Ahmet Omurtag

On the simulation of large populations of neurons

The dynamics of large populations of interacting neurons is investigated. Redundancy present in subpopulations of cortical networks is exploited through the introduction of a probabilistic description. A derivation of the kinetic equations for such subpopulations, under general transmembrane dynamics, is presented.The particular case of integrate-and-fire membrane dynamics is considered in detail. A variety of direct simulations of neuronal populations, under varying conditions and with as many as O(105) neurons, is reported. Comparison is made with analogous kinetic equations under the same conditions. Excellent agreement, down to fine detail, is obtained. It is emphasized that no free parameters enter in the comparisons that are made.

A population study of integrate-and-fire-or-burst neurons

Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the burstingbehavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate- and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population model and study a population of such LGN cells. This population model, the first simulation of its kind evolving in a two-dimensional phase space, is used to study the behavior of bursting populations in response to diverse stimulus conditions.

Dynamics of neuronal populations: the equilibrium solution

The behavior of an aggregate of neurons is followed by means of a population equation which describes the probability density of neurons as a function of membrane potential. The model is based on integrate-and-fire membrane dynamics and a synaptic dynamics which produce a fixed potential jump in response to stimulation. In spite of the simplicity of the model, it gives rise to a rich variety of behaviors. Here only the equilibrium problem is considered in detail. Expressions for the population density and firing rate over a range of parameters are obtained and compared with like forms obtained from the diffusion approximation. The introduction of the jump response to stimulation produces a delay term in the equations, which in turn leads to analytical challenges. A variety of asymptotic techniques render the problem solvable. The asymptotic resultsshow excellent agreement with direct numerical simulations.

The Approach of a Neuron Population Firing Rate to a New Equilibrium: An Exact Theoretical Result

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the populations evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.

Hybrid EEG-fNIRS asynchronous brain-computer interface for multiple motor tasks

Non-invasive Brain-Computer Interfaces (BCI) have demonstrated great promise for neuroprosthetics and assistive devices. Here we aim to investigate methods to combine Electroencephalography (EEG) and functional Near-Infrared Spectroscopy (fNIRS) in an asynchronous Sensory Motor rhythm (SMR)-based BCI. We attempted to classify 4 different executed movements, namely, Right-Arm—Left-Arm—Right-Hand—Left-Hand tasks. Previous studies demonstrated the benefit of EEG-fNIRS combination. However, since normally fNIRS hemodynamic response shows a long delay, we investigated new features, involving slope indicators, in order to immediately detect changes in the signals. Moreover, Common Spatial Patterns (CSPs) have been applied to both EEG and fNIRS signals. 15 healthy subjects took part in the experiments and since 25 trials per class were available, CSPs have been regularized with information from the entire population of participants and optimized using genetic algorithms. The different features have been compared in terms of performance and the dynamic accuracy over trials shows that the introduced methods diminish the fNIRS delay in the detection of changes.

EEG interpretation reliability and interpreter confidence: a large single-center study

The intrarater and interrater reliability (I&IR) of EEG interpretation has significant implications for the value of EEG as a diagnostic tool. We measured both the intrarater reliability and the interrater reliability of EEG interpretation based on the interpretation of complete EEGs into standard diagnostic categories and rater confidence in their interpretations and investigated sources of variance in EEG interpretations. During two distinct time intervals, six board-certified clinical neurophysiologists classified 300 EEGs into one or more of seven diagnostic categories and assigned a subjective confidence to their interpretations. Each EEG was read by three readers. Each reader interpreted 150 unique studies, and 50 studies were re-interpreted to generate intrarater data. A generalizability study assessed the contribution of subjects, readers, and the interaction between subjects and readers to interpretation variance. Five of the six readers had a median confidence of ≥99%, and the upper quartile of confidence values was 100% for all six readers. Intrarater Cohens kappa (κc) ranged from 0.33 to 0.73 with an aggregated value of 0.59. Cohens kappa ranged from 0.29 to 0.62 for the 15 reader pairs, with an aggregated Fleiss kappa of 0.44 for interrater agreement. Cohens kappa was not significantly different across rater pairs (chi-square=17.3, df=14, p=0.24). Variance due to subjects (i.e., EEGs) was 65.3%, due to readers was 3.9%, and due to the interaction between readers and subjects was 30.8%. Experienced epileptologists have very high confidence in their EEG interpretations and low to moderate I&IR, a common paradox in clinical medicine. A necessary, but insufficient, condition to improve EEG interpretation accuracy is to increase intrarater and interrater reliability. This goal could be accomplished, for instance, with an automated online application integrated into a continuing medical education module that measures and reports EEG I&IR to individual users.

