Time series analysis with delay differential equations (DDEs) reveals nonlinear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10dB to -30dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of nonlinearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A' under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.
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In recent years there has been a significant increase in the use of electroencephalography (EEG) and magnetoencephalography (MEG) to investigate changes in oscillatory brain activity associated with tinnitus with many conflicting results. Current view of the underlying mechanism of tinnitus is that it results from changes in brain activity in various structures of the brain as a consequence of sensory deprivation. This in turn gives rise to increased spontaneous activity and/or synchrony in the auditory centres but also involves modulation from non-auditory processes from structures of the limbic and paralimbic system. Some of the neural changes associated with tinnitus may be assessed non-invasively in humans with MEG and EEG (M/EEG) in ways which are superior to animal studies and other non-invasive imaging techniques. However, both MEG and EEG have their limitations and research results can be misinterpreted in the absence of sufficient understanding of these limitations. In this article, I intend to provide a brief review of these techniques, describe what the recorded signals reflect in terms of the underlying neural activity, and their strengths and limitations. I also discuss some pertinent methodological issues involved in tinnitus related studies and concludes with suggestions to minimise possible discrepancies between results. The overall message is that while MEG and EEG are extremely useful techniques, the interpretation of results from tinnitus studies requires much caution given the individual variability in oscillatory activity and the limits of these techniques.
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There is increasing evidence supporting dietary and alternative therapies for epilepsy, including the ketogenic diet, modified Atkins diet, and omega-3 fatty acids. Vitamin D is actively under investigation as a potential intervention for epilepsy. Vitamin D is fat soluble steroid which shows promise in animal models of epilepsy. Basic research has shed light on the possible mechanisms by which Vitamin D may reduce seizures, and animal data support the efficacy of Vitamin D in rat and mouse models of epilepsy. Very little clinical data exists to support the treatment of human epilepsy with Vitamin D, but positive findings from preliminary clinical trials warrant larger Phase I and II clinical trials in order to more rigorously determine the potential therapeutic value of Vitamin D as a treatment for human epilepsy.
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Objective: 1) To determine the brain connectivity pattern associated with clinical rigidity scores in Parkinson's disease (PD) and 2) to determine the relation between clinically-assessed rigidity and quantitative metrics of motor performance.Background: Rigidity, the resistance to passive movement, is exacerbated in PD by asking the subject to move the contralateral limb, implying that rigidity involves a distributed brain network. Rigidity mainly affects subjects when they attempt to move; yet the relation between clinical rigidity scores and quantitative aspects of motor performance are unknown.Methods: Ten clinically diagnosed PD patients (off medication) and ten controls were recruited to perform an fMRI squeeze-bulb tracking task that included both visually guided and internally guided features. The direct functional connectivity between anatomically defined regions of interest was assessed with Dynamic Bayesian Networks (DBNs). Tracking performance was assessed by fitting Linear Dynamical System (LDS) models to the motor performance, and was compared to the clinical rigidity scores. A cross-validated Least Absolute Shrinkage and Selection Operator (LASSO) regression method was used to determine the brain connectivity network that best predicted clinical rigidity scores.Results: The damping ratio of the LDS models significantly correlated with clinical rigidity scores (p < 10-4). An fMRI connectivity network in subcortical and primary and premotor cortical regions accurately predicted clinical rigidity scores (p < 10-5). Conclusions: A widely distributed cortical/subcortical network is associated with rigidity observed in PD patients, which reinforces the importance of altered functional connectivity in the pathophysiology of PD. PD subjects with higher rigidity scores tend to have less overshoot in their tracking performance, and damping ratio may represent a robust, quantitative marker of the motoric effects of increasing rigidity.
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Multiple sclerosis (MS) is a neurological disorder characterised by inflammatory demyelination and neurodegeneration in the central nervous system (CNS). Until recently, disease modifying treatment was based on agents requiring parenteral delivery, thus limiting long-term compliance. Basic treatments such as beta-interferon provide only moderate efficacy, and although therapies for second-line treatment and highly active MS are more effective, they are associated with potentially severe side effects. Fingolimod (Gilenya®) is the first oral treatment of MS and has recently been approved as single disease-modifying therapy in highly active relapsing-remitting multiple sclerosis (RRMS) for adult patients with high disease activity despite basic treatment (beta-interferon) and for treatment-naïve patients with rapidly evolving severe RRMS. At a scientific meeting that took place in Vienna on November 18th, 2011, experts from 10 Central and Eastern European countries discussed the clinical benefits and potential risks of fingolimod for MS, suggested how the new therapy fits within the current treatment algorithm and provided expert opinion for the selection and management of patients.
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Cognitive impairment in Parkinson’s disease (PD) has received little attention and as such, there are currently very few treatment options available. The aim of the present study was to evaluate the attention impairment in PD patients and to determine whether cognitive training might alleviate any such symptoms. The study, which included a pilot and experimental phase, involved assessing performance in a modified version of the Stroop task during functional magnetic resonance imaging (fMRI). The study was carried out in ten PD patients and ten paired healthy controls, half of the PD patients undergoing 6 months of cognitive training based on Sudoku exercises. The brain training programme improved the cognitive performance of the Parkinson’s patients in attention tasks and it provoked comparable patterns of cortical activation to those observed in controls. Based on these findings, we propose that cognitive training can contribute significantly to save brain resources in PD patients, maybe by readdressing the imbalance caused by the alterations to inhibitory circuitry.
