Implementation issues in approximate methods for stochastic Hodgkin-Huxley models.
Explore the source record for details and available documents.
Action Potentials↗
SEARCH · Search PubMed
Results for “Models, Neurological”
Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Increased computational accuracy in multi-compartmental cable models by a novel approach for precise point process localization.
Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional models assign a single potential to a compartment. This potential is associated with the membrane potential at the centre of the segment represented by the compartment. All input to that segment, independent of its location on the segment, is assumed to act at the centre of the segment with the potential of the compartment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the location of input to a segment on the model solution by partitioning the effect of this input between the axial currents at the proximal and distal boundaries of segments. For a given neuron, the new and traditional approaches to compartmental modelling use the same number of locations at which the membrane potential is to be determined, and lead to ordinary differential equations that are structurally identical. However, the solution achieved by the new approach gives an order of magnitude better accuracy and precision than that achieved by the latter in the presence of point process input.
Computer Simulation↗
Reduced model and simulation of neuron with passive dendritic cable: an eigenfunction expansion approach.
The neuron models with passive dendritic cables are often used for detailed cortical network simulations (Protopapas et al., 1998; Suarez et al., 1995). For this, the compartment model based on finite volume or finite difference discretization was used. In this paper, we propose an eigenfunction expansion approach combined with singular perturbation and demonstrate that the proposed scheme can achieve an order of magnitude accuracy improvement with the same number of equations. Moreover, it is also shown that the proposed scheme converges much faster to attain a given accuracy. Hence, for a network simulation of the neurons with passive dendritic cables, the proposed scheme can be an attractive alternative to the compartment model, that leads to a low order model with much higher accuracy or that converges faster for a given accuracy.
Algorithms↗
How can a patient blind to radial motion discriminate shifts in the center-of-motion?
Within biologically constrained models of heading and complex motion processing, localization of the center-of-motion (COM) is typically an implicit property arising from the precise computation of radial motion direction associated with an observer's forward self-motion. In the work presented here we report psychophysical data from a motion-impaired stroke patient, GZ, whose pattern of visual motion deficits is inconsistent with this view. We show that while GZ is able to discriminate direction in circular motions she is unable to discriminate direction in radial motion patterns. GZ's inability to discriminate radial motion is in stark contrast with her ability to localize the COM in such stimuli and suggests that recovery of the COM does not necessarily require an explicit representation of radial motion direction. We propose that this dichotomy can be explained by a circular template mechanism that minimizes a global motion error relative to the visual motion input, and we demonstrate that a sparse population of such templates is computationally sufficient to account for human psychophysical performance in general and in particular, explains GZ's performance. Recent re-analysis of the predicted receptive field structures in several existing heading models provides additional support for this type of circular template mechanism and suggests the human visual system may have available circular motion mechanisms for heading estimation.
Discrimination, Psychological↗
Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks.
We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states; (ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step; and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models-for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in [Formula: see text] operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, high-conductance states, our methods are designed to achieve statistical accuracy when very large time-steps are used. Moreover, our methods can also achieve trajectory-wise accuracy when small time-steps are used.
Algorithms↗
Robustness of the significance of spike synchrony with respect to sorting errors.
The aim of spike sorting is to reconstruct single unit spike times from extracellular multi-unit recordings. Failure in the identification of a spike (false negative) or assignment of a spike to a wrong unit (false positive) are typical examples of sorting errors. Their influence on cross-correlation measures has been addressed and it has been shown that correlation analysis of multi-unit signals may lead to incorrect interpretations. We formulate a model to study the influence of sorting errors on the significance of synchronized spikes, and thus are able to study if and how the significance changes in case of imperfect sorting. Here we explore the case of pairwise analysis of simultaneously recorded neurons. Interestingly, a decrease in the significance is observed in the presence of false positives, as well as for false negatives. Furthermore, false negative errors reduce the significance of synchronized spikes more strongly than false positives. Thus, conservative sorting strategies have a stronger tendency to lead to a loss of the significance of synchronization. We demonstrate that a detailed understanding of sorting techniques and their possible effects on subsequent data analyses is important in order to rule out inconsistencies in the interpretation of results.
Action Potentials↗
Non-parametric detection of temporal order across pairwise measurements of time delays.
