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J R Rosenberg

Publications and source records attributed to J R Rosenberg.

At least 19 recordsLinked to original sources
PubMed2006

Neural spike train synchronization indices: definitions, interpretations, and applications.

A comparison of previously defined spike train syncrhonization indices is undertaken within a stochastic point process framework. The second-order cumulant density (covariance density) is shown to be common to all the indices. Simulation studies were used to investigate the sampling variability of a single index based on the second-order cumulant. The simulations used a paired motoneurone model and a paired regular spiking cortical neurone model. The sampling variability of spike trains generated under identical conditions from the paired motoneurone model varied from 50% to 160% of the estimated value. On theoretical grounds, and on the basis of simulated data a rate dependence is present in all synchronization indices. The application of coherence and pooled coherence estimates to the issue of synchronization indices is considered. This alternative frequency domain approach allows an arbitrary number of spike train pairs to be evaluated for statistically significant differences, and combined into a single population measure. The pooled coherence framework allows pooled time domain measures to be derived, application of this to the simulated data is illustrated. Data from the cortical neurone model is generated over a wide range of firing rates (1-250 spikes/s). The pooled coherence framework correctly characterizes the sampling variability as not significant over this wide operating range. The broader applicability of this approach to multielectrode array data is briefly discussed.

Action Potentials↗
PubMed2005

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↗
PubMed2004

A note on the discrepancy between the predicted and observed speed of the propagated action potential in the squid giant axon.

The Hodgkin-Huxley model for the ionic currents in the membrane of the squid giant axon has become the standard model for the electrophysiological behaviour of many excitable cells. A strong test of the model predicted a travelling wave speed of 18.76 m/s for the propagated action potential in an axon with a reported speed of 21.2 m/s. This discrepancy between prediction and observation was considered satisfactory when the model was proposed 50 years ago, appears not to have been re-evaluated, but is unsatisfactory for a mature and important model. The separate and combined influences of measurement error and biological variability on the discrepancy between prediction and observation are quantified, as is the effect of using of a one-dimensional model to represent a three-dimensional axon. The main tool in this investigation is the use of simulation to study the behaviour of the Hodgkin-Huxley membrane model. These studies show that measurement error in combination with biological variability cannot account for the discrepancy between prediction and observation. Also, calculation shows that the one-dimensional description of the behaviour of the axon is adequate. Further calculation shows that the travelling wave description of the propagated action potential is valid only for sufficiently long axons. In shorter axons the propagated action potential is predicted to travel faster than the travelling wave; consequently under suitable experimental conditions the discrepancy between prediction and observation may be negligible.

Action Potentials↗
PubMed2004

From Maxwell's equations to the cable equation and beyond.

Maxwell's equations are taken as the starting point for the development of a mathematical model of a dendrite. The three-dimensional model of the evolution of the dendritic membrane potential based on these equations gives rise to a hierarchy of one-dimensional membrane equations. Under sufficiently strong assumptions, the first membrane equation is identical to the conventional cable equation. The second membrane equation explicitly includes the influence of dendritic taper and non-axial gradients in the intra-cellular potential. The procedure of starting from a three-dimensional model and extracting from it a one-dimensional approximation provides a prescription of how to incorporate three-dimensional properties of a dendrite in a one-dimensional representation, by contrast with an approach which aims to modify the traditional cable equation to take account of three-dimensional structure. Finite element methods are used to solve the membrane equations. An example based on a simple model of a tapered dendrite with differently placed distributions of synaptic input suggests that the effect of taper on the spike train output from the model is more important for distal synapses than those closer to the soma.

Animals↗
PubMed2003

Analytical and numerical construction of equivalent cables.

The mathematical complexity experienced when applying cable theory to arbitrarily branched dendrites has lead to the development of a simple representation of any branched dendrite called the equivalent cable. The equivalent cable is an unbranched model of a dendrite and a one-to-one mapping of potentials and currents on the branched model to those on the unbranched model, and vice versa. The piecewise uniform cable, with a symmetrised tri-diagonal system matrix, is shown to represent the canonical form for an equivalent cable. Through a novel application of the Laplace transform it is demonstrated that an arbitrary branched model of a dendrite can be transformed to the canonical form of an equivalent cable. The characteristic properties of the equivalent cable are extracted from the matrix for the transformed branched model. The one-to-one mapping follows automatically from the construction of the equivalent cable. The equivalent cable is used to provide a new procedure for characterising the location of synaptic contacts on spinal interneurons.

