Kinematic and vibration description of running pattern

Series on Biomechanics, Vol.31, No.4 (2017), 3-11

Kinematic and vibration description of running pattern using empirical mode decomposition X. Chiementina, M. Munerab,C. B. Machadoc, E. Abdid, D. Sá-Caputoe, M. Bernardo-Filhof, R.Taiara a

GRESPI, Moulin de la Housse, Université de Reims Champagne Ardenne, 51687 Reims Cedex 2; France b Escuela Colombiana de Ingeniería Julio Garavito, Bogotá D.C., Colombia c Biomedical Ultrasound Lab., Estácio de Sá University, R. Eduardo Luiz Gomes,134,Niterói, Rio de Janeiro, Brasil d Montclair State University, Upper Montclair, New Jersey, USA e Departamento de Biofísica e Biometria, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, Brazil. f Laboratório de Vibrações Mecânicas e Práticas Integrativas e Complementares, Universidade do Estado do Rio de Janeiro, 20551-030, Rio de Janeiro, RJ, Brasil

_____________________________________________________________________________________ Abstract Background: Running is the source of repeated shocks which can reach amplitude over 20g during a foot-ground contact generating stress vibration in humans. This study proposes to apply an advanced signal processing method which is the Empirical Modal Decomposition (EMD) to describe the vibration at the tibia after the impact in running. Methods: One participant completed 5 tests at 10 and 14 km/h on a treadmill using Rearfoot strike and Forefoot strike techniques. Accelerometric data were collected at a sampling frequency of 1344 Hz. The sports kinematics and vibrations generated by the impact were dissociated by a reconstruction scheme of Intrinsic Mode Functions (IMF). Then, Root Mean Square (RMS) values were computed before and after the EMD. Results: EMD method allows (i) dissociating three phases generated by the runner kinematics and by the foot/ground shock, (ii) to estimate an RMS value generated to the impact (RearFoot, 14km/h: 6m/s², 10km/h: 4.5m/s²; ForeFoot, 14km/h:11.2m/s², 10km/h: 8.1m/s²). This value depends on the running technique and on the speed. Conclusion: This study is orientated on the original methodology of the signal treatment. Like perspective we will focus on the assessment between the findings of the current work with the publications of other studies. Keywords: Empirical modal decomposition (emd), running, vibratory risk, signal treatment, biomechanics __________________________________________________________________________________________

1. Introduction Long distance running can increase the risk of degenerative disorders in lower extremities, particularly the knee joint [1]. The injuries are not caused by running itself, rather they are caused by either a structural weakness which the runner was born with, a postural weakness developed, or other stress caused by shoes or surfaces with poor shock attenuation capacities [2, 3]. In running, repeated impacts increase the risk of an overuse injury. That is why, to prevent injuries, many studies use the measure of acceleration, in particular at the tibia [4]. The components frequencies of the tibial acceleration for different pattern were described [5]. Other authors highlight that the surface has no effect on the tibial acceleration magnitude i.e. 10.3 to 12.4g. [6]. The numbers of studies using accelerometric analysis in running have increased over the past years. The interest in this subject is related to the emergence of Inertial Measurement Unit (IMU) in indoor and outdoor activities [7]. The IMUs are widely used attributable to good characteristics regarding the constraints of space, lightness and autonomy imposed for the measurement of human activities [8,9,10]. These devices have been deployed to evaluate the kinematics of athletes. However, their development have also allowed to conceive its use in the evaluation of vibratory risk [11,12]. Using this kind of sensors, acceleration have been measured at the tibia in running and walking to

