Research in our group focuses on the following areas:

(1) Multiscale analysis and modeling of the brain electrophysiology. The human electroencephalogram (EEG) is generated by the collective activities of ~100,000,000,000 cortical neurons. The spatial organization of neocortex extends from single neurons to submillimeter diameter cortical columns and neuronal clusters to large-scale networks organized over multiple brain regions. Similarly, the electrical activity spans a remarkable range of temporal scales from millisecond duration action potentials to ultra-slow local field potential oscillations lasting over a hundred seconds. Developing new efficient computational tools now allows simulating millions of neurons with realistic firing patterns. In this project, using combination of computational techniques, experimental recordings and data analysis we will establish a relationship between individual neuronal firing patterns and global EEG activity in normal awake and epileptic brain.

(2) Information processing in the olfactory system. Problems solved by the olfactory system are generally similar to those solved by other sensory systems such as vision or audition. Our research on olfaction is targeted to reveal the general principles and the neural circuitry involved in the encoding of sensory information in the brain. In collaboration with experimentalists, we construct detailed biophysical models of insect and vertebrate olfactory systems to study odor encoding, processing and learning. This study offers the promise of insight into a successful and perhaps optimal biological algorithm for processing complex information.

(3) "Electronic nose". Recently we started a new project targeted to develop new computational algorithms for electronic devices that process outputs from arrays of chemical sensors in the same way the olfactory system processes an output from olfactory sensory neurons. This highly non-linear processing can improve odor separation, reduce noise and increase sensitivity. Using reduced neuronal models, we build computationally efficient network models for chemical and biological agent detection that replicates the signal-processing mechanisms of the olfactory system found in insects.

(4) Mechanisms of focal and generalized spike-wave seizures. Our research on epilepsy is targeted to discover the cellular and network mechanisms underlying the transformation of normal brain oscillations to electrographic seizures. The long-term goal of this research is to design approaches that could be further developed to treat humans with trauma-induced epilepsy in clinical settings.

(5) Mechanisms and functional role of sleep oscillations. The goal of this research is to understand intrinsic and circuit mechanisms underlying sleep oscillations (such as slow-wave sleep rhythm) in the thalamocortical system. Sleep is essential for health and well-being. Sleep disturbances, increasingly caused by lifestyle and environmental factors, can be linked to a variety of mental disorders. Recent studies have reported that slow wave sleep may be essential for memory formation and consolidation. Revealing yet unknown mechanisms mediating this rhythm will aid our understanding of the origins of brain rhythms in both normal function and pathology.

To address these questions, we use broad spectrum of approaches ranging from detailed conductance based models developed from experimental data to different classes of simplified models that allow large-scale analysis with realistic network structure. In particularly, we develop a novel approach to studying large-scale networks of biological neurons based on difference equations (maps) to simulate neuron dynamics. The new models are able to replicate precisely spiking activity observed in different types of thalamic and cortical cells and interneurons and are designed to study a wide range of diverse processes (such as information processing) in large-scale anatomically realistic biological networks.

Some of our active projects

Oscillations in large-scale neural networks

M. Bazhenov and N. Rulkov

We develop a new computationally efficient approach to analyze large-scale networks of biological neurons. This approach is based on using difference equations (map) for simulation of neuron dynamics. The nonlinear maps produce very rich spectrum of dynamical behaviors while remaining simple and low-dimensional systems and, therefore, can be very computationally efficient. Conventional approach based on simulating ordinary differential equations (such as Hodgkin-Huxley type models) quickly reaches its limit when the number of elements in the network increases. It makes this approach impractical for studying those problems when the analyzed phenomena originate from a collective behavior of large neural ensembles. A map-based model of a neuron that realistically replicates the dynamical mechanisms underlying both its spiking and bursting activity and correctly captures the input-output processes opens new opportunities in the studies of large-scale network functionality. This approach will provide the basis for network simulations of different brain systems, including hundreds of thousands neurons, at the realistic time scales using conventional workstations.

Example of C++ code to simulate spiral wave dynamics in 2D network of regular spiking neurons and fast spiking interneurons:
C++ code to simulate 2D network - network2D.cpp.txt
Input file for network simulations - input2D.txt
To compile the code using GCC compiler: gcc network2D.cpp -lm -O2 -o network2D
To run simulations: network2D input2D.txt > tmp

Matlab code to simulate a network of 90 map-based RS neurons connected along a chain using excitatory connections is available here. It replicates fig 6 in N.Rulkov, I.Timofeev and M.Bazhenov. Oscillations in large-scale cortical networks: map-based model. Journal of Computational Neuroscience 17, 203�223, 2004
Main code: NetworkSim2.m
Function to calculate synaptic currents: Isynaptic.m
Function to simulate a regular spiking neuron (RS): RS2.m
Function to simulate a Fast spiking neuron (FS): FS2.m

LabView applet (MS Windows version) to simulate in real time response to DC pulse of a RS type map-based neuron is available here. Please install and run as Windows application: 2D-Map-RS

Click here to see movie of spiral wave dynamics. These neuron and network models are discussed in N.Rulkov, I.Timofeev and M.Bazhenov. Oscillations in large-scale cortical networks: map-based model. Journal of Computational Neuroscience 17, 203�223, 2004

Slow state transitions of sustained neural oscillations by activity-dependent modulation of intrinsic excitability

