Steady-state fluctuations of human walking

Caressed by music: Related preferences for velocity of touch and tempo of music?

Given that both hearing and touch are 'mechanical senses' that respond to physical pressure or mechanical energy and that individuals appear to have a characteristic internal or spontaneous tempo, individual preferences in musical and touch rhythms might be related. We explored this in two experiments probing individual preferences for tempo in the tactile and auditory modalities. Study 1 collected ratings of received stroking on the forearm and measured the velocity the participants used for stroking a fur. Music tempo preferences were assessed as mean beats per minute of individually selected music pieces and via the adjustment of experimenter-selected music to a preferred tempo. Heart rate was recorded to measure levels of physiological arousal. We found that the preferred tempo of favorite (self-selected) music correlated positively with the velocity with which each individual liked to be touched. In Study 2, participants rated videos of repeated touch on someone else's arm and videos of a drummer playing with brushes on a snare drum, both at a variety of tempos. We found that participants with similar rating patterns for the different stroking speeds did not show similar rating patterns for the different music beats. The results suggest that there may be a correspondence between preferences for favorite music and felt touch, but this is either weak or it cannot be evoked effectively with vicarious touch and/or mere drum beats. Thus, if preferences for touch and music are related, this is likely to be dependent on the specific type of stimulation.

Phase resetting and intermittent control at the edge of stability in a simple biped model generates 1/f-like gait cycle variability

The 1/f-like gait cycle variability, characterized by temporal changes in stride-time intervals during steady-state human walking, is a well-documented gait characteristic. Such gait fractality is apparent in healthy young adults, but tends to disappear in the elderly and patients with neurological diseases. However, mechanisms that give rise to gait fractality have yet to be fully clarified. We aimed to provide novel insights into neuro-mechanical mechanisms of gait fractality, based on a numerical simulation model of biped walking. A previously developed heel-toe footed, seven-rigid-link biped model with human-like body parameters in the sagittal plane was implemented and expanded. It has been shown that the gait model, stabilized rigidly by means of impedance control with large values of proportional (P) and derivative (D) gains for a linear feedback controller, is destabilized only in a low-dimensional eigenspace, as P and D decrease below and even far below critical values. Such low-dimensional linear instability can be compensated by impulsive, phase-dependent actions of nonlinear controllers (phase resetting and intermittent controllers), leading to the flexible walking with joint impedance in the model being as small as that in humans. Here, we added white noise to the model to examine P-value-dependent stochastic dynamics of the model for small D-values. The simulation results demonstrated that introduction of the nonlinear controllers in the model determined the fractal features of gait for a wide range of the P-values, provided that the model operates near the edge of stability. In other words, neither the model stabilized only by pure impedance control even at the edge of linear stability, nor the model stabilized by specific nonlinear controllers, but with P-values far inside the stability region, could induce gait fractality. Although only limited types of controllers were examined, we suggest that the impulsive nonlinear controllers and criticality could be major mechanisms for the genesis of gait fractality.

Modulations of the Optical Flow Did Not Induce Locomotor Pattern Fluctuations in Treadmill Walking in Man

We report an analysis of gait during human treadmill walking when visual information from the self-displacement velocity was modulated. Removing or sinusoidally modulating the frequency edge information in the optical flow did not induce significant changes in the walking velocity as analyzed using Fast Fourier Transform or in the spatiotemporal gait parameters. While low-frequency fluctuations in displacement speed increased, there was no significant change in locomotor cycle stability. When a constant frequency edge was provided, i.e., when a backward optical flow was added, stride length decreased as compared to the no-optical-flow condition and instantaneous fluctuations in stride amplitude increased. Temporal gait parameters did not change. These partial effects might be better explained by modifications in trunk balance. In humans, modulation of velocity information on self-motion cannot induce unintentional modulation of walking velocity and did not enhance fluctuations in the locomotor pattern. These results argue against the proprioceptive role of sagittal visual-motion information in control of stability of rhythmic leg movement, at least when other proprioceptive feedback sources are available.

