Assessment of Walking Stability of Elderly by Means of Nonlinear Time-Series Analysis and Simple Accelerometry

607 Assessment of Walking Stability of Elderly by Means of Nonlinear Time-Series Analysis and Simple Accelerometry Yasuaki OHTAKI, Muhammad ARIF, Akihiro SUZUKI, Kazuki FUJITA, Hikaru INOOKA, Ryoichi NAGATOMI and Ichiro TSUJI This study presents an assessment of walking stability in elderly people, focusing on local dynamic stability of walking. Its main objectives were to propose a technique to quantify local dynamic stability using nonlinear time-series analyses and a portable instrument, and to investigate their reliability in revealing the efficacyof anexercisetraining intervention for elderly people for improvement of walking stability. The method measured three-dimensional acceleration of the upper body, and computation of Lyapunov exponents, thereby directly quantifying the local stability of the dynamic system. Straight level walking of young and elderly subjects was investigated in the experimental study. We compared Lyapunov exponents of young and the elderly subjects, and of groups before and after the exercise intervention. Experimental results demonstrated that the exercise intervention improved local dynamic stability of walking. The proposed method was useful in revealing effects and efficacies of the exercise intervention for elderly people. Key Words: Biomechanics, Human Engineering, Information Processing and Signal Analysis, Walking Stability, Accelerometer, Nonlinear Time-Series Analysis, Medical Application 1. Introduction Falls pose a serious hazard to elderly people. Hip fractures caused by fall accidents account for more than 10% of elderly persons with bed-bound status in Japan. Furthermore, impaired mobility and fear of falling diminish a person s ability to perform activities of daily living (1), (2). Aging effects on motor control have been implicated as a key factor in adjusting posture during walking. Sensory feedback and muscular strength play impor- Received 7th June, 2005 (No. 05-4070) Graduate School of Engineering, Tohoku University, 6 6 04 Aza Aoba, Aramaki, Aoba-ku, Sendai 980 8579, Japan. E-mail: ohtaki@niche.tohoku.ac.jp Pakistan Institute of Engineering and Applied Science, P.O. Nilore, Islamabad, Pakistan Instruments Technology Research Co. Ltd., 2 1 40 Takamori, Izumi-ku, Sendai 981 3203, Japan Center for Preventive Medicine and Salutogenesis, Tohoku Fukushi University, 6 149 1 Kunimigaoka, Aobaku, Sendai 989 3201, Japan Graduate School of Medicine, Tohoku University, 2 1 Seiryo-machi, Aoba-ku, Sendai 980 8575, Japan tant roles in maintaining stability against the presence of unpredictable external perturbations or internal variations of gait. Although falls result from complex and multifactorial problems, falls among elderly persons might relate to their difficulty in maintaining walking stability. In addition, recent randomized controlled trials that have tested the effectiveness of intervention for elderly people have indicated that exercise training markedly increases their aerobic capacity and muscle strength, which might engender improvement of their postural stability (3), (4). Nevertheless, no practical technique has been demonstrated to evaluate their stability improvements in terms of walking stability. Traditionally, personal walking ability has been assessed in clinical fields with a main emphasis on quantifying the regional amounts of body sway or statistical mean deviation of gait variability. It has been reported that increased variability of gait patterns is related with an increased risk of falling in elderly persons (5), (6). Recently, some advanced techniques using nonlinear time series analyses have been proposed to investigate gait variability and dynamic stability in continuous walking (7) (10). Dynamic stability represents a resilient ability to main- JSME International Journal Series C, Vol. 48, No. 4, 2005

