**4.3 Experiments**

*Assistive and Rehabilitation Engineering*

valid [30, 33, 38, 39].

**Figure 11.**

between the two feet.

system and those given by the 3D-GA system.

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

accumulation of the digital integration error.

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

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

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

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

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

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.

**152**

two feet.

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

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

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 calculated to describe the robustness of event detection.

**Figure 12.** *Placement of rangefinder.*

**Figure 13.** *Joint angles of hemiparetic subject normalized in gait cycle.*

**Table 2** summarizes the results of the comparison of the accuracy between the proposed system and the 3D-GA system of joint angles and gait events as well as the robustness of the gait event detection. The RMSE estimates of joint angles are between 1.3° and 3.9° for hemiparetic patients and between 1.8° and 4° for healthy subjects. The CCs for stroke subjects are between 0.9 and 0.99. For healthy persons, they are between 0.91 and 0.99. In terms of the detection of gait events, the RSMEs for IC detection are between 45 and 14 ms for hemiparetic patients and between 16 and 24 ms for healthy persons. The FC event detection has a precision between 12 and 41 ms for hemiparetic patients and between 15 and 20 ms for healthy persons. The rates of detection of CI are between 93 and 100% for hemiparetic patients and between 95 and 100% for healthy persons. The rates of detection of FC are between 92 and 100% for hemiparetic patients and between 97 and 100% for healthy people.

**Figure 14** illustrates the correlation and concordance of the joint angles measured by the two systems. The coefficient of determination (r2 ) equals 0.98. The lower limits of agreement (95%) equal −3.6° and the upper limits of agreement (95%) equal 5.9°.

#### **4.4 Discussion**

This chapter describes the use of a wireless rangefinder to measure the feet relative distance in order to automatically detect the gait events (IC and FC) in everyday life condition and specially to consider the differences between normal and pathological walking.

To evaluate the precision and robustness of the proposed system, experiments have been carried out on hemiparetic and healthy persons. The estimated information delivered is compared with that from the 3D-GA system. Their comparison shows that the joint angles estimated with the proposed system are quite comparable to those of the reference system. In terms of the detection of gait events, thanks to the additional information given by the rangefinders, errors are rare. The system is very robust in the case of pathological walking.

In terms of detection of gait events, the results show a precision of 27 ms for IC events of hemiparetic patients and 22 ms for FC events. More than 98% of the events are correctly detected. The results show that this method has good accuracy and is especially robust for pathological gait. However, because of the limitation of the area detectable by the 3D-GA system, the comparison can be done only between the data captured in this area. So, even if the detection rate of the events of several persons reaches 100%, one can imagine that it is possible that some events are lost during the beginning and the end of the gait.

