Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly
This document summarizes a study that aimed to replicate the results of a previous paper on selectively stimulating neuronal fibers or cell bodies using different asymmetric biphasic current waveforms. The study developed a multi-compartment Hodgkin-Huxley neuronal model in MATLAB and simulated the response of populations of neurons to different stimulus waveforms. The results showed that an anodic-leading asymmetric biphasic waveform selectively activated fibers, while a cathodic-leading waveform preferentially activated cell bodies, consistent with the previous study.
Modeling Stochasticity and Gap Junction Dynamics: Integrate and Fire Modeldharmakarma
In this presentation, we describe a mathematical model for modeling the stochasticity of firing neurons based on a modified integrate and fire model that incorporates gap junction potential.
This master's thesis explores long-latency post-stimulus effects (PStEs) observed in stimulus-triggered averages of electromyography (EMG) recordings following intracortical microstimulation of the primary motor cortex in rhesus monkeys. The author develops a novel statistical method to identify significant long-latency PStEs up to 60ms after stimulation. Facilitatory PStEs were bimodal at 16ms and 46ms, while suppressive PStEs were bimodal at 14ms and 29ms. This work takes initial steps to characterize long-latency PStEs and investigate the neural pathways that may generate them.
Computational neuropharmacology drug designingRevathi Boyina
This document discusses computational neuropharmacology, which uses computational modeling approaches from neuroscience and dynamical systems theory integrated with traditional neuropharmacological methods to study drug effects on the brain and behavior. It describes how computational models are used in neuroscience to simulate neurons, neural circuits, and brain regions. It suggests computational neuropharmacology could help integrate molecular and systems-level descriptions of the nervous system to analyze drug effects on neural activity patterns and behavioral states. This may provide strategies for molecular screening of drugs and searching for target-specific drugs to shift pathological brain dynamics to normal patterns.
Zhou Changsong presents a document discussing the brain as a complex dynamical network system subject to constraints of cost and function. It aims to reconcile irregular neuronal spiking with neural avalanches through a biologically plausible neuronal network model and statistical physics analysis. The key findings are that the model shows coexistence of irregular spiking, oscillations, and critical avalanches through a dynamical mechanism of Hopf bifurcation in the mean field model that explains critical neural avalanches corresponding to irregular spiking in the microscopic neuronal network model. This multiscale variability in brain activity reflects principles of cost-efficient neural representation and dynamics.
Neural oscillations occur throughout the central nervous system and can be measured at different scales: microscopic (single neuron), mesoscopic (local groups of neurons), and macroscopic (between brain regions). At the microscopic level, neurons generate action potentials that form rhythmic spike trains. Groups of synchronized neurons give rise to local field potential oscillations. Interactions between brain areas also produce large-scale oscillations measured by EEG. Different neural oscillations have been linked to cognitive functions like perception and memory.
Neural oscillations occur throughout the central nervous system and can be measured at different scales: microscopic (single neuron), mesoscopic (local groups of neurons), and macroscopic (between brain regions). At the microscopic level, neurons generate action potentials that form rhythmic spike trains. Groups of synchronized neurons give rise to local field potential oscillations. Interactions between brain areas also produce large-scale oscillations measured by EEG. Different neural oscillations are linked to cognitive functions like perception and memory.
This is habilitation dissertation thesis on the importance of EEE and LPF phase for understanding of brain state dynamics of possible quantum coherent macroscopic phase
This document summarizes a study that aimed to replicate the results of a previous paper on selectively stimulating neuronal fibers or cell bodies using different asymmetric biphasic current waveforms. The study developed a multi-compartment Hodgkin-Huxley neuronal model in MATLAB and simulated the response of populations of neurons to different stimulus waveforms. The results showed that an anodic-leading asymmetric biphasic waveform selectively activated fibers, while a cathodic-leading waveform preferentially activated cell bodies, consistent with the previous study.
Modeling Stochasticity and Gap Junction Dynamics: Integrate and Fire Modeldharmakarma
In this presentation, we describe a mathematical model for modeling the stochasticity of firing neurons based on a modified integrate and fire model that incorporates gap junction potential.
This master's thesis explores long-latency post-stimulus effects (PStEs) observed in stimulus-triggered averages of electromyography (EMG) recordings following intracortical microstimulation of the primary motor cortex in rhesus monkeys. The author develops a novel statistical method to identify significant long-latency PStEs up to 60ms after stimulation. Facilitatory PStEs were bimodal at 16ms and 46ms, while suppressive PStEs were bimodal at 14ms and 29ms. This work takes initial steps to characterize long-latency PStEs and investigate the neural pathways that may generate them.
Computational neuropharmacology drug designingRevathi Boyina
This document discusses computational neuropharmacology, which uses computational modeling approaches from neuroscience and dynamical systems theory integrated with traditional neuropharmacological methods to study drug effects on the brain and behavior. It describes how computational models are used in neuroscience to simulate neurons, neural circuits, and brain regions. It suggests computational neuropharmacology could help integrate molecular and systems-level descriptions of the nervous system to analyze drug effects on neural activity patterns and behavioral states. This may provide strategies for molecular screening of drugs and searching for target-specific drugs to shift pathological brain dynamics to normal patterns.
Zhou Changsong presents a document discussing the brain as a complex dynamical network system subject to constraints of cost and function. It aims to reconcile irregular neuronal spiking with neural avalanches through a biologically plausible neuronal network model and statistical physics analysis. The key findings are that the model shows coexistence of irregular spiking, oscillations, and critical avalanches through a dynamical mechanism of Hopf bifurcation in the mean field model that explains critical neural avalanches corresponding to irregular spiking in the microscopic neuronal network model. This multiscale variability in brain activity reflects principles of cost-efficient neural representation and dynamics.
Neural oscillations occur throughout the central nervous system and can be measured at different scales: microscopic (single neuron), mesoscopic (local groups of neurons), and macroscopic (between brain regions). At the microscopic level, neurons generate action potentials that form rhythmic spike trains. Groups of synchronized neurons give rise to local field potential oscillations. Interactions between brain areas also produce large-scale oscillations measured by EEG. Different neural oscillations have been linked to cognitive functions like perception and memory.
Neural oscillations occur throughout the central nervous system and can be measured at different scales: microscopic (single neuron), mesoscopic (local groups of neurons), and macroscopic (between brain regions). At the microscopic level, neurons generate action potentials that form rhythmic spike trains. Groups of synchronized neurons give rise to local field potential oscillations. Interactions between brain areas also produce large-scale oscillations measured by EEG. Different neural oscillations are linked to cognitive functions like perception and memory.
This is habilitation dissertation thesis on the importance of EEE and LPF phase for understanding of brain state dynamics of possible quantum coherent macroscopic phase
Tognoli & Kelso, Society for Neuroscience 2009, diversity of 10Hz rhythms in ...EmmanuelleTognoli
This document discusses the heterogeneity of 10Hz rhythms seen in EEG data and proposes guidelines for their proper measurement and analysis. It presents a tentative dictionary of various 10Hz rhythms distinguished by their spatial distribution, frequency localization, and functional significance. It also puts forth a theory relating EEG spectral peaks to instantaneous brain oscillation patterns, and how the time scale of analysis impacts which patterns appear as peaks. Analyzing 10Hz rhythms at a fine spectral resolution and temporal scale can provide insights into distinct brain processes and functions.