608 tain certain continuous vibratory motion by accommodating internal or external perturbations. In other words, dynamic stability indicates robustness of periodic gait patterns when subjected to internal or external perturbations. Moreover, dynamic stability has two aspects: local stability and global stability. For this study, local stability is defined as the sensitivity of the dynamical system to small perturbations or gait variability which produced by one s locomotor system itself, whereas the global stability is defined as the capacity of the locomotor system to resist external perturbations such as slips or trips (11). Nonlinear time series analyses specifically elucidate temporal variations in the gait pattern. Dingwell et al. computed largest Lyapunov exponents to quantify the local dynamic stability of neuropathic patients (12). Buzzi et al. applied largest Lyapunov exponents in joint kinematics between elderly and young subjects, and reported that elderly subjects showed less dynamic stability than young ones (13). This study was intended to present a practical method to assess dynamic walking stability using a portable and wearable instrumentation unit, then to present its feasibility in assessing effects of an exercise intervention on walking performance in elderly people. The method employed a measurement of three-dimensional acceleration of the body, and computation of largest Lyapunov exponents of the time series acceleration data, which directly assess the local stability of the dynamic system. Straight walking in self-selected speed was investigated experimentally. First, differences in gait variability and local dynamic stability between elderly and young subjects were investigated. Secondly, effects and efficacies of six-month interventions, including aerobic exercise training for elderly persons, were investigated in an experimental study using the proposed method. 2. Experiment Seven healthy young adults (26.1 ± 1.9 yr)and 52 elderly persons (76.4 ± 4.3 yr) participated in our experiment. Detailed characteristics of the subjects are shown in Table 1. The elderly subjects were those who participated in the comprehensive geriatric assessment (The Tsurugaya Study) performed in the suburban district in Sendai City in 2002 2003 (14), (15). They were selected considering the following exclusion criteria: moderate to severe motor impairment or neurological deficit, history of coronary heart disease, joint pain or arthritis, mental or other conditions, history of fracture of a lower extremity or injurious fall within six months, and presence of cardiovascular abnormality revealed by exercise training. All subjects gave signed informed consent. The intervention was designed for elderly subjects as a five-month fall-prevention training program conducted and supervised by medical doctors and physical therapists. The training program was intended to improve both Series C, Vol. 48, No. 4, 2005 Table 1 Results for the continuous twelve steps (six strides) walking in comparison of a young and elderly subject. Significant differences (p < 0.05) are marked with asterisks Young Elderly Male/Female 5/2 28/24 Age 26.1 (1.9) 76.4 (4.3) Height [cm] 170.8 (4.5)* 154.8 (10.3)* Weight [kg] 58.46 (4.07)* 59.25 (12.88)* Step Number 14.4 (1.3)* 18.6 (2.2)* Cadence 109.2 (7.9)* 117.4 (9.9)* [step/min] Walking Speed 1.26 (0.03)* 1.06 (0.15)* [m/s] CV Gait Cycle 0.057 (0.020) 0.064 (0.053) SD Lateral 0.075 (0.024) 0.073 (0.028) SD Vertical 0.067 (0.021) 0.086 (0.039) SD Ant. post. 0.052 (0.014) 0.064 (0.026) LyEp Lateral 0.060 (0.016) 0.069 (0.029) LyEp Vertical 0.047 (0.026) 0.064 (0.032) LyEp Ant. post. 0.048 (0.027) 0.056 (0.026) static and dynamic body balance by strengthening muscular groups involved in standing and walking. Subjects attended two-hour classes once a week. The class training comprised stretching, balance training, and strength training including flexible rubber-band exercises. Functional physical capacities were measured in medical and fitness examinations before and after the intervention. Muscle strength and range of motion (ROM) of lower extremities are important determinants of the physical functional capacity of elderly persons. The passive ranges of knee flexion and ankle dorsiflexion angles were measured by an experienced physical therapist using a hand-held goniometer. The muscle strength of the lower leg extensors and hip abductors were examined using a calibrated dynamometer (Biodex 3; Biodex Medical Systems, New York, USA). The hip abductor muscle strength was divided by the bodyweight (BW). The functional reach test of