QUANTIFICATION OF DYNAMIC WALKING STABILITY OF ELDERLY BY USING NONLINEAR TIME-SERIES ANALYSIS AND SIMPLE ACCELEROMETRY

13 QUANTIFICATION OF DYNAMIC STABILITY OF ELDERLY BY

WALKING USING TIME-SERIES ANALYSIS AND

NONLINEAR SIMPLE ACCELEROMETRY

Y. Ohtaki 1, M. Arife, A. Suzuki :~ K. Fujita 4, R. Nagatomi 5, H. Inooka I 1New Industry Creation Hatchery Center, Tohoku University, 6-6-04 Aza Aoba, Aramaki, Aoba-ku, Sendal 9808579, JAPAN 2pakistan Institute of Engineering and Applied Science, PAKISTAN 3Instruments Technology Research Co. Ltd., Sendai, JAPAN 4Center for Preventive Medicine and Salutogenesis, Tohoku Fukushi University, Sendai, JAPAN '~Graduate School of Medicine, Tohoku University, Sendai, JAPAN

ABSTRACT This study presented a technique to assess dynamic walking stability utilizing a nonlinear timeseries analysis and a portable instrument. Main objective was to investigate its usefulness in the assessment of elderly walking. The method was consisted of measurement of three-dimensional acceleration of the upper body, and estimation of the Lyapunov exponents, thereby directly quantifying local dynamic stability while walking. Straight level walking of young and elderly subjects was investigated in the experimental study. Effects and efficacies of the interventions for the elderly were demonstrated by the proposed method. The experimental results suggested that the method was useful in revealing degree of improvements on the walking stability.

KEYWORDS Gait analysis, Walking stability, Portable instrument, Acceleration, Nonlinear time-series analysis, Aging, Medical application.

INTRODUCTION Falls cause a serious hazard to elderly people, hnpaired mobility due to injuries or a fear of falling diminish a person's ability to perform activities of daily living (Maki et al. 1991). Hip fracture due to fall accidents amounts to more than 10 % of bed-bound status of the elderly in Japan.

14 Although falling is a result of complex and multi-factorial problem, lack of postural control is one of the major contributing factors. Aging effects on the sensory feedback have been hypothesized to be a key factor in adjusting posture to maintain their balance against unpredictable external or internal variations of gait. In addition, recent randomized controlled trials that have tested the effectiveness of the intervention for elderly have indicated that exercise training significantly increase their aerobic capacity and muscle strength, which might result in improvement of the postural stability. Conventionally, clinicians have been assessed personnel walking ability based on performance of static balance tests and measure of simple gait factors (walking speed, cadence, step length, etc.), mostly focusing on quantifying regional amount of body sway, variability of gait factors or joint angles. Those methods provide a practical evaluation, however, the measure of static balance or gait variability itself does not mean that of dynamic stability of walking. Dynamic stability represents a resilient ability to maintain certain continuous cyclic movement by accommodating internal or external perturbations (Hurmuzlu et al. 1994). On the other hand variety of instruments have been used to quantify walking characteristics in a more precise manner, by means of the video-based motion capture system, goniometry, or force plates. However, those methods requires considerable setups, then limited to laboratorial environments. Recently, mechatronics progress made it possible to realize small and low power consumptive accelerometry as a testing tool applicable in the field of medical therapy(Aminian et al. 2002, Ohtaki et al. 2001, 2005). Some advanced algorithms have been also proposed to evaluate gait performances and dynamic walking stability basing on a simple accelerometry(Dingwell et al. 2000, 2001, Buzzi et al. 2003, Arif et al. 2004). Further application of those method to a physical assessment is strongly required to enhance efficiency and effectiveness of interventions. Nevertheless, it is still insufficient to investigate subsequent improvements on walking abilities in terms of the stability of dynamical system. This study was intended to present a practical method to assess walking stability by using a portable instrument, then to investigate its usefulness in the physical assessment for elderly people. The method employed a measurement of three-dimensional acceleration of the body, and an application of nonlinear time-series analysis which directly assess stability of the dynamical system. Straight level-walking of young and elderly subjects were investigated in the experiment. Moreover, its feasibility in assessing effects and efficacies of the five-month interventions including aerobic exercise training was investigated.

METHODOLOGY In this study, we focused on local dynamic stability which is defined as a sensitivity of the dynamical system to small perturbations in gait variability which produced by one's locomotor system itself. Lyapunov exponent estimation was applied to evaluate the local dynamic stability of walking. Firstly, state space was reconstructed from the obtained acceleration data after determining appropriate time delay and embedding dimension: y(t) = ( x ( t ) , x ( t + T),... , x ( t + ( d -

1)T)).

