Classical Cable Theory Research Articles

A Negative Slope Conductance of the Persistent Sodium Current Prolongs Subthreshold Depolarizations

Neuronal subthreshold voltage-dependent currents determine membrane properties such as the input resistance (Rin) and the membrane time constant (τm) in the subthreshold range. In contrast with classical cable theory predictions, the persistent sodium current (INaP), a non-inactivating mode of the voltage-dependent sodium current, paradoxically increases Rin and τm when activated. Furthermore, this current amplifies and prolongs synaptic currents in the subthreshold range. Here, using a computational neuronal model, we showed that the creation of a region of negative slope conductance by INaP activation is responsible for these effects and the ability of the negative slope conductance to amplify and prolong Rin and τm relies on the fast activation of INaP. Using dynamic clamp in hippocampal CA1 pyramidal neurons in brain slices, we showed that the effects of INaP on Rin and τm can be recovered by applying an artificial INaP after blocking endogenous INaP with tetrodotoxin. Furthermore, we showed that injection of a pure negative conductance is enough to reproduce the effects of INaP on Rin and τm and is also able to prolong artificial excitatory post synaptic currents. Since both the negative slope conductance and the almost instantaneous activation are critical for producing these effects, the INaP is an ideal current for boosting the amplitude and duration of excitatory post synaptic currents near the action potential threshold.

Dynamic behaviors of pretensioned cable AERORail structure

The AERORail, a new aerial transport platform, was chosen as the object of this work. Following a review of the literature on static behaviors, model tests on the basic dynamic mechanical characteristics were conducted. A series of 90 tests were completed with different factors, including tension force, vehicle load and vehicle speed. With regard to the proper tension and vehicle load, at a certain speed range, the tension increments of the rail’s cable were proved relatively small. It can be assumed that the change of tension is small and can be reasonably ignored when the tension of an entire span is under a dynamic load. When the tension reaches a certain range, the calculation of the cable track structure using classical cable theory is acceptable. The tests prove that the average maximum dynamic amplification factor of the deflection is small, generally no more than 1.2. However, when the vehicle speed reaches a certain value, the amplified factor will reach 2.0. If the moving loads increase, the dynamic amplification factor of dynamic deflection will also increase. The tension will change the rigidity of the structure and the vibration frequency; furthermore, the resonance speed will change at a certain tension. The vibration is noticeable when vehicles pass through at the resonance speed, and this negative impact on driving comfort requires the right velocity to avoid the resonance. The results demonstrate that more design details are required for the AERORail structure.

Repolarization features as detectable from electrograms and electrocardiograms

This contribution discusses the feasibility of extracting the major features of repolarization: its spatio-temporal behaviour, and how much of its global or local behaviour might be deduced from signals that can be observed experimentally. The analysis presented is based on source-volume-conductor configurations ranging from the classic cable theory, with sources derived from reaction diffusion computations, to a realistic thorax model comprising a whole heart model with electric sources represented by the equivalent electric double layer. The analysis focuses on the fact that the local activation recovery interval (ARI) at regions activated by expanding wave fronts is significantly longer than those activated by contracting ones. The consequences of this effect on observed magnitude and wave form of recorded signals are illustrated.

Experimental study on the cable rigidness and static behaviors of AERORail structure

This paper presented a new aerial platform-AERORail for rail transport and its structure evolution based on the elastic stiffness of cable; through the analysis on the cable properties when the cable supported a small service load with high-tensile force, summarized the theoretical basis of the AERORail structure and the corresponding simplified analysis model. There were 60 groups of experiments for a single naked cable model under different tensile forces and different services loads, and 48 groups of experiments for the cable with rail combined structure model. The experimental results of deflection characteristics were compared with the theoretical values for these two types of structures under the same conditions. It proved that the results almost met the classical cable theory. The reason is that a small deflection was required when this structure was applied. After the tension increments tests with moving load, it is verified that the relationships between the structure stiffness and tension force and service load are simple. Before further research and applications are made, these results are necessary for the determination of the reasonable and economic tensile force, allowable service load for the special span length for this new platform.

DYNAMICS OF SHALLOW CABLES UNDER TURBULENT WIND: A NONLINEAR FINITE ELEMENT APPROACH

In classic cable theory, vibrations are usually analyzed by writing the equations of motion in the neighborhood of the initial equilibrium configuration. Furthermore, a fundamental difference exists between out-of-plane motions, which basically corresponds to the linear behavior of a taut string and in-plane motion, where self-weight determines a sagged initial profile. This work makes use of a continuous approach to establish the initial shape of the cable when it is subjected to wind or fluid flow arbitrarily directed and employed a novel nonlinear finite element technique in order to investigate the dynamics present around the initial equilibrium shape of the cable. Stochastic solutions in the frequency domain are derived for a wind-exposed cable after linearization of the problem. By applying the proper orthogonal decomposition (POD) technique with the aim of reducing computational effort, an approach to simulate modal wind forces is proposed and applied to the nonlinear equations of motion.

