Scaling behavior in mitochondrial redox fluctuations

Scale-invariant long-range correlations have been reported in fluctuations of time-series signals originating from diverse processes such as heart beat dynamics, earthquakes, and stock market data. The common denominator of these apparently different processes is a highly nonlinear dynamics with competing forces and distinct feedback species. We report for the first time an experimental evidence for scaling behavior in NAD(P)H signal fluctuations in isolated mitochondria and intact cells isolated from the liver of a young (5-month-old) mouse. Time-series data were collected by two-photon imaging of mitochondrial NAD(P)H fluorescence and signal fluctuations were quantitatively analyzed for statistical correlations by detrended fluctuation analysis and spectral power analysis. Redox [NAD(P)H / NAD(P)(+)] fluctuations in isolated mitochondria and intact liver cells were found to display nonrandom, long-range correlations. These correlations are interpreted as arising due to the regulatory dynamics operative in Krebs' cycle enzyme network and electron transport chain in the mitochondria. This finding may provide a novel basis for understanding similar regulatory networks that govern the nonequilibrium properties of living cells.     

Long-range negative correlation of glucose dynamics in humans and its breakdown in diabetes mellitus

Diurnal fluctuations in glucose levels continuously monitored during normal daily life are investigated using an extended random walk analysis, referred to as detrended fluctuation analysis (DFA), in 12 nondiabetic subjects and 15 diabetic patients. The DFA exponent alpha = 1.25 +/- 0.29 for healthy individuals in the "long-range" (>2 h) regime is shown to be significantly (P < 0.01) smaller than the reference "uncorrelated" value of alpha = 1.5, suggesting that the instantaneous net effects of the dynamical balance of glucose flux and reflux, causing temporal changes in glucose concentration, are long-range negatively correlated. By contrast, in diabetic patients, the DFA exponent alpha = 1.65 +/- 0.30 is significantly (P < 0.05) higher than that in nondiabetic subjects, evidencing a breakdown of the long-range negative correlation. It is suggested that the emergence of such positive long-range glucose correlations in diabetic patients-indicating that the net effects of the flux and reflux persist for many hours-likely reflects pathogenic mechanisms of diabetes, i.e., the lack of long-term stability of blood glucose and that the long-range negatively correlated glucose dynamics are functional in maintaining normal glucose homeostasis.     

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

Hausdorff, Jeffrey M., Susan L. Mitchell, RenéeFirtion, C. K. Peng, Merit E. Cudkowicz, Jeanne Y. Wei, and Ary L. Goldberger. Altered fractal dynamics of gait: reducedstride-interval correlations with aging and Huntington's disease.J. Appl. Physiol. 82(1): 262-269, 1997.Fluctuationsin the duration of the gait cycle (the stride interval) display fractaldynamics and long-range correlations in healthy young adults. Wehypothesized that these stride-interval correlations would be alteredby changes in neurological function associated with aging and certaindisease states. To test this hypothesis, we compared thestride-interval time series of 1) healthy elderly subjects andyoung controls and of 2) subjects with Huntington's diseaseand healthy controls. Using detrended fluctuation analysis, we computed, a measure of the degree to which one stride interval is correlatedwith previous and subsequent intervals over different timescales. The scaling exponent  was significantly lower in elderlysubjects compared with young subjects (elderly: 0.68 ± 0.14; young:0.87 ± 0.15; P < 0.003). The scaling exponent  wasalso smaller in the subjects with Huntington's disease compared withdisease-free controls (Huntington's disease: 0.60 ± 0.24;controls: 0.88 ± 0.17; P < 0.005). Moreover,  was linearly related to degree of functional impairment in subjects withHuntington's disease (r = 0.78, P < 0.0005).These findings demonstrate that stride-interval fluctuations are morerandom (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.

     

Gait variability magnitude but not structure is altered in essential tremor

Essential tremor (ET) is a common tremor disorder affecting postural/action tremor of the upper extremities and midline. Recent research revealed a cerebellar-like deficit during tandem gait in persons with ET, though spatiotemporal variability during normal gait in ET has been relatively ignored. The first purpose of this study was to investigate gait variability magnitude and structure in ET as compared to healthy older adults (HOA). To address this issue, 11 ET and 11 age-matched HOAs walked on a treadmill for 5 min at preferred walking speeds. HOAs walked for an additional minute while speed-matched to an ET participant. The second purpose was to describe the clinical correlates of gait variability in this population. To address this aim, 31 persons with ET walked on a treadmill for 5 min and completed the Fahn–Tolosa–Marin Tremor Rating Scale. Gait variability magnitude was derived by calculating coefficients of variation in stride length, stride time, step length, step time, and step width. Gait variability structure was derived using a detrended fluctuation analysis technique. At preferred walking speeds, ET participants walked significantly slower with significantly increased variability magnitude in all five spatiotemporal gait parameters. At speed-matched walking, ET participants exhibited significantly higher step width variability. Gait variability structure was not different between groups. We also observed that gait variability magnitude was predicted by severity of upper extremity and midline tremors. This study revealed that self-selected gait in ET is characterized by high variability that is associated with tremor severity in the upper extremity and midline.     

