Nonlinear analysis of periodic waves in a neural field model.

Various types of brain activity, including motor, visual, and language, are accompanied by the propagation of periodic waves of electric potential in the cortex, possibly providing the synchronization of the epicenters involved in these activities. One example is cortical electrical activity propagating during sleep and described as traveling waves [Massimini et al., J. Neurosci. 24, 6862-6870 (2004)]. These waves modulate cortical excitability as they progress. Clinically related examples include cortical spreading depression in which a wave of depolarization propagates not only in migraine but also in stroke, hemorrhage, or traumatic brain injury [Whalen et al., Sci. Rep. 8, 1-9 (2018)]. Here, we consider the possible role of epicenters and explore a neural field model with two nonlinear integrodifferential equations for the distributions of activating and inhibiting signals. It is studied with symmetric connectivity functions characterizing signal exchange between two populations of neurons, excitatory and inhibitory. Bifurcation analysis is used to investigate the emergence of periodic traveling waves and of standing oscillations from the stationary, spatially homogeneous solutions, and the stability of these solutions. Both types of solutions can be started by local oscillations indicating a possible role of epicenters in the initiation of wave propagation.

Characterization of spatiotemporal dynamics in EEG data during picture naming with optical flow patterns.

In this study, we investigate the spatiotemporal dynamics of the neural oscillations by analyzing the electric potential that arises from neural activity. We identify two types of dynamics based on the frequency and phase of oscillations: standing waves or as out-of-phase and modulated waves, which represent a combination of standing and moving waves. To characterize these dynamics, we use optical flow patterns such as sources, sinks, spirals and saddles. We compare analytical and numerical solutions with real EEG data acquired during a picture-naming task. Analytical approximation of standing waves helps us to establish some properties of pattern location and number. Specifically, sources and sinks are mainly located in the same location, while saddles are positioned between them. The number of saddles correlates with the sum of all the other patterns. These properties are confirmed in both the simulated and real EEG data. In particular, source and sink clusters in the EEG data overlap with each other with median percentages around 60%, and hence have high spatial correlation, while source/sink clusters overlap with saddle clusters in less than 1%, and have different locations. Our statistical analysis showed that saddles account for about 45% of all patterns, while the remaining patterns are present in similar proportions.

Neurophysiological and behavioral effects of a 60 Hz, 1,800 µT magnetic field in humans.

The effects of time-varying magnetic fields (MF) on humans have been actively investigated for the past three decades. One important unanswered question is the potential for MF exposure to have acute effects on human biology. Different strategies have been used to tackle this question using various physiological, neurophysiological and behavioral indicators. For example, researchers investigating electroencephalography (EEG) have reported that extremely low frequency (ELF, <300 Hz) MF can increase resting occipital alpha rhythm (8-12 Hz). Interestingly, other studies have demonstrated that human motricity can be modulated by ELF MF: a reduction of anteroposterior standing balance or a decrease of physiological tremor intensity have been reported as consequences of exposure. However, the main limitation in this domain lies in the lack of results replication, possibly originating from the large variety of experimental approaches employed. Therefore, the present study aimed to investigate the effects of a 60 Hz, 1,800 µT MF exposure on neurophysiological (EEG) and neuromotor (standing balance, voluntary motor function, and physiological tremor) aspects in humans using a single experimental procedure. Though results from this study suggest a reduction of human standing balance with MF exposure, as well as an increase of physiological tremor amplitude within the frequency range associated with central nervous system contribution, no exposure effect appeared on other investigated parameters (e.g., EEG or voluntary motor control). These results suggest that 1 h of 60 Hz, 1,800 µT MF exposure may modulate human involuntary motor control without being detected in the cortical electrical activity.

Effects of acute hypoxia on postural and kinetic tremor.

