Index Introduction Wavelet Analysis Analysis of Distribution of COP Displacement Velocity New Methods in the Diagnosis of Standing Position Control Structure References

Introduction

Falls are not an uncommon event among elderly people. It is reported that 30–50% of elderly people experience at least one fall every year (Black et al., 1988; Tinetti et al., 1988) and falls are more common in females than males (Sheldon, 1948). Falls in the elderly can be fatal or can cause the elderly to become bedridden through injuries such as a femoral neck fracture or subdural hematoma.

The problem is that once elderly people have experienced a fall, they often become fixated by the fear of this happen-ing again, i.e. they suffer from so-called ‘post-fall syndrome’ (Maki et al., 1991). Elderly people with post-fall syndrome may limit their motility and rapidly reduce their range of activities. As a result, their lower limb muscular power weakens sharply, resulting in a further reduction of their activities of daily life (ADL). In other words, such falls in the elderly cause not only the direct loss of standing position control, but also indirectly cause further damage to that function, which in turn induces more falls, resulting in a vicious circle of declining health.

Therefore, it is important to preventatively maintain and manage the standing position control in elderly people by making an appropriate periodic examination before they have their first experience of falling. Irrespective of its type, each element in the complex human postural control system can ultimately be represented by the center of pressure (COP) displacement velocity, which has been reported to be a suitable measure for comprehensive evaluation of postural control systems (Prieto et al., 1996). The present study describes two new approaches that conveniently and effi-ciently analyze COP displacement velocity by examining the standing position control structure.

Wavelet Analysis

COP movements in a standing position can be complex, with short-term observations revealing random patterns, while long-term observations present some periodicity. Thus the normality/abnormality of COP displacement variation is clearly very difficult to determine.

The power spectrum has been used as a useful index to indicate variations in COP displacement, and is the best index to highlight movements with periodicity. However, while the continuous observation of COP displacement vari-ation can detect sudden movements, conventional indices for COP, including power spectrum measurements, cannot precisely express sudden movements.

Individuals with postural control system difficulties, such as people with Parkinson’s disease, have unusual COP dis-placement traces. Therefore any method of analysis can detect disorders of COP displacement; for example, the power spectrum of the COP displacement of an individual with Parkinson’s disease differs clearly from that of a healthy subject (Rocchi et al., 2002). However, COP displacement often shows just a single peak, which can be due to a significant reaction of the postural control system. Unfortunately, earlier fast Fourier transform (FFT) analysis methods overlook this pattern. The detection of a single, but significant, peak of COP displacement might reveal a hidden disorder of the postural control system, which could then be remedied. Such a method would contribute to the detection of the deterioration of postural control systems in elderly people, and improve their life conditions by allowing for adequate treatment. Therefore, an analysis method should not round off a single peak of COP displacement, much less exclude it.

Wavelet analysis, which is used to analyze various wave phenomena, has recently received attention. Newland (1993) demonstrated that the wavelet analysis method was better than FFT at detecting singularity, edges, and peaks on a continuous signal. According to Newland, the most dis-tinctive characteristic of this analytical method is that it can sensitively detect abnormal values as well as wave periodicity (Sakakibara, 1995; Ashino and Yamamoto, 1997; Kikuchi and Nakashizuka, 1997). More importantly, this method also allows analysis of periodicity over time, as is the case with short-time Fourier analysis (Loughlin et al., 1996).

The present study reports the results of COP swing analysis utilizing wavelet analysis, and notes the characteristics and benefits of this method. Data on COP displacement vari-ations were obtained from a 22-year-old male subject standing on a force platform (ANIMA: GI1822S) for 2 min. While in a standing position, the subject was asked to follow a directional acoustic signal in order to change the visual condition during the experiment. The signal was set to start 1 min after the subject took up his stance for the experiment. The distance between the subject’s feet on the force platform was 20 cm at the toe and 10 cm at the heel. Analog signals from the force platform were digitized with a sam-pling frequency of 20 Hz by an analog–digital (AD) converter integrated with a microcomputer. Figure 1 shows the COP displacement trace obtained from the standing subject. In each panel, the origins of the front–back and right–left directions have been translated to mean values. Standard deviations under each visual condition were as follows: 0.3176 cm (right–left direction) and 0.6352 cm (front–back direction) with the eyes open, 0.3773 cm (right–left direction) and 0.5707 cm (front–back direction) with the eyes closed, 0.4140 cm and 0.6498 cm with the eyes open to closed, and 0.3778 cm and 0.5947 cm with the eyes closed to open.

The COP trace shown in Figure 1 is a typical one, and reveals that the COP displacement ranges were ±1.5 cm for the right–left direction and ±2.5 cm for the front–back direction; thus there were no clear differences caused by visual conditions. A comparison of the standard deviations showed that in the right–left direction this was lowest (0.3176 cm) with the eyes open, while in the front–back direction it was lowest (0.5707 cm) with the eyes closed. Two reasons can be proposed for these results. The first is that the ranges of COP displacement would be almost the same under both visual conditions in the case of a healthy individual. The second is that the COP tracing diagram does not suit the display of events over the course of time. Therefore, it was found that the differences in visual conditions were not always reflected in the motion range of the COP trace.