The effects of sensory loss and walking speed on the orbital dynamic stability of human walking

Peripheral sensory feedback is believed to contribute significantly to maintaining walking stability. Patients with diabetic peripheral neuropathy have a greatly increased risk of falling. Previously, we demonstrated that slower walking speeds in neuropathic patients lead to improved local dynamic stability. However, all subjects exhibited significant local instability during walking, even though no subject fell or stumbled during testing. The present study was conducted to determine if and how significant changes in peripheral sensation and walking speed affect orbital stability during walking. Trunk and lower extremity kinematics were examined from two prior experiments that compared patients with significant neuropathy to healthy controls and walking at multiple different speeds in young healthy subjects. Maximum Floquet multipliers were computed for each time series to quantify the orbital stability of these movements. All subjects exhibited orbitally stable walking kinematics, even though these same kinematics were previously shown to be locally unstable. Differences in orbital stability between neuropathic and control subjects were small and, with the exception of knee joint movements (p=0.001), not statistically significant (0.380p0.946). Differences in knee orbital stability were not mediated by differences in walking speed. This was supported by our finding that although orbital stability improved slightly with slower walking speeds, the correlations between walking speed and orbital stability were generally weak (r(2)16.7%). Thus, neuropathic patients do not gain improved orbital stability as a result of slowing down and do not experience any loss of orbital stability because of their sensory deficits.     

Long-Range Correlations in Rectal Temperature Fluctuations of Healthy Infants during Maturation

Background

Control of breathing, heart rate, and body temperature are interdependent in infants, where instabilities in thermoregulation can contribute to apneas or even life-threatening events. Identifying abnormalities in thermoregulation is particularly important in the first 6 months of life, where autonomic regulation undergoes critical development. Fluctuations in body temperature have been shown to be sensitive to maturational stage as well as system failure in critically ill patients. We thus aimed to investigate the existence of fractal-like long-range correlations, indicative of temperature control, in night time rectal temperature (T_rec) patterns in maturing infants.

Methodology/Principal Findings

We measured T_rec fluctuations in infants every 4 weeks from 4 to 20 weeks of age and before and after immunization. Long-range correlations in the temperature series were quantified by the correlation exponent, α using detrended fluctuation analysis. The effects of maturation, room temperature, and immunization on the strength of correlation were investigated. We found that T_rec fluctuations exhibit fractal long-range correlations with a mean (SD) α of 1.51 (0.11), indicating that T_rec is regulated in a highly correlated and hence deterministic manner. A significant increase in α with age from 1.42 (0.07) at 4 weeks to 1.58 (0.04) at 20 weeks reflects a change in long-range correlation behavior with maturation towards a smoother and more deterministic temperature regulation, potentially due to the decrease in surface area to body weight ratio in the maturing infant. α was not associated with mean room temperature or influenced by immunization

Conclusions

This study shows that the quantification of long-range correlations using α derived from detrended fluctuation analysis is an observer-independent tool which can distinguish developmental stages of night time T_rec pattern in young infants, reflective of maturation of the autonomic system. Detrended fluctuation analysis may prove useful for characterizing thermoregulation in premature and other infants at risk for life-threatening events.     

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.     

Pupillary signs in diabetic autonomic neuropathy.

Pupillary function was investigated in 36 insulin-dependent diabetics and 36 controls matched for age and sex. About half of the diabetics had evidence of peripheral somatic or autonomic neuropathy, or both. The diabetic patients had abnormally small pupil diameters in the dark and less fluctuation in pupil size (hippus) during continuous illumination than the controls. They also had reduced reflex responses to light flashes of an intensity adjusted for individual retinal sensitivities. The pupillary findings were compared with results of five tests of cardiovascular function and five tests of peripheral sensory and motor nerve function. Almost all the patients with autonomic neuropathy had pupillary signs, which we therefore conclude are a common manifestation of diabetic autonomic neuropathy.     