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition

quantify the maximal acceleration [13], to detect asymmetry [14], and to compare the influence of different surfaces. 3 Other studies have also shown the efficiency of IMU to realise predictive maintenance [15,16]. More recently, it was shown a comparison between IMU and a piezoelectric sensor named “gold standard” to monitor the running activity in a bandwidth of 0-150Hz [17]. It showed a satisfactory spectral coherence in the 0-80Hz band. The IMUs in the perspective of defining the foot strike pattern using two accelerometers placed on the heel and metatarsal area were used [18] The identification of the foot strike pattern was completed by computing the time between heel and metatarsal acceleration peaks. This method has been used to differentiate two kinds of runners. Simultaneously, to quantify the influence of this foot strike pattern over the temporal parameters of peak amplitude or over a spectral parameter as the median frequency [19]. The measure of shock over this kind of measure from running cannot be realised directly on the raw signals because the vibration is lost in the kinematics. Accordingly, it is necessary to turn toward advanced signal allowing the process to extract embedded information. Taking into account the nonstationary nature of the running activity [20], the EMD proves an interesting part. The EMD were used to classify different daily activities, such as the uphill gait, downhill gait and normal gait. From this decomposition the author determined temporal and spectral parameters to apply a 64-mixture Gaussian Mixture Model classifier [21]. Overall classification accuracy of 96.02% was achieved for the different human gaits. One investigation used EMD to remove noise from area signals to improve the determinants in human gait recognition [22]. Other authors showed that the use of EMD is better than a multivariate multiscale entropy algorithm to discern small changes in the Center of Pressure (COP) signals in anteriorposterior and media-lateral directions between before and after use of vibration shoes [23] The balance stability improvement which was found with both methods stands at 61.5% with EMD against 30.8% with entropy. This paper proposes to apply an advanced signal processing method which is the EMD, to describe the vibratory phenomena perceived at the tibia after the impact in running A methodology based on the EMD is presented to dissociate the runner kinematics and the vibrations to which the runner is exposed. Finally, RMS values are computed for the evaluation of the risk regarding the displacement speed and the running technique used rear foot strike (RFS) and fore foot strikes (FFS). 2. Methods 2.1. EMD Description The empirical modal decomposition was developed [24]. The concept of the EMD is 1) to consider the signal on its local oscillation scale, 2) to withdraw the fastest oscillation from the signal and 3) to reiterate the process on the residue. This way the signal ( ) can be written as a finite combination of oscillations, Eq. 1. (1)

( )=∑

( )+ ( )

( ) is the oscillation, ( ) is the residue of the decomposition and is the number of IMF (or modes). The name of IMF (Intrinsec Modal Function) is given to this transformation because it is based on local oscillations of the signal ( ) and adapts itself to the signal. IMF must be of null mean, i.e. it crosses zero between two successive extreme and follows amplitude and frequency modulation law (oscillating behaviour) of mono-component type, naturally. The principle of decomposition is obtained via the diagram of decomposition presented in Table 1. In the algorithm two loops are distinguished, the first loop relates to the iteration on the number of IMF. This loop ends when the residue presents less than two extremes. The second loop corresponds to the sifting principle, i.e. the generation of an IMF which meets specific properties of IMFs. This loop stops when the IMF satisfies stopping criteria assuming that convergence exists. Without taking into account this last assumption, often defines a stopping criterion, such as the criterion suggested [25], Eq. 2.

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition Table 1 EMD Algorithm. IMF extraction Residue initialization r(n)Åy(n) Affectation h(n)År(n) Minima and maxima h(n)År(n) Estimation of lower (L(n)) and upper (U(n)) envelopes Calculate the local mean envelope μ(n) Estimation of the IMF(n)Åh(n)- μ(n) IMF? If no, affectation h(n)ÅIMF(n) and step 4; if yes, step 5 Extraction of the IMF r(n)Åh(n)-IMF(n) Is the decomposition completed? If no, step 3; if yes, end.

(2)

( )

( )=

( )

( )

The sifting loop stops when ( ) passes under a threshold ℎ 1 and when the product ( ) lies between ℎ 2 and .The authors proposes the following threshold values: ℎ 1 = 0.05, ℎ 2 = 10 ℎ 1, = 0.05 [25]. Strict criteria increase the number of IMF and the computing time. This can lead to signal over decomposition and a compromise is then necessary. 2.2. Proposition of decomposition of running pattern The collection of accelerations during running activities are the result of 1) accelerations caused by the movement kinematics of the lower limbs and 2) the shock created by the contact between the foot and the ground. The method presented in this paper allows separating those parts in order to extract new parameters. This paper proposes to decompose the signal ( ) in three signals ( ), ( ), ( ) representing respectively the vibration, the movement intra stride and the movement inter stride, Eq. 3. (3)

