Gait variability: methods, modeling and meaning

The study of gait variability, the stride-to-stride fluctuations in walking, offers a complementary way of quantifying locomotion and its changes with aging and disease as well as a means of monitoring the effects of therapeutic interventions and rehabilitation. Previous work has suggested that measures of gait variability may be more closely related to falls, a serious consequence of many gait disorders, than are measures based on the mean values of other walking parameters. The Current JNER series presents nine reports on the results of recent investigations into gait variability. One novel method for collecting unconstrained, ambulatory data is reviewed, and a primer on analysis methods is presented along with a heuristic approach to summarizing variability measures. In addition, the first studies of gait variability in animal models of neurodegenerative disease are described, as is a mathematical model of human walking that characterizes certain complex (multifractal) features of the motor control's pattern generator. Another investigation demonstrates that, whereas both healthy older controls and patients with a higher-level gait disorder walk more slowly in reduced lighting, only the latter's stride variability increases. Studies of the effects of dual tasks suggest that the regulation of the stride-to-stride fluctuations in stride width and stride time may be influenced by attention loading and may require cognitive input. Finally, a report of gait variability in over 500 subjects, probably the largest study of this kind, suggests how step width variability may relate to fall risk. Together, these studies provide new insights into the factors that regulate the stride-to-stride fluctuations in walking and pave the way for expanded research into the control of gait and the practical application of measures of gait variability in the clinical setting

Stratification of the phase clouds and statistical effects of the non-Markovity in chaotic time series of human gait for healthy people and Parkinson patients

In this work we develop a new method of diagnosing the nervous system diseases and a new approach in studying human gait dynamics with the help of the theory of discrete non-Markov random processes. The stratification of the phase clouds and the statistical non-Markov effects in the time series of the dynamics of human gait are considered. We carried out the comparative analysis of the data of four age groups of healthy people: children (from 3 to 10 year olds), teenagers (from 11 to 14 year oulds), young people (from 21 up to 29 year oulds), elderly persons (from 71 to 77 year olds) and Parkinson patients. The full data set are analyzed with the help of the phase portraits of the four dynamic variables, the power spectra of the initial time correlation function and the memory functions of junior orders, the three first points in the spectra of the statistical non-Markov parameter. The received results allow to define the predisposition of the probationers to deflections in the central nervous system caused by Parkinson's disease. We have found out distinct differencies between the five submitted groups. On this basis we offer a new method of diagnostics and forecasting Parkinson's disease.Comment: 15 pages, 5 figs, 3 Table

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Functional characterization of a minimal K+ channel expressed from a synthetic gene.

A gene for a slowly activating, voltage-dependent K(+) -selective channel was designed and synthesized on the basis of its known amino acid sequence. The synthetic gene was cloned into a transcription vector, and in vitro transcribed mRNA was injected into Xenopus oocytes for electrophysiological assay of the resulting ionic currents. The currents are voltage-dependent and highly selective for K+ over Na+. The selectivity among monovalent cations follows a familiar K(+)- channel sequence: K+ greater than Rb+ greater than NH4+ greater than Cs+ much greater than Na+, Li+. The currents are inhibited by Ba2+, Cs+, and tetraethylammonium (TEA), common pore blockers of K+ channels. Open-channel blockade by Cs+ (but not by Ba2+ or TEA) depends on applied voltage. The major inhibitory effect of Ba2+ is to alter channel gating by favoring the closed state; this effect is specific for Ba2+ and is relieved by external K+. The results argue that although the polypeptide expressed is very small for a eukaryotic ion channel, 130 amino acid residues in length, the ionic currents observed are indeed mediated by a genuine K(+) -channel protein. This synthetic gene is therefore well suited for a molecular analysis of the basic mechanisms of K(+) -channel function

Understanding Assistance in Dying: Arguments in Favor of the End of Life Option Act

Abstract There are many people in our society who are profoundly uncomfortable with the legalization of physician assistance in dying, previously known as physician - assisted suicide. The End of Life Option Act is designed to help people who are dying, who have no realistic chance for meaningful improvement of their health, and who are senselessly suffering from their condition. There are misconceptions regarding assisting in dying is the terminology itself. Article discusses the law, as well as, clarifies the vocabulary related to the topic. In conclusion the article raises the question: Is neglecting suffering consistent with the healers ethics

Persistent fluctuations in stride intervals under fractal auditory stimulation

Copyright @ 2014 Marmelat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.Commission of the European Community and the Netherlands Organisation for Scientific Research

Shedding light on walking in the dark: the effects of reduced lighting on the gait of older adults with a higher-level gait disorder and controls

OBJECTIVE: To study the effects of reduced lighting on the gait of older adults with a high level gait disorder (HLGD) and to compare their response to that of healthy elderly controls. METHODS: 22 patients with a HLGD and 20 age-matched healthy controls were studied under usual lighting conditions (1000 lumens) and in near darkness (5 lumens). Gait speed and gait dynamics were measured under both conditions. Cognitive function, co-morbidities, depressive symptoms, and vision were also evaluated. RESULTS: Under usual lighting conditions, patients walked more slowly, with reduced swing times, and increased stride-to-stride variability, compared to controls. When walking under near darkness conditions, both groups slowed their gait. All other measures of gait were not affected by lighting in the controls. In contrast, patients further reduced their swing times and increased their stride-to-stride variability, both stride time variability and swing time variability. The unique response of the patients was not explained by vision, mental status, co-morbidities, or the values of walking under usual lighting conditions. CONCLUSION: Walking with reduced lighting does not affect the gait of healthy elderly subjects, except for a reduction in speed. On the other hand, the gait of older adults with a HLGD becomes more variable and unsteady when they walk in near darkness, despite adapting a slow and cautious gait. Further work is needed to identify the causes of the maladaptive response among patients with a HLGD and the potential connection between this behavior and the increased fall risk observed in these patients

Scaling in Non-stationary time series I

Most data processing techniques, applied to biomedical and sociological time series, are only valid for random fluctuations that are stationary in time. Unfortunately, these data are often non stationary and the use of techniques of analysis resting on the stationary assumption can produce a wrong information on the scaling, and so on the complexity of the process under study. Herein, we test and compare two techniques for removing the non-stationary influences from computer generated time series, consisting of the superposition of a slow signal and a random fluctuation. The former is based on the method of wavelet decomposition, and the latter is a proposal of this paper, denoted by us as step detrending technique. We focus our attention on two cases, when the slow signal is a periodic function mimicking the influence of seasons, and when it is an aperiodic signal mimicking the influence of a population change (increase or decrease). For the purpose of computational simplicity the random fluctuation is taken to be uncorrelated. However, the detrending techniques here illustrated work also in the case when the random component is correlated. This expectation is fully confirmed by the sociological applications made in the companion paper. We also illustrate a new procedure to assess the existence of a genuine scaling, based on the adoption of diffusion entropy, multiscaling analysis and the direct assessment of scaling. Using artificial sequences, we show that the joint use of all these techniques yield the detection of the real scaling, and that this is independent of the technique used to detrend the original signal.Comment: 39 pages, 13 figure

A Proof of the Isoenergetic KAM-Theorem from the “Ordinary” One

A proof is given of the isoenergetic KAM-theorem for Hamiltonian systems, using the “ordinary” KAM-theorem and a transversality argument.