Invariant density analysis: modeling and analysis of the postural control system using Markov chains

In this paper, a novel analysis technique, invariant density analysis (IDA), is introduced. IDA quantifies steady-state behavior of the postural control system using center of pressure (COP) data collected during quiet standing. IDA relies on the analysis of a reduced-order finite Markov model to characterize stochastic behavior observed during postural sway. Five IDA parameters characterize the model and offer physiological insight into the long-term dynamical behavior of the postural control system. Two studies were performed to demonstrate the efficacy of IDA. Study 1 showed that multiple short trials can be concatenated to create a dataset suitable for IDA. Study 2 demonstrated that IDA was effective at distinguishing age-related differences in postural control behavior between young, middle-aged, and older adults. These results suggest that the postural control system of young adults converges more quickly to their steady-state behavior while maintaining COP nearer an overall centroid than either the middle-aged or older adults. Additionally, larger entropy values for older adults indicate that their COP follows a more stochastic path, while smaller entropy values for young adults indicate a more deterministic path. These results illustrate the potential of IDA as a quantitative tool for the assessment of the quiet-standing postural control system.     

The application of time-frequency methods to the analysis ofpostural sway

We apply time-frequency (TF) spectral analysis techniques, namely evolutionary spectral estimators, to postural sway data gathered during quiet standing and in response to external visual stimuli. These techniques provide insight into the time-varying properties of the human balance control systems during standing. We demonstrate by means of individual and group examples that the results of the TF methods can be used to characterize the behavior of the balance system for groups of patients and controls. Specifically we show that, for healthy control subjects, sway at a visual stimulus frequency toward and away from the subject shows an amplitude which decays in time. On the other hand, patients display a response whose amplitude at the stimulus frequency increases with time. Thus TF analysis yields insights into the time-varying nature of the postural control system     

Galvanic vestibular stimulation for analysis of postural adaptationand stability

Human postural dynamics was investigated in 12 normal subjects by means of a force platform recording body sway, induced by bipolar transmastoid galvanic stimulation of the vestibular nerve and labyrinth. The model adopted was that of an inverted segmented pendulum, the dynamics of postural control being assumed to be reflected in the stabilizing forces actuated by the feet as a result of complex muscular activity subject to state feedback of body sway and position. Time-series analysis demonstrates that a transfer function from stimulus to sway-force response with specific parameters can be identified. In addition, adaptation to the vestibular stimulus is demonstrated to exist, and the authors describe this phenomenon using quantification in terms of a postural adaptation time constant in the range of 40-50 s. The results suggest means to evaluate adaptive behavior and postural control in the erect human being which may be useful in the rehabilitation of individuals striving to regain upright stance     

Ambulatory center of mass prediction using body accelerations and center of foot pressure

The center of body mass (COM), center of foot pressure (COP), and body segment acceleration signals are commonly used to indicate movement performance and stability during standing activities and walking. For balance maintenance and restoration, the human brain is capable of estimating and predicting the COM even in the absence of visual or vestibular information. Thus, we hypothesized that the COM may be acquired through the processing of proprioceptive somatosensory information, represented by body segment accelerations, and an external spatial reference, the ground support, represented by the COP. To investigate this hypothesis, we modeled the relationships that exist between the COP and accelerometer data with the 3-D COM trajectory, during walking on firm and irregular surfaces. The models accounted for 99.85 +/- 0.20% and 99.77 +/- 0.39% of the resultant COM trajectory's variability for the firm and irregular surfaces, respectively. This corresponded to a percentage error between the estimated and actual resultant COM of 16.06 +/- 11.11% for the firm surface and 21.41 +/- 12.70% for the doweling surface. In turn, this translates into an absolute error between the true and actual resultant COM of 3.62 +/- 2.69 cm and 4.74 +/- 3.01 cm for the firm and doweling surfaces, respectively. The model is novel in that it does not require any calibration and provides a reasonably accurate estimation of the COM, which can be compared to the brain's balance performance. Hence, this model could be used instead of the cumbersome method of video motion analysis for COM calculation.     