Neuronal synchronization is often associated with small time delays, and these delays can change as a function of stimulus properties. Investigation of time delays can be cumbersome if the activity of a large number of neurons is recorded simultaneously and neuronal synchronization is measured in a pairwise manner (such as the cross-correlation histograms) because the number of pairwise measurements increases quadratically. Here, a non-parametric statistical test is proposed with which one can investigate (i) the consistency of the delays across a large number of pairwise measurements and (ii) the consistency of the changes in the time delays as a function of experimental conditions. The test can be classified as non-parametric because it takes into account only the directions of the delays and thus, does not make assumptions about the distributions and the variances of the measurement errors.
Algorithms↗
Mechanisms of seizure propagation in a cortical model.
We consider a mathematical model of mesoscopic human cortical ictal electrical activity. We compare the model results with ictal electrocortical data recorded from three human subjects and show how the two agree. We determine that, in the model system, seizures result from increased connectivity between excitatory and inhibitory cell populations, or from decreased connectivity within either excitatory or inhibitory cell populations. We compare the model results with the disinhibition and 4-AP models of epilepsy and suggest how the model may guide the development of new anticonvulsant therapies.
4-Aminopyridine↗
Systems-level modeling of neuronal circuits for leech swimming.
This paper describes a mathematical model of the neuronal central pattern generator (CPG) that controls the rhythmic body motion of the swimming leech. The systems approach is employed to capture the neuronal dynamics essential for generating coordinated oscillations of cell membrane potentials by a simple CPG architecture with a minimal number of parameters. Based on input/output data from physiological experiments, dynamical components (neurons and synaptic interactions) are first modeled individually and then integrated into a chain of nonlinear oscillators to form a CPG. We show through numerical simulations that the values of a few parameters can be estimated within physiologically reasonable ranges to achieve good fit of the data with respect to the phase, amplitude, and period. This parameter estimation leads to predictions regarding the synaptic coupling strength and intrinsic period gradient along the nerve cord, the latter of which agrees qualitatively with experimental observations.
Algorithms↗
On the dynamics of electrically-coupled neurons with inhibitory synapses.
We study the dynamics and bifurcations of noise-free neurons coupled by gap junctions and inhibitory synapses, using both delayed delta functions and alpha functions to model the latter. We focus on the case of two cells, as in the studies of Chow and Kopell (2000) and Lewis and Rinzel (2003), but also show that stable asynchronous splay states exist for globally coupled networks of N cells dominated by subthreshold electrical coupling. Our results agree with those of Lewis and Rinzel (2003) in the weak coupling range, but our Poincaré map analysis yields more information about global behavior and domains of attraction, and we show that the explicit discontinuous maps derived using delayed delta functions compare well with the continuous history-dependent, implicitly-defined maps derived from alpha functions. We find that increased bias currents, super-threshold electrical coupling and synaptic delays promote synchrony, while sub-threshold electrical coupling and fast synapses promote asynchrony. We compare our analytical results with simulations of an ionic current model of spiking cells, and briefly discuss implications for stimulus response modes of locus coeruleus and for central pattern generators.
Algorithms↗
Contrasting conceptions of perception and action.
Explore the source record for details and available documents.
Humans↗
The rise and fall in information-processing rates over the life span.
We surveyed studies that measured information-processing durations in groups of experimental subjects (children or elderly adults) and a group of college-aged control subjects. Some studies varied the type of processing while keeping the age of a subject group fixed. Process-durations in experimental subjects could be described by a multiplicative function of the control durations, regardless of the type of processing. Other studies varied the age of the subject groups while keeping the type of processing fixed. Process-durations declined during childhood, in a manner that could be described by a negative exponential function of age. Process-durations increased throughout middle- and old-age, in a manner that could be described by a positive exponential function of age. The sum of the two exponentials defined a U-shaped function that described process-durations over the life span. The most important studies varied both the type of processing and the age of the subject groups. An array of measurements of this kind could be described by a two-dimensional function that combined the multiplicative effect of process-duration and the exponential effects of age. The multiplicative effect of process-duration suggested that the execution of a processing sequence was conditioned by a single developmental parameter in both the experimental subject and the control subject. The exponential components determined the magnitude of the developmental parameter as the age of the subject changed. Given the global character of these effects, it seemed to us that the developmental mechanism may operate at a more elementary level than the information-processing stages conceived by cognitive theories. In a developmental framework, information processing may be reducible to a large number of small steps of a homogeneous duration or reliability, such as might be realized on a neural network. The exponential rate constants may be related to constant-probability hazards that act on one or another population of neural elements to create minute defects or incremental improvements. Their cumulative effects alter the functioning of the network over its lifetime, in a way that parallels the observed changes in process-durations.
