Comparison of brain-computer interface decoding algorithms in open-loop and closed-loop control.
Authors: Koyama, S. - Chase, S. M. - Whitford, A. S. - Velliste, M. - Schwartz, A. B. - Kass, R. E.
Journal: J Comput Neurosci
Neuroprosthetic devices such as a computer cursor can be controlled by the activity of cortical neurons when an appropriate algorithm is used to decode motor intention. Algorithms which have been proposed for this purpose range from the simple population vector algorithm (PVA) and optimal linear estimator (OLE) to various versions of Bayesian decoders. Although Bayesian decoders typically provide the most accurate off-line reconstructions, it is not known which model assumptions in these algorithms are critical for improving decoding performance. Furthermore, it is not necessarily true that improvements (or deficits) in off-line reconstruction will translate into improvements (or deficits) in on-line control, as the subject might compensate for the specifics of the decoder in use at the time. Here we show that by comparing the performance of nine decoders, assumptions about uniformly distributed preferred directions and the way the cursor trajectories are smoothed have the most impact on decoder performance in off-line reconstruction, while assumptions about tuning curve linearity and spike count variance play relatively minor roles. In on-line control, subjects compensate for directional biases caused by non-uniformly distributed preferred directions, leaving cursor smoothing differences as the largest single algorithmic difference driving decoder performance.
post to: CiteULike
Estimating short-run and long-run interaction mechanisms in interictal state.
Authors: Ozkaya, A. - Korurek, M.
Journal: J Comput Neurosci
We address the issue of analyzing electroencephalogram (EEG) from seizure patients in order to test, model and determine the statistical properties that distinguish between EEG states (interictal, pre-ictal, ictal) by introducing a new class of time series analysis methods. In the present study: firstly, we employ statistical methods to determine the non-stationary behavior of focal interictal epileptiform series within very short time intervals; secondly, for such intervals that are deemed non-stationary we suggest the concept of Autoregressive Integrated Moving Average (ARIMA) process modelling, well known in time series analysis. We finally address the queries of causal relationships between epileptic states and between brain areas during epileptiform activity. We estimate the interaction between different EEG series (channels) in short time intervals by performing Granger-causality analysis and also estimate such interaction in long time intervals by employing Cointegration analysis, both analysis methods are well-known in econometrics. Here we find: first, that the causal relationship between neuronal assemblies can be identified according to the duration and the direction of their possible mutual influences; second, that although the estimated bidirectional causality in short time intervals yields that the neuronal ensembles positively affect each other, in long time intervals neither of them is affected (increasing amplitudes) from this relationship. Moreover, Cointegration analysis of the EEG series enables us to identify whether there is a causal link from the interictal state to ictal state.
post to: CiteULike
A diffusion-activation model of CaMKII translocation waves in dendrites.
Authors: Earnshaw, B. A. - Bressloff, P. C.
Journal: J Comput Neurosci
Ca2+-calmodulin-dependent protein kinase II (CaMKII) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed that stimulating dendrites locally with a single glutamate/glycine puff induces a local translocation of CaMKII into spines that subsequently spreads in a wave-like manner towards the distal dendritic arbor. Here we present a mathematical model of the diffusion, activation and translocation of dendritic CaMKII. We show how the nonlinear dynamics of CaMKII diffusion-activation generates a propagating translocation wave, provided that the rate of activation is sufficiently fast. We also derive an explicit formula for the wave speed as a function of physiological parameters such as the diffusivity of CaMKII and the density of spines. Our model provides a quantitative framework for understanding the spread of CaMKII translocation and its possible role in heterosynaptic plasticity.
post to: CiteULike
Models of cortical networks with long-range patchy projections.
Authors: Voges, N. - Guijarro, C. - Aertsen, A. - Rotter, S.
Journal: J Comput Neurosci
The cortex exhibits an intricate vertical and horizontal architecture, the latter often featuring spatially clustered projection patterns, so-called patches. Many network studies of cortical dynamics ignore such spatial structures and assume purely random wiring. Here, we focus on non-random network structures provided by long-range horizontal (patchy) connections that remain inside the gray matter. We investigate how the spatial arrangement of patchy projections influences global network topology and predict its impact on the activity dynamics of the network. Since neuroanatomical data on horizontal projections is rather sparse, we suggest and compare four candidate scenarios of how patchy connections may be established. To identify a set of characteristic network properties that enables us to pin down the differences between the resulting network models, we employ the framework of stochastic graph theory. We find that patchy projections provide an exceptionally efficient way of wiring, as the resulting networks tend to exhibit small-world properties with significantly reduced wiring costs. Furthermore, the eigenvalue spectra, as well as the structure of common in- and output of the networks suggest that different spatial connectivity patterns support distinct types of activity propagation.
post to: CiteULike
Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression.