A population approach to cortical dynamics with an application to orientation tuning

A typical functional region in cortex contains thousands of neurons, therefore direct neuronal simulation of the dynamics of such a region necessarily involves massive computation. A recent efficient alternative formulation is in terms of kinetic equations that describe the collective activity of the whole population of similar neurons. A previous paper has shown that these equations produce results that agree well with detailed direct simulations. Here we illustrate the power of this new technique by applying it to the investigation of the effect of recurrent connections upon the dynamics of orientation tuning in the visual cortex. Our equations express the kinetic counterpart of the hypercolumn model from which Somers et al (Somers D, Nelson S and Sur M 1995 J. Neurosci. 15 5448–65) computed steady-state cortical responses to static stimuli by direct simulation. We confirm their static results. Our method presents the opportunity to simulate the data-intensive dynamical experiments of Ringach et al (Ringach D, Hawken M and Shapley R 1997 Nature 387 281–4), in which 60 randomly oriented stimuli were presented each second for 15 min, to gather adequate statistics of responses to multiple presentations. Without readjustment of the previously defined parameters, our simulations yield substantial agreement with the experimental results. Our calculations suggest that differences in the experimental dynamical responses of cells in different cortical layers originate from differences in their recurrent connections with other cells. Thus our method of efficient simulation furnishes a variety of information that is not available from experiment alone.

Tonic-clonic transitions in computer simulation

Summary: Network simulations can help identify underlying mechanisms of epileptic activity that are hard to isolate in biologic preparations. To be useful, simulations must be sufficiently realistic to make possible biologic and clinical prediction. This requirement for large networks of sufficiently detailed neurons raises challenges both with regard to computational load and the difficulty of obtaining insights with large numbers of free parameters and the large amounts of generated data. The authors have addressed these problems by simulating computationally manageable networks of moderate size consisting of 1,000 to 3,000 neurons with multiple intrinsic and synaptic properties. Experiments on these simulations demonstrated the presence of epileptiform behavior in the form of repetitive high-intensity population events (clonic behavior) or latch-up with near maximal activity (tonic behavior). Intrinsic neuronal excitability is not always a predictor of network epileptiform activity but may paradoxically produce antiepileptic effects, depending on the settings of other parameters. Several simulations revealed the importance of random coincident inputs to shift a network from a low-activation to a high-activation epileptiform state. Finally, a simulated anticonvulsant acting on excitability tended to preferentially decrease tonic activity.

Just-in-time connectivity for large spiking networks

The scale of large neuronal network simulations is memory limited due to the need to store connectivity information: connectivity storage grows as the square of neuron number up to anatomically relevant limits. Using the NEURON simulator as a discrete-event simulator (no integration), we explored the consequences of avoiding the space costs of connectivity through regenerating connectivity parameters when needed: just in time after a presynaptic cell fires. We explored various strategies for automated generation of one or more of the basic static connectivity parameters: delays, postsynaptic cell identities, and weights, as well as run-time connectivity state: the event queue. Comparison of the JitCon implementation to NEURONs standard NetCon connectivity method showed substantial space savings, with associated run-time penalty. Although JitCon saved space by eliminating connectivity parameters, larger simulations were still memory limited due to growth of the synaptic event queue. We therefore designed a JitEvent algorithm that added items to the queue only when required: instead of alerting multiple postsynaptic cells, a spiking presynaptic cell posted a callback event at the shortest synaptic delay time. At the time of the callback, this same presynaptic cell directly notified the first postsynaptic cell and generated another self-callback for the next delay time. The JitEvent implementation yielded substantial additional time and space savings. We conclude that just-in-time strategies are necessary for very large network simulations but that a variety of alternative strategies should be considered whose optimality will depend on the characteristics of the simulation to be run.

Dynamics of neural populations: Stability and synchrony

A population formulation of neuronal activity is employed to s tudy an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion for the critical gain at which time asynchronous behavior becomes unstable. At instability the dynamics can undergo a supercritical Hopf bifurcation and the population passes to a synchronous state. Under different conditions it can pass to synchrony through a subcritical Hopf bifurcation. And at high gain a network can reach a runaway state, in finite time, after which the network no longer supports bounded solutions. The introduction of time delayed feedback leads to a rich range of phenomena. For example, for a given external input, increasing gain produces transition from asynchrony, to synchrony, to asynchrony and finally can lead to divergence. Time delay is also shown to strongly mollify the amplitude of synchronous oscillations. Perhaps, of general importance, is the result that synchronous behavior can exist only for a narrow range of time delays, which range is an order of magnitude smaller than periods of oscillation.