dynamic balance criteria measures the maximum distance one can reach forward and laterally while maintaining a fixed base of support (16). For the walking test, we have developed a portable device consisted of IC accelerometers (±2 G, ADXL202E; Analog Devices Inc., MA, USA) with 16-bit duty cycle converter, Li-Ion batteries, microprocessor units, and a compact flash card. This equipment is sufficiently small and lightweight (100 55 18.5 mm, 97 g) to be carried without any restriction. Figure 1 shows that the equipment was attached to the center of the lower back, representing the center of gravity of the body using a back supporter. Three-dimensional acceleration as lateral, vertical and anteroposterior directions were measured by the portable equipment with sampling frequency of 100 Hz. All subjects wore rubber-soled walking shoes. Subjects JSME International Journal

609 Fig. 1 View of the experimental study. The subject (center) wore the portable instruments. Three-dimensional accelerations during walking were measured were instructed to walk at their self-selected speed on a 16 m straight track without any restriction. The beginning and the end of the strait track, separated by 3 m, were considered as transition phases of walking. Constant walking phase in the middle 10 m of the track was applied to the calculation. 3. Analysis Our nonlinear technique reveals temporal variations in the gait pattern. This variability was assumed to occur within the locomotor system, which provides the ability to accommodate perturbations. Lyapunov exponent estimation was applied to evaluate the local dynamic stability of walking. The methods are based on examining structural characteristics of a time series that is embedded in an appropriately constructed state space. First, the state space was properly reconstructed from the obtained acceleration data for each direction after determining the appropriate time delay and embedding dimension: y(t) = (x(t), x(t +τ),, x(t +(d 1)τ)). (1) Therein, y(t)represents the d dimensional state vector, x(t) is the original acceleration data, τ is the time delay, and d is the embedding dimension. A schematic representation of the reconstruction process is shown in Fig. 2. A valid state space must include a sufficient number of coordinates to unequivocally define the state of the attractor trajectories. Time delay τ was determined as a time when the autocorrelation coefficient of the data becomes less than the reciprocal value of the natural log. The embedding dimension d was determined using the global false nearest neighbors algorithm (17). In our case, the embedding dimension was four, to form a valid state space. Similar results were found for all directions and all subjects. Estimation of the largest Lyapunov exponent performed with the method proposed by Kantz (18).TheLyapunov exponent λ was defined as the following. D( t) = D(0)e λ t. (2) The notation D( t) denotes the displacement between Fig. 2 Reconstruction of an attractor trajectory in the state space (in case of the embedding dimension d = 3) neighboring trajectories after the t interval. The notation D(0) is the initial distance between neighboring points. The Lyapunov exponent λ quantifies the average exponential rate of divergence of neighboring trajectories in a reconstructed state space. That exponent is calculated as the slope of the average logarithmic divergence of the neighboring trajectories in the state space. A higher value of the Lyapunov exponent indicates a greater divergence of the attractor in the state space, that is, less stability of the dynamic system. We calculated the exponent from acceleration data of 12 continuous steps (six strides) for steady 10-m walking. Data were analyzed without filtering to avoid complications associated with linear filtering effects on nonlinear signals. It was also assumed that the level of measurement noise would be consistent for all data. We also evaluated traditional variability indexes for the gait factors. In order to recognize the gait cycle from time series data, distinct spikes in the vertical acceleration were detected as a heal strike instance. Subsequently, the step number, gait cycle (s), and cadence (step/min) were calculated. Coefficients of variation (CV) were calculated for gait cycle variation. Furthermore, each stride was normalized to 100 sample points, then variation of the acceleration waveform pattern in strides was evaluated as a mean value of the standard deviation (SD) across all data points (six- strides), as follows. The notation a i,n indicates i-th data point of the n-th stride. SD = Mean{S (1 100)}, S (i) = Std { } a i, 1 N, N = 12. (3) All above calculations were programmed using MAT- LAB (The Mathworks, Inc.). ANOVA was used to test for significant between group differences. All statistical investigations were processed using SPSS computer software (SPSS, Inc.). 