Slower speeds in patients with diabetic neuropathy lead to improved local dynamic stability of continuous overground walking

Patients with diabetic peripheral neuropathy are significantly more likely to fall while walking than subjects with intact sensation. While it has been suggested that these patients walk slower to improve locomotor stability, slower speeds are also associated with increased locomotor variability, and increased variability has traditionally been equated with loss of stability. If the latter were true, this would suggest that slowing down, as a locomotor control strategy, should be completely antithetical to the goal of maintaining stability. The present study resolves these seemingly paradoxical findings by using methods from nonlinear time series analysis to directly quantify the sensitivity of the locomotor system to local perturbations that are manifested as natural kinematic variability. Fourteen patients with severe peripheral neuropathy and 12 gender-, age-, height-, and weight-matched non-diabetic controls participated. Sagittal plane angles of the right hip, knee, and ankle joints and tri-axial accelerations of the trunk were measured during 10 min of continuous overground walking at self-selected speeds. Maximum finite-time Lyapunov exponents were computed for each time series to quantify the local dynamic stability of these movements. Neuropathic patients exhibited slower walking speeds and better local dynamic stability of upper body movements in the horizontal plane than did control subjects. The differences in local dynamic stability were significantly predicted by differences in walking speed, but not by differences in sensory status. These results support the hypothesis that reductions in walking speed are a compensatory strategy used by neuropathic patients to maintain dynamic stability of the upper body during level walking.     

Hemiplegic gait: a kinematic analysis using walking speed as a basis.

The kinematics of treadmill ambulation of stroke patients (N = 9) and healthy subjects (N = 4) was studied at a wide range of different velocities (i.e. 0.25-1.5 m s-1), with a focus on the transverse rotations of the trunk. Video recordings revealed, for both stroke patients and healthy subjects, similar relations between walking speed and stride length as well as stride frequency. The phase difference between pelvic and thoracic rotations (i.e. trunk rotation) and the total range of trunk rotation were almost linearly related to the walking speed. Healthy subjects showed a marked increase in pelvic rotation from 1 to 1.5 m s-1. Using dimensional analysis in a comparison between stroke patients and healthy subjects, invariances in the coordination of gait were found for stride length, stride frequency, pelvic rotation, and trunk rotation. Constant relations were obtained between, on the one hand, dimensionless velocity and, on the other, dimensionless stride length as well as stride frequency. Transitions were found between the velocities 0.75 and 1 m s-1 for dimensionless pelvic rotation and trunk rotation, indicating that, from this velocity range onwards, pelvic swing lengthens the stride: rotations of pelvis, thorax and trunk become tightly coordinated. On the basis of the dimensionless stride length, stride frequency, pelvic rotation and trunk rotation, deficits in the gait of stroke patients could be quantified. It is concluded that walking speed is an important control parameter, which should be used as a basic variable in the evaluation of the gait of stroke patients.     

Energy cost of walking and gait instability in healthy 65- and 80-yr-olds.

This study tested whether the lower economy of walking in healthy elderly subjects is due to greater gait instability. We compared the energy cost of walking and gait instability (assessed by stride to stride changes in the stride time) in octogenarians (G80, n = 10), 65-yr-olds (G65, n = 10), and young controls (G25, n = 10) walking on a treadmill at six different speeds. The energy cost of walking was higher for G80 than for G25 across the different walking speeds (P < 0.05). Stride time variability at preferred walking speed was significantly greater in G80 (2.31 +/- 0.68%) and G65 (1.93 +/- 0.39%) compared with G25 (1.40 +/- 0.30%; P < 0.05). There was no significant correlation between gait instability and energy cost of walking at preferred walking speed. These findings demonstrated greater energy expenditure in healthy elderly subjects while walking and increased gait instability. However, no relationship was noted between these two variables. The increase in energy cost is probably multifactorial, and our results suggest that gait instability is probably not the main contributing factor in this population. We thus concluded that other mechanisms, such as the energy expenditure associated with walking movements and related to mechanical work, or neuromuscular factors, are more likely involved in the higher cost of walking in elderly people.     

