Biomedical subjects

D M Durand

Publications and source records attributed to D M Durand.

7 recordsLinked to original sources

PubMed1996

A generalized cable equation for magnetic stimulation of axons.

During magnetic stimulation, electric fields are induced both on the inside (intracellular region) and the outside (extracellular region) of nerve fibers. The induced electric fields in each region can be expressed as the sum of a primary and a secondary component. The primary component arises due to an applied time varying magnetic field and is the time derivative of a vector potential. The secondary component of the induced field arises due to charge separation in the volume conductor surrounding the nerve fiber and is the gradient of a scalar potential. The question, "What components of intracellular fields and extracellular induced electric fields contribute to excitation?" has, so far, not been clearly addressed. In this paper, we address this question while deriving a generalized cable equation for magnetic stimulation and explicitly identify the different components of applied fields that contribute to excitation. In the course of this derivation, we review several assumptions of the core-conductor cable model in the context of magnetic stimulation. It is shown that out of the possible four components, only the first spatial derivative of the intracellular primary component and the extracellular secondary component of the fields contribute to excitation of a nerve fiber. An earlier form of the cable equation for magnetic stimulation has been shown to result in solutions identical to three-dimensional (3-D) volume-conductor model for the specific configuration of an isolated axon in a located in an infinite homogenous conducting medium. In this paper, we extend and generalize this result by demonstrating that our generalized cable equation results in solutions identical to 3-D volume conductor models even for complex geometries of volume conductors surrounding axons such as a nerve bundle of different conductivity surrounding axons. This equivalence in the solutions is valid for several representations of a nerve bundle such as anisotropic monodomain and bidomain models.

Animals↗

PubMed1995

Analysis of magnetic stimulation of a concentric axon in a nerve bundle.

In this paper, we present an analysis of magnetic stimulation of an axon located at the center of a nerve bundle. A three-dimensional axisymmetric volume conductor model is used to determine the transmembrane potential response along an axon due to induced electric fields produced by a toroidal coil. We evaluate four such models of an axon located in: 1) an isotropic nerve bundle with no perineurium, 2) an anisotropic nerve bundle without a perineurium, 3) an isotropic nerve bundle surrounded by a perineurium, and 4) an anisotropic nerve bundle surrounded by a perineurium. The transmembrane polarization computed along an axon for the above four models is compared to that for an axon located in an infinite homogeneous medium. These calculations indicate that a nerve bundle with no sheath has little effect on the transmembrane potential. However, the presence of a perinerium around the nerve bundle and anisotropy in the bundle significantly affects the shape of the transmembrane response. Therefore, during magnetic stimulation, nerve bundle anisotropy and the presence of perineurium must be taken into account for calculation of stimulus intensities for threshold excitation.

Animals↗

PubMed1994

Desynchronization of epileptiform activity by extracellular current pulses in rat hippocampal slices.

1. A single cathodic current pulse applied in the somatic CA1 region of the hippocampus was found to induce a large decrease in the amplitude of the population spike. 2. Intracellular recordings showed intense cellular firing suggesting the amplitude decrease could not be attributed to a decrease in neuronal firing. 3. Simultaneous intracellular and extracellular potentials were recorded to analyse the synchronization of neuronal firing in the CA1 region. Action potentials were synchronized with the first population spike but this synchronization decreased with subsequent spikes. Histograms of the phase of the action potentials displayed a normal distribution. 4. Histograms of the phases of the action potentials following the application of the 'singular stimulus' (one producing a singular response) revealed a uniform distribution of the phases suggesting that the neuronal population was desynchronized. 5. This desynchronization effect of the singular stimulus was verified by double intracellular recordings. The simultaneous firing of two neurons could be desynchronized by the application of the singular stimulus. 6. These findings indicate that it is possible to desynchronize a neuronal pool with the application of a single current pulse. In addition, the results show that it is possible for a neuronal population to fire a large number of action potentials with no resulting evoked potentials in the extracellular space.

Action Potentials↗

PubMed1994

Nonlinear parameter estimation by linear association: application to a five-parameter passive neuron model.

Linear associative memories (LAM) have been intensely used in the areas of pattern recognition and parallel processing for the past two decades. Application of LAM to nonlinear parameter estimation, however, has only been recently attempted. The process consists in converting the nonlinear function in the parameters into a set of linear algebraic equations. The nature of the linearized system and the factors influencing the accuracy of the parameter estimates have not yet been fully investigated. In this paper, LAM is applied to a nonlinear five-parameter model of the neuron. Ill-conditioning, which is often exhibited in LAM, is treated with the method of regularization as well as by the singular value decomposition (SVD). Simulation results indicate that the parameters estimated by LAM exhibit a remarkable robustness against additive white noise in comparison with the classical gradient optimization technique. Moreover, it is shown that regularization can be superior to SVD under certain conditions. Our results suggest that LAM can be used both as a noise reduction technique and as a stand-alone nonlinear parameter estimation algorithm. The comparison between LAM and a gradient technique show that, for this estimation problem, the LAM method can give more reliable estimates. Further improvements in estimation quality may still be achieved by the use of other forms of regularizing functions.

