Inter and intra-limb processes of gait control.

Inter and intra-limb processes of gait control. Simon B. Taylor, Rezaul K. Begg and Russell J. Best Biomechanics Unit, Centre for Rehabilitation, Exercise and Sport Science. Victoria University, Melbourne, Australia. Abstract This paper investigates a method for characterising the symmetric status of gait and the inter and intra-limb relationship of gait control. Previous research shows fluctuations of intra-limb stride intervals to have long-range correlations indicating scale-free (fractal like) phenomena. The presence of this phenomena in gait, and a method for its identification (detrended fluctuation analysis) provides a new approach to gait analysis. A single, healthy young adult subject, completed a thirty-minute treadmill test. Minimum foot clearance values and the time interval between their occurrences were taken at these successive bilateral events. Using detrended fluctuation analysis, we computed α (self-similarity parameter), a measure of the degree to which a single value in a series of data is correlated with a previous and subsequent value over different time scales. The results demonstrate long-range correlations of intra-limb spatial and temporal parameters in both limbs. The computed selfsimilarity parameter (α) indicates a symmetric relationship between limbs for temporal processes of gait. However, a similar computation and comparison for spatial processes of gait reveal an asymmetric relationship. The inter-limb spatial relationship demonstrates long-range correlations. The investigation demonstrates a new method for classifying gait symmetry and has implications for furthering knowledge on the coordination processes of gait control. I. INTRODUCTION In 999, a report by the Commonwealth Department of Health and Aged Care (CDHAC) [, 2] dedicated their attention towards the problem associated with the rise in the number of falls in elderly populations. The report detailed the need for addressing research gaps associated with the prevention of falls, and also, to identify those groups most at risk. One of these areas relates to identifying individuals at risk of falls so that intervention programs can be undertaken, which may cause a reduction in falls. Although some research has been aimed at finding a relationship between gait parameters and falls, currently there is no evidence of an objective method to confirm cause and effect relationship [3]. Interestingly, in a multi-factorial investigation, Hill et al. [4] found stance phase asymmetry to be amongst the two strongest predictors for the occurrence of a fall. Hence, the purpose of this paper is to investigate a method appropriate for characterising the symmetric status of gait. This can be addressed by combining two developing concepts in biological behaviour: Firstly, the measurement of long range, self-similar correlations in biological systems suggests that gait control mechanisms behave in a scale free (fractal like) process [5], and secondly, the principles of motor control, symmetry and inter-limb coordination dynamics [6]. Recently, Hausdorff et al., [5] developed a method (detrended fluctuation analysis (DFA)) to identify and characterise fluctuations (noise) in the stride intervals of gait. This method has an advantage over traditional methods because it can describe the fluctuating process that cause variance in the data.. DFA may be beneficial for characterising asymmetry in gait because it has the ability to identify the nature of various states contributing to the moment-tomoment changes that occur over multiple strides. Healthy gait is characterised by persistent long-range correlations, decaying in a power law fashion [5]. This implies a 'memory' effect within the neurophysiological control process, operating across hundreds of strides. Elderly, or pathological gait, shows a breakdown in long-range correlations, such that fluctuations approach white noise behaviour [7]. An important finding by Hausdorff et al., [7] demonstrates that when comparing single limb data between two subjects, the mean and standard deviation of a gait parameter may be almost identical, while the correlations inherent within the fluctuations can be significantly different. The parameters investigated will be measured at successive minimum foot clearance (see Figure.) events (i.e. periods occurring between left-to-right, left-to-left and right-to-right MFC events). Minimum foot clearance (MFC) is a precise end point control task, influenced by a multitude of factors [8]. The MFC event is considered an important parameter in understanding falls, specifically falls resulting from a trip [8]. The task of MFC is to avoid ground contact