( )=

( )+

( )+

( )

The EMD is applied over the raw signal recorded in the vertical direction. The result of IMFs will support for the reconstruction of the signals describing the running pattern. The reconstruction of the in the algorithm is signals is realized in three stages. First, to extract the kinematic part, a stop criterion defined. A Fourier transform is applied to the signal ( ). The fundamental frequency corresponding to for the time of the signal , the stride frequency , is extracted allowing to infer the number of strides Eq. 4. This number of strides is the stop criteria. The kinematic part is determined to a loop where the final IMFs are added. This loop is stopped when the number of oscillations passing through 0 is equal to the stop criteria. (4)

=⌊

. ⌋

Second, the part related to the shock foot/ground is determined adding the first IMFs until second criteria based on the Kurtosis. The Kurtosis is a temporal indicator sensitive to the signal singularities. It is defined as the ratio between a fourth moment about the mean and the square of a first moment about the mean. A value of 3 matches a Gaussian signal. The part related to the shock is defined as the addition of the IMFs until the Kurtosis is inferior to 4. Third, the kinematic part describing the stride pattern in the vertical direction correspond to the addition of the non-selected IMFs in the first and second part. Figure 1 represents the method for the signals reconstruction.

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition

Fig. 1. Algorithm for signal reconstruction

( ),

( ),

( )

2.3. Subject One subject (1.73m, 70kg) performed 20 sequences of running using two running techniques, RFS and FFS, and two displacement speeds, 10 and 14 km/h. Thus, 5 tests are realized by each configuration. Each test has duration of 80s. During all tests, the subject uses the same cotton socks and the same shoes. The signals were collected during a permanent regime in the treadmill for 10s. The signals were collected by an IMU (Hikob Fox, Villeurbanne, France) that has one tri-axial MEMS accelerometer. The use of this kind of sensor for the study of running activities has been validated [20]. The signals were collected in SD memory card with a sample frequency of 1344Hz. The analysis is accomplished in post-processing using Matlab software (Mathworks, Massachusetts). 3. Results 3.1. Example Prior to presenting the general results, this section illustrates the stages of the proposed method applied to the test at 14km/h and FFS. Figure 2 gives the temporal and spectral representations of the signal vertical acceleration. In those representations it is possible to recognise the stride pattern and the singularities that represent the foot/ground contact. The spectral domain provides harmonic series at the = ⌊10 × 1.47⌋ = 14. stride frequency, 1.47 Hz, giving us the stop criteria, Fig. 3 shows the EMD of the signal. In the decomposition 19 IMF are observed. The last IMFs represent the lower frequencies, which mean the kinematics and the gravity. The first IMFs represent the higher frequencies of the signal and the vibration caused by the impact.

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition

Fig. 2. Vertical acceleration in the temporal domain (top) and spectral domain (bottom) for a test FFS at 14 km/h

Fig. 3. IMFs result of the EMD for the test FFS at 14 km/h

The number of IMF which is a part of the vibratory response is determined by the decrease of the Kurtosis as a function of the IMFs number (Fig. 4). In this case, the first eight IMFs are taken to compose the vibratory part . The addition of the last 5 IMFs results in signals that have a number of crossings by zero of 29, which satisfies the stop criteria to make the kinematic part . Finally, the kinematic part during the stride is deduced from the IMFs which did not participate in the two other parts of the IMF from 9 to 11. In this case, Fig. 5 illustrates the results of the methodology to dissociate the vibration and the kinematics.

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition

Fig.4. Kurtosis represented as a function of the number of IMF added for a FFS test at 14 km/h.

Fig. 5. Results of the method proposed for a test FFS at 14 km/h. (Top left) Raw data (Top right) Vibratory component , (Middle right) Intra stride component , (Bottom right) Inter stride component .

