Estimation of the Effect of Cadence on Gait Stability in Young and Elderly People using Approximate Entropy Technique

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1 MEASUREMENT SCIENCE REVIEW, Volue 4, Section 2, 4 Estiation of the Effect of Cadence on Gait Stability in Young and Elderly People using Approxiate Entropy Technique M. Arif *, Y. Ohtaki **, R. Nagatoi ***, H. Inooka** * Departent of Coputer and Inforation Sciences, PIEAS, Islaabad, Pakistan ** Niche Lab., Tohoku University, Japan *** Dept. of Medicine and Science in Sports and Exercise, Tohoku University, Japan Abstract Walking stability of huan beings varies with age and reduces in the elderly people. Lesser walking stability causes any falls in the elderly people. In this paper, we have investigated the walking stability of young and elderly subjects using approxiate entropy, a non-linear tie series analysis ethod. Our ephasis in this paper is to investigate the walking stability using a portable instruentation that can be used in the daily life walking. The variability of the acceleration of the centre of gravity is analysed by using approxiate entropy technique and is used as an index to assess the walking stability of young and elderly people. By using the proposed ethod, it is possible to assess the walking stability of the elderly subjects and it is observed that the walking stability of elderly subjects decreases in the lateral direction. Moreover it is also possible to suggest a walking speed to the elderly subjects that can iprove their walking stability.. Introduction Noral ageing process causes any changes to neurouscular syste of a huan being restricting his walking capabilities. It is very iportant to study the age related changes in the walking gait of elderly subjects. Because these changes soeties result in an increase the nuber of falls during daily walking especially after the age of 75. Many researchers studied stability of huan walking gait and it was quoted that huan walking gait stability decreases with age increasing the risk of falls in elderly people. Many studies have been reported about the change in the kineatics paraeters with age [,2,3,4,5] but they require coplex systes (e.g. otion capture systes) and experients can only be perfored in the laboratory environents. Soe research is being done on the portable syste to calculate the kineatics paraeters in the daily life environent [3], but it requires any sensors attached to the body, which should be linked to a laptop coputer. Our ephasis is to find soe statistical index that can predict the walking stability using soe kind of lightweight portable instruentation which is easy to wear and handy to use. In this paper, we have proposed a ethod to predict the walking stability that can be used to predict the risk of fall in the elderly persons. In the daily life, huan beings walk in various changing environent very successfully despite of the fact that a huan body is a highly non-linear dynaic syste. During the walking, instability occurs between the steps when we shift our weight fro one leg to other. Centre of gravity (COG) of a walking person plays an iportant role in aintaining the dynaic stability of the walking. We change our location of COG fro one foot to another foot alternatively during walking. To aintain the dynaic stability, a huan walker tries to control the location of COG within the base area. The base area of a standing person is norally considered as his noral footprints. If the COG shifts outside the 29