lateral side of both the right and left shoe (fifth metatarsal head and the distal superior tip of the toe). Cameras and 2 have been positioned 9 meters from the center of the treadmill. The optical axis of cameras and 2 are perpendicular to the plane of progression. C. Data Analysis. MFC is calculated from a geometric model representing the two foot markers and a manually digitized point representing the outsole surface of the shoe. 'Peak Motus' provided the means to collect the raw data. This data was then 'screened' using a software program to determine temporal and spatial properties at MFC events. during the swing phase; hence, it is an important objective in the control of gait. Inter-limb symmetry is realised when the left and right limbs are identical in uncoupled frequencies and spatial orientation [9]. Symmetry can be broken through timing or spatial differences between the limbs. Principles from bimanual motor control experiments support the presence of asymmetric fluctuations inherent within inter-limb coordination [5,0]. Walter et al. [] using bimanual tasks, suggested that many inter-limb interactions are nonlinear. The methods that underlie the identification of asymmetric patterns, therefore, represent the hypothesis of the type of processes inherent in the biological system. Thus, an appropriate method for characterising asymmetric fluctuations may strengthen support of cause and effect relationships between predictors of falls, and the occurrence of falls. II. METHOD A. Subject One healthy young male participated in the current investigation. The subject characteristics were: age = 29 years, height =.82 m, body mass = 82.0 kg. The subject was free of the following exclusion criteria: any medical problems affecting balance and mobility; vision impairment; fall history; and impaired cognition. B. Equipment and Experimental Procedures. The camera set up follows recommended 2-d videography principles [2]. The walking trial was performed on a motorized treadmill. The experimental set up (Figure 2) and procedure was conducted at the Victoria University Biomechanics Laboratory (Flinders St. Campus). The subject completed a 30-minute walking trial at their selfselected gait velocity, as per Best et al. [3]. Data is collected from Cameras and 2 (50Hz). Two light emitting diodes (LED s) were positioned on the D. Quantifying spatiotemporal MFC correlations. To determine the degree of correlations within respective spatiotemporal parameters, time series data is obtained over the 30 minute walking trial. DFA is applied to the respective data series to identify selfsimilar processes, a criteria inherent in fractallike properties. A self-similarity scaling parameter (α) is computed from the time series data. Generating the scaling parameter involves several steps. Firstly, the specified time series data is integrated, mapping the original data to a self-similar process (equation ), where p i is the i th value for a given spatiotemporal parameter p; and, p (ave) is the average of the given parameter value. [ ] p i p k i ( ave) y k) = = ( () Determining self-similarity of the fluctuations in the integrated time series (y (k)) requires scaling different sized windows (n) of the data. To do this, the integrated time series, y(k), is detrended by subtracting the local trend, y n (k) (equation 2). F Figure 2. Experimental set up. [ y k y n k 2 ( ) ( )] ( n) (2) = N N k=

This creates a relationship between the average fluctuations F(n), and window size (n). If the fluctuations F(n) at different windows scale as a power-law with window size n, the integrated time series is self-similar. A linear relationship on a double log graph indicates the presence of selfsimilarity, where the slope of the gradient relating log F(n) to log n determines the value of the selfsimilarity parameter, α, where F(n) n α. Relationship between self-similarity and the nonintegrated time series. DFA calculates a scaling exponent (α) that describes the processes generating the fluctuations. These processes vary from random, white noise (α=0.5); long-range correlations (0.5<α<.0); /f noise (α=); and short-range correlations or Brownian noise (α=.5). With /f noise, the current value of the non-integrated time series data is believed to co-vary with not only its most recent value but also with its long-term history in a scale invariant fractal manner [4]. Spatial fluctuations in MFC values (cm) within and between limbs. Fluctuations in the output data of (i) the intra-limb MFC and (ii) the relative inter-limb MFC difference will be analysed. Fluctuations in the data will be characterised by the self-similarity parameter, α, obtained by DFA. This will reveal the process of how the limbs approach or disperse from an intended symmetric spatial orientation. Temporal fluctuations within stride-to-stride MFC intervals (seconds) of both limbs. MFC events will determine the interval time. Interval time series data will be analysed using DFA. The self-similarity parameter, α, will provide a means for comparing the temporal process between the limbs. II. RESULTS The results for the single subject are presented in Table. The descriptive statistics and the selfsimilarity scaling parameter, α, are recorded for the five spatiotemporal parameters. The temporal parameters are defined by the time interval between successive MFC occurrences. The spatial parameters involve inter and intra-limb relations. The observed intra-limb, MFC data for each limb is defined by 'mfc L-L' and 'mfc R-R'. Spatial inter-limb relations are defined by the MFC value difference between the left and right limbs ('mfc L-R'). Table. Inter and intra-limb temporal and spatial parameters for descriptive statistics and the selfsimilarity scaling parameter, α. Mean ± SD α Temporal parameters L-L mfc time (s).34 ±0.06 0.85 R-R mfc time (s).34 ±0.020 0.800 Spatial parameters mfc L-L (cm).42* ±0.99 0.803 mfc R-R (cm) 2.58* ±0.274 0.972 mfc L-R (cm).06 ±0.35 0.940 *Indicates a significant difference between left and right limbs (p <.00). MFC (cm) 4 3.5 3 2.5 2.5 right-left MFC difference (cm) Fluctuations in M FC v alues over time for the right limb. 50 00 50 Stride number (n) Figure 3. A sample of the time series data generated by the right limb, for n strides, against spatial MFC values Spatial difference between the left and right MFC values (cm) at their respective stride 2.5 number (n) 2.5 0.5 0 50 00 50 stride number (n) Figure 4. Spatial differences between concurrent left and right (step) MFC values (cm) at their respective stride number (n). A. Descriptive Statistics. The following gives an account of the intra-limb statistics. The mean and standard deviation for temporal stride intervals show no difference between the left and right limb. Alternatively, a significant difference (p <.00) exists