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Figure 1. COP traces in a standing position under four different visual conditions. Upper-left, eyes open; upper-right, eyes closed; lower-left, eyes open to closed; and lower-right, eyes closed to open. The COP in the front–back direction is plotted on the ordinate and in the left–right direction on the abscissa. Units for both directions are cm.

Figure 2 shows the front–back swing curves under the four different visual conditions in a standing position. Detailed comparisons between eyes open and eyes closed are shown in Figure 2, which demonstrates a spikier pattern with eyes closed. This suggests that there are certain differences of frequency components that depend on the differences in visual conditions. In this respect, Cernacek et al. (1973) found that the power of the frequency band of 0.125–0.375 Hz increased with eyes closed as compared with eyes open, and Prieto et al. (1996) reported that the 50% power frequency of adults was 0.285 Hz (±0.075) with eyes open and 0.320 Hz (±0.106) with eyes closed.

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Figure 2. COP curves in the front–back direction in a standing position under four visual conditions. From top to bottom: eyes open, eyes closed, eyes open to closed, and eyes closed to open. The COP position in the front–back direction is plotted on the ordinate and the elapsed time on the abscissa. Units are cm for the ordinate and seconds for the abscissa. The arrows in the figure indicate the starting points of the directional sounds.

These observations suggest that the COP swing with eyes closed had relatively higher spectral power around 0.3 Hz than with eyes open. Therefore, if the spiky pattern with eyes closed in Figure 2 is formed by the increased spectral power around 0.3 Hz, our results are generally consistent with pre-vious studies. When the visual condition was changed during the experiment in the standing position, spinosity appeared, a characteristic of eyes closed. These changes were due to the change of the visual condition during the measurement and had profound implications. However, since conventional Fourier analysis uses a series of COP swings as a minimum unit, it is difficult to detect precisely any sudden change during an experiment in a standing position, resulting in a high possibility of failing to ascertain the profound implications of this particular change. This study split the front–back swing curves of a standing position, shown in Figure 2, into individual frequency components by using wavelet analysis, and discusses the characteristics of this method.

Figure 3 shows the results of splitting the COP front–back swing of a standing position into each of the frequency components under the four visual conditions by applying wavelet analysis. The analysis yields the following functions;

g(0) = g(1) + g(2) + g(3) + g(4) + (5) + ··· + g(11).

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Figure 3. Results of wavelet analysis. COP displacement curve in the front-back direction were divided into the frequency components (g4, g5, g6) and all the components were compared each other. Upper-left, eyes open; lower-left, eyes closed; upper-right, eyes open to closed; and lower-right, eyes closed to open. The spectral power of swaying is plotted on the ordinate and the data number in order of their appearance on the abscissa.

where g(0) is the original COP displacement, e.g. the front–back swing curve in Figure 2. Generally, the largest function number will depend on the total number of data. The great amplitude of each function implies that an abundant frequency component is involved; this is the main reason why wavelet analysis has drawn the attention of many researchers. The results of wavelet analysis easily provide for partial periodicity on a series of complicated swing curves. Three functions, g(4), g(5), g(6), were compared to explain the differences of the frequency components due to the visual conditions used in this study. This example specifically compared the frequency components around 1.25, 0.6, and 0.3 Hz. Generally, each frequency component changed irrespective of the visual condition. However, comparisons of the same frequency band show that differences in visual conditions and spectral power were clearly greater with eyes closed. When the visual condition was changed at some midpoint during the experiment in the standing position, the characteristics of the spectral power both with eyes open and eyes closed appeared without any inconsistencies. In agreement with this change, the postural control mechanism was likely to be immediately changed as the visual condition changed. As is clear from the examples in Figure 3, when each frequency component is arranged over time by wavelet analysis, more detailed study is possible in relation to the size of the components in each frequency, and completely new interpretations may be derived. Therefore, if modulation of each element in a complicated standing position control system and the individual changes can be extracted from a changing COP swing curve, then based on the results of those extractions, appropriate preventative measures can be taken prior to any serious alteration in the standing position control structure.

Analysis of Distribution of COP Displacement Velocity

Of the many measurements associated with COP swing, displacement velocity is one of just a few detection methods that can precisely and consistently present differences by age and visual condition. Prieto et al. (1996) reported that the COP displacement velocities of young adults were 6.09 ± 1.79 mm/sec with eyes open and 8.89 ± 2.86 mm/sec with eyes closed, while those of elderly people were 12.2 ± 4.49 mm/sec with eyes open and 16.2 ± 6.43 mm/sec with eyes closed, showing that the COP displacement velocity became faster with increased age under both conditions.

The COP displacement velocity in these studies is the average of the COP normalized to the total excursion of the analysis interval. The instantaneous velocity of the COP displacement is rather more important than the average value, because the nature of falls in the elderly is usually a single, instantaneous, high-velocity moment. Earlier studies concerning the stability of the human standing posture have discussed average COP displacement velocity, and have failed to discuss the important aspect of instantaneous velocity.

