Characteristics of hand tremor time series

Tremor is classified into physiological, essential, and parkinsonian tremor by means of clinical criteria. The aim of our work was to extract quantitative features from the measurements of the acceleration of human postural hand tremor. Different mathematical methods were adopted and modified in order to separate these three types of tremor. Best discrimination between physiological and pathological tremors has been achieved by methods distinguishing nonlinear from linear behavior. On the other hand, methods separating different forms of nonlinear behavior have been found to be superior in discriminating parkinsonian and essential tremor. By these methods physiological and pathological tremors can be separated with an error rate below 20% and essential and parkinsonian tremor with an error rate below 10%. This may help to classify tremor time series by objective mathematical criteria and may increase the understanding of the pathophysiological differences underlying these kinds of tremor.     

Load dependence of simulated central tremor

Previous studies have argued that tremors of central versus peripheral origin can be distinguished based on their load dependence: the frequency of peripheral tremor decreases when a weight is added to the tremulous limb, while the frequency of central tremors remains unchanged. The present study scrutinizes the latter statement. We simulated central tremor using a simple network of coupled neural oscillators, which receives proprioceptive feedback from the motor periphery. The network produced a self-sustained, stable oscillation. When the gain of proprioceptive feedback was high, oscillation frequency decreased in the presence of an inertial load. When the gain was low, the oscillation frequency was load independent. We conclude that load dependence is not an exclusive property of peripheral tremors but may be found in tremors of central origin as well. Therefore, the load test is not sufficient to reject a central tremor origin. Received: 1 October 1998 / Accepted in revised form: 28 January 1999     

Energy and fractal characteristics of physiological and pathological tremors of the human hand

Tremors (involuntary shaking) were compared in healthy subjects and patients with the tremulous form of Parkinsonism sustaining isometric effort of the hand. For this purpose, fractal analysis and multilevel wavelet decomposition of tremor were used, and the energy characteristics determined on the basis of the spectral density of the energy of detailed components obtained at different levels of decomposition. The calculated fractal and energy characteristics of the tremor of healthy subjects were significantly lower than those of patients. If the patients took antiparkinsonian drugs at their usual doses, the characteristics shifted towards normal values. The decrease in the fractal dimension indicates an increase in the strength of the correlation in the dynamics of involuntary shaking. Thus, the characteristics studied allow not only physiological and pathological tremors to be discriminated, but also the strategy of selection of optimal drugs for relieving Parkinsonian tremor to be developed.     

Dynamical characterization of residual and non-native structures in a partially folded protein by (15)N NMR relaxation using a model based on a distribution of correlation times

A spectral density model based on a truncated lorentzian distribution of correlation times is used to analyze the nanosecond time-scale dynamics of the partially unfolded domain 2 of annexin I from its (15)N NMR relaxation parameters measured at three magnetic field strengths. The use of a distribution of correlation times enables the characterization of the dynamical features of the NH bonds of the protein in terms of heterogeneity of dynamical states in the nanosecond range. The variation along the sequence of the two dynamical parameters introduced, namely the center and the width of the distribution, points out the different types of residual secondary structures present in the D2 domain. Moreover, it allows a physically sensible interpretation of the dynamical behavior of the different residual helices and of the non-native structures. Also, a striking correspondence is found between the parameters obtained using an extended Lipari and Szabo model and the parameters obtained using the distribution of correlation times. This result led us to propose a specific interpretation of the model-free order parameter for internal motions in the nanosecond range in the case of unfolded states.     

Effectively desynchronizing deep brain stimulation based on a coordinated delayed feedback stimulation via several sites: a computational study

In detailed simulations we present a coordinated delayed feedback stimulation as a particularly robust and mild technique for desynchronization. We feed back the measured and band-pass filtered local filed potential via several or multiple sites with different delays, respectively. This yields a resounding desynchronization in a naturally demand-controlled way. Our novel approach is superior to previously developed techniques: It is robust against variations of system parameters, e.g., the mean firing rate. It does not require time-consuming calibration. It also prevents intermittent resynchronization typically caused by all methods employing repetitive administration of shocks. We suggest our novel technique to be used for deep brain stimulation in patients suffering from neurological diseases with pathological synchronization, such as Parkinsonian tremor, essential tremor or epilepsy.     