4. Result Figure 3 shows a typical example of acceleration waveforms measured respectively in the young subject in JSME International Journal Series C, Vol. 48, No. 4, 2005

610 Table 2 Comparison of a male elderly subject before and after the exercise intervention. The standard deviation is shown in parentheses. Significant differences (p < 0.05) ate marked with asterisks Fig. 3 Example of trunk acceleration during six strides (12 steps) walking in a young subject Before After N 28 Age 75.9 (4.2) 75.9 (4.2) Height [cm] 162.4 (7.0) 162.4 (7.0) Weight [kg] 65.6 (12.0) 66.3 (12.1) ROM Ankle [deg] 15.5 (5.2) 17.6 (5.6) ROM Knee [deg] 137.1 (10.8) 138.3 (7.9) Hip Abductors Strength [kg/bw] 1.22 (0.24)* 1.45 (0.31)* Leg Extension 683.5 (179.5) 686.2 (212.8) Power [watts] Functional Reach Forward [cm] 26.4 (4.8) 27.1 (5.0) Lateral [cm] 15.9 (2.4)* 19.7 (2.3)* Step Number 17.5 (1.4) 17.2 (1.2) Cadence 116.5 (11.1) 118.7 (7.9) [step/min] Walking Speed 1.27 (0.16) 1.31 (0.17) [m/s] CV Gait Cycle 0.067 (0.067) 0.068 (0.042) SD Lateral 0.076 (0.036) 0.072 (0.019) SD Vertical 0.089 (0.049) 0.081 (0.026) SD Ant. post. 0.068 (0.032) 0.083 (0.032) LyEp Lateral 0.065 (0.026)* 0.048 (0.018)* LyEp Vertical 0.057 (0.026) 0.046 (0.020) LyEp Ant. post. 0.051 (0.023)* 0.038 (0.018)* Fig. 4 Example of the trunk acceleration during six strides (12 steps) walking in an elderly subject lateral, vertical, and anterior posterior directions. Figure 4 shows the same elderly subject before intervention. That subject illustrated more variability than young subjects had in all directions. Table 1 shows results of analyses with comparison between young and elderly subjects. Significant differences were found in the step number, cadence, and walking speeds (p < 0.05). Elderly subjects walked significantly more slowly than young subjects. The Lyapunov exponents of elderly subjects were slightly higher than those of young subjects, indicating less local dynamic stability, but no statistical significance was observed (p = 0.05). It is noteworthy that elderly persons demonstrated almost identical instability at much slower walking speeds than did young subjects. Results suggested that aging diminished the local dynamic stability of walking, consequently decreasing elderly subjects walking speed to improve stability to compensate for variations of gait. Table 2 shows results of male elderly subjects with Series C, Vol. 48, No. 4, 2005 comparison between groups before and after the exercise intervention. Mean values of the right and the left side records were calculated for the ROM, the hip abductors muscle strength, the lower leg extensor power, and the functional reach. For male subjects, significant improvements were found in the hip abductors muscle strength and the lateral functional reach (p < 0.05). The Lyapunov exponents after the exercise intervention indicated significantly lower values in the lateral and the anteroposterior direction, which indicated improvement of local dynamic stability. Table 3 shows that female elderly subjects also presented significant improvements in the muscle strength of hip abductors and the lateral functional reach. Additionally, a significant increase of the forward functional reach and decrease of the step number were also observed. The Lyapunov exponents of the group after exercise intervention were significantly lower than those of the before group in all directions. No remarkable differences in SD and CV values were found between the groups before and after, in either male or female elderly subjects. According to those results, we hypothesized that strengths of hip abductors contributed to improvement of the local dynamic stability while walking. Figures 5 and 6 show relationships between the strength of hip abductors and the Lyapunov exponents in the group of after exercise JSME International Journal