Identification of development and autonomic nerve activity from heart rate variability in preterm infants

Heartbeat intervals, which are determined basically by regular excitations of the sinoatrial node, show significant fluctuation referred to as the heart rate variability (HRV). The HRV is mostly due to nerve activities through the sympathetic and parasympathetic branches of the autonomic nervous system (ANS). In recent years, it has been recognized that the HRV shows a greater complexity than ever expected, suggesting that it includes much information about ANS activities. In this study, we investigated relationship between HRV and development in preterm infants. To this end, heartbeat intervals were continuously recorded from 11 preterm infants in NICU. The recording periods were ranging from several days to weeks depending on the individuals. The HRV at various ages was then characterized by several indices. They include power spectrum as well as the mean and standard deviation of the series. For the power spectrum, the low-frequency band power (LF), high-frequency band power (HF), LF/HF (the ratio between LF and HF), beta (scaling exponent of the spectrum) were estimated. The detrended fluctuation analysis (DFA) was also employed to obtain short- and long-range scaling exponents. Each of these indices showed a correlation with the age. We showed that the long-range scaling exponent, derived from the DFA, was most significantly correlated with the age, suggesting that it could be a robust index to characterize the development of preterm infants.     

Somatosensory evoked potentials and magnetic resonance imaging in syringomyelia

Somatosensory evoked potentials (SEPs) to median and posterior tibial stimulation were obtained in 22 patients with syringomyelia. All patients had magnetic resonance imaging (MR) which defined the maximum transverse diameter of the syrinx as well as its longitudinal extension. SEP was abnormal in 16 (72%) patients. Median and posterior tibial SEPs were abnormal in 11 and 15 patients respectively. Both tests were abnormal in 10 patients. Ten patients showed absence of one or more central potentials (P/N13, N20, N22) and 7 patients demonstrated increased conduction times (N9–N20, P/N13–N20, N22–P40). The mean maximum transverse diameter of the syrinx was 7.5 mm in patients with normal SEPs and 16.2 mm in patients with abnormal SEPs. Abnormal SEP was observed in all 5 patients with loss of position sense, in 9 of 13 (69%) with loss of superficial pain and temperature, and 1 of 2 patients with motor deficit only. Central SEP abnormalities were observed in 3 of 5 patients with sensory deficits indistinguishable from a peripheral neuropathy and in 2 patients in the asymptomatic extremity. Three of 4 patients with syringomyelia and Chiari malformation had a normal SEP.     

Size Effects on Correlation Measures

The detection and quantification of long-range correlations in time series is a fundamental tool to characterize the properties of different dynamical systems, and is applied in many different fields, including physics, biology or engineering. Due to the diversity of applications, many techniques for measuring correlations have been designed. Here, we study systematically the influence of the length of a time series on the results obtained from several techniques commonly used to detect and quantify long-range correlations: the autocorrelation analysis, Hursts analysis, and detrended fluctuation analysis (DFA). Using the Fourier filtering method, we generate artificial time series with known and controlled long-range correlations and with a broad range of lengths, and apply on them the different correlation measures we have studied. Our results indicate that while the DFA method is practically unaffected by the length of the time series, and almost always provides accurate results, the results from Hursts analysis and the autocorrelation analysis strongly depend on the length of the time series.     

Noisy Interlimb Coordination Can Be a Main Cause of Freezing of Gait in Patients with Little to No Parkinsonism

Freezing of gait in patients with Parkinson’s disease is associated with several factors, including interlimb incoordination and impaired gait cycle regulation. Gait analysis in patients with Parkinson’s disease is confounded by parkinsonian symptoms such as rigidity. To understand the mechanisms underlying freezing of gait, we compared gait patterns during straight walking between 9 patients with freezing of gait but little to no parkinsonism (freezing patients) and 11 patients with Parkinson’s disease (non-freezing patients). Wireless sensors were used to detect foot contact and toe-off events, and the step phase of each foot contact was calculated by defining one stride cycle of the other leg as 360°. Phase-resetting analysis was performed, whereby the relation between the step phase of one leg and the subsequent phase change in the following step of the other leg was quantified using regression analysis. A small slope of the regression line indicates a forceful correction (phase reset) at every step of the deviation of step phase from the equilibrium phase, usually at around 180°. The slope of this relation was smaller in freezing patients than in non-freezing patients, but the slope exhibited larger step-to-step variability. This indicates that freezing patients executed a forceful but noisy correction of the deviation of step phase, whereas non-freezing patients made a gradual correction of the deviation. Moreover, freezing patients tended to show more variable step phase and stride time than non-freezing patients. Dynamics of a model of two coupled oscillators interacting through a phase resetting mechanism were examined, and indicated that the deterioration of phase reset by noise provoked variability in step phase and stride time. That is, interlimb coordination can affect regulation of the gait cycle. These results suggest that noisy interlimb coordination, which probably caused forceful corrections of step phase deviation, can be a cause of freezing of gait.