A statistical mechanical analysis of postural sway using non-Gaussian FARIMA stochastic models

In this paper, postural sway is modeled using a fractional autoregressive integrated moving average (FARIMA) family of models: the center-of-pressure (COP) motion is viewed in terms of a self-similar, anti-persistent random-walk process, obtained by fractionally summating non-Gaussian random variables, whose correlation structure for small time lags is shaped by a linear time-invariant low-pass filter. The model parameters are: the strength of the stochastic driving, e.g., the root mean square (rms) value of the time-difference COP motion; the DC gain, damping ratio and natural frequency of the filter; the Hurst exponent, which measures the random-walk antipersistence magnitude. In the proposed modeling procedure, a graphical estimator for determining the Hurst exponent is cascaded to a method for matching autoregressive (AR) models to fractionally difference COP motion via higher order cumulants. The effect of the presence or absence of vision on the model parameter values is discussed with regard to data from experiments on healthy young adults.     

Identification of human postural dynamics

Human postural dynamics was investigated for six healthy subjects using a force platform recording body sway induced by vibrators attached to the calf muscles. The model of body mechanics adopted was that of an inverted pendulum, the dynamics of postural control being assumed to be reflected in the stabilizing forces exerted on the platform by the feet as a result of complex muscular activity subject to state feedback of body sway and position. The approach to signal processing has been that of parametric identification of a transfer function representing the stabilized inverted pendulum. Posture control was quantified in three variables: swiftness, stiffness, and damping. It is shown that the identification fulfils ordinary statistical validation criteria, and it is conjectured that the state feedback parameters identified are suitable for use in assessing ability to maintain posture     

Balance prosthesis based on micromechanical sensors using vibrotactile feedback of tilt

A prototype balance prosthesis has been made using miniature, high-performance inertial sensors to measure lateral head tilt and vibrotactile elements mounted on the body to display head tilt to the user. The device has been used to study the feasibility of providing artificial feedback of head tilt to reduce postural sway during quiet standing using six healthy subjects. Two vibrotactile display schemes were used: one in which the individual vibrating elements, called tactors, were placed on the shoulders (shoulder tactors); another in which columns of tactors were placed on the right and left sides of the trunk (side tactors). Root-mean-square head-tilt angle (Tilt) and center of pressure displacement (Sway) were measured for normal subjects standing in a semi-tandem Romberg position with eyes closed, under four conditions: no balance aids; shoulder tactors; side tactors; and light touch. Compared with no balance aids, the side tactors significantly reduced Tilt (35%) and Sway (33%). Shoulder tactors also significantly reduced Tilt (44%) and Sway (17%). Compared with tactors, light touch resulted in less Sway, but more Tilt. The results suggest that healthy normal subjects can reduce their lateral postural sway using head tilt information as provided by a vibrotactile display. Thus, further testing with balance-impaired subjects is now warranted.     

Postural stability and stereo-ambiguity in man-designed visualenvironments

Our modern rectilinear visual environment contains visual stimuli for which evolution has not had time to optimally shape visual processing. One such stimulus, periodic stripes, is known to lead to visual depth ambiguity. In this paper we show that postural instability, as measured by the variance of fore and aft sway, is increased by viewing such stimuli. This instability may be the precursor of falls. Designers must evaluate the visual impressions conveyed by their systems in order to avoid postural instability due to visual ambiguity.     

Stiffness and Damping in Postural Control Increase With Age

Upright balance is believed to be maintained through active and passive mechanisms, both of which have been shown to be impacted by aging. A compensatory balance response often observed in older adults is increased co-contraction, which is generally assumed to enhance stability by increasing joint stiffness. We investigated the effect of aging on standing balance by fitting body sway data to a previously developed postural control model that includes active and passive stiffness and damping parameters. Ten young (24 $pm$ 3 years) and seven older (75 $pm$ 5 years) adults were exposed during eyes-closed stance to perturbations consisting of lateral pseudorandom floor tilts. A least-square fit of the measured body sway data to the postural control model found significantly larger active stiffness and damping model parameters in the older adults. These differences remained significant even after normalizing to account for different body sizes between the young and older adult groups. An age effect was also found for the normalized passive stiffness, but not for the normalized passive damping parameter. This concurrent increase in active stiffness and damping was shown to be more stabilizing than an increase in stiffness alone, as assessed by oscillations in the postural control model impulse response.      