Human physiological tremor is a complex phenomenon that is modulated by numerous mechanical, neurophysiological, and environmental conditions. Researchers investigating tremor have suggested that acute hypoxia increases tremor amplitude. Based on the results of prior studies, we hypothesized that human participants exposed to a simulated altitude of 4,500 m would display an increased tremor amplitude within the 6-12 Hz frequency range. Postural and kinetic tremors were recorded with a laser system in 23 healthy male participants before, during, and after 1 h of altitude-induced hypoxia. A large panel of tremor characteristics was used to investigate the effect of hypoxia. Acute hypoxia increased tremor frequency content between 6 and 12 Hz during both postural and kinetic tremor tasks (P < 0.05, F = 6.142, Eta(2) = 0.24 and P < 0.05, F = 3.767 Eta(2) = 0.14, respectively). Although the physiological mechanisms underlying the observed changes in tremor are not completely elucidated yet, this study confirms that acute hypoxia increases tremor frequency in the 6-12 Hz range. Furthermore, this study indicates that changes in physiological tremor can be detected at lower hypoxemic levels than previously reported (blood saturation in oxygen = 80.9%). The effects of hypoxia mainly result from a cascade of events starting with the activation of the hypothalamic-pituitary-adrenal axis causing in turn an increase in catecholamine release, leading to an augmentation of tremor amplitude in the 6- to 12-Hz interval and heart rate increase.

Modeling of post-stroke stimulation of cortical tissue.

Following a stroke, cortical networks in the penumbra area become fragmented and partly deactivated. We develop a model to study the propagation of waves of electric potential in the cortical tissue with integro-differential equations arising in neural field models. The wave speed is characterized by the tissue excitability and connectivity determined through parameters of the model. Post-stroke tissue damage in the penumbra area creates a hypoconnectivity and decreases the speed of wave propagation. It is proposed that external stimulation could restore the wave speed in the penumbra area under certain conditions of the parameters. Model guided cortical stimulation could be used to improve the functioning of cortical networks.

Neurologic signs of ciguatera disease: evidence of their persistence.

Ciguatoxins exert their effect on the voltage-sensitive sodium channels of the cellular membranes of all excitable tissues. This effect confers to ciguatera disease (CD) its neurologic hallmarks. A prospective study among French Polynesian adults over a two-month period was conducted to characterize and determine the persistence of neurologic symptoms of CD. We compared 47 patients with CD with 125 controls. In the acute phase of the disease, patients had mainly sensory disturbances as detected by an hypoesthesia on the palm of the hand and poorer sway performance compared with controls. Follow-up two months showed improvement of sway performance that eventually reaching control levels. However, for light-touch threshold, even if we observed a decrease threshold towards normal values, more than 50% of patients did not reach normal values 60 days after disease onset. Our results support the existence of neurologic impairments of CD and suggest their persistence for at least two months after onset.

New insights offered by a computational model of deep brain stimulation.

Deep brain stimulation (DBS) is a standard neurosurgical procedure used to treat motor symptoms in about 5% of patients with Parkinson's disease (PD). Despite the indisputable success of this procedure, the biological mechanisms underlying the clinical benefits of DBS have not yet been fully elucidated. The paper starts with a brief review on the use of DBS to treat PD symptoms. The second section introduces a computational model based on the population density approach and the Izhikevich neuron model. We explain why this model is appropriate for investigating macroscopic network effects and exploring the physiological mechanisms which respond to this treatment strategy (i.e., DBS). Finally, we present new insights into the ways this computational model may help to elucidate the dynamic network effects produced in a cerebral structure when DBS is applied.

Using wavelet analysis to detect the influence of low frequency magnetic fields on human physiological tremor.

The influence of extremely low frequency magnetic fields (ELF-MFs) on human physiological processes and, in particular, on motor activity is still not established with certainty. Using the wavelet-transform approach, changes in the characteristics of human finger micromovement are studied in the presence of a low intensity MF centred at the level of the head. Different approaches to nonstationary signal analysis involving real as well as complex wavelet functions are considered. We find evidence that ELF-MFs lead to more regular postural tremor and more homogeneous energy distribution.

The measurement of tremor using simple laser systems.