2 Measureent in Bioedicine M. Arif, Y. Ohtaki, R. Nagatoi, H. Inooka base area, instability occurs, which if not corrected by oving the body segents in appropriate directions, results in fall of the person. Therefore, oveent of COG of a person during walking is an iportant index to assess the stability of his walking pattern and can be used for the prediction of the falls in the elderly people. In fact, there is no noral walking pattern and the walking pattern varies fro person to person. These walking patterns are considered to be stable until and unless there is an evidence of fall of the person. During walking, huan tries to generate periodic series of otions. But due to the physiological liitations, these otions do not reain exactly periodic but contains soe variability or randoness in it. He does not try to correct this variability or randoness of these otions if it reains within stability liits. This variability present in the walking patterns are due to not only internal perturbation but also due to external perturbations. The aount of variability present in the walking pattern reflects the quality of neurouscular control of the huan being. Lesser the aount of variability eans better neurouscular control and walking stability. The variability or randoness of the walking pattern increases, as a person grows older. Many old people tend to lose the stability especially lateral stability. The aging effect on balance in elderly people is ore proinent in the lateral direction. Elderly people take steps ore laterally as copared to young people to restore the balance during walking [6,7]. In this paper, we have proposed a ethod to detect the variability of the COG using a portable 3D acceleration easureent syste attached to the body of the subject near the COG point. Two groups of subjects participated in the experients, naely, healthy young subjects and elderly healthy subjects. The variability of COG in analysed using approxiate entropy technique, which is an excellent ethod of predicting the coplexity or variability of deterinistic as well as stochastic signals [8,9]. Approxiate Entropy was ainly used in the analysis of heart rate variability [] and endocrine horone release pulsatility []. It is highly resistant to short strong transient interference (i.e. outliers or wild points). The influence of noise in the tie series signal can be suppressed by properly choosing the relevant paraeter of the approxiate entropy algorith. High value of the approxiate entropy indicates large variability or randoness in the tie series signal. The acceleration of the centre of gravity data in lateral, vertical and anterior/ posterior directions are analysed using approxiate entropy technique for both groups of subjects. Effect of age on the variability or irregularity of the acceleration of COG in lateral, vertical and anterior/ posterior directions is studied in this paper. 2. Signal coplexity/ variability by approxiate entropy Approxiate entropy (ApEn) is a technique that can be used to quantify the irregularity or variability of the tie series based on the statistics. This approach is a odel free approach and can be used for a relatively short finite tie series. Larger value of the approxiate entropy of a tie series corresponds to higher level of irregularity present in the tie series. It is different fro auto-correlation function and standard deviation because standard deviation used to quantify the degree of scattering of the data around their ean value. The tie order of the data is iaterial. On the other hand the tie order of the data is a crucial factor affecting the value of approxiate entropy. ApEn is an excellent technique to predict the variability of a tie series signal because it needs relatively saller data range to calculate the approxiate entropy and the influence of noise can be suppressed by properly choosing the relevant paraeter of the algorith. It can be applied to both deterinistic (chaotic) and stochastic signals and/or to their cobinations. In the phase flow diagra, the trajectories lying near to each other will reain close to each other in the regular type of otion and will occupy a fixed space of a certain diension. Hence ApEn can be calculated by calculating the probability of the two phase space trajectories, which are close to each other, will reain close to each other after certain tie [2]. 3

3 MEASUREMENT SCIENCE REVIEW, Volue 4, Section 2, 4 It can be expressed as the probability of values x i+ and x j+ lying within a certain tolerance region of size R given that x i and x j lie also within region, ( j+ i+ j i ) P x x R x x R () where i denotes the nor ( L or L 2 nors). We consider an (, J)-window which contains saples taken at interval of J. The eleents in the (, J)-window represent the coponents of an ebedding space. The value is the ebedding diension. Equation () for ebedding diension can be written in vector for as, P x x R (2) ( j i ) The conditional probability if the ebedding diension increases to + can be written as P x x R ( j( + ) i( + ) ) P( xj xi R) Taking the natural logarith of the above equation + Φ ( R) Φ ( R) (4) where Φ ( R) = ln( P( xj x i R) ) (5) The probabilities can be obtained by siple kernel based probability density function estiation ethods by defining the correlation su as Ci ( R ), where Φ ( R) = ln( Ci ( R)) and Ci ( R ) is defined as, N Ci ( R) = Θ( R nor( xi, x j)) (6) N j= Θ is the havyside function, s < Θ () s = (7) s and the nor can be defined as euclidean distance, ( ) 2 nor( x, x ) = x x (8) i j ik jk k= The value of R deterines the range within which neighbouring points in the phase space ust lie. Pincus has used the coplexity easure tered Approxiate Entropy (ApEn) and defined as, + ApEn(, R, N) =Φ ( R) Φ ( R) N + N (9) + = ln Cj ln Cj N + j= N j= For N>>, ApEn approxiate to, N C j ApEn(, R, N) = ln + () N j= C j Hence approxiate entropy is the difference between the frequency that all patterns having diension are close to each other and the frequency that all the patterns having (+)diension lies close to each other [9]. Pincus et. al [7] suggests, J = and R = rsd x, where SD x is the standard deviation of the original data, (3) 3