Characterizing and modeling the joint-level variability in human walking

Although human gait is often assumed to be periodic, significant variability exists. This variability appears to provide different information than the underlying periodic signal, particularly about fall risk. Most studies on variability have either used step-to-step metrics such as stride duration or point-wise standard deviations, neither of which explicitly capture the joint-level variability as a function of time. This work demonstrates that a second-order Fourier series for stance joints and a first-order Fourier series for swing joints can accurately capture the variability in joint angles as a function of time on a per-step basis for overground walking at the self-selected speed. It further demonstrates that a total of seven normal distributions, four linear relationships, and twelve continuity constraints can be used to describe how the Fourier series vary between steps. The ability of the proposed method to create curves that match human joint-level variability was evaluated both qualitatively and quantitatively using randomly generated curves.

Direct Evidence for Vision-based Control of Flight Speed in Budgerigars

We have investigated whether, and, if so, how birds use vision to regulate the speed of their flight. Budgerigars, Melopsittacus undulatus, were filmed in 3-D using high-speed video cameras as they flew along a 25 m tunnel in which stationary or moving vertically oriented black and white stripes were projected on the side walls. We found that the birds increased their flight speed when the stripes were moved in the birds’ flight direction, but decreased it only marginally when the stripes were moved in the opposite direction. The results provide the first direct evidence that Budgerigars use cues based on optic flow, to regulate their flight speed. However, unlike the situation in flying insects, it appears that the control of flight speed in Budgerigars is direction-specific. It does not rely solely on cues derived from optic flow, but may also be determined by energy constraints.

Identifying stride-to-stride control strategies in human treadmill walking

Variability is ubiquitous in human movement, arising from internal and external noise, inherent biological redundancy, and from the neurophysiological control actions that help regulate movement fluctuations. Increased walking variability can lead to increased energetic cost and/or increased fall risk. Conversely, biological noise may be beneficial, even necessary, to enhance motor performance. Indeed, encouraging more variability actually facilitates greater improvements in some forms of locomotor rehabilitation. Thus, it is critical to identify the fundamental principles humans use to regulate stride-to-stride fluctuations in walking. This study sought to determine how humans regulate stride-to-stride fluctuations in stepping movements during treadmill walking. We developed computational models based on pre-defined goal functions to compare if subjects, from each stride to the next, tried to maintain the same speed as the treadmill, or instead stay in the same position on the treadmill. Both strategies predicted average behaviors empirically indistinguishable from each other and from that of humans. These strategies, however, predicted very different stride-to-stride fluctuation dynamics. Comparisons to experimental data showed that human stepping movements were generally well-predicted by the speed-control model, but not by the position-control model. Human subjects also exhibited no indications they corrected deviations in absolute position only intermittently: i.e., closer to the boundaries of the treadmill. Thus, humans clearly do not adopt a control strategy whose primary goal is to maintain some constant absolute position on the treadmill. Instead, humans appear to regulate their stepping movements in a way most consistent with a strategy whose primary goal is to try to maintain the same speed as the treadmill at each consecutive stride. These findings have important implications both for understanding how biological systems regulate walking in general and for being able to harness these mechanisms to develop more effective rehabilitation interventions to improve locomotor performance.

The coupling of vision with locomotion in cortical blindness

Maintaining or modifying the speed and direction of locomotion requires the coupling of the locomotion with the retinal optic flow that it generates. It is shown that this essential behavioral capability, which requires on-line neural control, is preserved in the cortically blind hemifield of a hemianope. In experiments, optic flow stimuli were presented to either the normal or blind hemifield while the patient was walking on a treadmill. Little difference was found between the hemifields with respect to the coupling (i.e. co-dependency) of optic flow detection with locomotion. Even in the cortically blind hemifield, faster walking resulted in the perceptual slowing of detected optic flow, and self-selected locomotion speeds demonstrated behavioral discrimination between different optic flow speeds. The results indicate that the processing of optic flow, and thereby on-line visuo-locomotor coupling, can take place along neural pathways that function without processing in Area V1, and thus in the absence of conscious intervention. These and earlier findings suggest that optic flow and object motion are processed in parallel along with correlated non-visual locomotion signals. Extrastriate interactions may be responsible for discounting the optical effects of locomotion on the perceived direction of object motion, and maintaining visually guided self-motion.