Edgardo J. Arroyo is an Associate Research Scientist at Yale University School of Medicine who has extensive experience researching various aspects of myelin formation, degradation, and regeneration in the central and peripheral nervous systems. His research has focused on elucidating the cellular mechanisms and microanatomy of neuron-glial interactions using techniques such as immunohistochemistry, confocal microscopy, and biochemistry. He has studied topics such as the effects of spinal cord injury, stem cell transplantation, sodium channel expression after nerve damage, and how demyelination affects the molecular organization of nodes of Ranvier.
The document summarizes a study that demonstrated the ability to restore movement in a paralyzed human through intracortically recorded signals from the motor cortex linked to muscle activation. Specifically:
1) Researchers implanted an electrode array in the motor cortex of a participant with quadriplegia to record brain signals. Machine learning algorithms decoded the signals to control electrical stimulation of forearm muscles, allowing the participant to perform isolated finger movements and continuous control of six wrist/hand motions.
2) The participant achieved 70.4% accuracy on average in performing the trained motions. Accuracy for individual motions ranged from 93.1% to 97.3%. The system also allowed the participant to complete functional tasks.
3) Clinical
INHIBITION AND SET-SHIFTING TASKS IN CENTRAL EXECUTIVE FUNCTION OF WORKING ME...sipij
Understanding of neuro-dynamics of a complex higher cognitive process, Working Memory (WM) is
challenging. In WM, information processing occurs through four subsystems: phonological loop, visual
sketch pad, memory buffer and central executive function (CEF). CEF plays a principal role in WM. In this
study, our objective was to understand the neurospatial correlates of CEF during inhibition and set-shifting
processes. Thirty healthy educated subjects were selected. Event-Related Potential (ERP) related to visual
inhibition and set-shifting task was collected using 32 channel EEG system. Activation of those ERPs
components was analyzed using amplitudes of positive and negative peaks. Experiment was controlled
using certain parametric constraints to judge behavior, based on average responses in order to establish
relationship between ERP and local area of brain activation and represented using standardized low
resolution brain electromagnetic tomography. The average score of correct responses was higher for
inhibition task (87.5%) as compared to set-shifting task (59.5%). The peak amplitude of neuronal activity
for inhibition task was lower compared to set-shifting task in fronto-parieto-central regions. Hence this
proposed paradigm and technique can be used to measure inhibition and set-shifting neuronal processes in
understanding pathological central executive functioning in patients with neuro-psychiatric disorders.
Eeg time series data analysis in focal cerebral ischemic rat modelijbesjournal
The mammalian brain exists in a number of attractors. In order to characterize these attractors we have collected the time series data from the EEG recording of rat models. The time series was obtained by recording of the frontoparietal, occipital and temporal regions of the rat brain. Significant changes have
been observed in the dimensionalities of these brain attractors between the normal state, focal ischemic
state and the drug induced state. Thus, these three states were characterized by unique lyapunov exponents,
correlation dimensions and embedding dimensions. The inverse of the lyapunov exponent gave us the long
term coherence of the rat brain and was found to differ for the three states. The autocorrelation function
measured the mean similarity of the EEG signal with itself after a time t. The degree of decay was high indicating that there was maximum correlation in the time series. Thus, the autocorrelation functions clearly indicate the effect of focal cerebral ischemia and drugs induced on the rat brain.
The document discusses electrophysiology techniques used to study the electrical activity of neurons and other excitable cells. It begins by explaining that electrophysiology allows measurement of ionic currents across cell membranes and helps understand how cells and tissues function. Different techniques are then described, including intracellular recordings, patch clamp recordings, and extracellular recordings. The document outlines the historical development of the field and covers topics like resting membrane potentials, action potentials, ion channels, and how neurons encode and transmit information.
This document summarizes the molecular mechanisms underlying neuromuscular junction (NMJ) formation. It discusses how agrin, Lrp4, and Musk signaling pathways induce acetylcholine receptor clustering at the post-synaptic membrane. Wnt signaling is also involved in pre-patterning of acetylcholine receptors before nerve terminal arrival. NMJ formation involves precise interactions between motor neurons, muscle fibers, and glial cells. Defects in these molecular pathways can lead to myasthenia gravis or congenital myasthenia syndrome.
This document describes a model for how early orientation selectivity could emerge in the primary visual cortex based on the timing of incoming spikes from the lateral geniculate nucleus (LGN). The model shows that:
1) A wave of asynchronous spikes is generated in the LGN, with more strongly activated neurons firing earlier.
2) The timing of these incoming LGN spikes, combined with fast feedforward inhibition in visual cortex, allows a cortical pyramidal cell to develop orientation selectivity based on the order of spike latencies.
3) This mechanism provides automatic gain control, allowing the cortical neuron to respond selectively over a wide range of stimulus contrasts. It demonstrates how latency rank order coding could efficiently encode orientation information in the
A Novel Approach to Study the Effects of Anesthesia on Respiratory Signals by...IJECEIAES
General anesthesia plays a crucial role in many surgical procedures, and it therefore has an enormous impact on human health. There are no precise measures for maintaining the correct dose of anesthetic, and there is currently no fully reliable instrument to monitor depth of anesthesia. In this paper, a novel approach has been proposed for detecting the changes in synchronism of brain signals, taken from EEG machine. During the effect of anesthesia, there are certain changes in the EEG signals. Those signals show changes in their synchronism. This phenomenon of synchronism can be utilized to study the effect of anesthesia on respiratory parameters like respiration rate etc, and hence the quantity of anesthesia can be regulated, and if any problem occurs in breathing during the effect of anesthesia on patient, that can also be monitored.
General anesthesia plays a crucial role in many surgical procedures. It is a drug-induced, reversible state characterized by unconsciousness, anti-nociception or analgesia, immobility and amnesia. On rare occasions, however, the patient can remain unconscious longer than intended, or may regain awareness during surgery. There are no precise measures for maintaining the correct dose of anesthetic, and there is currently no fully reliable instrument to monitor depth of anesthesia. Although a number of devices for monitoring brain function or sympathetic output are commercially available, the anesthetist also relies on clinical assessment and experience to judge anesthetic depth. The undesirable consequences of overdose or unintended awareness might in principle be ameliorated by improved control if we could understand better the changes in function that occur during general anesthesia. Coupling functions prescribe the physical rule specifying how the inter-oscillator interactions occur. They determine the possibility of qualitative transitions between the oscillations, e.g. routes into and out of phase synchronization. Their decomposition can describe the functional contribution from each separate subsystem within a single coupling relationship. In this way, coupling functions offer a unique means of describing mechanisms in a unified and mathematically precise way. It is a fast growing field of research, with much recent progress on the theory and especially towards being able to extract and reconstruct the coupling functions between interacting oscillations from data, leading to useful applications in cardio respiratory interactions. In this paper, a novel approach has been proposed for detecting the changes in synchronism of brain signals, taken from EEG machine. During the effect of anesthesia, there are certain changes in the EEG signals. Those signals show changes in their synchronism. This phenomenon of synchronism can be utilized to study the effect of anesthesia on respiratory parameters like respiration rate etc, and hence the quantity of anesthesia can be regulated, and if any problem occurs in breathing during the effect of anesthesia on patient, that can also be monitored.