4 Measureent in Bioedicine M. Arif, Y. Ohtaki, R. Nagatoi, H. Inooka N N SDx = xn ( ) xn ( ) N N n= n= 2 () and r is a user defined paraeter which can reduce the influence of noise. Ebedding diension is related the dynaics of the underlying process in the tie series and can vary according to the coplexity of the dynaics. 3. Experiental setup Twenty six Subjects have participated in the experiental study and are divided into two groups. Group YNG consists of nine young healthy subjects having ages between 2 to 3 years (ean 24.7±6 years), body weight distribution is 63.±7 kgs and height distribution is 56.6±4 cs. Group OLD consists of seventeen elderly healthy subjects with no ajor disease having ages between to years (ean 69±6 years), body weight distribution is 56±8 kgs and height distribution is 54±7 cs. All subjects were asked to give signed infored consent. Most of the elderly subjects have good walking habit and soe of the elderly subjects are doing one hour exercise classes, once or twice a week in Sendai city silver centre, Sendai, Japan. All subjects were asked to walk with their self selected walking speed on a 5 straight walking track. In the next trial, they were asked to follow the tepo of a etronoe (sound signal) which was set to different walking speeds in ters of walking steps/inute. Four walking speeds,,, and steps/inute were selected for the experient. Sound signal of etronoe was sufficiently loud and can be heard easily while walking on the track. Acceleration of the COG during walking was easured by a portable 3D acceleration easureent syste ade by ITR Co. Ltd.(Japan), shown in Figure. The 3D acceleration easureent syste was placed on the trunk at about 55% of the subject's height as shown in the Figure 2. It is widely accepted that the COG of adult huans has been found to be slightly anterior to the second sacral vertebra [4] or approxiately 55% of a person's height [5]. Although it is very difficult to easure the acceleration at the exact location of the COG, but we assued that the acceleration of the trunk of subject at 55% height will represent the sae changes of acceleration as of COG. Acceleration of the COG was recorded in lateral, vertical and anterior/ posterior directions. In Figure 2, x direction refers to lateral direction, y direction refers to vertical direction and z direction refers to anterior/ posterior direction. The data fro the acceleroeter was sapled at the frequency of Hz. 4. Experiental results Acceleration data in lateral, vertical and anterior/ posterior directions are plotted in Figure 3 for a young and an old subject along with the step events. Coparing the acceleration data of young and elderly subject, a clear difference between the acceleration in lateral direction is visible in the Figure 3. In the case of elderly subject, the acceleration in lateral direction is ore irregular as copared to young subject. While walking on the straight path, the COG of the subject's body accelerates and de-accelerates in all three directions. Changes of acceleration in the lateral direction are ost critical in ters of walking stability. A huan can easily copensate any sudden change of acceleration or deceleration in the anterior/ posterior and vertical directions by changing the speed of walking or by changing the stride length or both. But it is difficult to copensate any sudden change in the acceleration in lateral direction and can easily cause a fall on the sideways while walking. Elderly people having lesser uscle strength than young people are ore prone to fall on sideways when subjected to sudden change in acceleration in lateral 32

5 MEASUREMENT SCIENCE REVIEW, Volue 4, Section 2, 4 2D Acceleroeter z 2D Acceleroeter y x Ni-MH Battery MPU PIC6LC63 Copact Flash TM Card (8MB - 28MB) Figure : Portable 3D acceleration easureent syste Figure 2: Position of Sensor Unit 33