Authors: Kilpatrick, Z. P. - Bressloff, P. C.
Journal: J Comput Neurosci
We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave.
post to: CiteULike
LFP spectral peaks in V1 cortex: network resonance and cortico-cortical feedback.
Authors: Kang, K. - Shelley, M. - Henrie, J. A. - Shapley, R.
Journal: J Comput Neurosci
This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the gamma-band (25-90 Hz) of the LFP power spectrum in macaque V1. The height and location of the gamma-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model's resonance frequency (ResF) was in the gamma-band and varied up or down in frequency depending on cortical feedback. The model's ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for gamma-band peaks in the LFP power spectrum of the primary visual cortex.
post to: CiteULike
CuBIC: cumulant based inference of higher-order correlations in massively parallel spike trains.
Authors: Staude, B. - Rotter, S. - Grun, S.
Journal: J Comput Neurosci
Recent developments in electrophysiological and optical recording techniques enable the simultaneous observation of large numbers of neurons. A meaningful interpretation of the resulting multivariate data, however, presents a serious challenge. In particular, the estimation of higher-order correlations that characterize the cooperative dynamics of groups of neurons is impeded by the combinatorial explosion of the parameter space. The resulting requirements with respect to sample size and recording time has rendered the detection of coordinated neuronal groups exceedingly difficult. Here we describe a novel approach to infer higher-order correlations in massively parallel spike trains that is less susceptible to these problems. Based on the superimposed activity of all recorded neurons, the cumulant-based inference of higher-order correlations (CuBIC) presented here exploits the fact that the absence of higher-order correlations imposes also strong constraints on correlations of lower order. Thus, estimates of only few lower-order cumulants suffice to infer higher-order correlations in the population. As a consequence, CuBIC is much better compatible with the constraints of in vivo recordings than previous approaches, which is shown by a systematic analysis of its parameter dependence.
post to: CiteULike
A biologically plausible model of time-scale invariant interval timing.
Authors: Almeida, R. - Ledberg, A.
Journal: J Comput Neurosci
The temporal durations between events often exert a strong influence over behavior. The details of this influence have been extensively characterized in behavioral experiments in different animal species. A remarkable feature of the data collected in these experiments is that they are often time-scale invariant. This means that response measurements obtained under intervals of different durations coincide when plotted as functions of relative time. Here we describe a biologically plausible model of an interval timing device and show that it is consistent with time-scale invariant behavior over a substantial range of interval durations. The model consists of a set of bistable units that switch from one state to the other at random times. We first use an abstract formulation of the model to derive exact expressions for some key quantities and to demonstrate time-scale invariance for any range of interval durations. We then show how the model could be implemented in the nervous system through a generic and biologically plausible mechanism. In particular, we show that any system that can display noise-driven transitions from one stable state to another can be used to implement the timing device. Our work demonstrates that a biologically plausible model can qualitatively account for a large body of data and thus provides a link between the biology and behavior of interval timing.
post to: CiteULike
Crossover inhibition in the retina: circuitry that compensates for nonlinear rectifying synaptic transmission.
Authors: Molnar, A. - Hsueh, H. A. - Roska, B. - Werblin, F. S.
Journal: J Comput Neurosci
In the mammalian retina, complementary ON and OFF visual streams are formed at the bipolar cell dendrites, then carried to amacrine and ganglion cells via nonlinear excitatory synapses from bipolar cells. Bipolar, amacrine and ganglion cells also receive a nonlinear inhibitory input from amacrine cells. The most common form of such inhibition crosses over from the opposite visual stream: Amacrine cells carry ON inhibition to the OFF cells and carry OFF inhibition to the ON cells ("crossover inhibition"). Although these synapses are predominantly nonlinear, linear signal processing is required for computing many properties of the visual world such as average intensity across a receptive field. Linear signaling is also necessary for maintaining the distinction between brightness and contrast. It has long been known that a subset of retinal outputs provide exactly this sort of linear representation of the world; we show here that rectifying (nonlinear) synaptic currents, when combined thorough crossover inhibition can generate this linear signaling. Using simple mathematical models we show that for a large set of cases, repeated rounds of synaptic rectification without crossover inhibition can destroy information carried by those synapses. A similar circuit motif is employed in the electronics industry to compensate for transistor nonlinearities in analog circuits.
post to: CiteULike
Dissecting cooperative calmodulin binding to CaM kinase II: a detailed stochastic model.