611 Table 3 Comparison of a female elderly subject before and after the exercise intervention. Significant differences (p < 0.05) ate marked with asterisks Before After N 24 Age 77.0 (4.5) 77.0 (4.5) Height [cm] 146.0 (5.2) 146.0 (5.2) Weight [kg] 51.9 (9.8) 51.6 (8.8) ROM Ankle [deg] 19.9 (7.5) 18.0 (5.5) ROM Knee [deg] 141.6 (15.4) 141.4 (15.2) Hip Abductors Strength [kg/bw] 0.89 (0.25)* 1.07 (0.28)* Leg Extension 252.8 (111.0) 264.4 (100.2) Power [watts] Functional Reach Forward [cm] 23.4 (5.2)* 24.7 (4.7)* Lateral [cm] 15.1 (2.5)* 18.0 (3.3)* Step Number 20.04 (2.27)* 19.67 (2.24)* Cadence 118.64 (8.56) 117.98 (8.42) [step/min] Walking Speed 1.14 (0.18) 1.16 (0.16) [m/s] CV Step 0.061 (0.032) 0.074 (0.038) SD Lateral 0.071 (0.018) 0.076 (0.023) SD Vertical 0.084 (0.025) 0.085 (0.031) SD Ant. post. 0.061 (0.017) 0.077 (0.021) LyEp Lateral 0.075 (0.032)* 0.056 (0.019)* LyEp Vertical 0.073 (0.038)* 0.048 (0.019)* LyEp Ant. post. 0.062 (0.029)* 0.043 (0.014)* Fig. 5 Relationships between the strength of hip abductors and Lyapunov exponents in male elderly subjects after the exercise intervention intervention, respectively, for the male and female elderly subjects. Remarkable correlations were observed in the female elderly subjects (p < 0.05), but not in the male elderly subjects. Hip abductors are known to contribute to stabilizing the pelvis in biped locomotion. Further investigation is required to ascertain specific effects of muscle building or balance training on improvement of walking stability. Results of the traditional variability index used in this study did not reveal significant differences between subjects before and the after the intervention. Elderly persons walking patterns reflect not only the direct effects of aging, but also some adaptive mechanisms developed to compensate for their diminished physical performance. They acquired their own gait pattern, engendering variability in the acceleration waveform. However, standard deviations merely provided a picture of the overall level of variability in the gait patterns. Although they provided a general picture of the level of variability, no information is apparent about any temporal structure of the variations involving with time (13). In contrast, the technique used to analyze nonlinear dynamic systems illustrates both spatial and temporal aspects of the data. In the experimental study, a short walking distance was chosen to avoid effects of fatigue from elderly persons walking. According to a pre-experiment, 16 m was Fig. 6 Relationships between the strength of hip abductors and Lyapunov exponents in female elderly subjects after the exercise intervention a feasible and proper condition to assess stable continuous walking. It is important to mention that estimation of Lyapunov exponents is sensitive to the data size and the observation time (17). Therefore, estimation accuracy of Lyapunov exponents was rather low in this study. However, we quantified the exponential rate of divergence of trajectories, which followed trends of Lyapunov exponents. Consequently, we assumed that our indices were reliable for this inter-subjective study to assess relative improvement of walking performance. The proposed method was adequate to quantify the nature of the dynamic system, which changes the states continuously while walking. It should also be emphasized that the method analyzes the dynamic stability of walking using a light-weight portable instrument that is easy to wear and convenient to use. A quantitative measure of walking stability might provide a promising method to assess personal risk of falls. It might also contribute to designing of proper training strategies and monitoring of JSME International Journal Series C, Vol. 48, No. 4, 2005