The document summarizes key concepts about the Hopfield model, an attractor neural network model inspired by physics. It discusses how memory is stored in the symmetric connectivity matrix through Hebbian learning of stored patterns. During recall, the network dynamics relax toward one of the stored memory patterns as an attractor state. This can be modeled deterministically or stochastically. The number of memories an N-neuron network can reliably store is approximately 0.15N.
Meller et al (2012) Single Unit Firing Rates In Macaque SI (In Review)David
A manuscript describing my recent doctoral work characterizing the cortical representation of cutaneous sensory information. Currently in review for publication
The researchers constructed a neural circuit in the computer simulation Swimmy to model the central pattern generator controlling a fish's swimming activity. They identified 8 neurons involved through experiments manipulating each neuron's activity. They concluded the circuit uses a mutually depressing inhibition oscillator mechanism, where two generator neurons (cells 23 and 11) directly inhibit each other through synaptic depression, controlling the firing patterns of the other neurons and generating the swimming rhythm. This allowed the simulated fish Swimmy to move its tail in alternating motions during swimming.
Electromyography Analysis for Person IdentificationCSCJournals
Physiological descriptions of the electromyography signal and other literature say that when we make a motion, the motor neurons of respective muscle get activated and all the innervated motor units in that zone produce motor unit action potential. These motor unit action potentials travel through the muscle fibers with conduction velocity and superimposed signal gets recorded at the electrode site. Here we have taken an analogy from the speech production system model as the excitation signal travels through vocal tract to produce speech; similarly, an impulse train of firing rate frequency goes through the system with impulse response of motor unit action potentials and travels along the muscle fiber of that person. As the vocal tract contains the speaker information, we can also separate the muscle fiber pattern part and motor unit discharge pattern through proper selection of features and its classification to identify the respective person. Cepstral and non uniform filter bank features models the variation in the spectrum of the signals. Vector quantization and Gaussian mixture model are the two techniques of pattern matching have been applied.
A Novel Approach For Detection of Neurological Disorders through Electrical P...IJECEIAES
This paper talks about the phenomenon of recurrence and using this concept it proposes a novel and a very simple and user friendly method to diagnose the neurological disorders by using the EEG signals.The mathematical concept of recurrence forms the basis for the detection of neurological disorders,and the tool used is MATLAB. Using MATLAB, an algorithm is designed which uses EEG signals as the input and uses the synchronizing patterns of EEG signals to determine various neurological disorders through graphs and recurrence plots
Neuron based time optimal controller of horizontal saccadic eye movementsAlireza Ghahari
A neural network model of biophysical neurons in the midbrain for controlling oculomotor
muscles during horizontal human saccades is presented. Neural circuitry that includes
omnipause neuron, premotor excitatory and inhibitory burst neurons, long lead burst neuron,
tonic neuron, interneuron, abducens nucleus and oculomotor nucleus is developed to
investigate saccade dynamics. The final motoneuronal signals drive a time-optimal
controller that stimulates a linear homeomorphic model of the oculomotor plant.
1) Statistical parametric mapping (SPM) allows researchers to perform voxel-wise statistical analysis on brain imaging data from techniques like positron emission tomography (PET), functional magnetic resonance imaging (fMRI), and voxel-based morphometry (VBM).
2) SPM uses the general linear model and random field theory to make statistical inferences about regionally specific responses while accounting for the analysis of many voxels across the brain.
3) Functional MRI detects the blood oxygen level dependent (BOLD) effect to map brain activity by measuring changes in deoxyhemoglobin levels that occur following neural activation.
This document describes an in vitro model using mouse hippocampal brain slices to study the recovery of functional connectivity in neural tissue after damage. The study found that regularly stimulating severed hippocampal slices with low frequency electrical pulses promoted the recovery of synaptic connections between the slices over time. Specifically, they observed fiber volley potentials and excitatory postsynaptic potentials reemerging between 20-40 minutes and 1 hour after initiating stimulation, respectively, suggesting the restoration of neural connectivity. The authors hypothesize that electrical stimulation enhances recovery by maintaining neural membrane function and propose this model could help investigate strategies to promote recovery from brain injury.
The presentation focuses on one of the important aspects of Neurophysiology-- The sesnsorimotor integration for planning and execution of movement.
It highlights on the brain regions associated with motor functions, the crosstalk between association areas, hierarchical levels of movement execution and the diseases related to it.
JAKBOS.COM | Nonton Film Online, Streaming Movie Indonesiajakbos
This document describes a study that evolved two types of neural networks - McCulloch-Pitts networks and spiking Integrate-And-Fire networks - to control autonomous agents performing a memory-dependent counting task. The task requires agents to remain still on food items for an exact number of time steps before consuming them, necessitating the development of a counting mechanism. The study found that spiking networks evolved more successfully and with simpler networks than McCulloch-Pitts networks to solve this task, demonstrating the advantage of spiking dynamics for problems requiring memory. Analysis of the evolved networks revealed their counting mechanisms and how spiking dynamics were utilized for counting.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Tognoli & Kelso, Society for Neuroscience 2009, diversity of 10Hz rhythms in ...EmmanuelleTognoli
This document discusses the heterogeneity of 10Hz rhythms seen in EEG data and proposes guidelines for their proper measurement and analysis. It presents a tentative dictionary of various 10Hz rhythms distinguished by their spatial distribution, frequency localization, and functional significance. It also puts forth a theory relating EEG spectral peaks to instantaneous brain oscillation patterns, and how the time scale of analysis impacts which patterns appear as peaks. Analyzing 10Hz rhythms at a fine spectral resolution and temporal scale can provide insights into distinct brain processes and functions.
Edgardo J. Arroyo is an Associate Research Scientist at Yale University School of Medicine who has extensive experience researching various aspects of myelin formation, degradation, and regeneration in the central and peripheral nervous systems. His research has focused on elucidating the cellular mechanisms and microanatomy of neuron-glial interactions using techniques such as immunohistochemistry, confocal microscopy, and biochemistry. He has studied topics such as the effects of spinal cord injury, stem cell transplantation, sodium channel expression after nerve damage, and how demyelination affects the molecular organization of nodes of Ranvier.
The document summarizes a study that demonstrated the ability to restore movement in a paralyzed human through intracortically recorded signals from the motor cortex linked to muscle activation. Specifically:
1) Researchers implanted an electrode array in the motor cortex of a participant with quadriplegia to record brain signals. Machine learning algorithms decoded the signals to control electrical stimulation of forearm muscles, allowing the participant to perform isolated finger movements and continuous control of six wrist/hand motions.
2) The participant achieved 70.4% accuracy on average in performing the trained motions. Accuracy for individual motions ranged from 93.1% to 97.3%. The system also allowed the participant to complete functional tasks.
3) Clinical
INHIBITION AND SET-SHIFTING TASKS IN CENTRAL EXECUTIVE FUNCTION OF WORKING ME...sipij
Understanding of neuro-dynamics of a complex higher cognitive process, Working Memory (WM) is
challenging. In WM, information processing occurs through four subsystems: phonological loop, visual
sketch pad, memory buffer and central executive function (CEF). CEF plays a principal role in WM. In this
study, our objective was to understand the neurospatial correlates of CEF during inhibition and set-shifting
processes. Thirty healthy educated subjects were selected. Event-Related Potential (ERP) related to visual
inhibition and set-shifting task was collected using 32 channel EEG system. Activation of those ERPs
components was analyzed using amplitudes of positive and negative peaks. Experiment was controlled
using certain parametric constraints to judge behavior, based on average responses in order to establish
relationship between ERP and local area of brain activation and represented using standardized low
resolution brain electromagnetic tomography. The average score of correct responses was higher for
inhibition task (87.5%) as compared to set-shifting task (59.5%). The peak amplitude of neuronal activity
for inhibition task was lower compared to set-shifting task in fronto-parieto-central regions. Hence this
proposed paradigm and technique can be used to measure inhibition and set-shifting neuronal processes in
understanding pathological central executive functioning in patients with neuro-psychiatric disorders.