Quantification of movement pathologies is an important challenge of the clinical and research laboratories today. Basically, two problems must be addressed. The first one is to find the appropriate technology; the second is to develop adequate measures from the raw data which will best discriminate between health and pathology. In this paper, we propose a simple method to record and analyse tremor and other microdisplacements of the upper extremities based on the recording of position by laser analog sensors. Any microcomputer equipped to perform analog-digital conversion is compatible for use with this system. The performance of the laser system is examined and compared with the performance of accelerometers. Finally, data recorded with a laser analog sensor from a patient with Parkinson's disease and a control subject are presented. This new laser-based quantitative method may prove to be an important tool in early and differential diagnosis of neurodegenerative diseases of the central nervous system.

The measurement of tremor using a velocity transducer: comparison to simultaneous recordings using transducers of displacement, acceleration and muscle activity.

Precise kinematic measurements of tremor have historically been obtained using accelerometers. However, current technology permits precise measurements in velocity and displacement. The primary advantage of velocity recording is that only one step of integration or differentiation is required for either displacement or acceleration. A method is presented of measuring finger tremor using a laser system that transduces velocity precisely. Measurements of postural finger tremor thus obtained were compared to those simultaneously obtained from a laser system that transduces displacement, from an accelerometer and from surface electromyography (EMG) of the extensor digitorum communis. A range of amplitude and frequency content was obtained by testing control subjects and subjects with Parkinson's disease. The velocity transducer showed excellent correspondence of amplitude and frequency measurement with the displacement transducer. Measures of absolute and relative amplitude correlated well (r > or = 0.96 in amplitude measures in displacement, velocity and acceleration), and high coherence was found throughout the frequency range of interest. Measurements by the accelerometer generally showed poorer correspondence with those of the other instruments. EMG measurements showed good correspondence in some trials but poorer correspondence in others, attributed to the low level of muscle activity required in the task. Precise kinematic measurements appear to be highly sensitive to neuromotor impairment.

Relationships between electromyography and kinematics in human stepping strategies.

Kinematic and electromyographic (EMG) parameters were analyzed on phase plane diagrams of human stepping motions performed over an obstacle of varying height. A videomotion analysis system was used to record the displacement of 5 reflective markers placed on the subject's lower limb joints. Surface bipolar electrodes were placed on the rectus and biceps femoris muscles. Results revealed systematic differences in the EMG patterns of the rectus femoris between initial and subsequent trials in the 3 conditions of obstacle height. In the initial trials there was an episode of EMG activity right before or during the transition from knee flexion to extension. In the subsequent trials this episode was shifted toward maximum knee extension velocity, leaving a period of silence between the initial burst and this episode. On the other hand, the biceps femoris was rarely silent and particularly active during the flexion phase, reflecting its possible role in active knee flexion and postural control during the dynamic phase of stepping. The increase in phase plane size with obstacle height appears related to the amplitude of the initial EMG burst of the rectus femoris. Phase plane diagrams combined with EMG appear to be an appropriate approach to explore the dynamics of human movement strategies. The results suggest that control mechanisms for the flexion and extension phases are different and may be involved in fine tuning the stepping strategy for subsequent trials.

Accelerometric measurement of involuntary movements during pallidal deep brain stimulation of patients with generalized dystonia.

Accelerometric activity during rest and posture was quantified in the upper dominant limb of 14 patients with primary or secondary dystonia and five healthy control subjects. Data were recorded before and after bilateral implantation of the stimulating electrodes in the Globus Pallidus internus. Clinical evaluation was based on the Burke-Marsden-Fahn's Dystonia Rating Scale (BMFDRS). For the patient group, I(t), the integral (i.e. area) of the acceleration power spectrum over the total frequency range (0.6-16 Hz) decreased as the clinical state of the patients improved following deep brain stimulation (p < 0.01) during rest and posture. Ten days after surgery, there were no I(t) differences between control subjects and patients (p > 0.05). A significant correlation was found between the global BMFDRS scores and I(t) for rest (p < 0.01) but not for posture. No significant correlation was found between I(t) and a partial BMFDRS score for the right arm for rest or posture. The integral I(t) provides a valid indicator of the motor activity generated by the arm of the patient but further analyses are needed to monitor patients' progress not only during their hospitalization but also after they are released from the hospital, and to understand why this measure does not correlate with partial BMFDRS scores.