Linear Models↗

PubMed1994

Reconstruction of hippocampal CA1 pyramidal cell electrophysiology by computer simulation.

1. We have developed a 16-compartment model that reproduces most of the features of the CA1 pyramidal cell electrophysiology observed experimentally. The model was constructed using seven active ionic conductances: gNa, gCa, gDR, gCT, gA, gM, and gAHP whose kinetics have been, inferred, in most cases, from the available voltage-clamp data obtained from these cells. We focussed the simulation on the initial and late accommodation, the slow depolarization potential and the spike broadening during repetitive firing, because their mechanisms are not well understood. 2. Current-clamp records were reproduced by iterative adjustments to the ionic maximum conductances, scaling and/or "reshaping" of the gates' time constant within the experimental voltage-clamp data, and shifting the position of the steady-state gate opening. The final properties of the ionic channels were not significantly different from the voltage-clamp experiments. 3. The resulting model reproduces all four after-potentials that have been recorded to follow activation of the cell. The fast, medium, and slow after-hyperpolarization potentials (AHPs) were, respectively, generated by ICT, IM, and IAHP. Furthermore, the model suggests that the mechanisms underlying the depolarization after potential (DAP) is mostly due to passive recharging of the soma by the dendrites. 4. The model also reproduces most of the firing features experimentally observed during injection of long current pulses. Model responses showed a small initial decrease in the firing frequency during a slow underlying depolarization potential, followed by a more significant frequency decrease. Moreover, a gradual broadening of the action potential and loss of the fast AHP were also observed during the initial high-frequency firing, followed, as the firing frequency decreased, by a gradual recovery of the spikes' original width and fast AHP amplitude increase. 5. A large reduction of the K repolarizing current was required to reproduce the spike broadening and reduction of the fast AHP experimentally observed in CA1 cells during repetitive firing responses. The incorporation of a transient Ca- and voltage-dependent K current (ICT) into the model successfully reproduced these experimental observations. In contrast, we were unable to reproduce this phenomenon when a large persistent Ca- and voltage-dependent K current (generally named IC) was included in the model. These results suggest that there is a strong contribution to action-potential repolarization and fast AHP by a transient Ca- and voltage-dependent K current (ICT). 6. The two accommodation steps were induced by a progressively enlargement of two K currents IM (initial) and IAHP (late).(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed1993

Effects of induced electric fields on finite neuronal structures: a simulation study.

In this paper we present an analysis of magnetic stimulation of finite length neuronal structures using computer simulations. Models of finite neuronal structures in the presence of extrinsically applied electric fields indicate that excitation can be characterized by two driving functions: one due to field gradients and the other due to fields at the boundaries of neuronal structures. It is found that boundary field driving functions play an important role in governing excitation characteristics during magnetic stimulation. Simulations indicate that axons whose lengths are short compared to the spatial extent of the induced field are easier to excite than longer axons of the same diameter. Simulations also indicate that independent cellular dendritic processes are probably not excited during magnetic stimulation. Analysis of the temporal distribution of induced fields indicates that the temporal shape of the stimulus waveform modulates excitation thresholds and propagation of action potentials.

Animals↗

PubMedDate not supplied

Magnetic stimulation of axons in a nerve bundle: effects of current redistribution in the bundle.

Recently, we developed a model of magnetic stimulation of a concentric axon in an anisotropic nerve bundle. In that earlier paper, we considered a single axon surrounded by a nerve bundle represented as a homogeneous anisotropic monodomain medium. In this paper we extend our previous calculations to examine excitation of axons within a nerve bundle without neglecting the presence of other axons in the nerve bundle. A three-dimensional axial symmetry volume conductor model is used to determine the transmembrane potential response along an axon due to induced electric fields produced by a toroidal coil. Our principal objective is to examine the effect of current redistribution to other axons in the bundle on excitation characteristics. We derive the transmembrane potential along an axon for two currently available models of current redistribution: the biodomain model and the spatial--frequency monodomain model. Results indicate that a reduction in the transmembrane potential along an axon due to the presence of other nerve fibers in the bundle is observed. Axons located at the periphery of a nerve bundle have lower thresholds and different excitation sites compared with axons located near the center of a nerve bundle.

Axons↗