Eeg time series data analysis in focal cerebral ischemic rat modelijbesjournal
The mammalian brain exists in a number of attractors. In order to characterize these attractors we have collected the time series data from the EEG recording of rat models. The time series was obtained by recording of the frontoparietal, occipital and temporal regions of the rat brain. Significant changes have
been observed in the dimensionalities of these brain attractors between the normal state, focal ischemic
state and the drug induced state. Thus, these three states were characterized by unique lyapunov exponents,
correlation dimensions and embedding dimensions. The inverse of the lyapunov exponent gave us the long
term coherence of the rat brain and was found to differ for the three states. The autocorrelation function
measured the mean similarity of the EEG signal with itself after a time t. The degree of decay was high indicating that there was maximum correlation in the time series. Thus, the autocorrelation functions clearly indicate the effect of focal cerebral ischemia and drugs induced on the rat brain.
The document discusses electrophysiology techniques used to study the electrical activity of neurons and other excitable cells. It begins by explaining that electrophysiology allows measurement of ionic currents across cell membranes and helps understand how cells and tissues function. Different techniques are then described, including intracellular recordings, patch clamp recordings, and extracellular recordings. The document outlines the historical development of the field and covers topics like resting membrane potentials, action potentials, ion channels, and how neurons encode and transmit information.
This document summarizes the molecular mechanisms underlying neuromuscular junction (NMJ) formation. It discusses how agrin, Lrp4, and Musk signaling pathways induce acetylcholine receptor clustering at the post-synaptic membrane. Wnt signaling is also involved in pre-patterning of acetylcholine receptors before nerve terminal arrival. NMJ formation involves precise interactions between motor neurons, muscle fibers, and glial cells. Defects in these molecular pathways can lead to myasthenia gravis or congenital myasthenia syndrome.
This document describes a model for how early orientation selectivity could emerge in the primary visual cortex based on the timing of incoming spikes from the lateral geniculate nucleus (LGN). The model shows that:
1) A wave of asynchronous spikes is generated in the LGN, with more strongly activated neurons firing earlier.
2) The timing of these incoming LGN spikes, combined with fast feedforward inhibition in visual cortex, allows a cortical pyramidal cell to develop orientation selectivity based on the order of spike latencies.
3) This mechanism provides automatic gain control, allowing the cortical neuron to respond selectively over a wide range of stimulus contrasts. It demonstrates how latency rank order coding could efficiently encode orientation information in the
A Novel Approach to Study the Effects of Anesthesia on Respiratory Signals by...IJECEIAES
General anesthesia plays a crucial role in many surgical procedures, and it therefore has an enormous impact on human health. There are no precise measures for maintaining the correct dose of anesthetic, and there is currently no fully reliable instrument to monitor depth of anesthesia. In this paper, a novel approach has been proposed for detecting the changes in synchronism of brain signals, taken from EEG machine. During the effect of anesthesia, there are certain changes in the EEG signals. Those signals show changes in their synchronism. This phenomenon of synchronism can be utilized to study the effect of anesthesia on respiratory parameters like respiration rate etc, and hence the quantity of anesthesia can be regulated, and if any problem occurs in breathing during the effect of anesthesia on patient, that can also be monitored.
General anesthesia plays a crucial role in many surgical procedures. It is a drug-induced, reversible state characterized by unconsciousness, anti-nociception or analgesia, immobility and amnesia. On rare occasions, however, the patient can remain unconscious longer than intended, or may regain awareness during surgery. There are no precise measures for maintaining the correct dose of anesthetic, and there is currently no fully reliable instrument to monitor depth of anesthesia. Although a number of devices for monitoring brain function or sympathetic output are commercially available, the anesthetist also relies on clinical assessment and experience to judge anesthetic depth. The undesirable consequences of overdose or unintended awareness might in principle be ameliorated by improved control if we could understand better the changes in function that occur during general anesthesia. Coupling functions prescribe the physical rule specifying how the inter-oscillator interactions occur. They determine the possibility of qualitative transitions between the oscillations, e.g. routes into and out of phase synchronization. Their decomposition can describe the functional contribution from each separate subsystem within a single coupling relationship. In this way, coupling functions offer a unique means of describing mechanisms in a unified and mathematically precise way. It is a fast growing field of research, with much recent progress on the theory and especially towards being able to extract and reconstruct the coupling functions between interacting oscillations from data, leading to useful applications in cardio respiratory interactions. In this paper, a novel approach has been proposed for detecting the changes in synchronism of brain signals, taken from EEG machine. During the effect of anesthesia, there are certain changes in the EEG signals. Those signals show changes in their synchronism. This phenomenon of synchronism can be utilized to study the effect of anesthesia on respiratory parameters like respiration rate etc, and hence the quantity of anesthesia can be regulated, and if any problem occurs in breathing during the effect of anesthesia on patient, that can also be monitored.
The document summarizes key concepts about the Hopfield model, an attractor neural network model inspired by physics. It discusses how memory is stored in the symmetric connectivity matrix through Hebbian learning of stored patterns. During recall, the network dynamics relax toward one of the stored memory patterns as an attractor state. This can be modeled deterministically or stochastically. The number of memories an N-neuron network can reliably store is approximately 0.15N.
Meller et al (2012) Single Unit Firing Rates In Macaque SI (In Review)David
A manuscript describing my recent doctoral work characterizing the cortical representation of cutaneous sensory information. Currently in review for publication
The researchers constructed a neural circuit in the computer simulation Swimmy to model the central pattern generator controlling a fish's swimming activity. They identified 8 neurons involved through experiments manipulating each neuron's activity. They concluded the circuit uses a mutually depressing inhibition oscillator mechanism, where two generator neurons (cells 23 and 11) directly inhibit each other through synaptic depression, controlling the firing patterns of the other neurons and generating the swimming rhythm. This allowed the simulated fish Swimmy to move its tail in alternating motions during swimming.
Electromyography Analysis for Person IdentificationCSCJournals
Physiological descriptions of the electromyography signal and other literature say that when we make a motion, the motor neurons of respective muscle get activated and all the innervated motor units in that zone produce motor unit action potential. These motor unit action potentials travel through the muscle fibers with conduction velocity and superimposed signal gets recorded at the electrode site. Here we have taken an analogy from the speech production system model as the excitation signal travels through vocal tract to produce speech; similarly, an impulse train of firing rate frequency goes through the system with impulse response of motor unit action potentials and travels along the muscle fiber of that person. As the vocal tract contains the speaker information, we can also separate the muscle fiber pattern part and motor unit discharge pattern through proper selection of features and its classification to identify the respective person. Cepstral and non uniform filter bank features models the variation in the spectrum of the signals. Vector quantization and Gaussian mixture model are the two techniques of pattern matching have been applied.