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Time series analysis with delay differential equations (DDEs) reveals nonlinear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson's disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10dB to -30dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of nonlinearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A' under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.
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In recent years there has been a significant increase in the use of electroencephalography (EEG) and magnetoencephalography (MEG) to investigate changes in oscillatory brain activity associated with tinnitus with many conflicting results. Current view of the underlying mechanism of tinnitus is that it results from changes in brain activity in various structures of the brain as a consequence of sensory deprivation. This in turn gives rise to increased spontaneous activity and/or synchrony in the auditory centres but also involves modulation from non-auditory processes from structures of the limbic and paralimbic system. Some of the neural changes associated with tinnitus may be assessed non-invasively in humans with MEG and EEG (M/EEG) in ways which are superior to animal studies and other non-invasive imaging techniques. However, both MEG and EEG have their limitations and research results can be misinterpreted in the absence of sufficient understanding of these limitations. In this article, I intend to provide a brief review of these techniques, describe what the recorded signals reflect in terms of the underlying neural activity, and their strengths and limitations. I also discuss some pertinent methodological issues involved in tinnitus related studies and concludes with suggestions to minimise possible discrepancies between results. The overall message is that while MEG and EEG are extremely useful techniques, the interpretation of results from tinnitus studies requires much caution given the individual variability in oscillatory activity and the limits of these techniques.
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There is increasing evidence supporting dietary and alternative therapies for epilepsy, including the ketogenic diet, modified Atkins diet, and omega-3 fatty acids. Vitamin D is actively under investigation as a potential intervention for epilepsy. Vitamin D is fat soluble steroid which shows promise in animal models of epilepsy. Basic research has shed light on the possible mechanisms by which Vitamin D may reduce seizures, and animal data support the efficacy of Vitamin D in rat and mouse models of epilepsy. Very little clinical data exists to support the treatment of human epilepsy with Vitamin D, but positive findings from preliminary clinical trials warrant larger Phase I and II clinical trials in order to more rigorously determine the potential therapeutic value of Vitamin D as a treatment for human epilepsy.
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Objective: 1) To determine the brain connectivity pattern associated with clinical rigidity scores in Parkinson's disease (PD) and 2) to determine the relation between clinically-assessed rigidity and quantitative metrics of motor performance.Background: Rigidity, the resistance to passive movement, is exacerbated in PD by asking the subject to move the contralateral limb, implying that rigidity involves a distributed brain network. Rigidity mainly affects subjects when they attempt to move; yet the relation between clinical rigidity scores and quantitative aspects of motor performance are unknown.Methods: Ten clinically diagnosed PD patients (off medication) and ten controls were recruited to perform an fMRI squeeze-bulb tracking task that included both visually guided and internally guided features. The direct functional connectivity between anatomically defined regions of interest was assessed with Dynamic Bayesian Networks (DBNs). Tracking performance was assessed by fitting Linear Dynamical System (LDS) models to the motor performance, and was compared to the clinical rigidity scores. A cross-validated Least Absolute Shrinkage and Selection Operator (LASSO) regression method was used to determine the brain connectivity network that best predicted clinical rigidity scores.Results: The damping ratio of the LDS models significantly correlated with clinical rigidity scores (p < 10-4). An fMRI connectivity network in subcortical and primary and premotor cortical regions accurately predicted clinical rigidity scores (p < 10-5). Conclusions: A widely distributed cortical/subcortical network is associated with rigidity observed in PD patients, which reinforces the importance of altered functional connectivity in the pathophysiology of PD. PD subjects with higher rigidity scores tend to have less overshoot in their tracking performance, and damping ratio may represent a robust, quantitative marker of the motoric effects of increasing rigidity.
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Multiple sclerosis (MS) is a neurological disorder characterised by inflammatory demyelination and neurodegeneration in the central nervous system (CNS). Until recently, disease modifying treatment was based on agents requiring parenteral delivery, thus limiting long-term compliance. Basic treatments such as beta-interferon provide only moderate efficacy, and although therapies for second-line treatment and highly active MS are more effective, they are associated with potentially severe side effects. Fingolimod (Gilenya®) is the first oral treatment of MS and has recently been approved as single disease-modifying therapy in highly active relapsing-remitting multiple sclerosis (RRMS) for adult patients with high disease activity despite basic treatment (beta-interferon) and for treatment-naïve patients with rapidly evolving severe RRMS. At a scientific meeting that took place in Vienna on November 18th, 2011, experts from 10 Central and Eastern European countries discussed the clinical benefits and potential risks of fingolimod for MS, suggested how the new therapy fits within the current treatment algorithm and provided expert opinion for the selection and management of patients.
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