Stochastic Simulation of Delay-Induced Circadian Rhythms in Drosophila

Circadian rhythms are ubiquitous in all eukaryotes and some prokaryotes. Several computational models with or without time delays have been developed for circadian rhythms. Exact stochastic simulations have been carried out for several models without time delays, but no exact stochastic simulation has been done for models with delays. In this paper, we proposed a detailed and a reduced stochastic model with delays for circadian rhythms in Drosophila based on two deterministic models of Smolen et al. and employed exact stochastic simulation to simulate circadian oscillations. Our simulations showed that both models can produce sustained oscillations and that the oscillation is robust to noise in the sense that there is very little variability in oscillation period although there are significant random fluctuations in oscillation peeks. Moreover, although average time delays are essential to simulation of oscillation, random changes in time delays within certain range around fixed average time delay cause little variability in the oscillation period. Our simulation results also showed that both models are robust to parameter variations and that oscillation can be entrained by light/dark circles. Our simulations further demonstrated that within a reasonable range around the experimental result, the rates that dclock and per promoters switch back and forth between activated and repressed sites have little impact on oscillation period.     

A spatial stochastic neuronal model with Ornstein–Uhlenbeck input current

 We consider a spatial neuron model in which the membrane potential satisfies a linear cable equation with an input current which is a dynamical random process of the Ornstein–Uhlenbeck (OU) type. This form of current may represent an approximation to that resulting from the random opening and closing of ion channels on a neuron's surface or to randomly occurring synaptic input currents with exponential decay. We compare the results for the case of an OU input with those for a purely white-noise-driven cable model. The statistical properties, including mean, variance and covariance of the voltage response to an OU process input in the absence of a threshold are determined analytically. The mean and the variance are calculated as a function of time for various synaptic input locations and for values of the ratio of the time constant of decay of the input current to the time constant of decay of the membrane voltage in the physiological range for real neurons. The limiting case of a white-noise input current is obtained as the correlation time of the OU process approaches zero. The results obtained with an OU input current can be substantially different from those in the white-noise case. Using simulation of the terms in the series representation for the solution, we estimate the interspike interval distribution for various parameter values, and determine the effects of the introduction of correlation in the synaptic input stochastic process. Received: 5 March 2001 / Accepted in revised form: 7 August 2001     

A biologically plausible model of time-scale invariant interval timing

The temporal durations between events often exert a strong influence over behavior. The details of this influence have been extensively characterized in behavioral experiments in different animal species. A remarkable feature of the data collected in these experiments is that they are often time-scale invariant. This means that response measurements obtained under intervals of different durations coincide when plotted as functions of relative time. Here we describe a biologically plausible model of an interval timing device and show that it is consistent with time-scale invariant behavior over a substantial range of interval durations. The model consists of a set of bistable units that switch from one state to the other at random times. We first use an abstract formulation of the model to derive exact expressions for some key quantities and to demonstrate time-scale invariance for any range of interval durations. We then show how the model could be implemented in the nervous system through a generic and biologically plausible mechanism. In particular, we show that any system that can display noise-driven transitions from one stable state to another can be used to implement the timing device. Our work demonstrates that a biologically plausible model can qualitatively account for a large body of data and thus provides a link between the biology and behavior of interval timing.     