Using frequency domain characteristics to discriminate physiologic and parkinsonian tremors.

The manner in which characteristics of time series in the frequency domain can enhance discrimination between physiologic and parkinsonian tremor when tremor amplitude is low was examined. Rest tremor and postural tremor with and without visual feedback were recorded twice in the two hands of a group of patients with Parkinson's disease (PD) (n = 21) and a group of healthy control subjects (n = 30) using displacement laser systems. Recordings were analyzed quantitatively using amplitude and seven frequency domain characteristics. Postural tremor with no visual feedback allowed the most efficient discrimination between the two groups of subjects especially in velocity and acceleration (derived from displacement) and allowed identification of more patients with PD as separate from the range observed in the control group. Moreover, the frequency domain characteristics that were investigated identified the majority of the patients even when amplitude did not. After eliminating redundant (correlated) characteristics, it was found that the frequency composition of tremor in PD can be described adequately with four characteristics, which are the most reliable, independent, and discriminative elements for detecting early or subtle modifications in tremor. Also, a series of finger flexions was found to enhance physiologic tremor but not tremor in PD. Discrimination of low-amplitude tremor in PD from normal physiologic tremor is enhanced by examining the median frequency of oscillations, the concentration of power in the power spectrum, and the distribution of power in particular ranges. Tremor measurement should not be limited to acceleration data as some information is more visible in velocity time series.

Using time domain characteristics to discriminate physiologic and parkinsonian tremors.

Tremor amplitude and frequency do not always clearly differentiate subjects with particular pathologies from control subjects or from subjects with other pathologies, especially in early stages of a disease. For patients with early stages of Parkinson's disease (PD) the discriminative power of amplitude was compared with that of other time domain characteristics of tremor recordings that are probably not evident clinically. Postural tremor with and without visual feedback and rest tremor were recorded in both hands of a group of patients with Parkinson's disease (n = 21) and a group of healthy control subjects (n = 30) using displacement lasers. Velocity and acceleration data were derived from displacement data. Twelve time domain characteristics were calculated on each recording and the discriminating power of each was evaluated using the worse hand in each case. Postural tremor with no visual feedback separates the two groups of subjects most efficiently, especially in velocity and acceleration. Tremor in Parkinson's disease (in comparison to normal physiologic tremor) has a specific morphology, has a distinctive histogram, is more periodic, and contains indications of nonlinearity in the underlying dynamics. There may also be greater difference in amplitude between the two hands and time asymmetry in tremor of patients with PD. A series of finger flexions seems to enhance normal tremor but not tremor in PD and may thus aid in discrimination. Discrimination of tremor attributable to PD from normal physiologic tremor can be enhanced by measuring time domain characteristics subtler than amplitude, particularly when amplitude itself is not large. Tremor measurement should not be limited to acceleration data because some information is more visible in other variables.

Can tremor be used to measure the effect of chronic mercury exposure in human subjects?

Clinical and quantitative studies in which tremor was used to evaluate the effect of chronic exposure to organic and inorganic mercury in human subjects during the last 20 years were identified in MEDLINE and BIOLOGICAL ABSTRACTS. In the selected studies, methods varied widely by types of transducers used, anatomical locations of tremor testing, tasks executed by the subjects, types of tremor recorded and durations of trials. Measurements of tremor in these studies also varied by frequency, amplitude, waveform and reproducibility. Typically measures of variability were not included. Results obtained depended heavily on the methods and analyses used. We suggest that, although many contradictions and discrepancies have been noted in these studies, tremor can probably be used to measure the effect of chronic mercury exposure. This would involve more rigorous and uniform recording procedures and analyses. Specific suggestions proposed include: realizing the limitations of accelerometric data; considering the effect of weight on the tested limb; controlling recording conditions; selecting samples more carefully; recording other physiological variables besides tremor; using tasks and manoeuvres that unmask subclinical abnormalities in tremor; reporting frequency, amplitude, waveform and variability of tremor; understanding the limitations of power spectra analysis; separating tremor characteristics according to types of mercury exposure; and considering supraspinal influences that both vision and voluntary movements have on tremor.