Authors: Byrne, M. J. - Putkey, J. A. - Waxham, M. N. - Kubota, Y.
Journal: J Comput Neurosci
Calmodulin (CaM) is a major Ca(2+) binding protein involved in two opposing processes of synaptic plasticity of CA1 pyramidal neurons: long-term potentiation (LTP) and depression (LTD). The N- and C-terminal lobes of CaM bind to its target separately but cooperatively and introduce complex dynamics that cannot be well understood by experimental measurement. Using a detailed stochastic model constructed upon experimental data, we have studied the interaction between CaM and Ca(2+)-CaM-dependent protein kinase II (CaMKII), a key enzyme underlying LTP. The model suggests that the accelerated binding of one lobe of CaM to CaMKII, when the opposing lobe is already bound to CaMKII, is a critical determinant of the cooperative interaction between Ca(2+), CaM, and CaMKII. The model indicates that the target-bound Ca(2+) free N-lobe has an extended lifetime and may regulate the Ca(2+) response of CaMKII during LTP induction. The model also reveals multiple kinetic pathways which have not been previously predicted for CaM-dissociation from CaMKII.
post to: CiteULike
Recurrent networks with short term synaptic depression.
Authors: York, L. C. - van Rossum, M. C.
Journal: J Comput Neurosci
Cortical circuitry shows an abundance of recurrent connections. A widely used model that relies on recurrence is the ring attractor network, which has been used to describe phenomena as diverse as working memory, visual processing and head direction cells. Commonly, the synapses in these models are static. Here, we examine the behaviour of ring attractor networks when the recurrent connections are subject to short term synaptic depression, as observed in many brain regions. We find that in the presence of a uniform background current, the network activity can be in either of three states: a stationary attractor state, a uniform state, or a rotating attractor state. The rotation speed can be adjusted over a large range by changing the background current, opening the possibility to use the network as a variable frequency oscillator or pattern generator. Finally, using simulations we extend the network to two-dimensional fields and find a rich range of possible behaviours.
post to: CiteULike
From Wikipedia,
Computational Neuroscience is an interdisciplinary science that links the diverse fields of neuroscience, cognitive science, electrical engineering, computer science, physics and applied mathematics together. It serves as the primary theoretical method for investigating the function and mechanism of the nervous system. Computational neuroscience traces its historical roots to the work of people such as Andrew Huxley, Alan Hodgkin, and David Marr. Hodgkin and Huxley developed the voltage clamp and created the first mathematical model of the action potential. David Marr's work focused on the interactions between neurons, suggesting computational approaches to the study of how functional groups of neurons within the hippocampus and neocortex interact, store, process, and transmit information. Computational modeling of biophysically realistic neurons and dendrites began with the work of Wilfrid Rall, with the first multicompartmental model using cable theory.
Computational neuroscience is distinct from psychological connectionism and theories of learning from disciplines such as machine learning, neural networks and statistical learning theory in that it emphasizes descriptions of functional and biologically realistic neurons and their physiology and dynamics. These models capture the essential features of the biological system at multiple spatial-temporal scales, from membrane currents, protein and chemical coupling to network oscillations and learning and memory. These computational models are used to test hypotheses that can be directly verified by current or future biological experiments.
Currently, the field is undergoing a rapid expansion. There are many software packages, such as NEURON, that allow rapid and systematic in silico modeling of realistic neurons. Blue Brain, a collaboration between IBM and École Polytechnique Fédérale de Lausanne, aims to construct a biophysically detailed simulation of a cortical column on the Blue Gene supercomputer.
Single Neuron Modeling
Even single neurons have complex biophysical characteristics. Hodgkin and Huxley's original model only employed two voltage-sensitive currents, the fast-acting sodium and the inward-rectifying potassium. Though successful in predicting the timing and qualitative features of the action potential, it nevertheless failed to predict a number of important features such as adaptation and shunting. We now believe that there are a wide variety of voltage-sensitive currents, and the implications of the differing dynamics, modulations and sensitivity of these currents is an important topic of computational neuroscience (for reference, see Johnston and Wu, 1994).