Electrotonic Signals along Intracellular Membranes May Interconnect Dendritic Spines and Nucleus

Synapses on dendritic spines of pyramidal neurons show a remarkable ability to induce phosphorylation of transcription factors at the nuclear level with a short latency, incompatible with a diffusion process from the dendritic spines to the nucleus. To account for these findings, we formulated a novel extension of the classical cable theory by considering the fact that the endoplasmic reticulum (ER) is an effective charge separator, forming an intrinsic compartment that extends from the spine to the nuclear membrane. We use realistic parameters to show that an electrotonic signal may be transmitted along the ER from the dendritic spines to the nucleus. We found that this type of signal transduction can additionally account for the remarkable ability of the cell nucleus to differentiate between depolarizing synaptic signals that originate from the dendritic spines and back-propagating action potentials. This study considers a novel computational role for dendritic spines, and sheds new light on how spines and ER may jointly create an additional level of processing within the single neuron.

A second level of plasticity and expanded memory capacity: theoretical predictions of the Cable-In-Cable theory

Event Abstract Back to Event A second level of plasticity and expanded memory capacity: theoretical predictions of the Cable-In-Cable theory Isaac Shemer1* and Sten Grillner1 1 Karolinska Institute, Sweden Cable-In-Cable (CIC) theory is a passive cable theory that has been recently described as an extension to the conventional cable theory proposing explanations to some puzzling experimental observations 1. The CIC theory considers the fact that the endoplasmatic reticulum (ER) forms a continuum from the cell soma to the heads of the dendritic spines 2,3,4 and suggests that post-synaptic potentials may be more accurately described by the CIC system, where synaptic currents travel simultaneously in the medium between the cell membrane and the ER, and within the ER-lumen (see figure). The principal description of neuronal processing suggests that synaptic potentials received by the dendrites are conveyed passively via the cell soma to the initial segment of the axon (the ‘Integration Zone’), where action-potentials are triggered following a momentary integration of these potentials. The classic cable theory predicts that the effect an arbitrary synaptic activity has on the Integration Zone is mainly dominated by two synapse-specific properties: (1) the efficacy of the individual synapses and (2) the electrotonic distance to the Integration Zone. As a result, the impact an individual synaptic activity would have on the Integration Zone, is expected to diminish as the post synaptic potential become weaker or as the electrotonic distance from the Integration Zone increases. While large body of experimental evidence shows that synaptic efficacy increases with distance from the soma 5,6, theoretical consideration originating from classic cable theory, considers this as a self-defeating strategy 7. CIC theory predicts that the effect an arbitrary synaptic activity has on the Integration Zone is additionally determined by a third parameter. This parameter, which can largely modulate the efficacy a given synaptic activity may have on the Integration Zone, is synapse-specific and is independent of the transmembrane-potential at the postsynaptic part (synaptic efficacy). Simulating the CIC prediction using realistic parameters suggests: (1) A potential resolution to the above-mentioned debate about the efficacy of the observed increase in synaptic efficacy over distance; (2) a novel computational role for dendritic spines; (3) a new compensatory mechanism influencing the electrotonic attenuation of distal synaptic inputs as well as (4) a second dimension of synaptic plasticity; These findings are not limited to a narrow set of parameters and can be reproduced over a wide range of parameters. Conclusion: The CIC theory employs the intracellular architecture and the associated electrophysiology to unfold predictions that may be regarded as counter-intuitive to views originating from conventional cellular electrophysiology.

Elastodynamic Analysis of Aerial Refueling Hose Using Curved Beam Element

The elastodynamic analysis of an aerial refueling hose by classic cable theory suffers the singularity problem when the hose slackens under dynamic loadings. The difficulty is addressed and overcome by modeling the refueling hose with a new three-noded locking-free curved beam element. The large deformations and rotations of curved beams are formulated in terms of an updated Lagrangian framework with consistently coupled quintic polynomial displacement fields to satisfy the membrane locking-free condition. The stability and accuracy of the new element is validated by experiments involving an instrumented free-swinging steel cable. Good agreement is observed between the experimental results and the predictions of the new element. The numerical capability of modeling a refueling hose and drogue system has been demonstrated by simulating 1) the oscillation of hose due to the disturbance from the tanker and the vortex-induced velocity and 2) a receiver coupling with a hose reel malfunction. The analysis results show clearly the formation and propagation of oscillations along the hose, the consequent whipping near the drogue, and the associated variation of hose tension. The results of new element agree well with field observations and existing analysis results.

Elastodynamic analysis of low tension cables using a new curved beam element

In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.