Standardization of a neuromotor test battery: the CATSYS system.

Interindividual and intraindividual variability in neuromotor behaviors is expected and normal. Early changes in neuromotor behaviors associated with neurodegenerative disorders or neurotoxic effects are often subtle and fluctuating in their characteristics. Therefore, their detection at an early stage is particularly difficult without precise recording instruments. The CATSYS system developed by Danish Product Development (DPD) is a portable device recording four measures of neuromotor control including tremor, reaction time, hand coordination and postural sway. The aim of this study is to develop a set of normative data. One hundred and fifty healthy men and women were divided into five age groups: (1) 20 to 29 years (n=30); (2) 30 to 39 years (n=30); (3) 40 to 49 years (n=30); (4) 50 to 59 years (n=30); (5) 60 to 70 years (n=30). All participants were free of neurological deficits at the time of testing and they were tested individually for approximately 30 min. Hand coordination was measured with prono-supination and finger-tapping movements executed at constant and accelerated rhythms. Reaction time was assessed in both hands using a hand held switch activated by the thumb. Postural tremor was quantified in both hands during 24.6 sec. by asking the subject to hold a stylus horizontally at 10 cm in front of his/her navel. The stylus contained a biaxial accelerometer. Postural sway was tested by asking the subject to stand on a force platform for 75 sec. under four conditions: (1) eyes open; (2) eyes closed; (3) eyes open standing on a foam pad; and (4) eyes closed standing on a foam pad. ANOVAs and multiple comparison tests were performed and the results were examined taking into account age, gender and experimental condition effects.

Quantification of neuromotor function for detection of the effects of manganese.

The effect of low level exposure to manganese (Mn) was examined in 297 subjects from southwest Quebec. Blood manganese (MnB) levels as well as other possibly relevant variables were obtained. We tested equipment and analysis procedures that we have developed to quantify aspects of motor function thought to be affected by exposure to toxins, in particular, rapid alternating movements, rapid and precise pointing movements, and tremor. (1) The eurythmokinesimeter measures timing and precision of contacts between a hand-held stylus and a pair of metal targets (proximal/distal). This roughly approximates the finger-to-nose test of the UPDRS. Characteristics quantifying speed, precision and regularity of the movements were calculated, as well as multiple contacts due to tremor and an index based on Fitts' Law eliminating the effect of the trade-off between speed and precision. (2) The diadochokinesimeter accurately measures rapid rotation of the forearms (pronation/supination). Characteristics quantifying the range, speed, period, shape and regularity of the oscillatory movements were calculated, as well as the smoothness of the movement on a fine scale and the coordination between the two hands. (3) Postural tremor of the arm and hand was measured using the accelerometry-based "TREMOR" system of Danish Product Development. We used the amplitude and frequency characteristics provided by the TREMOR system: intensity, center frequency, dispersion and harmonic index. Previous studies have shown that these tests are sufficiently sensitive to detect small differences in performance of different groups of subjects, with indications that some characteristics are also specific to particular conditions. In this study, significant though small effects related to age and gender were found in many of the characteristics. When effects of other variables are removed, low-level exposure to Mn was found to be associated with a decrease in ability to perform regular, rapid and precise pointing movements, a decrease in ability to attain high maximum rotation speeds in rapid alternating movements, and an increase in regularity of tremor oscillations. Moreover, the effects are age-related for levels of MnB 7.5, micrograms/L.

Manganese neurotoxicity, a continuum of dysfunction: results from a community based study.