Development and decline of upright gait stability

Upright gait is a peculiar characteristic of humans that requires the ability to manage upper body dynamic balance while walking, despite the perturbations that are generated by movements of the lower limbs. Most of the studies on upright gait stability have compared young adults and the elderly to determine the effects of aging. In other studies, the comparison was between healthy subjects and patients to examine specific pathologies. Fewer researches have also investigated the development of upright gait stability in children. This review discusses these studies in order to provide an overview of this relevant aspect of human locomotion. A clear trend from development to decline of upright gait stability has been depicted across the entire lifespan, from toddlers at first steps to elderly. In old individuals, even if healthy, the deterioration of skeletal muscle, combined with sensorial and cognitive performance, reduces the ability to maintain an upright trunk during walking, increasing the instability and the risk of falls. Further, the pathological causes of altered development or of a sudden loss of gait stability, as well as the environmental influence are investigated. The last part of this review is focused on the control of upper body accelerations during walking, a particularly interesting topic for the recent development of low-cost wearable accelerometers.

Multifractal detrended fluctuation analysis of human gait diseases

In this paper multifractal detrended fluctuation analysis (MFDFA) is used to study the human gait time series for normal and diseased sets. It is observed that long range correlation is primarily responsible for the origin of multifractality. The study reveals that the degree of multifractality is more for normal set compared to diseased set. However, the method fails to distinguish between the two diseased sets.

The representation of egocentric space in the posterior parietal cortex

The posterior parietal cortex (PPC) is the most likely site where egocentric spatial relationships are represented in the brain. PPC cells receive visual, auditory, somaesthetic, and vestibular sensory inputs; oculomotor, head, limb, and body motor signals; and strong motivational projections from the limbic system. Their discharge increases not only when an animal moves towards a sensory target, but also when it directs its attention to it. PPC lesions have the opposite effect: sensory inattention and neglect. The PPC does not seem to contain a "map" of the location of objects in space but a distributed neural network for transforming one set of sensory vectors into other sensory reference frames or into various motor coordinate systems. Which set of transformation rules is used probably depends on attention, which selectively enhances the synapses needed for making a particular sensory comparison or aiming a particular movement.

New insights into anterior cruciate ligament deficiency and reconstruction through the assessment of knee kinematic variability in terms of nonlinear dynamics

PURPOSE

Injuries to the anterior cruciate ligament (ACL) occur frequently, particularly in young adult athletes, and represent the majority of the lesions of knee ligaments. Recent investigations suggest that the assessment of kinematic variability using measures of nonlinear dynamics can provide with important insights with respect to physiological and pathological states. The purpose of the present article was to critically review and synthesize the literature addressing ACL deficiency and reconstruction from a nonlinear dynamics standpoint.

METHODS

A literature search was carried out in the main medical databases for studies published between 1990 and 2010.

RESULTS

Seven studies investigated knee kinematic variability in ACL patients. Results provided support for the theory of "optimal movement variability". Practically, loss below optimal variability is associated with a more rigid and very repeatable movement pattern, as observed in the ACL-deficient knee. This is a state of low complexity and high predictability. On the other hand, increase beyond optimal variability is associated with a noisy and irregular movement pattern, as found in the ACL-reconstructed knee, regardless of which type of graft is used. This is a state of low complexity and low predictability. In both cases, the loss of optimal variability and the associated high complexity lead to an incapacity to respond appropriately to the environmental demands, thus providing an explanation for vulnerability to pathological changes following injury.

CONCLUSION

Subtle fluctuations that appear in knee kinematic patterns provide invaluable insight into the health of the neuromuscular function after ACL rupture and reconstruction. It is thus critical to explore them in longitudinal studies and utilize nonlinear measures as an important component of post-reconstruction medical assessment.

LEVEL OF EVIDENCE

II.