6 Measureent in Bioedicine M. Arif, Y. Ohtaki, R. Nagatoi, H. Inooka Young Suject Data Old Subject Data.6.6 Lateral Acc Lateral Acc X Data X Data Vertical Acc Vertical Acc X Data X Data Ant./Post. Acc Ant./Post. Acc X Data X Data Step Event.5 Step Event Tie (sec.) Tie (sec.) Figure 3: 3D Acceleration data of young and old subjects direction. The irregularity in the acceleration data shows an increase probability of fall in the elderly people as visible in Figure 3. We have applied the technique of approxiate entropy to estiate the irregularity or coplexity in the tie series signal of the acceleration of COG in lateral, vertical and anterior/ posterior directions for young and elderly subjects for different walking speeds. Approxiate entropy technique usually applied to the tie series of a finite length and represents the irregularity of the whole tie series. Approxiate entropy shows the variability or coplexity of the walking pattern. This variability reflects the response of dynaic systes involved in walking against internal as well as external perturbations. For exaple, any deforation of joints or weakness of leg uscles will effect the quality of control during walking and will produce ore variability in the walking pattern of the subject which in our case is the acceleration of the COG. More variability in the acceleration data of COG eans less walking stability. Moreover neurological disorder associated with age ay cause poor otion generation during walking and ay induce ore variability in the walking patterns of the patient. In our experients, we are interested in calculating the approxiate entropy on various tie instants and the calculations are required to be fast such that it can be applied to the online onitoring of the approxiate entropy of walking data of a subject. In our analysis, a window of constant size is defined and whole data of each subject is divided into any data segents. The size of window is not tie but a certain nuber of steps taken during walking. Hence the window size can be varied in the tie doain according to the tie taken by the subject per step of walking but will be fixed in ters of the nuber of walking steps. Let the acceleration data a having length of N is recorded, in which a subject has taken M nuber of walking steps, given as, [ a(), a(2),..., a( N) ] a (2) 34

7 MEASUREMENT SCIENCE REVIEW, Volue 4, Section 2, 4 Let a be converted into nuber of walking steps doain as under, [ α(), α(2),..., α( N )] α (3) Here α () = [ a(), a(2),..., a( k )], (2) = [ a(), a(2),..., a( k )] α and vice versa. The variables k and k 2 are the nuber of tie steps per walking step. For instance, recording the data at sapling period of Hz, tie taken for the first walking step equals to.5 seconds eans that k will be equal to 5 data points and tie taken for the second walking step equals to.52 seconds eans that k 2 will be equal to 52 data points and vice versa. Applying a window having size of J walking steps will decopose the acceleration data entioned in equation (3) into M - J data segents. A data segent a w (i) is defined as, [ α α α ] 2 α ( i) = ( i), ( i+ ),..., ( i+ J) (4) w for i =,2,... M J. Approxiate entropy of each data segent a w (i) will then be calculated and averaged over all data segents for every subject. Ebedding diension for all the data analysis is set to be 4 and R is set to be.3sd, SD is the standard deviation of the data segent. Window size is selected as 6 walking steps. Four walking speeds are selected for the experients, which are steps/inute (Slow walking), steps/inute (Noral walking), steps/inute (Noral Walking) and steps/inute (Fast walking). Walking speed is controlled by the sound signals of a etronoe and all the subjects are asked to walk on the tepo of etronoe. Figure 4 shows the walking speed of each subject for four pre-set walking speeds. Young subjects can aintain the walking speed by hearing the etronoe sound in all the cases except in fast walking ode ( steps/inute). Whereas, elderly subjects showed soe variation in keeping up the desired walking speed in alost all cases. The COG acceleration data of young subjects is analysed first. Approxiate entropy of lateral acceleration of COG is plotted in Figure 5 for different walking speeds for all young subjects. The figure suggests that all the young subjects have iniu approxiate entropy value near their noral walking speeds (steps/inute). The average noral walking speed of the young subjects is 4±4 steps/inute. Walking on the speed different fro their noral walking speed, slower or faster, increases the variability of the lateral acceleration showing ore instability which is reflected in the figure as high value of approxiate entropy. This behaviour shows that subjects have adjusted their walking speed in a way to optiise their walking stability. Approxiate entropy values of the lateral acceleration for elderly subjects are shown in Figure 6 for different walking speeds. It is evident fro the figure that elderly subjects ake two groups. One Group exhibits the sae behaviour as of young subjects showing iniu value of approxiate entropy near their noral walking speed. But subject nuber, 6, 3, and 7 have shown different kind of behaviour, i.e. showing ore value of approxiate entropy near their noral walking speeds. Noral walking speeds for elderly subjects are plotted in Figure 7 (black circle shows ean value and bar shows the standard deviation of the walking speed). Noral walking speed for these subjects are 27, 2, 23 and 28 (steps/inute) respectively. It suggests that these subjects are unable to optiise their walking stability by choosing proper walking speed. For exaple, subject nuber can iprove his walking stability by lowering his walking speed. Subject nuber 6 do not show any significant difference of approxiate entropy value for various walking speeds. Hence subject nuber 6 has lesser walking stability 35