Analysis of the posture control system under fixed andsway-referenced support conditions

To delineate the relative roles of each of the feedback sensors in the posture control system such as the visual, vestibular, and proprioceptive sensors, an identification technique was applied to measurements of antero-posterior sway angles of the body and ankle moments under the following conditions: standing on a fixed support with eyes open (ox), standing on a fixed support with eyes closed (cx), standing on a sway-referenced support with eyes open (os), and standing on a sway-referenced support with eyes closed (cs). Frequency response functions from the sway angle to the ankle moment were calculated. Gain and phase characteristics for conditions (os) and (cs) were similar to those of Nashner's (1972) vestibular model in the high-frequency range, which shows that the vestibular system may be dominant. The gain was higher under condition (cx) than under (ox). Judging from the phase characteristics, this was probably due to increased weighting of the proprioceptive sensor over the vestibular sensor. There was a tendency for gain to increase as balance tasks became more demanding     

一种基于Radon变换的时频分析方法

针对CW脉冲和线性调频(LFM)信号,利用Radon变换沿直线积分的特性,将其与时频分布(TFD)结合在一起,抑制多频率分量信号各个分量之间的交叉项干扰,提高时频分布的时频二维分辨力。通过仿真数据验证算法具有良好的时频分辨能力以及抑制交叉项干扰能力。     

The time-frequency distributions of nonstationary signals based ona Bessel kernel

A kernel based on the first kind Bessel function of order one is proposed to compute the time-frequency distributions of nonstationary signals. This kernel can suppress the cross terms of the distribution effectively. It is shown that the Bessel distribution (the time-frequency distribution using Bessel kernel) meets most of the desirable properties with high time-frequency resolution. A numerical alias-free implementation of the distribution is presented. Examples of applications in time-frequency analysis of the heart's sound and Doppler blood flow signals are given to show that the Bessel distribution can be easily adapted to two very different signals for cardiovascular signal processing. By controlling a kernel parameter, this distribution can be used to compute the time-frequency representations of transient deterministic and random signals. The study confirms the potentials of the proposed distribution in nonstationary signal analysis     

Center of mass approximation and prediction as a function of body acceleration

In order to maintain postural stability, the central nervous system must maintain equilibrium of the total center of body mass (COM) in relation to its base of support. Thus, the trajectory of the COM provides an important measure of postural stability. Three different models were developed to estimate the COM and the results tested on 16 subjects: namely a neural network, an adaptive fuzzy interface system and a hybrid genetic algorithm sum-of-sines model. The inputs to the models were acquired via two accelerometers, one representing the trunk segment placed on T2 and the second representing the limb segment placed on the shank below the knee joint. The portability, ease of use and low cost (compared with video motion analysis systems) of the accelerometers increases the range of clinics to which the system will be available. The subjects performed a multisegmental movement task on fixed and foam surfaces, thus covering a relatively wide dynamic scope. The results are encouraging for obtaining COM estimates that have clinical applications; the genetic sum-of-sines model was found to be superior when compared to the other two models.     

A Quiet Standing Index for Testing the Postural Sway of Healthy and Diabetic Adults Across a Range of Ages

A quiet standing index is developed for tracking the postural sway of healthy and diabetic adults over a range of ages. Several postural sway features are combined into a single composite feature C that increases with age a. Sway features are ranked based on the r ²-values of their linear regression models, and the composite feature is a weighted sum of selected sway features with optimal weighting coefficients determined using principal component analysis. A performance index based on both reliability and sensitivity is used to determine the optimal number of features. The features used to form C include power and distance metrics. The quiet standing index is a scalar that compares the composite feature C to a linear regression model f(a) using C ^'(a) = C/f(a). For a motionless subject, C ^' = 0, and when the composite feature exactly matches the healthy control (HC) model, C ^' = 1. Values of C ^' >> 1 represent excessive postural sway and may indicate impaired postural control. Diabetic neurologically intact subjects, nondiabetic peripheral neuropathy subjects (PN), and diabetic PN subjects (DPN) were evaluated. The quiet standing indexes of the PN and DPN groups showed statistically significant increases over the HC group. Changes in the quiet standing index over time may be useful in identifying people with impaired balance who may be at an increased risk of falling.     

多分量线性调频信号的Wigner-Ville分布交叉项去除

针对多分量线性调频信号WVD（Wigner-Ville Distribution）检测中的交叉项问题,提出一种交叉项去除方法.利用自项和交叉项的频率特性,将WVD时频矩阵进行坐标旋转,在变换域上滤波去除交叉项.理论推导了矩阵旋转变换公式以及旋转后自项和交叉项的表达式,并且针对缓慢震荡的交叉项受滤波器性能限制不能完全去除的情况,提出能量加权的方法进行改进.仿真和实验结果验证,该方法不仅能够去除交叉项,且不会降低分辨率.     