Clinicians’ Tendencies to Under-Rate Parkinsonian Tremors in the Less Affected Hand

The standard assessment method for tremor severity in Parkinson’s disease is visual observation by neurologists using clinical rating scales. This is, therefore, a subjective rating that is dependent on clinical expertise. The objective of this study was to report clinicians’ tendencies to under-rate Parkinsonian tremors in the less affected hand. This was observed through objective tremor measurement with accelerometers. Tremor amplitudes were measured objectively using tri-axis-accelerometers for both hands simultaneously in 53 patients with Parkinson’s disease during resting and postural tremors. The videotaped tremor was rated by neurologists using clinical rating scales. The tremor measured by accelerometer was compared with clinical ratings. Neurologists tended to under-rate the less affected hand in resting tremor when the contralateral hand had severe tremor in Session I. The participating neurologists corrected this tendency in Session II after being informed of it. The under-rating tendency was then repeated by other uninformed neurologists in Session III. Kappa statistics showed high inter-rater agreements and high agreements between estimated scores derived from the accelerometer signals and the mean Clinical Tremor Rating Scale evaluated in every session. Therefore, clinicians need to be aware of this under-rating tendency in visual inspection of the less affected hand in order to make accurate tremor severity assessments.     

Vitamins E and C prevent the impairment of retention of an inhibitory avoidance task caused by arginine administration

S-adenosylmethionine (SAMe) is present in all tissues and functions as the sole donor of methyl groups in over 100 different methylation reactions. Recent reports suggest that direct intraventricular injection of SAMe induces Parkinsonian like symptoms in rats including seizures, tremors, hyperkinesia and abnormal posture. In order to assess the influence of SAMe on rat behavior we have undertaken a study to examine the effect of 3 different forms of SAMe. Guide cannulae were sterotaxically implanted into the lateral ventricle of male SD rats ( n = 5 for each group) using either ketamine or chloral hydrate anesthesia. 48 h post surgery the rats received a 5-μL injection containing 1 μmol of either SAMe-toluenedisulfonate, SAMe-butanedisulfonate, SAMe-chloride, or vehicle (butanedisulfonate, toluenedisulfonate or saline). Locomotor activity was monitored using the TruScan monitoring system and by videotape recording for 1 h. The videotape was reviewed by one of the authors (RD-A) who is experienced with animal models of epilepsy. SAMe injected animals had frequent myoclonic and tonic seizures, and occasional generalized clonic seizures. SAMe induced behavioral seizures and tremors occurred only in rats that had previously been anesthetized with chloral hydrate, and not in rats that received ketamine. The number of movements recorded during the 1-h period were significantly increased in SAMe injected animals compared to control groups in both chloral hydrate and ketamine anethetized rats. Our studies indicate that there is an anesthetic dependency for SAMe induced seizures and tremors.     

Analytical theory of the control equations for protein synthesis in the Goodwin model

The analytical expressions, and their convergent series expansions, for the time period and various time averages of the dynamical quantities are derived for the Goodwin model. The radius of convergence of the series expansions is also calculated. The changes necessary to fully take into account the restrictions on dynamical variable, following from the positivity of physical quantities of the model, for the statistical mechanical treatment of the system are also discussed.     

Poster Sessions AP10: Learning,Memory and Behavior. S‐adenosylmethionine induced seizures are anesthetic dependant

S‐adenosylmethionine (SAMe) is present in all tissues and functions as the sole donor of methyl groups in over 100 different methylation reactions. Recent reports suggest that direct intraventricular injection of SAMe induces Parkinsonian like symptoms in rats including seizures, tremors, hyperkinesia and abnormal posture. In order to assess the influence of SAMe on rat behavior we have undertaken a study to examine the effect of 3 different forms of SAMe. Guide cannulae were sterotaxically implanted into the lateral ventricle of male SD rats (n = 5 for each group) using either ketamine or chloral hydrate anesthesia. 48 h post surgery the rats received a 5‐μL injection containing 1 μmol of either SAMe‐toluenedisulfonate, SAMe‐butanedisulfonate, SAMe‐chloride, or vehicle (butanedisulfonate, toluenedisulfonate or saline). Locomotor activity was monitored using the TruScan monitoring system and by videotape recording for 1 h. The videotape was reviewed by one of the authors (RD‐A) who is experienced with animal models of epilepsy. SAMe injected animals had frequent myoclonic and tonic seizures, and occasional generalized clonic seizures. SAMe induced behavioral seizures and tremors occurred only in rats that had previously been anesthetized with chloral hydrate, and not in rats that received ketamine. The number of movements recorded during the 1‐h period were significantly increased in SAMe injected animals compared to control groups in both chloral hydrate and ketamine anethetized rats. Our studies indicate that there is an anesthetic dependency for SAMe induced seizures and tremors.     

Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations

Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.     

The impact of food contaminants on the bioavailability of trace metals.

Organic solvents, detergents, organochloric compounds, pesticides, mycotoxins, residues of veterinary drugs and metals are examples for food contaminants; they are usually present at very low concentrations. Their impact on absorption and distribution kinetics of essential trace metals, if there is any, can be mediated by three types of mechanisms: 1. In animal experiments, contaminants like T-2 mycotoxins or 2,3,7,8 tetrachlorodibenzodioxin inhibited absorptive or excretory mechanisms at high concentrations which, however, are usually not found in food. 2. Food contaminants with metal binding properties can interact with essential metals in the intestinal lumen or during transfer through the intestinal mucosa and affect their absorption according to the rules of complex chemistry. To balance the effect of endogenous metal-binding food constituents, they should be present in comparably high quantities. Usually, however, the concentration of contaminants is approx. 6 orders of magnitude lower than that of endogenous food ligands. 3. Contaminating metals may interfere with the regulated absorption, distribution, and excretion kinetics of essential metals. Such mechanisms may be amplified by vicious cycles. In general, however, food contaminations with metals are too low to have an impact on the bioavailability of essential metals.     

Quantifying Spike Train Oscillations: Biases,Distortions and Solutions

Estimation of the power spectrum is a common method for identifying oscillatory changes in neuronal activity. However, the stochastic nature of neuronal activity leads to severe biases in the estimation of these oscillations in single unit spike trains. Different biological and experimental factors cause the spike train to differentially reflect its underlying oscillatory rate function. We analyzed the effect of factors, such as the mean firing rate and the recording duration, on the detectability of oscillations and their significance, and tested these theoretical results on experimental data recorded in Parkinsonian non-human primates. The effect of these factors is dramatic, such that in some conditions, the detection of existing oscillations is impossible. Moreover, these biases impede the comparison of oscillations across brain regions, neuronal types, behavioral states and separate recordings with different underlying parameters, and lead inevitably to a gross misinterpretation of experimental results. We introduce a novel objective measure, the "modulation index", which overcomes these biases, and enables reliable detection of oscillations from spike trains and a direct estimation of the oscillation magnitude. The modulation index detects a high percentage of oscillations over a wide range of parameters, compared to classical spectral analysis methods, and enables an unbiased comparison between spike trains recorded from different neurons and using different experimental protocols.     

A mathematical model of hematopoiesis--I. Periodic chronic myelogenous leukemia

Periodic chronic myelogenous leukemia (PCML) is an interesting dynamical disease of the hematopoietic system in which oscillating levels of circulating leukocytes, platelets and/or reticulocytes are observed. Typically all of these three differentiated cell types have the same oscillation period, but the relation of the oscillation mean and amplitude to the normal levels is variable. Given the appearance of the abnormal Philadelphia chromosome in all of the nucleated progeny of the hematopoietic stem cells (HSCs), the most parsimonious conclusion is that chronic myelogenous leukemia, and its periodic variant, arise from derangements partially involving the dynamics of the stem cells. Here, we have synthesized several previous mathematical models of HSC dynamics, and models for the regulation of neutrophils, platelets and erythrocytes into a comprehensive model for the regulation of the hematopoietic system. Based on estimates of parameters for a typical normal human, we have systematically explored the changes in some of these parameters necessary to account for the quantitative data on leukocyte, platelet and reticulocyte cycling in 11 patients with PCML. Our results indicate that the critical model parameter changes required to simulate the PCML patient data are an increase in the amplification in the leukocyte line, an increase in the differentiation rate from the stem cell compartment into the leukocyte line, and the rate of apoptosis in the stem cell compartment. Our model system is particularly sensitive to changes in stem cell apoptosis rates, suggesting that changes in the numbers of proliferating stem cells may be important in generating PCML.     