Action Potentials↗
PubMed2002

An investigation into the influence of boundary condition specification in finite difference methods on the behaviour of passive and active neuronal models.

Neuronal models provide a major aid to understanding the behaviour of individual neurons and networks of neurons. The solution of the model equations by finite difference methods is widespread because of the inherent simplicity of the technique. Error in the finite difference approach due to spatial and temporal discretisation is shown to be equivalent to a mis-specification of membrane current density. The effect of this mis-specification on the accuracy of the solution to the model equations is shown to depend on the structure of the model and its input, as well as the size of the discretisation intervals themselves. Through a theoretical analysis, illustrated by a number of examples on passive and active dendrites, this article demonstrates that the accuracy with which core current is implemented numerically at segment end-points in elementary models influences the behaviour of the numerical solution of these models, and consequently any physiological conclusions drawn from them.

Animals↗
PubMed2001

The interaction between membrane kinetics and membrane geometry in the transmission of action potentials in non-uniform excitable fibres: a finite element approach.

By solving the partial differential equations for an axonal segment using a finite element method, the interaction between membrane kinetics and axonal inhomogeneities, measured by their influence on propagated action potentials and stochastic spike trains, is investigated for Morris-Lecar and Hodgkin-Huxley membrane models. To facilitate comparisons of both kinetic models, parameter values are matched to give approximately the same speed for propagated action potentials. In all cases examined, the Morris-Lecar membrane model is more sensitive to geometric inhomogeneities than the comparable Hodgkin-Huxley membrane model. This difference in sensitivity can, in part, be attributed to significant differences in the membrane current supplied by each kinetic model ahead of the action potential. Also, the Morris-Lecar membrane model did not generate reflected action potentials whereas these were observed over a narrow range of geometric parameters for the comparable Hodgkin-Huxley membrane model. Simulations using stochastic spike train input showed that the presence of a sharp flare could significantly modify the statistical characteristics of the spike train output. The behaviour of action potentials governed by Morris-Lecar kinetics were more sensitive to changes in axonal geometry than those generated by comparable Hodgkin-Huxley kinetics. As a consequence of the fine balance between membrane kinetics and axon geometry, local changes in membrane properties, such as those caused by synaptic activity, can be expected to have a strong influence on the behaviour of stochastic spike trains at regions of changing axonal geometry.

Action Potentials↗
PubMed2001

An analysis of the dependence of saccadic latency on target position and target characteristics in human subjects.

BACKGROUND: Predictions from conduction velocity data for primate retinal ganglion cell axons indicate that the conduction time to the lateral geniculate nucleus for stimulation of peripheral retina should be no longer than for stimulation of central retina. On this basis, the latency of saccadic eye movements should not increase for more peripherally located targets. However, previous studies have reported relatively very large increases, which has the implication of a very considerable increase in central processing time for the saccade-generating system. RESULTS: In order to resolve this paradox, we have undertaken an extended series of experiments in which saccadic eye movements were recorded by electro-oculography in response to targets presented in the horizontal meridian in normal young subjects. For stationary or moving targets of either normal beam intensity or reduced red intensity, with the direction of gaze either straight ahead with respect to the head or directed eccentrically, the saccadic latency was shown to remain invariant with respect to a wide range of target angular displacements. CONCLUSIONS: These results indicate that, irrespective of the angular displacement of the target, the direction of gaze or the target intensity, the saccade-generating system operates with a constant generation time.

Adult↗
PubMed2001

Equivalence transformations for dendritic Y-junctions: a new definition of dendritic sub-unit.

A sequence of equivalence transformations is used to represent the mathematical model of a simply branched neuron with non-homogeneous membrane properties and non-uniform geometry by an entirely equivalent model of an unbranched structure. The analysis indicates how neuronal morphology, in combination with its biophysical properties, shapes neuronal output in response to current input. The equivalence transformations described here reveal the types of operations that are likely to feature in the analysis of complex multi-branched structures, neuronal or otherwise. These transformations provide a new definition of dendritic sub-unit and a basis of a mechanism for characterising local and non-local signal processing within dendritic structures. It is anticipated that the capacity to transform biological neurons into an equivalent unbranched structure will make an important contribution to the understanding of the functional role of neuron geometry as well as to the construction of silicon neurons with realistic biological properties.

Dendrites↗
PubMed2001

Dendritic subunits determined by dendritic morphology.