between the left and right limbs for the MFC events. The range of MFC values recorded for the right limb was between.743 cm and 3.49 cm, and 0.8 cm and 2.46 cm for the left limb. B. Temporal stride-to-stride relationship within limbs. The self-similarity parameter for the stride interval of the left limb (α=0.85) is approximately the same as the right limb (α=0.800) (Table ). This suggests persistent long-range correlations within the stride-to-stride interval of both limbs, over hundreds of strides. Also, the mean and standard deviation of the respective right and left stride interval is almost equal. C. Spatial inter and intra stride-to-stride relationship. The respective spatial orientation between the left and right limbs is somewhat different to the timing between MFC events. A significant difference is shown between the left and the right spatial process (α=0.803 and α=0.972 respectively). Interestingly, the right MFC series (α=0.972) approaches /f noise, indicating a presence of both long range and short-range correlations. The structure of the fluctuations for the spatial parameter 'mfc R-R' is shown in Figure 3. Inter-limb MFC difference ('mfc L-R') fluctuations are shown in Figure 4. Some similar characteristics in the line graph structure for both 'mfc R-R' and 'mfc L-R' are evident upon inspection. Spatial symmetry, expressed in the difference between successive left and right MFC occurrences, shows a relatively high variability in consideration to the mean. Also, persistent long-range correlations are shown to occur within the spatial inter-limb relationship, where α=0.940. III. DISCUSSION This study investigated a new method for characterising inter and intra-limb gait control. The advantage of the DFA allows a greater understanding of the control processes of gait compared with traditional statistical methods. Traditional methods generally fail to account for the asymmetric fluctuations of inter-limb coordination and how the gait processes can be characterised over hundreds of strides. Hence, traditionally, where data is obtained from several trials, important phenomena within the parameters being measured can easily be missed. This investigation demonstrates that the precise end point motor control task, of successive intra-limb and inter-limb MFC events, is influenced by a memory effect in both temporal and spatial processes. The results of this study did not demonstrate discrepancies in comparisons between the first order statistics and the self-similarity scaling method for intra-limb analysis, as reported by Hausdorff et al. [7]. Future studies involving more subjects (healthy, elderly and pathological) will allow comparisons between differential statistics and the scaling parameter. The stride interval fluctuations between minimum foot clearance events are consistent with those found by Hausdorff et al. [5,7], who reported on the stride interval of heel contact events. The results of this study do not show inter-limb relationship in temporal coordination between the limbs. Their means, standard deviations and more importantly, their respective self-similarity parameter, does, however, suggest the necessary features of a symmetric relationship. Further analysis methods are required to confirm this rationale. Comparing the differences found between left and right intra-limb self-similarity parameters, suggests a break in the reflective spatial orientation, hence asymmetric behaviour. The persistent long-range correlations found in the spatial difference fluctuations, however, indicate a coordinating relationship. Turvey et al. [6] identified three complex and separate organisational levels, trying to establish both spatial and temporal symmetry. Although spatial symmetry is rarely achieved (Figure 4.), interestingly, the relative spatial changes follow long-range correlations (α=0.94); hence, indicating that each MFC event is either dependent upon the contra-lateral limb (a localised coordinating relationship) or higher order mechanisms (a coordinating control center). The implications of an inter-limb relationship not exhibiting long-range correlations would suggest a breakdown in the coordinating mechanisms of gait control, maybe leading to asymmetric behaviour, whereby identification is possible only from methods that account for fractal like processes, such as detrended fluctuation analysis. Future Applications and Implications. To further understand the control mechanisms of gait and symmetry relations between limbs, future applications of this form of gait analysis will need to be performed upon a larger number of subjects of various population groups and the effect treadmill speed has on the self-similarity parameter. The implications of this procedure and its applications may advance our understanding of gait control and

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