Figure 4a shows a COP trace obtained from a 21-year-old subject standing for 2 min with eyes open on a force platform (see section above). Figure 4a shows the COP displacement in both directions within a 15 mm range. The analysis of the COP displacement velocity was done as follows: (1) the root mean squares (RMS) of both directions were calculated, (2) a grid diagram based on the RMS values was created as shown in Figure 4b, (3) the COP tracing diagram was overlaid on the grid diagram (Figure 4c), (4) the position of each point on the COP tracing diagram was determined, and (5) the displacement velocity of each COP was calculated. Figure 5 shows how the displacement velocity of each COP was determined. Here, the distances from N - 1 to N and N to N + 1 (d₁ and d₂) were determined. The displacement time from N - 1 to N + 1 was 0.1 sec because of the sampling frequency of 20 Hz used in this study, and thus the displacement velocity from N - 1 to N + 1 could be expressed as (d₁ + d₂) × 10 mm/sec. The value obtained from the above formula was defined as the COP displacement velocity at N in the present study. The COP displacement velocities of all points, except the first and last points, were similarly determined.

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Figure 4. Method of defining the position of each COP point on the grid diagram made from RMS values. (a) COP tracing diagram, units for both directions are in cm; (b) the grid diagram made from RMS values; (c) the position of each COP point on the grid diagram.

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Figure 5. Method to calculate displacement velocity at each COP. d1, distance between N - 1 and N; d2, distance between N and N + 1. See text.

The COP displacement velocities obtained were integrated for each grid as shown in Figure 6. The mean COP displacement velocity was then determined for each grid. Figure 7 shows the mean COP displacement velocities on the grid diagram of the measured values from the present study. The COP of the subject moved within -2 RMS to +RMS in the right–left direction, and -1.5 RMS to +1.5 RMS in the front–back direction. The mean COP displacement velocities tended to be higher in both directions in the outer grids. The COP displacement velocities in two grids (C-4 and C-7) exceeded 4 mm/sec. When the cut-off value was set at 3.5 mm/sec, the COP displacement velocity was relatively higher in five grids (H-6, G-7, and F-8 in addition to C-4 and C-7). The results in Figure 7 suggest that the COP displacement velocities continuously varied for a standing subject.

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Figure 6. Definitions of each grid. The direction from A to J corresponds to the direction from heel to toe. The smaller the number, the farther the COP is to the left side; and the greater the number, the farther the COP is to the right side.

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Figure 7. Averages of the COP displacement velocity (mm/sec) in each grid.

A contour drawing using the level of the COP displacement velocities calculated on the basis of the distribution of the COP displacement velocities shown in Figure 7 is shown in Figure 8, which visually indicates the differences in the COP displacement velocities by region. An overview of Figure 8 gives an appearance like a ‘crown’, since the center is depressed and the fringes have some projections. That is, the COP displacement velocity was faster at the fringe of the tracing diagram and slower in the center.

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Figure 8. Distribution of the COP displacement velocity.

Generally, the COP displacement velocity in elderly peo-ple is faster than in young adults, and their 50% and 95% power frequencies of the COP swing are in a higher fre-quency band than those of young adults (Myklebust and Myklebust, 1989; Prieto et al., 1996). These facts predict that the COP displacement velocity in elderly people has a larger projection at the fringes with weaker depression at the center as compared with young adults. Therefore, if the distribution of the COP displacement velocity is visualized and allows for an easy detection of points with abnormally high velocity and extent of depression at the center, a mild alteration of the subject’s postural control system, which could not be distinguished by outer appearances, can be made.

New Methods in the Diagnosis of Standing Position Control Structure

As described above, since the effect of each element in the complicated postural control structure is ultimately reflected in the COP displacement velocity, the study of standing-position COP displacement velocities in the elderly is important (Prieto et al., 1996). The present study shows that wavelet analysis of COP displacement velocity, and analysis of COP displacement velocity distribution could quickly and easily detect changes in both measurements.

The causes of falls in the elderly include functional and morphological disorders of the body due to aging (Orimo, 1992). Examples are orthostatic hypotension and cerebral vascular disorder; cerebellar disorder, Parkinson’s disease, and posterior funiculus disorder of the nervous system; joint pain, fracture/dislocation, and lowered muscular power in the lower locomotor system; and cataracts and glaucoma. Even if no diagnosis of pathological change has been made, the elderly are usually assumed to be suffering from such disorders; thus even ‘normal’ elderly people are at a risk of falling.

When a standing position is maintained, full use of the functions of various organs is possible, thus a defect in one organ does not always lead to critical damage (Nashner et al., 1985; Black et al., 1988). For this reason, if a minor dysfunction of the standing position control structure can be ascertained and treated properly before an elderly person has their first experience of falling, any lowering of their ADL due to a fall might be prevented. The two approaches to analyzing COP displacement velocity described in the present study are useful methods to evaluate any changes to the standing position control structure caused by aging, and can be used as diagnostic methods to maintain and manage this structure in elderly people.