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**Joint angles**

**Knee**

**Hip**

**CI**

**CF**

**Ankle**

**RMSE (°)**

Hemiparetic patients

1 2 3 4 5 6 7 8 9 10 11

> Mean

Healthy persons

1 2 3 4

> Mean

**Table 2.**

*Comparison between the proposed system and the 3D-GA system.*

2.7 3.25

0.93

2.60

0.99

2.20

0.98

20.25

97.50

15.00

98.50

0.93

3

0.99

2.8

0.98

16

100

12

100

4

0.91

1.8

0.99

1.5

0.99

21

95

20

97

3.1

0.94

3.7

0.98

1.2

0.99

24

98

13

97

3.2

0.92

1.9

0.99

3.3

0.97

20

97

15

100

2.5 2.75

0.94

2.53

0.99

3.13

0.97

26.91

98.73

22.00

98.55

0.95

1.3

0.99

3.6

0.99

30

93

24

92

1.9

0.97

1.8

0.99

1.6

0.99

14

100

17

100

2.9

0.93

3.1

0.97

3.6

0.91

28

98

15

97

3.6

0.90

2.4

0.99

3

0.99

19

100

12

100

3.9

0.95

3.5

0.98

3.5

0.97

35

100

41

100

2.6

0.91

2.5

0.99

2.7

0.98

15

100

13

100

2.6

0.94

2.9

0.99

2.6

0.98

45

98

42

98

1.8

0.92

3.9

0.98

3.9

0.92

20

100

22

100

2.4

0.97

2.6

0.99

3.8

0.94

25

97

17

100

3.9

0.92

1.9

0.98

3.8

0.98

22

100

22

2.1

0.95

1.9

0.99

2.3

0.98

43

100

17

100

**CC**

**RMSE (°)**

**CC**

**RMSE (°)**

**CC**

**RMSE (ms)**

**Rate (%)**

**RMSE (ms)**

**Rate (%)**

**Gait events**

*An Embedded Gait Analysis System for CNS Injury Patients*

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

97


### *An Embedded Gait Analysis System for CNS Injury Patients DOI: http://dx.doi.org/10.5772/intechopen.83826*

*Assistive and Rehabilitation Engineering*

*Joint angles of hemiparetic subject normalized in gait cycle.*

**Table 2** summarizes the results of the comparison of the accuracy between the proposed system and the 3D-GA system of joint angles and gait events as well as the robustness of the gait event detection. The RMSE estimates of joint angles are between 1.3° and 3.9° for hemiparetic patients and between 1.8° and 4° for healthy subjects. The CCs for stroke subjects are between 0.9 and 0.99. For healthy persons, they are between 0.91 and 0.99. In terms of the detection of gait events, the RSMEs for IC detection are between 45 and 14 ms for hemiparetic patients and between 16 and 24 ms for healthy persons. The FC event detection has a precision between 12 and 41 ms for hemiparetic patients and between 15 and 20 ms for healthy persons. The rates of detection of CI are between 93 and 100% for hemiparetic patients and between 95 and 100% for healthy persons. The rates of detection of FC are between 92 and 100% for hemiparetic patients and between 97 and 100% for healthy people. **Figure 14** illustrates the correlation and concordance of the joint angles mea-

) equals 0.98. The

sured by the two systems. The coefficient of determination (r2

is very robust in the case of pathological walking.

during the beginning and the end of the gait.

lower limits of agreement (95%) equal −3.6° and the upper limits of agreement

This chapter describes the use of a wireless rangefinder to measure the feet relative distance in order to automatically detect the gait events (IC and FC) in everyday life condition and specially to consider the differences between normal

To evaluate the precision and robustness of the proposed system, experiments have been carried out on hemiparetic and healthy persons. The estimated information delivered is compared with that from the 3D-GA system. Their comparison shows that the joint angles estimated with the proposed system are quite comparable to those of the reference system. In terms of the detection of gait events, thanks to the additional information given by the rangefinders, errors are rare. The system

In terms of detection of gait events, the results show a precision of 27 ms for IC events of hemiparetic patients and 22 ms for FC events. More than 98% of the events are correctly detected. The results show that this method has good accuracy and is especially robust for pathological gait. However, because of the limitation of the area detectable by the 3D-GA system, the comparison can be done only between the data captured in this area. So, even if the detection rate of the events of several persons reaches 100%, one can imagine that it is possible that some events are lost

**154**

(95%) equal 5.9°.

**Figure 13.**

**4.4 Discussion**

and pathological walking.

**Table 2.**

*Comparison between the proposed system and the 3D-GA system.*

**Figure 14.** *Correlation (a) and Bland-Altman plot (b).*

**Figure 15.** *CI nondetectable case.*

The proposed system provides good accuracy in determining hemiparetic events but has a limitation. The method uses the relative distance between the feet as the main source of information to determine the IC event. Then, the FC is searched between two IC events. As a result, if the IC event is not correctly determined, the FC event cannot be detected. As shown in **Figure 11**, the IC events of both feet correspond to the local maximum of the relative distance signal of the feet. If the peaks corresponding to the IC are very attenuated, the risk of no longer detecting the IC event increases (**Figure 15**). This figure shows the relative distance and inclinations of the two feet. The colored areas represent the areas where the peaks on the distance signal corresponding to the IC must be observed. In green zones, significant peaks are observable; in red zones, most peaks are very attenuated or undetectable. This system cannot then be used on people that walk with a maximum distance of the feet very close to the length of the step during the double phase support. In practice, for all persons that have a minimum relative distance between feet larger than 20 cm, this system works properly.