8 Measureent in Bioedicine M. Arif, Y. Ohtaki, R. Nagatoi, H. Inooka steps/in. steps/in. steps/in steps/in. steps/in steps/in. steps/in. steps/in. (a) Young subjects (b) Elderly subjects Figure 4: Walking speed of young and elderly subjects when tep is controlled by etronoe.. Approxiate Entropy steps/in. steps/in. steps/in. steps/in Figure 5: Approxiate Entropy of lateral acceleration data of individual young subjects 36

9 MEASUREMENT SCIENCE REVIEW, Volue 4, Section 2, 4. Approxiate Entropy steps/in. steps/in. steps/in. steps/in Figure 6: Average approxiate entropy values of young and elderly subjects for different walking speeds in lateral direction independent of his walking speed. Subject nuber 3, siilar to subject 6, also has high values of approxiate entropy for all walking speed and shows a little iproveent if he decreases his walking speed to steps/inute. Subject nuber 7 can increase his walking stability significantly if he walks slower than his noral walking speed. Hence by using the above entioned result, it is possible to suggest the elderly people about their walking speed that can increase their walking stability. Mean values of approxiate entropy for young and elderly subjects walking by different walking speeds are plotted in Figure 8 which showed a U shape curve. In the figure, bar shows the standard deviation of the approxiate entropy. Both young and elderly subjects have showed the sae trend that is the values of approxiate entropy is lower near their noral walking speeds. The approxiate entropy value for elderly subjects is higher than young subjects in the walking speed of steps/inute and steps/inute (p<.5) suggesting the fact that young subjects show ore lateral walking stability as copared to elderly subjects. The approxiate entropy values for young and old are not statistical significant for the walking speed of steps/inute and steps/inute. Experiental results suggest that the effect of age is proinent in the acceleration in lateral direction and the variability or coplexity of lateral acceleration increases in the elderly subjects. Hence the walking stability of the elderly subjects decreases in the lateral direction putting the subjects on ore risks of lateral falls. Moreover, young subjects always try to adjust their noral walking speed to axiize their walking stability. For other walking speeds, slower or faster, their walking stability decreases. Elderly subjects also try to optiise their walking stability by changing their noral walking speeds. In soe cases, it is observed that their noral walking style is less stable and they can iprove their walking stability by decreasing their walking speeds. 37

10 Measureent in Bioedicine M. Arif, Y. Ohtaki, R. Nagatoi, H. Inooka Noral Figure 7: Noral walking speed of elderly subjects.8 Approxiate Entropy Young Elderly. Figure 8: Average approxiate entropy values of young and elderly subjects for different walking speeds in lateral direction 38