Excessive manganese (Mn) has been associated with neurobehavioral deficits and neurological and/or neuropsychiatric illness, but the level at which this metal can cause adverse neurotoxic effects, particularly with long-term exposure, is still unknown. The objective of the present study was to assess nervous system functions in residents exposed to manganese from a variety of environmental sources. A random stratified sampling procedure was used to select participants; persons with a history of workplace exposure to Mn and other neurotoxic substances were excluded. A self-administered questionnaire provided data on socio-demographic variables. Blood samples were analyzed for total manganese (MnB), lead, mercury and serum iron. Nervous system assessment included computer and hand-administered neurobehavioral tests, computerized neuromotor tests, sensory evaluation and a neurological examination. The present analyses include 273 persons (151 women and 122 men); MnB range: 2.5 micrograms/L-15.9 micrograms/L (median: 7.3 micrograms/L). Multivariate analyses were used and neuro-outcomes were examined with respect to MnB, taking into account potential confounders and covariables. Results were grouped according to neurofunctional areas and MANOVA analyses revealed that higher MnB (7.5 micrograms/L) was significantly associated with changes in coordinated upper limb movements (Wilks' lambda = 0.92; p = 0.04) and poorer learning and recall (men: Wilks' lambda = 0.77; p = 0.002; women: Wilks' lambda = 0.86; p = 0.04). Further analyses revealed that with increasing log MnB (Simple regression: p < 0.05) performance on a pointing task was poorer, frequency dispersion of hand-arm tremor decreased, while harmonic index increased, and the velocity of a pronation/supination arm movement was slower. An Mn-age interaction was observed for certain motor tasks, with the poorest performance observed among those _50 y and in the higher MnB category. Differences between genders suggest that men may be at greater risk than women, although effects were also observed in women. These findings are consistent with the hypothesis that Mn neurotoxicity can be viewed on a continuum of dysfunction, with early, subtle changes at lower exposure levels.

Diadochokinesimetry: a study of patients with Parkinson's disease and manganese exposed workers.

Diadochokinesia, the ability to perform rapid alternating movements is often impaired in patients with extrapyramidal disease. It is a common sign among patients with Parkinsonism or manganism. In the present study we compare patients with Parkinson's disease (n = 11), workers formerly exposed to manganese (n = 10) and control subjects (n = 11) performing rapid alternating hand movements for 5 s under four conditions repeated twice (natural cadence and maximal speed with one or two hands). Data recorded using a diadochokinesimeter built in our laboratory and connected to a 486/33 microcomputer were digitized in real time while subjects rotated back and forth hand held foam spheres connected to flexible rods articulated with optical encoders. Significant differences were found between control subjects and patients with Parkinson's disease, but not with manganese exposed workers, in most variables examined. However, trajectory length (a combination of movement amplitude and velocity) indicated that manganese exposed workers and patients with Parkinson's disease were significantly different from the controls in functional asymmetries between right and left hand. In addition, workers and patients tend to have marked differences between the performance of right and left hands. Improved quantitative measurement of rapid alternating movements may prove to be an important tool in early and differential diagnosis of Parkinson's disease and manganese exposure.

Fluctuations in tremor at rest and eye movements during ocular fixation in subjects with Parkinson's disease.

This exploratory study investigates possible relationships between fluctuations in tremor at rest (TR) and fluctuations in eye movement amplitude during ocular fixation. TR of the hand and eye movements were analyzed in five subjects with Parkinson's disease (PD) and five age-matched controls. TR was recorded using a position laser system and eye movements were recorded using an infrared reflectometry technique (Ober2). TR amplitudes were significantly larger in the group of subjects with PD than in the control group (p/=0.05). Changes in TR amplitude were not systematically correlated with modifications of eye movement amplitude in either group. However, occasional but distinct monocular oscillations were found in subjects with PD. Coherence values between frequencies of TR from the tested hand (3.5-7Hz) and frequencies of oscillatory eye movements (within the same frequency band) were clearly higher for the eye ipsilateral to the side of the body most affected by the disease in three subjects with PD. It is believed that these monocular oscillations may be a consequence of PD. Results from two previously published exploratory studies are integrated with the present results and new avenues of research are proposed.