Center of Mass Compensation during Gait in Hip Arthroplasty Patients: Comparison between Large Diameter Head Total Hip Arthroplasty and Hip Resurfacing

Objective. To compare center of mass (COM) compensation in the frontal and sagittal plane during gait in patients with large diameter head total hip arthroplasty (LDH-THA) and hip resurfacing (HR). Design. Observational study. Setting. Outpatient biomechanical laboratory. Participants. Two groups of 12 patients with LDH-THA and HR recruited from a larger randomized study and 11 healthy controls. Interventions. Not applicable. Main Outcome Measures. To compare the distance between the hip prosthetic joint center (HPJC) and the COM. The ratio (R_HPJC-COM) and the variability (CV_HPJC-COM) were compared between groups. Hip flexor, abductor, and adductor muscle strength was also correlated between groups while radiographic measurements were correlated with the outcome measures. Results. In the frontal plane, HR shows less variability than healthy controls at push-off and toe-off and R_HPJC-COM is correlated with the muscle strength ratios (FR_ABD) at heel contact, maximal weight acceptance, and mid stance. In the sagittal plane, LDH-THA has a higher R_HPJC-COM than healthy controls at push-off, and CV_HPJC-COM is significantly correlated with FR_FLEX. Conclusions. One year after surgery, both groups of patients, LDH-THA and HR, demonstrate minor compensations at some specific instant of the gait cycle, in both frontal and sagittal planes. However, their locomotion pattern is similar to the healthy controls.

Does the nervous system depend on kinesthetic information to control natural limb movements?

This target article draws together two groups of experimental studies on the control of human movement through peripheral feedback and centrally generated signals of motor commands. First, during natural movement, feedback from muscle, joint, and cutaneous afferents changes; in human subjects these changes have reflex and kinesthetic consequences. Recent psychophysical and microneurographic evidence suggests that joint and even cutaneous afferents may have a proprioceptive role. Second, the role of centrally generated motor commands in the control of normal movements and movements following acute and chronic deafferentation is reviewed. There is increasing evidence that subjects can perceive their motor commands under various conditions, but that this is inadequate for normal movement; deficits in motor performance arise when the reliance on proprioceptive feedback is abolished either experimentally or because of pathology. During natural movement, the CNS appears to have access to functionally useful input from a range of peripheral receptors as well as from internally generated command signals. The unanswered questions that remain suggest a number of avenues for further research.

Implications of neural networks for how we think about brain function

Engineers use neural networks to control systems too complex for conventional engineering solutions. To examine the behavior of individual hidden units would defeat the purpose of this approach because it would be largely uninterpretable. Yet neurophysiologists spend their careers doing just that! Hidden units contain bits and scraps of signals that yield only arcane hints about network function and no information about how its individual units process signals. Most literature on single-unit recordings attests to this grim fact. On the other hand, knowing a system's function and describing it with elegant mathematics tell one very little about what to expect of interneuronal behavior. Examples of simple networks based on neurophysiology are taken from the oculomotor literature to suggest how single-unit interpretability might decrease with increasing task complexity. It is argued that trying to explain how any real neural network works on a cell-by-cell, reductionist basis is futile and we may have to be content with trying to understand the brain at higher levels of organization.

Does human gait exhibit comparable and reproducible long-range autocorrelations on level ground and on treadmill?

Stride duration of young healthy subjects walking at spontaneous speed fluctuates over the long-term in a very complex way. The presence of long-range autocorrelations among these fluctuations has already been highly suggested for subjects walking on level ground, but the mathematical methods used among studies are variable. Moreover, despite the frequent use of a treadmill in research and in rehabilitation, the presence of such autocorrelations was nearly exclusively assessed during level-ground walking. The first aim of this study was to confirm the presence of long-range autocorrelations among stride duration variability on level ground with a good level of confidence. The stride duration fluctuations of 10 young healthy subjects were assessed on a 37-meter-long track using an integrated approach that combines the results of rescaled range analysis and power spectral analysis. Secondly, the results obtained from treadmill tests were compared with the outcomes of the level-ground walking tests in order to challenge the persistence of the long-range autocorrelations during treadmill walking. Finally, the third aim of this study was to test the reproducibility of the outcomes by comparing the results obtained on the treadmill during two different trials. The outcomes of this study provide significant evidence to confirm the hypothesis that long-range autocorrelations are present among stride duration variability, not only on level ground but also on the treadmill. The reproducibility of the results obtained during treadmill walking further validates the use of a treadmill to assess the long-term fluctuations of gait.