A theoretical framework is presented in which arbitrarily branched dendritic structures with nonhomogeneous membrane properties and nonuniform geometry can be transformed into an equivalent unbranched structure (equivalent cable). Rall's equivalent cylinder is seen to be one part of the equivalent cable in the special case of dendrites satisfying the Rall criteria. The relation between the branched dendrite and its equivalent unbranched representation is uniquely defined by an invertible mapping that connects configurations of inputs on the branched structure with those on the unbranched structure, and conversely. This mapping provides a new definition of dendritic subunit and provides a mechanism for characterizing local and nonlocal signal processing within dendritic structures.

Animals↗
PubMed2000

Coherence between low-frequency activation of the motor cortex and tremor in patients with essential tremor.

BACKGROUND: In healthy people, rhythmic activation of the motor cortex in the 15-30 Hz frequency range accompanies and contributes to voluntarily-generated postural contractions of contralateral muscle. In patients with Parkinson's disease, an abnormal low-frequency activation of the motor areas of the cortex occurs and has been directly linked to the characteristic 3-6 Hz rest tremor of this disease. We therefore investigated whether the motor cortex is involved in the transmission of the rhythmic motor drive responsible for generating essential tremor. METHODS: Non-invasive recordings of activity from the hand area of the motor cortex were made from six patients with essential tremor by magnetoencephalography. The recordings were made simultaneously with the electromyogram recorded from contralateral finger muscles during periods of postural tremor. A statistical spectral analysis was done to determine at which frequencies the two signals were correlated. FINDINGS: Spectral analysis of the electromyogram signals showed a significant low-frequency component at the frequency of the tremor bursts. However, there was no coherence between magnetoencephalogram and electromyogram recordings at the tremor frequency, indicating that no correlation existed between the tremor signal and low-frequency activity recorded from the primary motor cortex in individuals with essential tremor. Coherence at frequencies higher than the tremor frequency was similar to that in healthy individuals performing voluntary postural contractions. INTERPRETATION: The absence of significant coherence between the magnetoencephalogram and electromyogram at tremor frequencies suggests that in essential tremor the tremor is imposed on the active muscle through descending pathways other than those originating in the primary motor cortex. These findings challenge the model widely used to explain the efficacy of neurosurgical treatment of essential tremor, are in contrast to those of previous studies of parkinsonian rest tremor, and highlight an important difference in the pathophysiology of essential and parkinsonian tremor.

Adolescent↗
PubMed1999

The unilateral and bilateral control of motor unit pairs in the first dorsal interosseous and paraspinal muscles in man.

1. The discharges of two motor units were identified in an intrinsic hand muscle (first dorsal interosseous, FDI) or an axial muscle (lumbar paraspinals, PSP) in ten healthy subjects. Each motor unit was situated in the homologous muscle on either side of the body (bilateral condition) or in the same muscle (ipsilateral condition). The relationship between the times of discharge of the two units was determined using coherence analysis. 2. Motor unit pairs in the ipsilateral FDI showed significant coherence over the frequency bands 1-10 Hz and 12-40 Hz. Motor units in the ipsilateral PSP were significantly coherent below 5 Hz. In contrast there was no significant coherence at any frequency up to 100 Hz in the bilateral FDI condition and only a small but significant band of coherence below 2 Hz in the bilateral PSP condition. 3. Common drive to motor units at frequencies of < 4 Hz was assessed by cross-correlation of the instantaneous frequencies of the motor units. A significantly higher coefficient was found in the ipsilateral FDI, ipsi- and bilateral PSP compared with shifted, unrelated data sets. This was not the case for the bilateral FDI condition. 4. The presence of higher frequency coherence ( > 10 Hz) in the ipsilateral FDI condition and its absence in ipsilateral PSP is consistent with a more direct and influential cortical supply to the intrinsic hand muscles compared with the axial musculature. The presence of low frequency drives (< 4 Hz) in the bilateral PSP condition and its absence in the bilateral FDI condition is consistent with a bilateral drive to axial, but not distal, musculature by the motor pathways responsible for this oscillatory input.

Adult↗
PubMed1999

The origin of ocular microtremor in man.

A novel technique for the study of human eye movements was used to investigate the frequency components of ocular drift and microtremor in both eyes simultaneously. The tangential components of horizontal eye accelerations were recorded in seven healthy subjects using light-weight accelerometers mounted on scleral contact lenses during smooth pursuit movements, vestibulo-ocular reflexes and eccentric gaze with and without fixation. Spectral peaks were observed at low (up to 25 Hz) and high (60-90 Hz) frequencies. A multivariate analysis based on partial coherence analysis was used to correct for head movement. After correction, the signals were found to be coherent between the eyes over both low- and high-frequency ranges, irrespective of task, convergence or fixation. It is concluded that the frequency content of ocular drift and microtremor reflects the patterning of low-level drives to the extra-ocular muscle motor units.