A Non-Incremental Nonlinear Finite Element Solution for Cable Problems

In this investigation, a nonlinear finite element method for the large deformation and rotation of cable problems is presented. This method is based on finite element absolute nodal coordinate formulation that guarantees the continuity of all displacement gradients and leads to a constant mass matrix. The classical cable theory is first reviewed and the assumptions used in this linear theory are defined in order to demonstrate the basic differences between the linear theory and the nonlinear finite element formulation proposed in this paper for cable applications. The elastic cable forces in the absolute nodal coordinate formulation are obtained using a general continuum mechanics approach that accounts for the effect of all geometric nonlinearities. It is shown in this investigation that the use of the general continuum mechanics approach leads to a simpler and more efficient formulation as compared to the use of the assumptions of the linear theory that employs a local finite element coordinate system. The results obtained using the absolute nodal coordinate formulation show a good agreement with the results obtained using the classical cable theory when linear cable problems are considered. In particular it is shown that the use of perturbation methods to linearize the finite element equations of motion leads to modal characteristics results that are in a good agreement with the linear theory. The results of this investigation obtained using explicit numerical integration also show the potential of the proposed finite element formulation in the nonlinear analysis of cables that experience large rotations and deformations. The generalization of the procedure presented in this paper to three-dimensional cable problems is demonstrated and the computer implementation in multibody algorithms is discussed.

Detecting and estimating signals in noisy cable structures, II: information theoretical analysis.

This is the second in a series of articles that seek to recast classical single-neuron biophysics in information-theoretical terms. Classical cable theory focuses on analyzing the voltage or current attenuation of a synaptic signal as it propagates from its dendritic input location to the spike initiation zone. On the other hand, we are interested in analyzing the amount of information lost about the signal in this process due to the presence of various noise sources distributed throughout the neuronal membrane. We use a stochastic version of the linear one-dimensional cable equation to derive closed-form expressions for the second-order moments of the fluctuations of the membrane potential associated with different membrane current noise sources: thermal noise, noise due to the random opening and closing of sodium and potassium channels, and noise due to the presence of "spontaneous" synaptic input. We consider two different scenarios. In the signal estimation paradigm, the time course of the membrane potential at a location on the cable is used to reconstruct the detailed time course of a random, band-limited current injected some distance away. Estimation performance is characterized in terms of the coding fraction and the mutual information. In the signal detection paradigm, the membrane potential is used to determine whether a distant synaptic event occurred within a given observation interval. In the light of our analytical results, we speculate that the length of weakly active apical dendrites might be limited by the information loss due to the accumulated noise between distal synaptic input sites and the soma and that the presence of dendritic nonlinearities probably serves to increase dendritic information transfer.

How does an electric field defibrillate cardiac muscle?

Cardiac fibrillation is caused by an irregular wave propagation. Fibrillation can be eliminated by a strong electric field (5 kV, 20 A, 2 msec). The mechanism of this phenomenon (defibrillation) is not known. The principal difficulty, as shown in experiments and confirmed by classical cable theory, is that the changes in transmembrane potential, e, induced by electric field, decay exponentially with distance from the electrodes. We study wave suppression by an electric field in generic excitable media. In excitable media consisting of separate cells (similar to biological tissues), we have found a suppression of rotating waves and defibrillation induced by strong electric field, contrary to what happens in continuous media. We show that the spatially periodic component of e which arises in cellular media is responsible for defibrillation. We have found that (i) it does not decay with distance; (ii) it can excite quiescent cells and terminate excitation in excited cells; (iii) the coupling between cardiac cells is a crucial parameter affecting the amplitude of the spatially periodic component of e, and the efficiency of defibrillation. New experiments on cardiac muscle are proposed.

Magnetic coil stimulation of straight and bent amphibian and mammalian peripheral nerve in vitro: locus of excitation.

1. According to classical cable theory, a magnetic coil (MC) should excite a linear nerve fibre in a homogeneous medium at the negative-going first spatial derivative of the induced electric field. This prediction was tested by MC stimulation of mammalian phrenic and amphibian sciatic nerve and branches in vitro, immersed in Ringer solution within a trough, and identifying the sites of excitation by recording responses of similar latency to local electrical stimulation. Subsequently, the identified sites of excitation were compared with measurements of the induced electric field and its calculated first spatial derivative. A special hardware device was used to selectively reverse MC current direction and to generate predominantly monophasic- or polyphasic-induced pulse profiles whose initial phases were identical in polarity, shape and amplitude. When using the amphibian nerve preparation, a complication was excitation at low threshold points related to cut branches. 2. Reversal of monophasic current resulted in latency shifts corresponding approximately to the distance between induced cathode and anode. The location of each site of excitation was at, or very near, the negative-going first spatial derivative peaks of the induced electric field measured parallel to the straight nerve. Significantly, excitation of the nerve did not occur at the peak of the induced electric field above the centre of the 'figure of eight' MC junction. 3. A polyphasic pulse excited the nerve at both sites, by the negative-going first phase at one location, and approximately 150 microseconds later, by the reversed negative-going second phase at the other location. Polyphasic and monophasic pulses elicited responses with similar latency when the induced current flowed towards the recording electrode. 4. Straddling a nerve with non-coding solid lucite cylinders created a localized spatial narrowing and increase in the induced electric field, resulting in a lowered threshold of excitation. The corresponding closer spacing between first spatial derivative peaks was exhibited by a significant reduction in latency shift when MC current direction was reversed. 5. When a nerve is bent and the induced current is directed along the nerve towards the bend, the threshold of excitation is reduced there. Increasing the angle of the bend from 0 deg to more than 90 deg graded the decrease in threshold. 6. In a straight nerve the threshold was lowest when current was directed towards the cut end.(ABSTRACT TRUNCATED AT 400 WORDS)