ACL deficiency affects stride-to-stride variability as measured using nonlinear methodology

Previous studies suggested that the small fluctuations present in movement patterns from one stride to the next during walking can be useful in the investigation of various pathological conditions. Previous studies using nonlinear measures have resulted in the development of the "loss of complexity hypothesis" which states that disease can affect the variability and decrease the complexity of a system, rendering it less able to adjust to the ever changing environmental demands. The nonlinear measure of the Lyapunov Exponent (LyE) has already been used for the assessment of stride-to-stride variability in the anterior cruciate ligament (ACL) deficient knee in comparison to the contralateral intact knee. However, there is biomechanical evidence that after ACL rupture, adaptations are also present in the contralateral intact knee. Thus, our goal was to investigate stride-to-stride variability in the ACL deficient knee as compared to a healthy control knee. Seven subjects with unilateral ACL deficiency and seven healthy controls walked at their self-selected speed on a treadmill, while three-dimensional knee kinematics was collected for 80 consecutive strides. A nonlinear measure, the largest LyE was calculated from the resulted knee joint flexion-extension data of both groups. Larger LyE values signify increased variability and increased sensitivity to initial conditions. Our results showed that the ACL deficient group exhibited significantly less variable walking patterns than the healthy control. These changes are not desirable because they reflect decreases in system's complexity, which indicates narrowed functional responsiveness, according to the "loss of complexity hypothesis." This may be related with the increased future pathology found in ACL deficient patients. The methods used in the present paper showed great promise to assess the gait handicap in knee injured patients.

Dynamics of visuo-spatial remembering: a study of information structuring in memory

We studied the process by which learning a pattern of motor activity reaches a steady-state characterized by a reduction in fluctuations. The stimuli consisted of eight visually presented dots that appeared sequentially. In a 20-trial learning phase, participants reproduced the positions of the eight dots after each presentation. Next, they reproduced the pattern 40 times without renewed presentation. In one condition, spatial distances between the dots were proportional to the intervals between their appearances; in the other they were not proportional. We analyzed how the reproduction stabilized at the configuration and dot levels. In proportional as well as non-proportional conditions, stabilization occurs at different time scales for the configuration and dot levels. The stabilization rate differed between proportional and non-proportional conditions. These results are discussed in the framework of dynamical systems.

Gait dynamics, fractals and falls: finding meaning in the stride-to-stride fluctuations of human walking

Until recently, quantitative studies of walking have typically focused on properties of a typical or average stride, ignoring the stride-to-stride fluctuations and considering these fluctuations to be noise. Work over the past two decades has demonstrated, however, that the alleged noise actually conveys important information. The magnitude of the stride-to-stride fluctuations and their changes over time during a walk - gait dynamics - may be useful in understanding the physiology of gait, in quantifying age-related and pathologic alterations in the locomotor control system, and in augmenting objective measurement of mobility and functional status. Indeed, alterations in gait dynamics may help to determine disease severity, medication utility, and fall risk, and to objectively document improvements in response to therapeutic interventions, above and beyond what can be gleaned from measures based on the average, typical stride. This review discusses support for the idea that gait dynamics has meaning and may be useful in providing insight into the neural control of locomotion and for enhancing functional assessment of aging, chronic disease, and their impact on mobility.

Complexity analysis of stride interval time series by threshold dependent symbolic entropy

The stride interval of human gait fluctuates in complex fashion. It reflects the rhythm of the locomotor system. The temporal fluctuations in the stride interval provide us a non-invasive technique to evaluate the effects of neurological impairments on gait and its changes with age and disease. In this paper, we have used threshold dependent symbolic entropy, which is based on symbolic nonlinear time series analysis to study complexity of gait of control and neurodegenerative disease subjects. Symbolic entropy characterizes quantitatively the complexity even in time series having relatively few data points. We have calculated normalized corrected Shannon entropy (NCSE) of symbolic sequences extracted from stride interval time series. This measure of complexity showed significant difference between control and neurodegenerative disease subjects for a certain range of thresholds. We have also investigated complexity of physiological signal and randomized noisy data. In the study, we have found that the complexity of physiological signal was higher than that of random signals at short threshold values.

GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (<1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5 < alpha < 1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha < 0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).