A Novel Approach For Detection of Neurological Disorders through Electrical P...IJECEIAES
This paper talks about the phenomenon of recurrence and using this concept it proposes a novel and a very simple and user friendly method to diagnose the neurological disorders by using the EEG signals.The mathematical concept of recurrence forms the basis for the detection of neurological disorders,and the tool used is MATLAB. Using MATLAB, an algorithm is designed which uses EEG signals as the input and uses the synchronizing patterns of EEG signals to determine various neurological disorders through graphs and recurrence plots
Neuron based time optimal controller of horizontal saccadic eye movementsAlireza Ghahari
A neural network model of biophysical neurons in the midbrain for controlling oculomotor
muscles during horizontal human saccades is presented. Neural circuitry that includes
omnipause neuron, premotor excitatory and inhibitory burst neurons, long lead burst neuron,
tonic neuron, interneuron, abducens nucleus and oculomotor nucleus is developed to
investigate saccade dynamics. The final motoneuronal signals drive a time-optimal
controller that stimulates a linear homeomorphic model of the oculomotor plant.
1) Statistical parametric mapping (SPM) allows researchers to perform voxel-wise statistical analysis on brain imaging data from techniques like positron emission tomography (PET), functional magnetic resonance imaging (fMRI), and voxel-based morphometry (VBM).
2) SPM uses the general linear model and random field theory to make statistical inferences about regionally specific responses while accounting for the analysis of many voxels across the brain.
3) Functional MRI detects the blood oxygen level dependent (BOLD) effect to map brain activity by measuring changes in deoxyhemoglobin levels that occur following neural activation.
This document describes an in vitro model using mouse hippocampal brain slices to study the recovery of functional connectivity in neural tissue after damage. The study found that regularly stimulating severed hippocampal slices with low frequency electrical pulses promoted the recovery of synaptic connections between the slices over time. Specifically, they observed fiber volley potentials and excitatory postsynaptic potentials reemerging between 20-40 minutes and 1 hour after initiating stimulation, respectively, suggesting the restoration of neural connectivity. The authors hypothesize that electrical stimulation enhances recovery by maintaining neural membrane function and propose this model could help investigate strategies to promote recovery from brain injury.
The presentation focuses on one of the important aspects of Neurophysiology-- The sesnsorimotor integration for planning and execution of movement.
It highlights on the brain regions associated with motor functions, the crosstalk between association areas, hierarchical levels of movement execution and the diseases related to it.
JAKBOS.COM | Nonton Film Online, Streaming Movie Indonesiajakbos
This document describes a study that evolved two types of neural networks - McCulloch-Pitts networks and spiking Integrate-And-Fire networks - to control autonomous agents performing a memory-dependent counting task. The task requires agents to remain still on food items for an exact number of time steps before consuming them, necessitating the development of a counting mechanism. The study found that spiking networks evolved more successfully and with simpler networks than McCulloch-Pitts networks to solve this task, demonstrating the advantage of spiking dynamics for problems requiring memory. Analysis of the evolved networks revealed their counting mechanisms and how spiking dynamics were utilized for counting.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
indian journal of pharmaceutical science 21 pdf.pdfnareshkotra
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
This document discusses the pathogenesis and diagnosis of schizophrenia from the perspective of mitochondrial dysfunction and nonlinear dynamics analysis. It summarizes that:
1) Schizophrenia is thought to result from an interplay between genetic and environmental factors that disrupt brain development, and recent research implicates mitochondrial dysfunction caused by disruption of multiple genes.
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3) Quantum biophysical semeiotics clinical evaluation techniques can detect an inherited real risk of schizophrenia even in asymptomatic individuals by examining microvascular function and complexity of oscillations. This allows for early pre-clinical diagnosis
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
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Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
international research journal of engineering and technology 3 nov.pdfnareshkotra
The International Journal of Mechanical Engineering Research and Technology is an international online journal in English published Quarterly offers a fast publication schedule whilst maintaining a proper peer review and the use of recommended electronic formats for an article delivery expedites the process of All submitted research articles are subjected to an immediate rapid screening by the editors consultation with the Editorial Board or others working in the field as assure that they are likely to be the level of interest and importance of appropriate for the journal.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
ugc list of approved journals 02 nov.pdfnareshkotra
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
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Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
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The International Journal of Mechanical Engineering Research and Technology is an international online journal in English published a Quarterly offers a fast publication schedule with maintaining a rigorous peer review and the use of recommended electronic formats and articles of delivery expedites and the process of All submitted research articles are subjected to the rapid screening by the editors consultation with the Editorial Board or others working in the field of appropriate to ensure that they are much a like to be the level of interest and importance of appropriate for the journal.
Neuro Quantology is an international, interdisciplinary, open-access, peer-reviewed journal that publishes original research and review articles on the interface between quantum physics and neuroscience. The journal focuses on the exploration of the neural mechanisms underlying consciousness, cognition, perception, and behavior from a quantum perspective. Neuro Quantology is published monthly.
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science journal.pdf
1. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
50
Original article1
Controlling Synchronization of Modified
FitzHugh-Nagumo Neurons Under External
Electrical Stimulation
Deepak Mishra, Abhishek Yadav, Sudipta Ray and Prem K. Kalra
Abstract
We report control of synchronization between pair of coupled neurons under
external electrical stimulation. A nonlinear controlling mechanism is proposed for
keeping the coupled system in synchronized state. We studied transitions between
synchrony and asynchrony because of variation in coupling strength. We discuss the
dynamical analysis for the Modified FitzHugh-Nagumo neuron model in detail. This
work focuses the application of control system theory for understanding possible
synchronization phenomena in a pair of biological neuron models.
Key Words: modified FitzHugh-Nagumo, nonlinear controller, synchronization,
coupled neurons
NeuroQuantology 2006; 1: 50-67
Introduction
Determining the dynamical behavior of an ensemble of coupled neurons is an important
problem in computational neuroscience. Commonly used models for the study of individual
neuron which display spiking behavior include (a) Integrate-and-Fire neuron model and its
variants (b) FitzHugh-Nagumo model (c) Hodgkin-Huxley model and (d) Morris-Lecar model
(Gerstner, 2002; FitzHugh, 1969; Nagumo, 1962; Hodgkin, 1952; Koch, 1999; Abbott, 2001).
From the very beginning of the research in the field of computational neuroscience, people
deal with single neuron and its behavior. Present trends of research include investigation of
Corresponding authors: Department of Electrical Engineering, Indian Institute of Technology Kanpur, India,
e-mail: dkmishra@iitk.ac.in, ayadav.iitk@gmail.com, sray@iiita.ac.in, kalra@iitk.ac.in
2. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
51
the behavior of neurons considered in a network and their way to fire synchronously. It is
assumed that the activities in the brain are synchronous and underlying interests for
synchronization of nonlinear oscillators in physical and biological systems range from novel
communication strategies to understand how large and small neural assemblies efficiently
and sensitively achieve desired functional goal (Pinto, 2000).
The dynamics of many neural ensembles such as central pattern generators or
thalamo-cortical circuits poses questions related to the cooperative behavior of neurons.