3.2. General Results All the signals were decomposed by EMD and the reconstruction is realised using the proposed model. Table 2 shows the mean number the IMF determined for each configuration (technique-speed) and the repartition of those IMFs to reconstruct the signals ( ), ( ), ( ). Table 2 illustrates that the FFS technique generates the higher number of IMF proving that the signal is more singular than the RFS technique. This last demands more of the shoe damping. This damping produces a lower acceleration during the foot/ground contact, thus the exited frequency range is lower, generating smaller number of IMF. The FFS technique presents 3.6 and 5.4 IMF more for the speeds of 10 and 14 km/h respectively. This seems pertinent as a result of vibration generated by shock, causes an important number of IMFs. By comparing the number of IMFs that constitute the 3 signals, it can be highlighted that the signal is constituted by a number of IMFs. More variable (CV=36.2%) that the number of IMF constitutes and (CV= 7.9%). Thus, the technique and the displacement speed influences largely the first IMFs and the signal .

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition Table 2 Number of IMF determined for each test after EMD and IMF repartition for the three components; m± std. N° IMF IMF Number FFS - 10km/h 1.0±0.0 – 8.0±0.7 16.4±0.6 9.0±0.7 – 10.4±1.1 11.4±1.1 – 16.4±0.6 FFS - 14km/h

1.0±0.0 – 11.2±0.8

19.0±0.7

12.2±0.8 – 13.4±0.9 14.4±0.9 – 19.0±0.7 RFS - 10km/h

1.0±0.0 – 5.0±0.7

12.8±0.5

6.0±0.7 – 7.2±0.5 8.2±0.5 – 12.8±0.5 RFS - 14km/h

1.0±0.0 – 5.2±0.5

13.6±0.6

6.2±0.5 – 7.6±0.6 8.6±0.6 – 13.6±0.6

3.3. Root mean square (RMS) values Using the reconstruction of the signals, the kinematic and the vibratory parts are dissociated. Consequently the RMS values are lower when calculated with the proposed model, table 3. The results show that removing the kinematic component, the RMS values are divided by approximately 2.5 according to speed and running technique. On the raw data, an increase of 4km/h causes an increase of 6.0m/s² e and 4.0m/s² for the FFS and RFS techniques, respectively. On the signals obtained by the proposed model, the increases are 3.1m/s² and 1.5m/s² for the FFS and RFS techniques respectively. This increase is lower when calculated using the proposed model since it does not take under consideration the variation in the RMS caused by the kinematics. Moreover, in all cases an increase in the speed caused an increase in the RMS value. It can be highlighted that the FFS technique at the higher speed caused the higher level of energy on the signals. A change in the technique induces a variation of 0.7 and 2.7 m/s² for the speeds of 10 and 14km/h respectively over the raw signals, and a variation of 3.6 and 5.2 m/s² on the signals obtained with the proposed model. As a result this method allows revealing the characteristics linked to the changes in the running technique. Table 3 Root mean square values ( Raw data FFS - 10km/h FFS - 14km/h RFS - 10km/h RFS - 14km/h

(m/s²) 15.3±1.4 21.3±0.7 14.6±0.9 18.6±1.7

) With model proposed (m/s²) 8.1±1.7 11.2±1.6 4.5±1.1 6.0±1.6

This estimation of energy only in the vibratory part of the signal could be useful to compare different conditions in running and link them to different risk of injuries.