11 MEASUREMENT SCIENCE REVIEW, Volue 4, Section 2, 4 5. Discussion In this paper, we have analysed the walking stability of elderly and young subjects while walking on a controlled pace. At the noral walking speed, the walking stability of elderly subjects has decreased. It is also worth entioning that the elderly subjects were the participants of the exercise class at Sendai Silver Centre. So they ay have better balance as copared to the noral elderly subjects or elderly subjects having soe physiological probles. We have also investigated the effect of the walking speed in steps/inute on their walking stability. The ost iportant finding is that young subjects inherently optiise their walking speed to axiize the walking stability. As persons grew old, they try to adjust their walking speed to achieve the axiu walking stability achievable. We have not found any study relating the walking speed with walking stability. Though, in the literature, it is entioned that elderly people reduce their walking speed to iprove their walking stability. Elderly subjects exhibits gait pattern characterized by reduced velocity, shorter step length and increased step tiing variability [6]. But the perception of correct walking speed by elderly people ay not be correct. In this paper, we have presented a ethodology that can be used to suggest the optial walking speed for the elderly subjects to be ore stable during walking. 6. Conclusion In this paper, we have investigated the walking stability of young and elderly subjects in noral walking and when their walking speed is controlled. The results suggest that the variability in the walking pattern increases with age showing lesser walking stability. Young and elderly subjects try to optiise their walking stability by selecting a proper walking speed in the noral walking. But in soe cases, elderly subjects shows less walking stability at their noral walking speed and can iprove their walking stability by lowering their walking speed. Age related effects on walking stability in vertical and anterior/ posterior directions are not significant between young and elderly subjects. Acknowledgeents: The authors acknowledge the help of Sendai city silver centre for providing assistance in arranging the subjects to participate in our experients. References [] D.A. Winter, A.E. Patla, J.S. Frank and S.E. Walt, Bioechanical walking pattern changes in the fit and healthy elderly persons, Phy. Ther., vol. 7, pp , 99. [2] J.O. Judge, R.B. Davis and S. Ounpuu, Step length reductions in advanced age: the role of ankle and hip kinetics, J. Gerontol., vol. 5, pp , 996. [3] B.M. Nigg, V. Fisher and J.L. Rousky, Gait characteristics as a function of age and gender, Gait and Posture, vol. 2, pp. 23-2, 994. [4] K.M. Ostrosky, J.M. Vanswearingen, R.G. Burdett and Z. Gee, Coparison of gait characteristics in young and old subjects, Phys. Ther., vol. 74, pp , 994. [5] D.C. Kerrigen, M.K. Todd, U.D. Crose, L.A. Lipstiz and J.J. Collins, Bioechanical gait alterations independent of speed in the healthy elderly: Evidence for specific liiting ipairents, Arch. Phys. Med. Rehabil., vol. 79, pp , 998. [6] W.E. McIlory, B.E. Maki, Age related changes in copensatory stepping in response to unpredictable perturbation, J. Gerontol Med Sci, 5A, M , 996. [7] M.W. Rogers, Disorder of posture, balance and gait in Parkinson s disease, In: Studenski S.A. ed. Clinics in Geriatic Medicine: Gait and balance disorders, Philadelphia PA: W.B. Saunders Copany, p ,

12 Measureent in Bioedicine M. Arif, Y. Ohtaki, R. Nagatoi, H. Inooka [8] S. Pincus, Approxiate Entropy (ApEn) as a coplexity easure, Chaos, vol.5, pp. - 7, 995. [9] M. Akay, Nonlinear bioedical signal processing Volue II: Dynaic analysis and odeling, IEEE Press,. [] D. Sapoznikov, et al., Detection of regularities in heart rate variations by linear and nonlinear analysis: power spectru versus approxiate entropy, Coput. Methods Progras Bioed., vol. 48, p. -9, 995. [] S.M. Pincus, Older ales secrete luteinizing horone and testosterone ore irregularly and joint ore asynchronously, than younger ales, Proc. Natl. Acad. Sci. USA, vol. 93, pp. 4-45, 996. [2] I. Rezek, Inforation Dynaics in Physiological Control Systes, PhD thesis, Iperial College of Science, Technology and Medicine, 997. [3] Ohtaki, K. Sagawa, and H. Inooka, A Method for Gait Analysis in A Daily Living Environent Using Body-ounted Instruents, JSME International Journal, Series C, Vol. 44, No. 4, pp ,. [4] W. Braune, O. Fischer, On the Centre of Gravity of the Huan Body Translated (fro 889 original) by PGJ Maquet and R Furong. Berlin: Springer-Verlag 984. [5] FA Hellebrandt, RH Tepper, GLBraun, Location of the cardinal anatoical orientation planes passing through the center of weight in young adult woen Aerican Journal of Physiology, pp. 2: 465, 938. [6] HB Menz, SR Lord, RC Fitzpatrick, Age-related differences in walking stability Age and Ageing Vol. 32 No. 2, pp , 3.

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