Each neuron independently may show irregular behavior while ensembles of different
neurons can synchronize in order to process biological information or produce regular,
rhythmic activity (Elson, 1999). How do the dissimilar neurons synchronize? How do they
inhibit noise and intrinsic fluctuations? What are the parameters responsible for such
synchronization and regularization? Answers to these and similar questions may be found
through simulations and experiments that enable one to follow qualitatively the cooperative
dynamics of neurons as intrinsic synaptic parameters are varied (Elson, 1999). However,
these problems did not receive many opportunities for extensive study. Many cells are
linked together by specialized inter-cellular pathways known as gap junction. There are two
types of possible couplings among neurons namely weak coupling and strong coupling,
defined on the basis of the magnitude of coupling strength. In my paper (Mishra, 2004), the
effect of coupling strength on dynamics of coupled neurons is studied.
In recent years, there has been tremendous interest for the study of the
synchronization of chaotic systems. The synchronous and asynchronous behavior of
neurons is one of the important research topics (Jiang, 2004; Thompson, 1999). Application
of nonlinear active controller for maintaining synchronism among neurons is one of the
issues addressed in (Ucar, 2004). The phenomenon of synchronism gives rise to different
dynamical behaviors such as chaotic synchronization etc. In (Mishra, 2004; Mishra, 2005),
nonlinear dynamical analysis on single and coupled modified FitzHugh-Nagumo model under
steady current stimulation is carried out. Also the effect of parameter variation on its
behavior is investigated.
In many papers (Pinto, 2000; Ucar, 2004; Rinzel, 1987; Elson, 1999) dynamical
analysis on various neuron models is carried out under steady current input. The variations
3. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
52
in the external stimulus may bring the system to unstable state from a stable one. However,
biological rhythms, such as, cardiac and circadian rhythms arise from activity of multiple
oscillators with dispersed intrinsic frequencies (Chang, 2000). Variety of complex dynamical
behavior including phase locked limit cycles, quasi-periodicity, intermittency and chaos are
observed in literature (Thompson, 1999) for sinusoidal external fields. Chang et.al. (Chang,
2000), investigated the stability of the output rhythm of these sympathetic oscillators for a
periodic driving force.
In this paper, a nonlinear controller has been designed to synchronize a coupled
modified FitzHugh-Nagumo model. Dynamical characteristics of modified FitzHugh-Nagumo
neuron model under external stimulation are discussed first. With the variation of the
stimulation and the initial condition, the complex behavior is revealed. The response of a
model of two neurons coupled with a gap junction is investigated and the significance of
coupling coefficient is studied next. We propose a nonlinear active controller for the
synchronization of a pair of coupled neurons. Numerical results in support of our findings
are also presented. At last, we conclude our work.
Dynamics of Modified FitzHugh-Nagumo Neuron Model
The modified FitzHugh-Nagumo equations are a set of three coupled differential equations
which exhibit the qualitative behavior observed in neurons, viz quiescence, excitability and
periodicity (Rinzel, 1987). The system can be represented as
)
cos(
)
/
(
)
(
,
)
(
)
(
)
(
3
/
.
.
3
.
t
A
t
F
Where
dy
c
x
y
bw
a
x
w
t
F
y
w
x
x
x
Ω
Ω
=
−
+
−
=
−
+
=
+
+
−
−
=
ε
φ
(1)
The function F(t) represents the external stimulus. The variable x represents the
potential difference between the dendritic spine head and its surrounding medium, w is
recovery variable and y represents the slowly moving current in the dendrite. In this
4. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
53
model, x and w together make up a fast subsystem relative to y . The Jacobian at
equilibrium point (x*, w*, y*) is found to be
−
−
−
−
−
=
d
b
x
J
ε
ε
φ
φ
0
0
1
1
1 2
(2)
If at a neighborhood of a particular value µ0 of the parameter µ, there exists a
pair of eigenvalues of J(µ) of the form α(µ) ± iβ(µ) such that α(µ) = 0, β(µ) ≠ 0, then
no other eigenvalue of J(µ0) will be an integral multiple of iβ(µ0). Thus J(µ0) has a pair
of pure imaginary eigenvalues. This helps in understanding the dynamics of the model at
the equilibrium point.
Dynamics of Single Uncoupled Modified FitzHugh-Nagumo Neuron Model
The dynamical set of equations of a single uncoupled modified FitzHugh-Nagumo system is
given in equations (1). The system parameters used for simulations are a = 0.7, b = 0.8, c =
-0.775, φ = 0.08, ε = 0.0001 and d = 1.0. The calculated equilibrium point for the system at
F(t) = 0 is: (x*, w*, y*) = (-1.0292, -0.4115, 0.2542). Eigenvalues at these points are: (λ1,
λ2, λ3) = (-0.0002, -0.061+j0.283, -0.061+j0.283).
We found that the set of equations are asymptotically stable around the
equilibrium points at F(t) = 0. The variations in the external stimulus bring the system to
unstable state (periodic oscillation). We analyze the response of the model by subjecting it
under the following electrical stimulation
)
cos(
)
/
(
)
( t
A
t
F Ω
Ω
= (3)
Here, A represents the magnitude of the stimulus and Ω refers to the frequency
of given stimulus. The stimulus frequency is varied while keeping the magnitude at a fixed
value of A = 0.71, since at this particular value of A, modified FitzHugh-Nagumo neuron
model gives periodic spiking. Simulation results at different stimulus frequencies are shown
in Figure 1 and Figure 2. Time response for the neuron at Ω = 0.07 is shown in Figure 1(a)
and phase portrait is drawn in Figure 1(b). Similar responses for Ω = 0.127 are shown in
Figure 2. It is observed that with the variation in stimulus frequency, the neuron shows
5. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
54
complex chaotic behavior. Hence the stimulus frequency can be considered as a significant
parameter that affects the behavior of neuron.
Fig.1 Time responses and phase portrait for modified FitzHugh-Nagumo model at stimulus frequency Ω =
0.07 (a) Time response (b) phase portrait.
Fig.2 Time responses and phase portrait for modified FitzHugh-Nagumo model at stimulus frequency Ω =
0.07 (a) Time response (b) phase portrait.
Bifurcation analysis with Ω as the parameter
We have investigated behavioral change in the dynamics of modified FitzHugh-Nagumo
model with respect to Ω by plotting leading Lyapunov exponents, and bifurcation diagram in
Figure 3. It is observed that modified FitzHugh-Nagumo model exhibits stable, periodic and
chaotic behavior for different value of Ω. Thus the frequency of injected stimulus plays
important role and its variation alters the dynamics of model. The Lyapunov exponent is
positive for Ω = 0.127.
6. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
55
Fig.3 Plots of Leading Lyapunov exponent and bifurcation diagram with Ω as bifurcation parameter. (a) Leading
Lyapunov exponent; (b) Bifurcation diagram.
Dynamics of Coupled Modified FitzHugh-Nagumo Neuron Model
We studied the characteristics of an uncoupled modified FitzHugh-Nagumo neuron in the
previous section. In this section, we extend our analysis for coupled neuron models. A
system of two coupled neurons can be expressed as:
j
i
j
i
X
c
X
f
dt
dX
j
i
i
≠
=
+
=
2
,
1
,
)
(
arctan
)
(
(4)
where Xij ∈ Rn (xi or xj) represents state variable of the two oscillating neurons,
function f: Rn →Rn defines the dynamics of a single neuron in the absence of coupling,
and c is the coupling matrix. Complete synchronization occurs when the coupled chaotic
oscillators asymptotically exhibit identical behaviors, i.e., when || X1(t)-X2(t)|| →0 as t →∞,
for any initial condition. The synchronization is dependent on the coupling matrix c. The
dynamical equations for the coupled modified FitzHugh-Nagumo neuron model are given in
equations (5).
