A5003658702- Neural dynamics and brain function
- Nonlinear Dynamics and Pattern Formation
- stochastic dynamics and bifurcation
- Neuroscience and Neuropharmacology Research
- Photoreceptor and optogenetics research
- Mathematical and Theoretical Epidemiology and Ecology Models
- Neurological disorders and treatments
- Neuroscience and Neural Engineering
- Ion channel regulation and function
- Neural Networks and Applications
- Differential Equations and Numerical Methods
- Advanced Mathematical Modeling in Engineering
- Quantum chaos and dynamical systems
- Nonlinear Differential Equations Analysis
- Nonlinear Waves and Solitons
- Nonlinear Partial Differential Equations
- Sleep and Wakefulness Research
- Advanced Mathematical Physics Problems
- Functional Brain Connectivity Studies
- Circadian rhythm and melatonin
- Connexins and lens biology
- Stability and Controllability of Differential Equations
- Biochemical Analysis and Sensing Techniques
- Gene Regulatory Network Analysis
- Neuroscience of respiration and sleep
The Ohio State University
2014-2023
National Institute of Diabetes and Digestive and Kidney Diseases
1998
National Institutes of Health
1992-1998
Brandeis University
1998
University of Pittsburgh
1998
New Jersey Institute of Technology
1996
Boston University
1996
University of Rochester
1991
Michigan State University
1986-1988
Leiden University
1986
Based on recent experimental data, we have developed a conductance-based computational network model of the subthalamic nucleus and external segment globus pallidus in indirect pathway basal ganglia. Computer simulations analysis this illuminate roles coupling architecture network, associated synaptic conductances, modulating activity patterns displayed by network. Depending relationships these parameters, can support three general classes sustained firing patterns: clustering, propagating...
We study image segmentation on the basis of locally excitatory, globally inhibitory oscillator networks (LEGION), whereby phases oscillators encode binding pixels. introduce a lateral potential for each so that only with strong connections from their neighborhood can develop high potentials. Based concept potential, solution to remove noisy regions in an is proposed LEGION, it suppresses corresponding but without affecting those major regions. show resulting network separates into several...
A novel class of locally excitatory, globally inhibitory oscillator networks (LEGION) is proposed and investigated. The model each corresponds to a standard relaxation with two time scales. In the network, an jumping up its active phase rapidly recruits oscillators stimulated by same pattern, while preventing other from up. Computer simulations demonstrate that network achieves both synchronization within blocks are connected regions desynchronization between different blocks. This lays...
A class of differential equations that model electrical activity in pancreatic beta cells is considered. It demonstrated these must give rise to both bursting solutions and, for different values the parameters, continuous spiking. We also consider how number spikes per burst changes as parameters are varied. This transition may be continuous, which case period solution increases significantly and then decreases. Hence, small perturbations cause macroscopic solution. chaotic dynamics due...
Consideration is given to a system of reaction-diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical-biochemical systems. These are the FitzHugh–Nagumo type contain three parameters. For certain ranges parameters exhibits two stable singular points. A perturbation construction illustrate that there may exist both pulse transition traveling waves. complete, rigorous, description these waves set how velocities vary...
The therapeutic effectiveness of deep brain stimulation (DBS) the subthalamic nucleus (STN) may arise through its effects on inhibitory basal ganglia outputs, including those from internal segment globus pallidus (GPi). Changes in GPi activity will impact thalamic targets, representing a possible pathway for STN-DBS to modulate ganglia-thalamocortical processing. To study effect activity, we examined thalamocortical (TC) relay cell responses an excitatory input train under variety signals,...
Astrocytes are extensively coupled through gap junctions into a syncytium. However, the basic role of this major brain network remains largely unknown. Using electrophysiological and computational modeling methods, we demonstrate that membrane potential ( V M ) an individual astrocyte in hippocampal syncytium, but not single, freshly isolated cell preparation, can be well‐maintained at quasi‐physiological levels when recorded with reduced or K + free pipette solutions alter equilibrium to...
Inhibition in oscillatory networks of neurons can have apparently paradoxical effects, sometimes creating dispersion phases, fostering synchrony the network. We analyze a pair biophysically modeled and show how rates onset decay inhibition interact with timescales intrinsic oscillators to determine when stable is possible. that there are two different regimes parameter space which combinations time constants other parameters regulate whether synchronous state stable. also discuss...
The propagation of activity is studied in a spatially structured network model γ-aminobutyric acid–containing (GABAergic) neurons exhibiting postinhibitory rebound. In contrast to excitatory-coupled networks, recruitment spreads very slowly because cells fire only after the postsynaptic conductance decays, and with two possible modes. If connection strength decreases monotonically distance (on-center), then occurs discontinuous manner. self- nearby connections are absent (off-center), can...
The Hodgkin–Huxley equations model the propagation of electrical signals in a nerve axon. Here we give examples mathematics inspired by this model. presentation is organized chronologically, beginning with brief introduction to underlying biology and description Mathematical issues related both single cell dynamics large neuronal networks are discussed, along applications neurological disease.
A network of excitatory neurons within the pre-Bötzinger complex ({\mbox{pre-BötC}}) mammalian brain stem has been found experimentally to generate robust, synchronized population bursts activity. An calibrated model for {\mbox{pre-BötC}} cells yields typical square-wave bursting behavior in absence coupling, over a certain parameter range, with quiescence or tonic spiking outside this range. Previous simulations showed that introduction synaptic coupling extends range significantly and...
Abstract Syncytial isopotentiality, resulting from a strong electrical coupling, emerges as physiological mechanism that coordinates individual astrocytes to function highly efficient system in brain homeostasis. However, whether syncytial isopotentiality occurs selectively certain regions or is universal astrocytic networks remains unknown. Here, we have explored the correlation of with different astrocyte subtypes various regions. Using nonphysiological K + ‐free/Na electrode solution...
Neuronal persistent activity has been primarily assessed in terms of electrical mechanisms, without attention to the complex array molecular events that also control cell excitability. We developed a multiscale neocortical model proceeding from network level assess contributions calcium (Ca2+) regulation hyperpolarization-activated cyclic nucleotide-gated (HCN) channels providing additional and complementary support continuing activation network. The contained 776 compartmental neurons...
We develop geometric dynamical systems methods to determine how various components contribute a neuronal network's emergent population behaviors. The results clarify the multiple roles inhibition can play in producing different rhythms. Which rhythms arise depends on interacts with intrinsic properties of neurons; nature these interactions underlying architecture network. Our analysis demonstrates that fast inhibitory coupling may lead synchronized if either cells within network or is...
Thalamic reticularis, thalamocortical, and cortical cells participate in the 7–14-hz spindling rhythm of early sleep slower delta rhythms deeper sleep, with different firing patterns. In this case study, showing interactions intrinsic synaptic properties, a change conductance one kind cell effectively rewires thalamocortical circuit, leading to transition from rhythm. The two make uses fast (GABA A ) slow B inhibition generated by thalamic reticularis cells.
Subthalamic nucleus neurons exhibit reverse spike-frequency adaptation. This occurs only at firing rates of 20-50 spikes/s and higher. Over this same frequency range, there is an increase in the steady-state frequency-intensity (F-I) curve's slope (the secondary range). Specific blockade high-voltage activated calcium currents reduced F-I curve Blockade calcium-dependent potassium current enhanced range firing. A simple model that exhibited these properties used spike-triggered conductances...