A dynamical model for the basal ganglia-thalamo-cortical oscillatory activity and its implications in Parkinson’s disease

We propose to investigate brain electrophysiological alterations associated with Parkinson’s disease through a novel adaptive dynamical model of the network of the basal ganglia, the cortex and the thalamus. The model uniquely unifies the influence of dopamine in the regulation of the activity of all basal ganglia nuclei, the self-organised neuronal interdependent activity of basal ganglia-thalamo-cortical circuits and the generation of subcortical background oscillations. Variations in the amount of dopamine produced in the neurons of the substantia nigra pars compacta are key both in the onset of Parkinson’s disease and in the basal ganglia action selection. We model these dopamine-induced relationships, and Parkinsonian states are interpreted as spontaneous emergent behaviours associated with different rhythms of oscillatory activity patterns of the basal ganglia-thalamo-cortical network. These results are significant because: (1) the neural populations are built upon single-neuron models that have been robustly designed to have eletrophysiologically-realistic responses, and (2) our model distinctively links changes in the oscillatory activity in subcortical structures, dopamine levels in the basal ganglia and pathological synchronisation neuronal patterns compatible with Parkinsonian states, this still remains an open problem and is crucial to better understand the progression of the disease.Electronic supplementary materialThe online version of this article (10.1007/s11571-020-09653-y) contains supplementary material, which is available to authorized users.     

Characterising neurological time series data using biologically motivated networks of coupled discrete maps

Artificial biochemical networks (ABNs) are a class of computational dynamical system whose architectures are motivated by the organisation of genetic and metabolic networks in biological cells. Using evolutionary algorithms to search for networks with diagnostic potential, we demonstrate how ABNs can be used to carry out classification when stimulated with time series data collected from human subjects with and without Parkinson's disease. Artificial metabolic networks, composed of coupled discrete maps, offer the best recognition of Parkinsonian behaviour, achieving accuracies in the region of 90%. This is comparable to the diagnostic accuracies found in clinical diagnosis, and is significantly higher than those found in primary and non-expert secondary care. We also illustrate how an evolved classifier is able to recognise diverse features of Parkinsonian behaviour and, using perturbation analysis, show that the evolved classifiers have interesting computational behaviours.     

Characterizing Deep Brain Stimulation effects in computationally efficient neural network models

Background  

Recent studies on the medical treatment of Parkinson's disease (PD) led to the introduction of the so called Deep Brain Stimulation (DBS) technique. This particular therapy allows to contrast actively the pathological activity of various Deep Brain structures, responsible for the well known PD symptoms. This technique, frequently joined to dopaminergic drugs administration, replaces the surgical interventions implemented to contrast the activity of specific brain nuclei, called Basal Ganglia (BG). This clinical protocol gave the possibility to analyse and inspect signals measured from the electrodes implanted into the deep brain regions. The analysis of these signals led to the possibility to study the PD as a specific case of dynamical synchronization in biological neural networks, with the advantage to apply the theoretical analysis developed in such scientific field to find efficient treatments to face with this important disease. Experimental results in fact show that the PD neurological diseases are characterized by a pathological signal synchronization in BG. Parkinsonian tremor, for example, is ascribed to be caused by neuron populations of the Thalamic and Striatal structures that undergo an abnormal synchronization. On the contrary, in normal conditions, the activity of the same neuron populations do not appear to be correlated and synchronized.