Propagation of dendritic spikes mediated by excitable spines: a continuum theory

1. Neuroscientists are currently hypothesizing on how voltage-dependent channels, in dendrites with spines, may be spatially distributed or how their numbers may divide between spine heads and the dendritic base. A new cable theory is formulated to investigate electrical interactions between many excitable and/or passive dendritic spines. The theory involves a continuum formulation in which the spine density, the membrane potential in spine heads, and the spine stem current vary continuously in space and time. The spines, however, interact only indirectly by voltage spread along the dendritic shaft. Active membrane in the spine heads is modeled with Hodgkin-Huxley (HH) kinetics. Synaptic currents are generated by transient conductance increases. For most simulations the membrane of spine stems and dendritic shaft is assumed passive. 2. Action-potential generation and propagation occur as localized excitatory synaptic input into spine heads causes a few excitable spines to fire, which then initiates a chain reaction of spine firings along a branch. This sustained wavelike response is possible for a certain range of spine densities and electrical parameters. Propagation is precluded for spine stem resistance (Rss) either too large or too small. Moreover, even if Rss lies in a suitable range for the local generation of an action potential (resulting from local synaptic excitatory input), this range may not be suitable to initiate a chain reaction of spine firings along the dendrite; success or failure of impulse propagation depends on an even narrower range of Rss values. 3. The success or failure of local excitation to spread as a chain reaction depends on the spatial distribution of spines. Impulse propagation is unlikely if the excitable spines are spaced too far apart. However, propagation may be recovered by redistributing the same number of equally spaced spines into clusters. 4. The spread of excitation in a distal dendritic arbor is also influenced by the branching geometry. Input to one branch can initiate a chain reaction that accelerates into the sister branch but rapidly attenuates as it enters the parent branch. In branched dendrites with many excitable and passive spines, regions of decreased conductance load (e.g., near sealed ends) can facilitate attenuating waves and enhance waves that are successfully propagating. Regions of increased conductance load (e.g., near common branch points) promote attenuation and tend to block propagation. Non-uniform loading and/or nonuniform spine densities can lead to complex propagation characteristics. 5. Some analytic results of classical cable theory are generalized for the case of a passive spiny dendritic cable.(ABSTRACT TRUNCATED AT 400 WORDS)

Correlation between in vivo transmembrane action potential durations and activation-recovery intervals from electrograms. Effects of interventions that alter repolarization time.

Classic cable theory was used to analyze the relation between the activation-recovery interval measured from unipolar electrograms and transmembrane action potential duration. Theoretic analysis demonstrated that the temporal derivative of the extracellular potential is proportional to a spatial weighting of the third temporal derivative of the transmembrane action potentials along a cable with uniform propagation in a homogeneous medium. Thus, the activation-recovery interval, measured as the interval between times of minimum derivative (Vmin) of the QRS and maximum derivative (Vmax) of the T wave, should be related to action potential duration, measured as the interval between times of Vmax of the upstroke and Vmin of the downstroke of the transmembrane action potential. This relation was examined experimentally in 12 anesthetized dogs. Unipolar electrograms and transmembrane action potentials were recorded simultaneously from sites within 2 mm of each other during control states, cardiac sympathetic nerve stimulation, localized epicardial warming, and graded reductions in myocardial perfusion. The heart was paced from several sites. There was close correlation between activation-recovery interval and action potential duration measurements taken during cardiac sympathetic nerve stimulation and local epicardial warming (r = 0.96 and 0.99 for cardiac sympathetic nerve stimulation and warming, respectively). In five animals in which coronary perfusion pressure was gradually lowered, the variables correlated closely over a range of values from 62 to 212 msec (r = 0.98). However, although the overall correlation was good and mean differences between activation-recovery interval and action potential duration were small, in individual cases there were differences up to 24 msec.(ABSTRACT TRUNCATED AT 250 WORDS)