Estimation of Gait Stability based on Accelerometer Signals Hector Moncada-Gonzalez, Ruth M. Aguilar-Ponce, and J. Luis Tecpanecatl-Xihuitl School of Sciences Universidad Autonoma de San Luis Potosi San Luis Potosi, Mexico
[email protected] phases that completes the walking cycle. The stability of the walking cycle can be defined as a repetition of a walking cycle with minimal variation between cycles. The amount of variability present in the walking pattern reflects the neuromuscular control of the person. When the amount of variability is high, means that the person has a poor stability, while a small amount of variability reflect a high stability.
Abstract— an estimation of gait stability based on accelerometer signal is presented. The walking process of a human body is a complex task that involves the muscular, joint and nervous systems. The gait cycle is divided into swing and stance phases. Gait stability is defined as repetition of the gait cycle with minimum variability. In order to assets the gait stability a series of parameter are estimated, such parameters include, duration of the gait cycle, length of the left and right step, average speed of the gait and number of samples per cycle. The first step toward establish gait stability is estimated the beginning and ending of a cycle. This process is achieved by a series of filter that isolated 2Hz component that is produce by heel strike. Once the cycles have been localized, the rest of the parameters are estimated. The algorithm was tested on a set of 40 healthy persons from ages 20 to 59. The results show that the stability decreases with age, as expected, since our neuromotor system deteriorates with age.
Our proposal is to estimate walking stability through accelerometer signals that are capture by a smart phone. Smart phone has a set of sensor such as accelerometer, gyroscope, proximity, etc. Additionally, smart phone counts with a processing unit, and communication unit that include a series of protocols such as Bluetooth, WI-FI and Cellular Network. A triaxial accelerometer is included in most smart phone that provide information of the acceleration on the three planes of a human body, transverse, frontal and sagittal planes illustrated in Figure 1. The plane that provides more information about the walking cycle is the sagittal. The acceleration signal in this plane is analyzed to acquire the variability of the walking cycle.
Keywords—gait stability, accelerometer signals, smart phone
I.
INTRODUCTION
A natural process of ageing causes changes in the neuromuscular system of a human being, decreasing their ability of performs daily activities. Walking gait stability suffer negative changes that results in an increasing number of falls during daily activities in elderly subjects. There have been several studies that reported the changes in kinematics parameters with age [1, 2]. However, the reports have been done using complex systems that requires special spaces to record a series of movements using markers in the body to assets the estimation on the walking stability [3]. Even though the results are precise, the experiments must be done in a laboratory, and cannot be done while performing normal activities during the day. There are several systems that are estimating the walking stability through a set of sensor strapped in the body and sending the information to a computer that analyses the signals and estimates the stability [4]. .
Fig. 1. Human Body planes: sagittal, transverse and frontal.
Additionally, human gait estimation has been used to assets the recovery process of patients after a surgery. Human gait encompasses the interaction of muscle, joint and nervous systems that changes the center of gravity on each leg repeatedly. The gait hast two phases: stance and swing. The stance phase is when the foot is on the ground, and swing phase comprehend when the same foot is no longer in contact with the ground. The gait consists of series of stance and swing
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The rest of the paper is organized as follows, in section II discuses the parameter that are calculated to assets the variability, while section III shows the implementation of the proposed estimation. Section IV presents the results and finally section V provides our conclusion.
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II.
VARIABILITY MEASUREMENT OF THE WALKING CYCLE
The walking cycle consist of stance and swing phases, which include the following movements in each phase: heel strike marks the beginning of a gait cycle and represents the point at which the gravity center of a human is in the lowest position. Then the plantar surface of the foot touches the ground, after that the other foot swings to pass to stance phase. At this point the center of gravity is the highest position. Then the hell loses contact with the ground and pushes to initiate a plantar flex. The toe leaves the ground to finish the stance phase and initiates the swing phase. Acceleration starts when the foot leaves ground to enter into midswing phase that coincide with midstance phase of the other foot. Finally deceleration is the action of the muscles to slow the leg and stabilize the foot to achieve the next heel strike. These phases can be clearly observed in the acceleration signal obtained from the sagittal plane by a smart phone strapped in the thigh as shown in Figure 2.
Lowpass Filter
Derivative Filter
Nonlinear Transformation
Average Filter
Thresholding
Fig. 3. Process to estimate the beginning of each gait cycle
The threshold is established dynamically based on the signal of each individual. The threshold is calculated using the following equation:
(2) where amax denotes the maximum acceleration value in the sagittal plane. 6
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Acceleration Signal in Sagittal Plane
Aceleracion
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Fig. 4. Output of the Lowpass Filter
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Fig. 2. Accelerometer signal from the sagittal plane.
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In order to calculate the variability of the gait cycle, the first step is to estimate when a cycle finish and starts the next. A set of accelerometer signals of 40 healthy persons between the ages of 20 and 50 years old were analyzed. In each signal the heel strike cause a spike that was localized at 2 Hz. Therefore, the beginning and end of a cycle can be established by detecting such spike. In order to detect it, a lowpass filter is used to retain only the values from 0 to 2Hz. The isolation of this component is illustrated in Figure 4. The spike can be highlighted using a derivative filter. The derivative filter shows the change rate on the signal. The 4th order derivative filter has the following transfer function:
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Fig. 5. Output of the derivative Filter 0.7
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A nonlinear transformation emphasizes the spike and gets rid of the negative values by squaring the values of each sample. The results of the derivative filter and the nonlinear transformation is shown in Figure 5 and 6. Then an average filter of 7th order is used. After this process, a threshold that is dynamically selected estimates the beginning of a cycle. Figure 3 illustrates the process of detecting the beginning of a cycle.