Tau and Kappa effects in physical space: the case of audition

The organization of spatio-temporal information in an auditory memory task was studied in two experiments. Stimuli consisted of four different configurations of eight sequentially presented beeps. In two configurations, the stimuli were space-time congruent, with (constant or variable) inter-stimulus distances corresponding to (constant or variable) inter-stimulus time intervals. In the other two configurations, the stimuli were space-time incongruent, with (constant or variable) inter-stimulus distances not corresponding to (variable or constant) inter-stimulus time intervals. After a learning phase consisting of 20 presentations of the target configuration, participants reproduced the spatial (Experiment 1) or temporal (Experiment 2) characteristics of the target 60 times in succession without re-examining the target configuration. Accuracy (with respect to the target) and variability (between responses) were found to evolve independently. In the incongruent space-time conditions, effects of variable inter-stimulus time intervals or distances on the reproduction of, respectively, constant distances (Tau effect) or constant time intervals (Kappa effect) were observed, while the reverse was not the case. Thus, dimensional interference occurred when the dimension to be ignored was variable. The results are discussed in the light of the distinction between properties of the stabilized mental image and the process of stabilization.

Reliability of the long-range power-law correlations obtained from the bilateral stride intervals in asymptomatic volunteers whilst treadmill walking

Stride intervals measured during steady-state walking are irregular. These stride interval fluctuations are not random but exhibit long-range power-law correlation (alpha) such that a given stride interval is 'influenced' by earlier variations in the stride intervals. To estimate alpha, one requires a minute long sequence of right or left side stride interval data. However, to obtain a reliable alpha point estimate, the minimal stride sequence length is unknown. Additionally, it is unknown if the right and left side alpha are equivalent. In this study, the within-day and the right and left side reliabilities of alpha point estimates were examined in 23 volunteers performing three 8-min treadmill walks. In addition, eight volunteers were retested on three additional days to estimate between-day reliability. The standard error of measurement (S.E.M.) and the within- and between-day intraclass correlation (ICC) values, and their 95% confidence intervals, each calculated using the combined right and left leg 8-min alpha estimates were acceptable [0.047 (0.044-0.051); 0.914 (0.882-0.932) and 0.769 (0.689-0.815), respectively]. The left alpha (0.688 +/- 0.93) was greater than the right alpha (0.664 +/- 0.094), albeit this finding was underpowered (0.55). The alpha point estimates obtained from the full 8-min walks provided minimal S.E.M. and maximal within- and between-day ICCs. However, the minimal S.E.M. was statistically indistinguishable from the 6- and 7-min walk durations and all of the within-day and between-day ICCs were similar except for the 3- and 8-min between-day ICCs. This study suggests that data from four 3 min, three 6 min or two 8 min walk duration trials provide reliable alpha point estimates from a short series of short treadmill walks.

Dynamics of Balancing Space and Time in Memory: Tau and Kappa Effects Revisited

In 3 experiments, the authors studied the organization of spatiotemporal information in memory. Stimuli consisted of configurations of dots, presented sequentially. The stimuli were either proportional, with interdot distances corresponding to interdot durations, or not proportional, with interdol distances not corresponding to interdot durations. After a learning phase, participants reproduced the spatial (Experiment 1), temporal (Experiment 2), or spatial and temporal (Experiment 3) characteristics of the target 60 times in succession. In the nonproportional conditions, effects of variable interdot durations or distances on the reproduction of, respectively, constant distances (tau effect) or durations (kappa effect) were observed, whereas no such effects were observed when variable distances or durations were to be produced. Tau and kappa effects influenced the accuracy but not the variability of responses. The results are discussed in light of the distinction between properties of the stabilized mental image and the process of stabilization.

Electromyographic analysis of locomotion for healthy and hemiparetic subjects--study of performance variability and rail effect on treadmill

This study quantified the performance variability and effect of rail support on the ankle joint for normal and hemiparetic subjects during treadmill walking. Muscle activities of the anterior tibialis (TA) and medial gastrocnemius (MG) from six hemiparetic patients and 14 healthy subjects were assessed with EMG linear envelope and variance ratio of consecutive strides at self-selected cadences. Our results indicate that (1) performance consistency of the hemiparetic patients was significantly undermined; (2) habituated process during treadmill walking was notable in the MG but not in the TA; and (3) rail support could reduce performance variability of the ankle antagonist pairs.