The two systems are coupled with different coupling parameters, say gc and g’c,
with rest of the parameter values kept identical.
(a) (b)
7. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
56
)
(
,
)
(
)
2
cos(
)
2
/
(
)
arctan(
'
)
(
3
/
)
(
),
(
)
2
cos(
)
2
/
(
)
arctan(
)
(
3
/
2
2
.
2
2
2
.
2
1
2
2
3
2
2
.
2
1
1
.
1
1
1
.
1
2
1
1
3
1
1
.
1
dy
c
x
y
bw
a
x
w
t
A
x
g
t
F
y
w
x
x
x
dy
c
x
y
bw
a
x
w
t
A
x
g
t
F
y
w
x
x
x
c
c
−
+
−
=
−
+
=
Ω
Ω
+
+
+
+
−
−
=
−
+
−
=
−
+
=
Ω
Ω
+
+
+
+
−
−
=
ε
φ
π
π
ε
φ
π
π
(5)
We have carried out the analysis in the presence of external electrical stimulus of
magnitude A = 0.7 and frequency Ω = 0.127, the values for which the model exhibits
complex chaotic response.
The results for strongly coupled neuron models are shown in Figure 4. The
coupling strengths are: gc = 0.9 and g’c = 0.9. The coupled modified FitzHugh-Nagumo
neurons are synchronous, but the response is chaotic. Time courses for the variables x1 and
x2 are shown in Figure 4(a). The synchronism among the neurons is evident from the plot
between x1 and x2, which is almost a straight line as shown in Figure 4(b).
We analyze a loosely coupled neural system, where the values for coupling
coefficient are kept as gc = 0.009 and g’c = 0.009. The responses of coupled neurons are
asynchronous. The firing of one neuron is out of phase with the other neuron. The time
courses for x1 and x2, when system is loosely coupled, are shown in Figure 5(a). Figure 5(b)
shows the plot between x1 and x2.
The coupling among neurons can be weak and strong, so we have taken effect of
unequal (Weak-Strong) coupling. This is done by keeping one of the neuron in strongly
coupled state and other in weakly coupled state i.e. by keeping gc = 0.9 and g’c = 0.009,.
The response with these values of coupling strengths is shown in Figure 6. The time courses
for variables x1 and x2 are plotted in Figure 6(a). The responses of the variable x1 and x2 are
not in complete synchronism but they are trying to achieve a synchronous state. The same
can be observed from phase portrait of x1 and x2 drawn in Figure 6(b). In this case, neurons
try to maintain synchronization, but they are not in exact synchronism. In order to bring
this coupled system in synchronism, we need an active controller. In the next section, a
control mechanism is explained which keeps the coupled neurons in exact synchronism by
applying a control input to one of the pairs of neurons.
8. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
57
Fig.4 Response of coupled modified FitzHugh-Nagumo neuron models (equations 5) with coupling strengths
gc= 0.9 and g’c= 0.9. (a) The time courses for variables x1 and x2 (b) Phase portrait of the components of
oscillations.
Fig.5 Response of coupled modified FitzHugh-Nagumo neuron models (equations 5) with coupling strengths gc
= 0.9 and g’c = 0.009. (a) The time courses for variables x1 and x2 (b) Phase portrait of the components of
oscillations.
The findings in the analysis of coupling strength effects support the hebbian
hypothesis. According to Donald Hebb, if input from neuron A often contributes to the
firing of neuron B, then the synapse from A to B should be strengthened (Dyan, 2001). Thus
it can be stated that the coupling between the pair of neuron is one of the important
parameter to be studied for exploring the intricacies of the coupled system.
Nonlinear Active Controller for a Pair of Coupled Modified FitzHugh-Nagumo System
It is found in previous section that because of unequal coupling strength we observe
asynchrony among pair of neurons. In this section, we propose a control mechanism which
can bring the two systems into exact synchronism. The schematic diagram for two coupled
neurons is shown in Figure 7. The method is based on the Lyapunov stability theory.
9. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
58
Fig.6 Response for coupled modified FitzHugh-Nagumo neuron model (equations 5) with coupling strengths gc
= 0.009 and g’c = 0.009. (a) The time courses for variable x1 and x2 (b) Phase portrait of the components of
oscillations.
Fig. 7 Schematic diagram of two coupled neurons controlled by an active controller.
Responses for Uncontrolled Pair of Neurons
To begin with, we show the results for two uncontrolled coupled pairs of neurons whose
dynamical equations can be given by the following set of equations.
)
(
,
)
(
)
2
cos(
)
2
/
(
)
arctan(
'
)
(
3
/
)
(
),
(
)
2
cos(
)
2
/
(
)
arctan(
)
(
3
/
2
2
.
2
2
2
.
2
1
2
2
3
2
2
.
2
1
1
.
1
1
1
.
1
2
1
1
3
1
1
.
1
dy
c
x
y
bw
a
x
w
t
A
x
g
t
F
y
w
x
x
x
dy
c
x
y
bw
a
x
w
t
A
x
g
t
F
y
w
x
x
x
c
c
−
+
−
=
−
+
=
Ω
Ω
+
+
+
+
−
−
=
−
+
−
=
−
+
=
Ω
Ω
+
+
+
+
−
−
=
ε
φ
π
π
ε
φ
π
π
(6)
)
(
),
(
)
2
cos(
)
2
/
(
)
arctan(
'
)
(
3
/
)
(
),
(
)
2
cos(
)
2
/
(
)
arctan(
)
(
3
/
4
4
.
4
4
4
.
4
3
4
4
3
4
4
.
4
3
3
.
3
3
3
.
3
4
3
3
3
3
3
.
3
dy
c
x
y
bw
a
x
w
t
A
x
n
t
F
y
w
x
x
x
dy
c
x
y
bw
a
x
w
t
A
x
n
t
F
y
w
x
x
x
c
c
−
+
−
=
−
+
=
Ω
Ω
+
+
+
+
−
−
=
−
+
−
=
−
+
=
Ω
Ω
+
+
+
+
−
−
=
ε
φ
π
π
ε
φ
π
π
(7)
10. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
59
The parameters used for the uncontrolled coupled pair of neurons are same as used for
earlier analysis. The only changes are in the values of coupling coefficients. The coefficient
values used are: gc = g’c = 0.6 and nc = n’c = 0.02. Simulation results for this model are
drawn in Figure 8. The time evolutions of the variables x1 and x3 are shown in Figure 8(a).
The corresponding phase portrait between x1 and x3 is plotted in Figure 8(b). Error curves
for uncontrolled system are plotted in Figure 9. It is evident from these figures that the pairs
of neurons are in asynchronous state.
Fig.8 Responses of pair of coupled neurons (equations 6 and 7) used in the absence of nonlinear active
controller at different coupling strengths gc = 0.6 and nc= 0.02. (a) Time courses for variables x1 and x3 (b)
Phase portrait of the components of oscillations
(b)
(a)
11. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
60
Responses for controlled pair of neurons
In order to bring the synchronism among these neurons we proposed a control law. The
equations given in (7) are replaced by the set of coupled system given by equations (8),
which incorporates the control input. Thus,
Fig. 9 The error curves for the variables in modified FitzHugh-Nagumo system (equations 6 and 7) at coupling
strengths gc = 0.6 and g’c = 0.02. (a) Error signals e1, e2 and e3 (b) Error signals e4, e5 and e6.
