycle. Opposite, because of the gait asymmetry of the hemiparetic patient, the median local maximum is slightly offset from the

therefore necessary to determine the gait events.

*IMU signals and gait events of a stroke subject.*

**4.1 Proposed method**

**Figure 8.**

local maximum.

middle point of the gait cycle.

**150**

*Distance between feet during walk.*

Compared to the acceleration and angular velocity signals, the foot distance signal is simpler to use for the recognition of gait events as the extrema are more significant. The IC event can be highlighted by searching for the local maximum of the foot distance signal.

**Figure 11** shows the relationship binding the distance between the two feet and the IC event. In this figure, the blue curve is the relative distance between feet during the walk of the hemiparetic patient. This distance is captured by the 3D-GA system. The red dots correspond to the IC events determined manually by visual inspection. Green triangles are the local maximums of the distance. Local maxima are very close to the IC events determined manually. Feet distance can then be an alternative, simpler, and more robust method than existing ones.

However, local maxima only allow determining that an IC event is produced by a foot. To distinguish, the foot that produces the IC event is the one that has just finished its swing phase, because the opposite foot is in its **support** phase. The acceleration experienced by the foot that produces the IC event must be significantly greater than that of the opposite foot before the IC event. Comparing the accelerations of both feet for a time just before the IC event occurs is the way to identify the foot that produces this event.

After the IC events have been correctly determined, it is then possible to partition and normalize the recording in gait cycles. Between two IC events on the same foot, there must be a FC produced by this foot. Even if the local maxima that correspond to the IC events are attenuated and become undetectable, the local maxima

**Figure 10.** *Distance between feet normalized in gait cycle.*

**Figure 11.** *Relationship between the IC event and the distance between feet.*

that correspond to the FC events are still detectable. The method for determining FC using the signal from gyrometer, which is presented in different studies, remains valid [30, 33, 38, 39].

In the following, the new embedded sensor for measuring the relative distance between feet to determine the IC event is described. The data from this new sensor are coupled with data provided by the IMU to determine the FC event. The accuracy of this method is evaluated by comparing the results provided by the proposed system and those given by the 3D-GA system.

The distance between feet can be measured either by measuring the displacements of the two feet independently or by a direct measurement of the distance between the two feet.

Theoretically, the displacement of the foot can be calculated with data from the IMU attached to the foot. After estimating the attitude of the foot, a reference transformation can be made to transform the acceleration measured in the sensor coordinate system to the fixed coordinate system. By double integration on the acceleration of the foot, the three-dimensional displacement of the foot can be reckoned. But unbounded drifts will appear because of the sensor noise and the accumulation of the digital integration error.

Several studies propose different methods based on the algorithm called "zero velocity update" (ZUPT), which aim at reducing this error [40–43]. These methods are based on the detection of the period during which the foot is considered as static or quasi-static according to the information measured by the accelerometer or the gyrometer, supposing that the foot velocity is equal to zero during these periods. These methods limit the error introduced by the first integration applied to the accelerations to obtain the foot speed. However, no correction is applied to the second integration applied to the speed to calculate the displacement. This implies an accumulation of error over time on the calculation of movement of the foot. The study in [44] shows that the same displacement calculated with data from two IMUs does not give the same result. The errors depend on the style of locomotion and the gait speed as well as the type of environment in which walking is performed [45]. For this reason, none of the studies cited use the movements relative between the two feet.

In order to find a solution, a direct real-time measurement of the relative distance of the feet will be made by a wireless rangefinder that will complement the wireless system. The rangefinder measures the distance directly by measuring the time of fight (ToF) of an electromagnetic wave, thus avoiding complex calculations.

**153**

**Figure 12.**

*Placement of rangefinder.*

*An Embedded Gait Analysis System for CNS Injury Patients*

**4.2 Measurement of feet distance with ultra-wideband (UWB) rangefinder**

To determine gait events using foot distance signal, a pair of rangefinder modules (based on DM1000 [46]) is added to the system. The rangefinders are connected to the sensor nodes on the feet. To obtain the best performance of the distance measurement, the two rangefinders are placed at the medial side of foot, close to the heel, antennas face to face, as shown in **Figure 12**. The feet relative distance provided by the modules is coupled with the information from sensors on the feet to determine the IC and EC events and the times they occur. The rangefinders are sampled at 100 Hz. **Figure 3** illustrates the main organization and role of the

Experiments are conducted to evaluate the accuracy of the proposed system including the gait event detection and joint angle estimation. Experiments are performed in a gait analysis laboratory equipped with 3D-GA system. Totally, 11 hemiparetic patients, 4 females and 7 males 51.7 ± 18.2 years old, participated in the experiments. About, 4 healthy people, 1 female and 3 male aged 24 ± 3.1 years, participated in the experiments. The persons were equipped with both markers for 3D-GA system and proposed wearable system during experiment. All persons have been asked to walk 6 times on a straight course of 8 m with self-selected confirmable speed. The walking scenarios are captured by 3D-GA system at 100 Hz and at 70 Hz by the proposed wearable system. The embedded system's records are re-sampled at 100 Hz so that they can be compared

**Figure 13** illustrates the joint angles of a hemiparetic patient normalized in gait cycles. In this figure, the red curves represent the joint angles of the left side (healthy side) and the blue curves represent the joint angles of the right side (paretic side). The dotted curves are the angles measured by the 3D-GA system and

The two systems are compared by evaluating the accuracy of the gait event detection (IC and FC) and the joint angle estimation. IC and FC events' RSMEs are used to evaluate the accuracy of gait event detection, and the detection rate is

the solid lines are the angles estimated by the proposed wearable system.

*DOI: http://dx.doi.org/10.5772/intechopen.83826*

elements of the final system.

point-to-point with those of the 3D-GA system.

calculated to describe the robustness of event detection.

**4.3 Experiments**