Stride variability in human gait: the effect of stride frequency and stride length

This study focused on spatial and temporal variability of the stride in human gait. We determined the role of stride frequency (F) and stride length (L) on those parameters. Eight healthy subjects walked on a treadmill using 25 different FL combinations (0.95<L<1.5 m, and 0.8<F<1.26 Hz). The results showed that spatial and temporal variabilities tend to increase in concert with respect to change in stride parameters. In addition, stride variability was found (1) to be minimal at F=1 Hz; and (2) to increase with smaller L. During additional trials, subjects walked freely at various speeds. Although it is generally hypothesized that freely chosen behaviors are optimal in terms of variability, our data show that this is not always the case in human gait.

When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations

We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different "neural centers", reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood including a decrease in the correlation and volatility exponents with maturation.

A review of analytical techniques for gait data. Part 1: Fuzzy, statistical and fractal methods

In recent years, several new approaches to gait data analysis have been explored, including fuzzy systems, multivariate statistical techniques and fractal dynamics. Through a critical survey of recent gait studies, this paper reviews the potential of these methods to strengthen the gait laboratory's analytical arsenal. It is found that time-honoured multivariate statistical methods are the most widely applied and understood. Although initially promising, fuzzy and fractal analyses of gait data remain largely unknown and their full potential is yet to be realized. The trend towards fusing multiple techniques in a given analysis means that additional research into the application of these two methods will benefit gait data analysis.

Nonlinear time series analysis of normal and pathological human walking

Characterizing locomotor dynamics is essential for understanding the neuromuscular control of locomotion. In particular, quantifying dynamic stability during walking is important for assessing people who have a greater risk of falling. However, traditional biomechanical methods of defining stability have not quantified the resistance of the neuromuscular system to perturbations, suggesting that more precise definitions are required. For the present study, average maximum finite-time Lyapunov exponents were estimated to quantify the local dynamic stability of human walking kinematics. Local scaling exponents, defined as the local slopes of the correlation sum curves, were also calculated to quantify the local scaling structure of each embedded time series. Comparisons were made between overground and motorized treadmill walking in young healthy subjects and between diabetic neuropathic (NP) patients and healthy controls (CO) during overground walking. A modification of the method of surrogate data was developed to examine the stochastic nature of the fluctuations overlying the nominally periodic patterns in these data sets. Results demonstrated that having subjects walk on a motorized treadmill artificially stabilized their natural locomotor kinematics by small but statistically significant amounts. Furthermore, a paradox previously present in the biomechanical literature that resulted from mistakenly equating variability with dynamic stability was resolved. By slowing their self-selected walking speeds, NP patients adopted more locally stable gait patterns, even though they simultaneously exhibited greater kinematic variability than CO subjects. Additionally, the loss of peripheral sensation in NP patients was associated with statistically significant differences in the local scaling structure of their walking kinematics at those length scales where it was anticipated that sensory feedback would play the greatest role. Lastly, stride-to-stride fluctuations in the walking patterns of all three subject groups were clearly distinguishable from linearly autocorrelated Gaussian noise. As a collateral benefit of the methodological approach taken in this study, some of the first steps at characterizing the underlying structure of human locomotor dynamics have been taken. Implications for understanding the neuromuscular control of locomotion are discussed. (c) 2000 American Institute of Physics.

Dynamic markers of altered gait rhythm in amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is a disorder marked by loss of motoneurons. We hypothesized that subjects with ALS would have an altered gait rhythm, with an increase in both the magnitude of the stride-to-stride fluctuations and perturbations in the fluctuation dynamics. To test for this locomotor instability, we quantitatively compared the gait rhythm of subjects with ALS with that of normal controls and with that of subjects with Parkinson's disease (PD) and Huntington's disease (HD), pathologies of the basal ganglia. Subjects walked for 5 min at their usual pace wearing an ankle-worn recorder that enabled determination of the duration of each stride and of stride-to-stride fluctuations. We found that the gait of patients with ALS is less steady and more temporally disorganized compared with that of healthy controls. In addition, advanced ALS, HD, and PD were associated with certain common, as well as apparently distinct, features of altered stride dynamics. Thus stride-to-stride control of gait rhythm is apparently compromised with ALS. Moreover, a matrix of markers based on gait dynamics may be useful in characterizing certain pathologies of motor control and, possibly, in quantitatively monitoring disease progression and evaluating therapeutic interventions.