612 their progress. 5. Conclusion This study described a technique for assessing dynamic stability of walking using nonlinear time-series analyses with a portable instrument. The proposed method was concluded to be feasible for revealing effects and efficacies of exercise interventions for elderly persons. The method might be useful for scoring the degree of improvement in terms of walking stability. This method is readily applicable in the clinical field. Further application of the present technique might help to predict personal risks of falls. Acknowledgment We are grateful to the Sendai Silver Center and Miyagi Physical Therapist Association for their cooperation in our study. This research was aided by a grant from the Japanese Ministry of Education, Culture, Sports, Science and Technology. References ( 1 ) Tinetti, E.M., Speechley, M. and Ginter, F.S., Risk Factors for Falls among Elderly Persons Living in the Community, New England Journal of Medicine, Vol.319 (1988), pp.1701 1707. ( 2 ) Maki, B.E., Holliday, P.J. and Topper, A.K., Fear of Falling and Postural Performance in the Elderly, Journal of Gerontology: Medical Sciences, Vol.46 (1991), pp.123 131. ( 3 ) Fujita, K., Nagatomi, R., Hozawa, A., Ohkubo, T., Sato,K.,Anzai,Y.,Sauvaget,C.,Watanabe,Y.,Tamagawa, A. and Tsuji, I., Effects of Exercise Training on Physical Activity in Older People: A Randomized Control Trial, Journal of Epidemiology, Vol.13, No.2 (2003), pp.120 125. ( 4 ) Rogers, M.E., Fernandez, J.D. and Bohlken, R.M., Training to Reduce Postural Sway and Increase Functional Reach in the Elderly, Journal of Occupational Rehabilitation, Vol.11, No.4 (2002), pp.291 297. ( 5 ) Bloem, R.B., Haan, J., Lagaay, A.M., Beek, W., Wintzen, A.R. and Roos, R.A.C., Investigation of Gait in Elderly Subjects over 88 Years of Age, Journal of Geriatric Psychiatry and Neurology, Vol.5 (1992), pp.78 84. ( 6 ) Morris, J.R.W., Accelerometry A Technique for the Measurement of Human Body Movements, Journal of Biomechanics, Vol.6 (1973), pp.729 736. ( 7 ) Hurmuzlu, Y. and Basdogan, C., On the Measurement of Dynamic Stability of Human Locomotion, Journal of Biomechanical Engineering, Vol.116 (1994), pp.30 36. ( 8 ) Arif, M., Ohtaki, Y., Ishihara, T. and Inooka, H., Analysis of Aging Effect on Human Walking Gait Using Detrended Fluctuation Analysis Technique, International Journal of HWRS, Vol.3, No.4 (2002). ( 9 ) Arif, M., Ohtaki, Y., Nagatomi, R. and Inooka, H., Estimation of the Effect of Cadence on Gait Stability in Young and Elderly People Using Approximate Entropy Technique, Measurement Science Review, Vol.4 (2004), pp.29 40. (10) Ohtaki, Y., Iijima, Y., Arif, M., Suzuki, A., Nagatomi, R. and Inooka, H., Assessment of Walking Stability by Lyapunov Exponent Estimation, Proceedings of the Second EMBS/BMES Conference, (2002), pp.2475 2476. (11) Dingwell, J.B., Cusumano, J.P., Sternad, D. and Cavanagh, P.R., Slower Speeds in Patients with Diabetic Neuropathy Lead to Improved Local Dynamic Stability of Continuous Overground Walking, Journal of Biomechanics, Vol.33 (2000), pp.1269 1277. (12) Dingwell, J.B.D. and Cavanagh, P.R., Increased Variability of Continuous Overground Walking in Neuropathic Patients Is Only Indirectly Related to Sensory Loss, Gait and Posture, Vol.14 (2001), pp.1 10. (13) Buzzi, U.H., Stergiou, N., Kurz, M.J., Hageman, P.A. and Heidel, J., Nonlinear Dynamics Indicates Aging Affects Variability during Gait, Clinical Biomechanics, Vol.18 (2003), pp.435 443. (14) Awata, S., Seki, T., Koizumi, Y., Sato, S., Hozawa, A., Omori, K., Kuriyama, S., Arai, H., Nagatomi, R., Matsuoka, H. and Tsuji, I., Factors Associated with Suicidal Ideation in an Elderly Urban Japanese Population: A Community-Based, Cross-Sectional Study, Psychiatry and Clinical Neurosciences, Vol.59 (2005), pp.327 336. (15) Hozawa, A., Ohmori, K., Kuriyama, S., Shimazu, T., Niu, K., Watando, A., Ebihara, S., Matsui, T., Ichiki, M., Nagatomi, R., Sasaki, H. and Tsuji, I., C-Reactive Protein and Peripheral Artery Disease among Japanese Elderly: The Tsurugaya Project, Hypertension Research, Vol.27 (2004), pp.955 961. (16) Newton, R.A., Validity of the Multi-Directional Reach Test: A Practical Measure for Limits of Stability in Older Adults, Journal of Gerontology: Medical Sciences, Vol.56A, No.4 (2001), pp.248 252. (17) Cao, L., Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series, Physica D, Vol.110 (1997), pp.43 50. (18) Kantz, H., A Robust Method to Estimate the Lyapunov Exponent of a Time Series, Physics Letters A, Vol.185 (1994), pp.77 87. Series C, Vol. 48, No. 4, 2005 JSME International Journal