(1)

Where, y(t) is the d dimensional state vector, x(t) is the original acceleration data, T is the time delay, and d is the embedding dimension. A Schematic representation of the reconstruction process was shown in Figure 1. A valid state space must include a sufficient number of coordinates to unequivocally define the state of the attractor trajectories. Time delay T was determined as a time when autocorrelation coefficient of the data gets lower than the reciprocal value of natural

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log. Embedding dimension d was determined by using the global false nearest neighbors algorithm (Cao 1997). In our case, the embedding dimension was four, to form a valid state space. Lyapunov exponent quantifies the average exponential rate of divergence of neighboring trajectories in a reconstructed state space. The estimation of the largest Lyapunov exponent performed with the method proposed by Kantz (Kantz 1994). The Lyapunov exponent A was defined as the following. D(At) = D(O)e :~xt (2) The notation D(At) denotes the displacement between neighboring trajectories after The notation At interval. D(0) is the initial distance between neighboring point. Lyapunov exponent A quantifies the average exponential rate of divergence of neighboring trajectories in a reconstructed state space. A Higher value of Lyapunov exponent indicates a larger divergence of the attractor in the state space, suggesting less stability of the dynamical system. We calculated the exponent from ten steps acceleration data in steady state of the walking trial. Data were analyzed without filtering to avoid complications associated with filtering nonlinear signals.

EXPERIMENT We developed a portable device consisted of monolithic IC accelerometers (-t-2 G, ADXL202E; Analog Devices Inc., MA, USA) with 16-bit duty cycle converter, Li-Ionic batteries, micro processor units and CompactFlash card. This equipment is small (100x55x18.5 mm) and lightweight enough to carry without any restriction. The equipment was attached to the center of lower back representing the center of gravity of the body using a back supporter, as shown in Figure 2. Three-dimensional acceleration as lateral, vertical, and anteroposterior direction were measured by the portable equipment with sampling frequency of 100 Hz. Seven healthy young adults (25.0 + 1.6 yr.) and fifty-four elderly adults aged (76.7 + 4.6 yr.) participated in the experiment. All subjects gave signed informed consent. Prior to the experiment, physical conditions and exercise habit were examined by questionnaires. The subjects 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 3 m were considered as transition phases of the walking. Constant walking phase in middle 10 m of the track was applied to the calculation.

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Figure 2" View of a subject wearing the portable instrument by using a back supporter.

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Figure 3: Typical examples of accelerations as measured in healthy young subject and an elderly before the intervention. Firstly, we investigated the dynamic stability in comparison with the young and the elderly subjects. Secondly, we demonstrated efficacy and effectiveness of the intervention for elderly, quantifying degree of improvements on the walking stability. The intervention program was designed for elderly living in the community through the continuous five-month training conducted by medical doctors and physical therapists. The training program was intended to improve aerobic and physical performance by strengthening the muscular group involved in standing and walking. Subjects attended two-hour classes once a week.

RESULT Figure 3 shows typical examples of acceleration waveforms as measured in healthy young subject (left) and an elderly subject before the intervention (right). The elderly presented clear fluctuations on the waveforms, resulted in large value of the Lyapunov exponents. Figure 4 illustrates average values of the estimated Lyapunov exponents comparing with the young and the elderly in the direction of lateral, vertical, and anteroposterior respectively. The lower and upperlines of the

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Figure 4 Comparison of Lyapunov exponents between young and all elder subjects. The lower and upperlines of the box are 25th amd 75th percentiles.

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Figure 5" Comparison of Lyapunov exponents between the pre-intervention and the post-intervention subject in the elderly.

box are the 25th and 75th percentiles. The line in the middle of the box is the median. The wiskers shows the extent of the rest of the data. Elderly subjects generally exhibited higher value indicating much instability in all direction, but no statistical significance was observed except in the vertical direction (p <0.05). Figure 5 shows the average value of the estimated Lyapunov exponent comparing with the pre-intervention and the post-intervention in elderly subjects. The post-intervention illustrates significantly smaller value of the exponent in all direction (p <0.05). The result, suggested that the inethod feasibly reveals the effects of the interventions on the improvement of walking stability in elderly. In the experiment, a short walking distance was chosen to avoid effects of fatigue from elderly persons' walking. It is important to mention that estimation of Lyapunov exponents is sensitive to the data size and the observation time. 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. The proposed method was adequate to quantify the nature of the dynamic system while walking. A quantitative measure of the walking stability may provides an essential tool for assessing personnel risk of falls, designing proper treatments, and monitoring progress and emcacy of the intervention.

CONCLUSION This study presented a technique for assessing dynamic stability of walking using nonlinear timeseries analysis with a portable instrument. This method is easily applicable and reliable in the clinical field and daily situations. The experimental results suggested that the proposed method

18 quantify degree of improvements in walking stability, which contributes to ascertain the effectiveness of exercise intervention for elderly. Further application of the present technique may help predicting personal risk of falls.

ACKNOWLEDGMENT We are grateful to Dr.I.Tsuji at Graduate School of Medicine, Tohoku University, Sendail Silver Center, and Miyagi Physical Therapist Association for their cooperation in our study. This research is grant aided by Japanese Ministry of Education, Culture, Sports, Science and Technology.

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