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Fig. 6. Squaring of the signal
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The average velocity can be estimated dividing the total estimated distance by the duration of the test.
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(5)
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where Lcycle and Tcycle are the distance and duration of each cycle. The length of the left step is estimated through the following equation [4],
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Fig. 7. Output of the Average Filter
(6)
Once each cycle is detected, then the variability of the cycle is measure in terms of duration of each cycle, number of samples per cycle, average velocity during the cycle and step length for right and left foot.
where ai are the sample of the acceleration signal in the sagittal plane of the cycle, Nc is the number of samples per cycle. Tcycle is the duration of the cycle and p is the difference between the highest values of the cycle i and the cycle i+1. The parameter k was determined experimentally and is k = 750 for males and k=630 for females [5].
A. Parameter Estimation for each Cycle The Android sensor framework includes a timestamp with each sample of the accelerometer. Therefore, the duration of a cycle can be estimated by subtracting the timestamp of the beginning of a cycle i form the timestamp of the beginning of the cycle i+1. The number of samples per cycle is estimated in similar manner.
B. Stability estimation Once the parameter estimation has been done, a set of measurement of each cycle can express the regularity of the gait cycle. In order to estimate the variability of the gait cycle, the mean and variance of each set of parameter is calculated. Then, the stability can be estimated by:
In order to estimate the length of each step, an estimation of the total length of a complete cycle is performed based on the acceleration signals. The distance is estimated using the following equation:
(7)
C. Implementation of Proposed Algorithm The proposed algorithm for gait stability estimation was implemented in a Smart Phone with Android 4.0 operating system. Android offers a sensor framework that includes sensor manager, event monitoring, description of an event and sensor handlers.
(3) where ai is the sample of the acceleration signal in the sagittal plane of the cycle, Nc is the number of samples per cycle. The parameter m must be adjusted for each individual. The distance that each person walks in a single cycle depends on height, weight, and gender. Women walk differently than men and this causes that the length of the step even if they are of the same height and weight is different. In order to incorporate these parameters into our equation, m is a variable defined as follows:
The implementation of the algorithm was done in a consumer-producer paradigm. Where the producer thread is obtaining samples of the triaxial accelerometer and stores them in a blocking queue, while the consumer thread takes the data and estimates the previously discussed parameters. The filters used in the estimation of the beginning of each cycle where implemented using symmetric structures to save time and power. The resulting application has an interface that offers the possibility of store different profiles per individual. The profile stores name, age, gender and the parameter m that help us to determine the distance walked by cycle. Figure 8 shows the interface of the application.
(4) where dr is the real distance that the person walk, Lcycle is the distance per cycle, and NC is the number of cycles estimated in the duration of the walking period. This parameter must be set only one time during the training phase. The parameter has an initial value of m=0.98, the process of calculation this parameter is iterative until de error between the estimated distance and the real distance is under a predetermined threshold.
III.
RESULTS
In order to establish the effectiveness of our algorithm, a set of test were directed including 40 human subjects. The individuals ages varying from 20 to 50, 10 individuals per
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TABLE II.
decade. The smart phone was strapped at the tight of each person. The distance walked by each person was 30 meters and each individual walk two times the same distance.
AVERAGE GAIT STABILITY
Age Range
Gait Stability Estimation
20 - 29 30 - 39 40 - 49 50 - 59
1.6780 1.8660 1.8487 0.9672
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Gait Stability Estimation
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Fig. 8. User Interface of the Resulting Application
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The set of resulting signals were analyzed and the mean values for each parameter in the age range are shown in Table 1. TABLE I.
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35 Age
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50
Fig. 9. Gait stability estimation
ACKNOWLEDGMENT
AVERAGE OF ESTIMATED PARAMETERS
Age Range
20-29
30 - 39
40-49
50-59
Number of Cycles
22.1
21.1
20.8
22.6
Duration of cycle (sec)
1.11
1.05
1.09
1.11
Number of samples per cycle
110.36
105
108
111.2
Left Step Length
0.8003
0.8305
0.8070
0.8105
Right Step Length
0.6358
0.6703
0.7069
0.5944
Average velocity
1.3150
1.4398
1.4027
1.2633
Hector Moncada-Gonzalez thanks CONACYT under the contract 275556.
the
support
of
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[2]
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[4]
The average gait stability estimation for each group of individuals is reported in Table 2. These results agreed with the results achieved by Zhang et. al. using a complex system including video recording with markers in the subject’s bodies. Figure 9 shows the gait stability against age. The figure shows that persons in between the ages of 30 to 39 have high gait stability compare with individuals in their 20’s or 40’s. At early 20’s the neuromotor system still developing while at late 20’s the stability is higher denoting a mature individual.
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