Adult↗
PubMed1999

Coherent cortical and muscle discharge in cortical myoclonus.

There is increasing evidence in man that the cortical drive to motor neurons is rhythmic. This oscillatory drive may be exaggerated in patients with cortical myoclonus. Spectral analysis of surface bipolar EEG and EMG activity was performed in eight such patients. Only three cases had evidence of giant cortical evoked potentials or a cortical correlate on back-averaging at the time of study. In six subjects, significant coherence between contralateral and vertex EEG and EMG was observed in ranges similar to that previously reported for normal subjects (15-30 and 30-60 Hz). Three out of these six subjects also had significant coherence at higher frequencies (up to 175 Hz). All eight patients had a correlate in the cumulant density estimate between EEG and contralateral EMG. EMG lagged EEG by about 14, 25 and 35 ms for the muscles of the forearm, hand and foot, respectively. These delays were estimated from the slope of the phase curves and the timing of the peaks in the cumulant density estimates, and are appropriate for conduction in fast pyramidal pathways. The results provide clear evidence of a cortical drive synchronizing muscle discharge over a broad range of frequencies in patients with cortical myoclonus. Fourier analysis is a promising technique in the diagnosis and investigation of such patients.

Adolescent↗
PubMed1999

Load-independent contributions from motor-unit synchronization to human physiological tremor.

This study describes two load-independent rhythmic contributions from motor-unit synchronization to normal physiological tremor, which occur in the frequency ranges 1-12 Hz and 15-30 Hz. In common with previous studies, we use increased inertial loading to identify load-independent components of physiological tremor. The data consist of simultaneous recordings of tremor acceleration from the third finger, a surface electromyogram (EMG), and the discharges of pairs of single motor units from the extensor digitorum communis (EDC) muscle, collected from 13 subjects, and divided into 2 data sets: 106 records with the finger unloaded and 84 records with added mass from 5 to 40 g. Frequency domain analysis of motor-unit data from individual subjects reveals the presence of two distinct frequency bands in motor-unit synchronization, 1-12 Hz and 15-30 Hz. A novel Fourier-based population analysis demonstrates that the same two rhythmic components are present in motor-unit synchronization across both data sets. These frequency components are not related to motor-unit firing rates. The same frequency bands are present in the correlation between motor-unit activity and tremor and between surface EMG activity and tremor, despite a significant alteration in the characteristics of the tremor with increased inertial loading. A multivariate analysis demonstrates conclusively that motor-unit synchronization is the source of these contributions to normal physiological tremor. The population analysis suggests that single motor-unit discharges can predict an average of 10% of the total tremor signal in these two frequency bands. Rectified surface EMG can predict an average of 20% of the tremor; therefore within our population of recordings, the two components of motor-unit synchronization account for an average of 20% of the total tremor signal, in the frequency ranges 1-12 Hz and 15-30 Hz. Our results demonstrate that normal physiological tremor is a complex signal containing information relating to motor-unit synchronization in different frequency bands, and lead to a revised definition of normal physiological tremor during low force postural contractions, which is based on using both the tremor spectra and the correlation between motor-unit activity and tremor to characterize the load-dependent and the load-independent components of tremor. In addition, both physiological tremor and rectified EMG emerge as powerful predictors of the frequency components of motor-unit synchronization.

Adult↗
PubMed1998

Identification of patterns of neuronal connectivity--partial spectra, partial coherence, and neuronal interactions.

The cross-correlation histogram has provided the primary tool for inferring the structure of common inputs to pairs of neurones. While this technique has produced useful results it not clear how it may be extended to complex networks. In this report we introduce a linear model for point process systems. The finite Fourier transform of this model leads to a regression type analysis of the relations between spike trains. An advantage of this approach is that the full range of techniques for multivariate regression analyses becomes available for spike train analysis. The two main parameters used for the identification of neural networks are the coherence and partial coherences. The coherence defines a bounded measure of association between two spike trains and plays the role of a squared correlation coefficient defined at each frequency lambda. The partial coherences, analogous to the partial correlations of multiple regression analysis, allow an assessment of how any number of putative input processes may influence the relation between any two output processes. In many cases analytic solutions may be found for coherences and partial coherences for simple neural networks, and in combination with simulations may be used to test hypotheses concerning proposed networks inferred from spike train analyses.

Animals↗