(a)
(b)
12. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
61
)
(
)
(
),
(
)
(
)
(
)
2
cos(
)
2
/
(
)
arctan(
)
(
3
/
3
3
.
3
3
3
.
3
4
3
3
3
3
3
.
3
t
dy
c
x
y
t
bw
a
x
w
t
t
A
x
n
t
F
y
w
x
x
x
c
b
a
c
µ
ε
µ
φ
µ
π
π
+
−
+
−
=
+
−
+
=
+
Ω
Ω
+
+
+
+
−
−
=
)
(
)
(
),
(
)
(
)
(
)
2
cos(
)
2
/
(
)
arctan(
'
)
(
3
/
4
4
.
4
4
4
.
4
3
4
4
3
4
4
.
4
t
dy
c
x
y
t
bw
a
x
w
t
t
A
x
n
t
F
y
w
x
x
x
f
e
d
c
µ
ε
µ
φ
µ
π
π
+
−
+
−
=
+
−
+
=
+
Ω
Ω
+
+
+
+
−
−
=
(8)
Errors between the variables are calculated as
2
4
6
2
4
5
2
4
4
1
3
3
1
3
2
1
3
1
,
,
,
,
y
y
e
w
w
e
x
x
e
y
y
e
w
w
e
x
x
e
−
=
−
=
−
=
−
=
−
=
−
=
(9)
Ideally, the rate of change of error must be zero in order to achieve exact synchronism.
Derivative of the error signals are given by
2
.
4
.
6
.
2
.
4
.
5
.
2
.
4
.
4
.
1
.
3
3
.
1
.
3
.
2
.
1
.
.
3
1
.
,
,
,
,
y
y
e
w
w
e
x
x
e
y
y
e
w
w
e
x
x
e
−
=
−
=
−
=
−
=
−
=
−
=
⋅
(10)
The calculated error signal for the system is given by following equations
f
e
d
c
c
c
b
a
c
c
de
e
e
be
e
e
x
g
x
n
x
x
e
e
e
e
de
e
e
be
e
e
x
g
x
n
x
x
e
e
e
e
µ
ε
µ
φ
µ
µ
ε
µ
φ
µ
+
−
−
=
+
−
=
+
−
+
+
−
+
−
=
+
−
−
=
+
−
=
+
−
+
+
−
+
−
=
)
(
,
)
(
)
arctan(
'
)
arctan(
'
3
/
3
/
)
(
,
)
(
)
arctan(
)
arctan(
3
/
3
/
6
4
6
.
5
4
5
.
1
3
3
2
3
4
6
5
4
4
.
2
1
3
.
3
1
.
2
2
4
3
1
3
3
2
3
1
.
1
(11)
We proposed the control law for µa, µb, µc, µd and µf in equations (12). They are
expressed as in equation (12).
1
1
2
4
3
1
3
3
3
2
1
,
)
arctan(
)
arctan(
3
/
3
/
de
be
x
g
x
n
x
x
e
e
Ke
c
b
c
c
a
ε
µ
φ
µ
µ
=
−
=
+
−
−
+
−
+
−
=
6
5
1
3
3
2
3
4
6
5
4
1
,
)
arctan(
'
)
arctan(
'
3
/
3
/
de
be
x
g
x
n
x
x
e
e
e
K
f
e
c
c
d
ε
µ
φ
µ
µ
=
−
=
+
−
−
+
−
+
−
=
(12)
The systems given in (6) and (8) will approach synchronization for any initial conditions by
the control law given by (12). We construct the Lyapunov function
)
)(
2
/
1
( 2
6
2
5
2
4
2
3
2
2
2
1 e
e
e
e
e
e
V +
+
+
+
+
= (13)
13. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
62
The differential of the Lyapunov function along the trajectory of system (11) is
6
.
6
5
.
5
4
.
4
3
.
3
2
.
2
1
.
1 e
e
e
e
e
e
e
e
e
e
e
e
V +
+
+
+
+
= (14)
Substituting above into (14) results in
0
)
( 2
6
2
5
2
4
2
3
2
2
2
1
.
<
−
−
−
−
−
−
= e
e
e
e
e
e
V (15)
which gives asymptotic stability of the system by Lyapunov stability theory. This means that
the coupled systems (6) and (8) are synchronized for any initial conditions.
Results of the controlled pair of coupled modified FitzHugh-Nagumo neurons are
shown in Figure 10. The time evolutions of variables x1 and x3 are shown in Figure 10(a).
Phase portrait for variables x1 and x3 is plotted in Figure 10(b). It is evident that the set of
coupled neurons is now in exact synchronism. The control signal profile is shown in Figure
11. This shows the time evolution of controller activity. The error profile drawn for the
system is shown in Figure 12. The system is operated without any controller till t=250 msec
and it is switched to controlling mode after this time instant. It is observed from the error
profile that, as soon as the controller comes into action, system achieves complete
synchronism.
The description of a nonlinear controller for maintaining synchronism is given. We
compared the results with a nonlinear coupled neuron model in the absence of controlling
mechanism. It is found that the application of active controller for maintaining synchronism
in nonlinear systems is very effective and can be used in real life applications.
14. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
63
Fig. 10 Responses of pair of coupled neurons (equations 6 and 8) with nonlinear active controller. The
responses are generated at different coupling strengths i.e. gc = 0.6 and nc = .02. (a) Time courses for variables
x1 and x3 (b) Phase portrait of the components of oscillations.
(a)
(b)
15. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
64
Fig. 11 Responses of pair of coupled neuron used with nonlinear active controller at different coupling
strengths gc = 0.6 and nc = 0.02. (a) Control signals (equations 11) µa, µb and µc (b) Control signals (equations
11) µd, µe and µf for keeping the system in synchronism.
(b)
(a)
16. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
65
Fig. 12 Responses for pair of coupled neuron used with nonlinear active controller at different coupling
strengths gc = 0.6 and nc = 0.02. (a) Error signals (equations 9) e1, e2 and e3 (b) Error signals (equations 9) e4,
e5 and e6.
(b)
(a)
17. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
66
Conclusion
In this paper, the characteristics of three dimensional modified FitzHugh-Nagumo neuron
model is studied. Dynamical behavior of the modified FitzHugh-Nagumo system under
external electrical stimulation is presented and it is verified that the introduction of periodic
stimulation modifies the dynamics of biological system by presenting the dynamical behavior
for the modified FitzHugh-Nagumo system under external electrical stimulation. The
responses of the system for different stimulus frequencies are shown. The synchronization
of two coupled neurons subjected to external electrical stimulation is studied. The behavior
of coupled neurons with the variation in coupling strength is also studied. A nonlinear active
controller description is provided at the end. It is shown that this controller can maintain
the synchronous behavior among strongly-weakly coupled neurons. The methodology for
determining control law is presented. We compared these results with the response of a
nonlinear coupled neuron model in the absence of controlling mechanism. It is found that
the application of active controller for maintaining synchronism in nonlinear system is very
effective and can be used in real life applications.
18. NeuroQuantology 2006|Issue 1|Page 50-67
Mishra et al. FitzHugh-Nagumo Neurons
ISSN 1303 5150 www.neuroquantology.com
67
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