一种低副瓣无混叠的线性调频信号时频分析方法

作为通信与勘探中广泛使用的一类信号,线性调频信号的参数分析经常采用基于Wigner-Ville分布(WVD)的时频分析方法。该方法具有高时频分辨率,但在交叉项、高副瓣以及频谱混叠问题上存在缺陷。该文提出一种名为空间变迹重排Wigner-Ville分布(SVA-rWVD)的时频分析方法,结合空间变迹技术(SVA)的副瓣抑制能力及短时傅里叶变换(STFT)的无混叠无交叉项特性,得到一个新的时频分布。基于单分量和多分量线性调频信号的仿真实验结果表明,该方法得到的时频分布可以降低副瓣水平至–40 dB以下同时消除交叉项及频谱混叠现象。     

Measures of postural steadiness: differences between healthy youngand elderly adults

Measures of postural steadiness are used to characterize the dynamics of the postural control system associated with maintaining balance during quiet standing. The objective of this study was to evaluate the relative sensitivity of center-of-pressure (COP)-based measures to changes in postural steadiness related to age. A variety of time and frequency domain measures of postural steadiness were compared between a group of twenty healthy young adults (21-35 years) and a group of twenty healthy elderly adults (66-70 years) under both eyes-open and eyes-closed conditions. The measures that identified differences between the eyes-open and eyes-closed conditions in the young adult group were different than those that identified differences between the eye conditions in the elderly adult group. Mean velocity of the COP was the only measure that identified age-related changes in both eye conditions, and differences between eye conditions in both age groups. The results of this study will be useful to researchers and clinicians using COP-based measures to evaluate postural steadiness     

Characteristics of transients among periodic attractors controlledby high-frequency injection in a chaotic laser diode

We numerically studied statistics of the transient response time when switching between periodic attractors obtained through chaos control with a high-frequency injection method in a laser diode that is subject to optical feedback. Each transient response time significantly depends on its position in the starting attractor, whereas the statistical distributions of the response times for many transients are determined almost entirely by the final attractor. The average transient response time is 40 times larger than the round time in the controlled periodic attractors. The transient response time is also strongly affected by the external cavity length. The shortest average transient response time is obtained at a minimum external cavity length and a zero phase difference between the laser field and the feedback light field     

Postural control adaptation during galvanic vestibular and vibratory proprioceptive stimulation

The objective for this study was to investigate whether the adaptation of postural control was similar during galvanic vestibular stimulation and during vibratory proprioceptive stimulation of the calf muscles. Healthy subjects were tested during erect stance with eyes open or closed. An analysis method designed to consider the adaptive adjustments was used to evaluate the motion dynamics and the evoked changes of posture and stimulation response. Galvanic vestibular stimulation induced primarily lateral body movements and vibratory proprioceptive stimulation induced anteroposterior movements. The lateral body sway generated by the galvanic stimulation was proportionally smaller and contained more high-frequency movements (> 0.1 Hz) than the anteroposterior body sway induced by the vibratory stimulation. The adaptive adjustments of the body sway to the stimulation had similar time course and magnitude during galvanic and vibratory stimulation. The perturbations induced by stimulation were gradually reduced within the same time range (15-20 s) and both kinds of stimulation induced a body leaning whose direction was dependent on stimulus. The similarities in the adjustment patterns suggest that postural control operates in the same way independent of the receptor systems affected by the disturbance and irrespective of whether the motion responses were induced in a lateral or anteroposterior direction.     

Block Diagram Reduction of the Interconnected Linear Time-Varying Systems in the Time-Frequency Domain

The problem of obtaining the time-frequency domain input-output model of a linear time-varying (LTV) system formed by linking the time-frequency domain blocks describing LTV subsystems is considered. Simultaneous input-output transformation of the constituent LTV subsystems modeled in terms of two-dimensional impulse responses into time-frequency domain is developed. It is shown that this transformation gives rise to the time-frequency domain subsystem representation which lends itself easily to: 1) deriving composition rules for obtaining the simplified overall interconnection model, and 2) revealing the constraints on individual subsystem modeling that need to be satisfied to admit such simplification. These composition rules are developed for the reduction of standard topologies including series, parallel, and feedback interconnections. The reduction of a more complicated topology using these rules is demonstrated.