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition

4. Conclusions This paper proposes to quantify the vibratory dose in which a runner is exposed. This dose is given by measure of RMS after a stage of decomposition by EMD and reconstruction of the three signals representing the vibration generated by foot/ground impact, the kinematics in a stride and the kinematics between strides. The number of IMFs retained to describe the vibration is in average 17.7 and 13.2, respectively for the FFS and the RFS techniques. The estimated dose depends on the running technique adopted by the runner and on its speed. This study is orientated on the methodology of the signal processing. For this reason few comparison with results coming from bibliography were made. Perspective wise, we will focus on the assessment between the findings of the current work with the publications of other authors. References [1] Clancy WG., 1980. Runners’ injuries, Part two. Evaluation and treatment of specific injuries. Am J Sports Med 8, 4, 287–289. [2] Sheehan G., 1984.Running wild, The Physician and Sports medicine; 12,12, 43–43. [3] Kim W, Voloshin AS., 1992. Dynamic loading during running on various surfaces. Human Movement Science 11,6, 675–689. [4] Hreljac, A.,2004.Impact and overuse injuries in runners.Medicine and science in sports and exercise;36, 845–9. [5] Gruber A.H, Boyer K.A., Derrick T.R., Hamill J., 2014. Impact shock frequency components and attenuation in rearfoot and forefoot running. Journal of Sport and Health Scienc; 3 , 2, 113-121. [6] Fu W, Fang Y, Shuo Liu DM, Wang L, Ren S, Liu Y., 2015, Surface effects on in-shoe plantar pressure and tibial impact during running. Journal of Sport and Health Scienc; 4 , 4, 384-39. [7] Mayagoita RE, Nene VA, Veltink PH., 2002. Accelerometer and rate gyroscope measurement of kinematics: an inexpensive alterative to motion analysis system. Journal of Biomechanic, 35,4, 537–42. [8] Boyd LJ, Ball K, Aughey RJ., 2011.The reliability of MinimaxX accelerometers for measuring physical activity in Australian football. International journal of sports physiology and performance; 6,3, 311–21. [9] Lee JB., 2010. Identifying symmetry in running gait using a single inertial sensor. Journal of Science and Medicine in Sport; 13, 559–563. [10] Patterson M, McGrath D, Caulfield B., 2011. Using a tri-axial accelerometer to detect technique breakdown due to fatigue in distance runners: a preliminary perspective. IEEE Engineering in Medicine and Biology Society. Annual Conference, 6511–4. [11] Fong DTP, Chan YY., 2010.The use of wearable inertial motion sensors in human lower Limb biomechanics studies: a systematic review. Sensors; 10,12, 11556–65. [12] Liu K., 2009. Novel approach to ambulatory assessment of human segmental orientation on a wearable sensor system. Journal of biomechanics; 42,16, 2747–52. [13] Lafortune M., 1991. Three-dimensional acceleration of the tibia during walking and running. Journal of Biomechanics; 24,10, 877-86. [14] Moran K., 2015. Detection of Running Asymmetry Using a Wearable Sensor System. Procedia Engineering; 112,180–183. [15] Maruthi G, Panduranga Vittal K., 2005. Electrical Fault Detection in Three Phase Squirrel Cage Induction Motor by Vibration Analysis using MEMS Accelerometer. International Conference on Power Electronics and Drives Systems, 838–843. [16] Korkua S., 2010. Wireless health monitoring system for vibration detection of induction motors. IEEE Industrial and Commercial Power Systems Technical Conference - Conference Record. IEEE, 1–6. [17] Provot T., 2015. Reliability of inertial measurement units applied to vibration signal during running. In 21th Congress of the European Society of Biomechanics, Czech Republic. [18] Giandolini M., 2014. A simple field method to identify foot strike pattern during running. Journal of Biomechanics; 47,07, 1588-93. [19] Giandolini M., 2015. Effect of foot strike pattern on axial and transverse shock severity during ownhill trail running. In 33rd International Conference on Biomechanics in Sports. [20] Kurz M, Stergiou N., 2003.The spanning set indicates that variability during the stance period of running is affected by footwear, Gait & Posture; 17 , 2, 132-135. [21] Ning W., 2008.Accelerometry based classification of gait patterns using empirical mode decomposition. International Conference on Acoustics, Speech and Signal Processing; 617–620. [22] Hatzinakos AD., 2012. Determinants in Human Gait Recognition. J. of Information Security; 03, 02, 77–85. [23] Wei Q., 2012. Multivariate Multiscale Entropy Applied to Center of Pressure Signals Analysis: An Effect of

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X. Chiementin et al./ Kinematic and vibration description of running pattern using empirical mode decomposition Vibration Stimulation of Shoes. Entropy; 14,12, 2157–2172. [24] Huang NE., 1998. The empirical mode ecomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences; 454, 1971, 903–995. [25] Rilling G, Flandrin P, Gonçalvès P., 2003. On empirical mode decomposition and its algorithms. In IEEEEURASIP workshop on nonlinear signal and image processing; 8–11.

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