F. Frohlich and M. Bazhenov

Sustained oscillatory activity is generally mediated by neurons which are either in tonic firing or bursting mode depending on their level of excitability. Little is known, however, about the dynamics and mechanisms of transitions between tonic firing and bursting in cortical networks. Here, we use a computational model of a neocortical circuit with extracellular potassium dynamics to show that activity-dependent modulation of intrinsic excitability can lead to sustained oscillations with slow transitions between two distinct firing modes - fast run (tonic spiking or fast bursting with spike doublets or triplets) and slow bursting. These transitions are caused by a bistability with hysteresis between tonic firing and slow bursting in individual pyramidal cells for elevated extracellular potassium concentration. Balanced excitation and inhibition stabilizes a network of pyramidal cells and inhibitory interneurons in the bistable region and causes sustained periodic alternations between fast run and slow bursting. Neocortical paroxysmal activity in anesthetized cats during spike-wave seizures exhibit qualitatively similar slow transitions between two distinct oscillatory firing regimes. We therefore predict that extracellular potassium dynamics causes alternating episodes of fast and slow oscillatory states in both normal and epileptic neocortical networks.

Spatio-temporal dynamics of the locust antennal lobe and odor representation

S. Haney and M. Bazhenov

Odor simulation evokes complex spatio-temporal patterns of activity in the projection neurons (PNs) of the locust antennal lobe (AL). These patterns consisting of fast (20-30Hz) oscillations and slower temporal structure of alternating de- and hyperpolarizing epochs are the evidence of the complex intrinsic dynamics induced by odor; this dynamics can optimize odor representation and thus contribute to odor discrimination. In zebrafish the slow temporal patterning in mitral cells appears to play a major role in the decorrelation of odor representations [Science: 5505:835, 2001]. Here we tested with computational model the hypothesis that locust AL intrinsic dynamics can serve similar task. Upon odor presentation, the fast (about 20 Hz) field potential oscillations arised and were maintaining by interaction between excitatory PNs and inhibitory local neurons (LNs); stimulus-specific slow temporal structure was induced by slow inhibitory synapses between neurons. When similar odors were presented, the response patterns of PNs were strongly overlapped at first. During following few hundred of msec, the overlap between similar odor representations was reduced and the initial clusters of activated PNs disappeared; cross-correlation between PN activity patterns was reduced by 30-50%. Correlation increased again following brief activity increase after stimuli termination. Thus our model predicts that Al intrinsic dynamics depending on interaction between PNs and LNs can amplify small differences between a like odors thus improving odor discriminability.

Localized connectivity changes alter pan-network activity patterns: implications to early post-traumatic epilepsy and neurogeneration

E. Ohanyon and M. Bazhenov

This study examines the effect of changes in network structure on its activity. Previously, using recurrent connectionist models, we have shown that localized changes in network connectivity are sufficient to cause fundamental changes in network dynamics and may account for early post-traumatic epilepsy. In order to test the universality of this principle, we examined whether these effects would hold in more detailed models. To this end, we used neural network models composed of up to 10,000 map-based units individually capable of exhibiting spiking behavior. Simulations in these spiking models showed that changes in network structure following localized removal of cells were sufficient to account for the initiation and propagation of hyper-excited oscillatory activity. In effect, boundary units whose activity would otherwise be dampened by their interactions with neighbors were now more likely to fire. The network level propensity for hyper-excitability showed sensitivity to both the size of the lesion as well as the spatio-temporal properties of initial activity and noise. The models suggest that changes in network structure may account for early post-traumatic epilepsy even in the absence of changes to intrinsic cellular properties. The massive changes in oscillations and propagation patterns seen following the removal of cells also highlight the importance of examining the contribution of chronic changes in the network structure to brain dynamics following neurodegeneration in Alzheimer's, Parkinson's and Transmissible Spongiform Encephalopathies.

Odor identity and concentration coding in the model of the locust olfactory system  

C. Assisi and M. Bazhenov    

The first olfactory relay in the locust, the antennal lobe, consists of a tightly interconnected network of excitatory projection neurons (PNs) and inhibitory interneurons (LNs). Stimulation of the antennal lobe by presenting an odor to the antenna leads to field potential oscillations resulting from a distributed, coherent population response. Both the identity and the concentration of odors can be encoded in the spatiotemporal firing patterns of antennal lobe activity. By what mechanism, then, are these spatiotemporal patterns organized, and how can the identity and the intensity of odors be disambiguated? Here, we use a realistic computational model of the locust olfactory system to study its response properties for different odor concentrations. The input to the antennal lobe (an odor) was simulated as firing from olfactory receptor neurons to a set of PNs. Individual PNs were assumed to be maximally sensitive to a particular odor with a distribution of lesser sensitivity for other odors. An increase in concentration was simulated by recruiting additional PNs while keeping their input below that of the preferred PNs. We demonstrate that the simulated antennal lobe network preserves the salient properties seen in the experiment, including odor and concentration based clustering, while retaining the LFP oscillations at approximately 20 Hz. A dimension reduction analysis revealed that PN responses for different odor concentrations are grouped into clusters with different clusters corresponding to different odors. When odor representations at each time point were considered as instantaneous vectors of activity across a whole PN population, the activity due to different odors and concentrations could be easily separated. The PN activities for different odors diverged within a few cycles of the LFP oscillation while the activity corresponding to different concentrations of a particular odor evolved along neighboring trajectories.