The computational functions of complex dendrites are also under intense investigation. There is a large body of literature regarding how different currents interact with geometric properties of neurons (for reference, see Koch, 1998).
Development, Axonal Patterning and Guidance
How do axons and dendrites form during development? How do axons know where to target and how to reach these targets? How do neurons migrate to the proper position in the central and peripheral systems? How do synapses form? We know from molecular biology that distinct parts of the nervous system release distinct chemical cues, from growth factors to hormones that modulate and influence the growth and development of functional connections between neurons.
Theoretical investigations into the formation and patterning of synaptic connection and morphology is still nascent. One hypothesis that has recently garnered some attention is the minimal wiring hypothesis, which postulates that the formation of axons and dendrites effectively minimizes resource allocation while maintains maximal information storage. (for a review, see Chklovskii, 2004)
Sensory processing
Models of sensory processing understood within a theoretical framework is credited to Horace Barlow. Somewhat similar to the minimal wiring hypothesis described in the preceding section, Barlow understood the processing of the early sensory systems to be a form of efficient coding, where the neurons encoded information which minimized the number of spikes. Experimental and computational work have since supported this hypothesis in one form or another.
Current research in sensory processing is divided among biophysical modelling of different subsystems and more theoretical modelling function of perception. Current models of perception have suggested that the brain performs some form of Bayesian inference and integration of different sensory information in generating our perception of the physical world.
Memory and synaptic plasticity
Earlier models of memory are primarily based on the postulates of Hebbian learning. Biologically relevant models such as Hopfield net have been developed to address the properties of associative, rather than content-addressable style of memory that occur in biological systems. These attempts are primarily focusing on the formation of medium-term and long-term memory, localizing in the hippocampus. Models of working memory, relying on theories of network oscillations and persistent activity, have been built to capture some features of the prefrontal cortex in context-related memory. (For review, see Durstewitz et al, 2000)
One of the major problems in biological memory is how it is maintained and changed through multiple time scales. Unstable synapses are easy to train but also prone to stochastic disruption. Stable synapses forget less easily, but they are also harder to consolidate. One recent computational hypothesis involves cascades of plasticity (Fusi et al, 2004) that allow synapses to function at multiple time scales. Stereochemically detailed models of the acetylcholine receptor-based synapse with Monte Carlo method, working at the time scale of microseconds, have been built (Coggan et al, 2005). It is likely that computational tools will contribute greatly to our understanding of how synapses function and change in relation to external stimulus in the coming decades.
Behaviors of Networks
Biological neurons are connected to each other in a complex, recurrent fashion. These connections are, unlike most artificial neural networks, sparse and most likely, specific. It is not known how information is transmitted through such sparsely connected networks. It is also unknown what the computational functions, if any, of these specific connectivity pattern are.
The interactions of neurons in a small network can be often reduced to simple models such as the Ising model. The statistical mechanics of such simple systems are well-characterized theoretically. There have been some recent evidence that suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions (Schneidman et al, 2006; Shlens et al, 2006.) It's unknown, however, whether such descriptive dynamics impart any important computational function. With the emergence of two-photon microscopy and calcium imaging, we now have powerful experimental methods with which to test the new theories regarding neuronal networks.
Cognition, Discrimination and Learning
Computational modeling of higher cognitive functions has only begun recently. Experimental data comes primarily from single unit recording in primates. The frontal lobe and parietal lobe function as integrators of information from multiple sensory modalities. There are some tentative ideas regarding how simple mutually inhibitory functional circuits in these areas may carry out biologically relevant computation (Machens et al, 2005).
The brain seems to be able to discriminate and adapt particularly well in certain contexts. For instance, human beings seem to have an enormous capacity for memorizing and recognizing faces. One of the key goals of computational neuroscience is to dissect how biological systems carry out these complex computations efficiently and potentially replicate these processes in building intelligent machines.
Consciousness
The ultimate goal of neuroscience is to be able to explain the every day experience of conscious life. Francis Crick and Christof Koch made some attempts in formulating a consistent framework for future work in neural correlates of consciousness (NCC), though much of the work in this field remains speculative. (for a review, see Koch and Crick, 2003)