Adolescent↗
Right hemisphere involvement in depression: toward a neuropsychological theory of negative affective experiences.
Several lines of inquiry provide converging evidence for a critical role for the right cerebral hemisphere in negative affective experiences. This research includes the assessment of affective consequences of both focal cerebral lesions and pharmacological inactivation of one or the other hemisphere, as well as experimental and physiological techniques assessing differential hemispheric activation. The specific nature of right hemispheric involvement is conceptualized as a tendency to become activated by aversive experiences, and once activated, to process stimuli in a manner consistent with the right hemisphere's more negative affective tone. A theory of right hemisphere involvement in depressive affect is presented in detail and its relevance to clinical phenomena, e.g., the co-occurrence of depression and pain, and sex differences in depression, is examined, as is congruence with cognitive theories of depression.
Affective Symptoms↗
An artificial neural network analogue of learning in autism.
An artificial neural network is simulated that shares formal qualitative similarities with the selective attention and generalization deficits seen in people with autism. The model is based on neuropathological studies which suggest that affected individuals have either too few or too many neuronal connections in various regions of the brain. In simulations where the model was taught to discriminate children with autism from children with mental retardation, having too few simulated neuronal connections led to relatively inferior discrimination of the two groups in a training set and, consequently, relatively inferior generalization of the discrimination to a novel test set. Too many connections produced excellent discrimination but inferior generalization because of overemphasis on details unique to the training set. It is concluded that, within the context of the current model, the neuropathological observations that have been described in the literature are sufficient to explain some of the unique pattern recognition and discrimination learning abilities seen in some people with autism as well as their problems with generalization and concept acquisition. The model generates testable hypotheses that have implications for understanding the pathogenesis, treatment, and phenomenology of autism.
Analysis of Variance↗
Thalamo-tectal projections in the frog.
Explore the source record for details and available documents.
Animals↗
The morphometry of the branching pattern in dendrites of the visual cortex pyramidal cells.
An analysis has been made of the three-dimensional branching structure for the basal and apical dendrites of cortical neurons in an adult rabbit. The real branching angles of basal dendrites and apical oblique branches are in the same range, but differ from those of the apical main shaft. Therefore, several different parts of the apical dendrite have to be distinguished on anatomical grounds, coincident with the presynaptic areas distinguished in the literature. The bifurcations of basal dendrites are essentially symmetrical. The mode of outgrowth, however, is non-symmetrical. Redirection of dendrites will, therefore, occur. This redirection is often not complete, so that a large variability of branching angles results. The possible significance of the observed symmetry is discussed.
Animals↗
Three-dimensional branching structure of pyramidal cell dendrites.
Explore the source record for details and available documents.
Animals↗
Auditory event-related potentials in the squirrel monkey: parallels to human late wave responses.
Event-related potentials (ERPs) were recorded from the brain surface in squirrel monkeys during the presentation of two auditory stimulus paradigms which have previously been utilized to elicit scalp-recorded ERPs in humans. In the first paradigm, inter-stimulus interval (ISI) was systematically varied during the presentation of a series of tone pips. The tones produced a negative (70 ms)-positive (130 ms) sequence of components similar in morphology to the human scalp-recorded N1-P2 'vertex' potential. The amplitude of the N70 and P130 components recorded from midline electrodes decreased with decreasing ISI, as previously shown for the human vertex potential. However, this amplitude change with ISI was not observed in ERPs recorded from lateral frontal and temporal electrodes. These results agree with previous studies of monkeys and humans which suggest at least two different sources contribute to N1-P2 components recorded in response to tones. The effects of stimulus probability and novelty on ERP morphology and amplitude were studied in the second paradigm. ERPs elicited by frequent (P = 0.92) and infrequent (P = 0.08) tone pips presented in an unpredictable order were compared. N70 - P130 components were produced by both stimuli, and the infrequent stimuli also elicited a broad, long latency (300 ms) positive complex that decreased in amplitude with repeated presentations. In humans the same infrequent auditory stimuli produce a frontally distributed late positive component that has been interpreted as indicating the activation of orientation mechanisms or of a 'mismatch detector'. These data suggest that in these paradigms squirrel monkeys exhibit ERPs which are similar in several respects to ERPs recorded to identical stimuli in humans.
Animals↗