Maturation of gait dynamics: stride-to-stride variability and its temporal organization in children

In very young children, immature control of posture and gait results in unsteady locomotion. In children of approximately 3 yr of age, gait appears relatively mature; however, it is unknown whether the dynamics of walking change beyond this age. Because stride dynamics depend on neural control, we hypothesized that motor control would continue to develop beyond age 3. To test this hypothesis, we measured the gait cycle duration on a stride-by-stride basis in 50 healthy 3- to 14-yr-old children (25 girls). Measurements of stride-to-stride variability were significantly larger both in the 3- and 4-yr-old children, compared with the 6- and 7-yr-old children, and in the 6- and 7-yr-old children, compared with the 11- to 14-yr-old children. Measurements of the temporal organization of gait also revealed significant age-dependent changes. The effects of age persisted even after adjusting for height. These findings indicate that mature stride dynamics may not be completely developed even in healthy 7-yr-old children and that different aspects of stride dynamics mature at different ages.

Multiple-time scales analysis of physiological time series under neural control

We discuss multiple-time scale properties of neurophysiological control mechanisms, using heart rate and gait regulation as model systems. We find that scaling exponents can be used as prognostic indicators. Furthermore, detection of more subtle degradation of scaling properties may provide a novel early warning system in subjects with a variety of pathologies including those at high risk of sudden death.

Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington's disease

Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P < 0.003). The scaling exponent alpha was also smaller in the subjects with Huntington's disease compared with disease-free controls (Huntington's disease: 0.60 +/- 0.24; controls: 0.88 +/-0.17; P < 0.005). Moreover, alpha was linearly related to degree of functional impairment in subjects with Huntington's disease (r = 0.78, P < 0.0005). These findings demonstrate that strike-interval fluctuations are more random (i.e., less correlated) in elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.

Increased walking variability in elderly persons with congestive heart failure

OBJECTIVES

To determine the effects of congestive heart failure on a person's ability to walk at a steady pace while ambulating at a self-determined rate.

SETTING

Beth Israel Hospital, Boston, a primary and tertiary teaching hospital, and a social activity center for elderly adults living in the community.

PARTICIPANTS

Eleven elderly subjects (aged 70-93 years) with well compensated congestive heart failure (NY Heart Association class I or II), seven elderly subjects (aged 70-79 years) without congestive heart failure, and 10 healthy young adult subjects (aged 20-30 years).

MEASUREMENTS

Subjects walked for 8 minutes on level ground at their own selected walking rate. Footswitches were used to measure the time between steps. Step rate (steps/minute) and step rate variability were calculated for the entire walking period, for 30 seconds during the first minute of the walk, for 30 seconds during the last minute of the walk, and for the 30-second period when each subject's step rate variability was minimal. Group means and 5% and 95% confidence intervals were computed.

MAIN RESULTS

All measures of walking variability were significantly increased in the elderly subjects with congestive heart failure, intermediate in the elderly controls, and lowest in the young subjects. There was no overlap between the three groups using the minimal 30-second variability (elderly CHF vs elderly controls: P < 0.001, elderly controls vs young: P < 0.001), and no overlap between elderly subjects with and without congestive heart failure when using the overall variability. For all four measures, there was no overlap in any of the confidence intervals, and all group means were significantly different (P < 0.05).

Distortions and fluctuations in topographic memory

Two experiments dealing with the learning of a space by map or by navigation approached the questions of equivalency of the cognitive processes involved in spatial information and of response fluctuation. In the first experiment, 11 subjects were asked to situate, six times, 18 locations on a blank map. In the second experiment, the subjects were first given 3 min to learn a map with 12 locations marked, and then asked to reproduce it. The task was repeated six times, using three different maps. This gave us several trials per subject, so that distortion could be distinguished from response fluctuation. In Experiment 1, the range of values was the same for response inaccuracy and response fluctuation; in Experiment 2, the range was greater for response inaccuracy than for response fluctuation. The results showed that space learning by navigation and space learning by map involve different cognitive processes.