Uniform Cables Research Articles

Cell-to-cell heterogeneity in ion channel conductance impacts substrate vulnerability to arrhythmia.

Determining whether an ectopic depolarization will lead to a self-perpetuating arrhythmia is of critical importance in determining arrhythmia risk, so it is necessary to understand what factors impact substrate vulnerability. This study sought to explore the impact of cell-to-cell heterogeneity in ion channel conductance on substrate vulnerability to arrhythmia by measuring the duration of the vulnerable window in computational models of one-dimensional cables of ventricular cardiomyocytes. We began by using a population of uniform cable models to determine the mechanisms underlying the vulnerable window phenomenon. We found that in addition to the known importance of GNa, the conductances GCa,L and GKr also play a minor role in determining the vulnerable window duration. We also found that a steeper slope of the repolarizing action potential during the vulnerable window correlated with a shorter vulnerable window duration in uniform cables. We applied our understanding from these initial simulations to an investigation of the vulnerable window in heterogeneous cable models. The heterogeneous cables displayed a great deal of intra-cable variation in vulnerable window duration, highly sensitive to the cardiomyocytes in the local environment of the ectopic stimulus. Coupling strength modulated not only the magnitude of the vulnerable window duration but also the extent of intra-tissue variability in vulnerable window duration.NEW & NOTEWORTHY We investigate the impact of cell-to-cell heterogeneity in ion channel conductance on substrate vulnerability to arrhythmia by measuring the vulnerable window duration in computational cardiomyocyte cable models. We demonstrate a wide range of intra-cable variability in vulnerable window duration (VWD) and show how this is changed by ion channel block and coupling strength perturbations.

Numerical analysis and cable activation in hybrid bending-active structures with multiple cables

Recent applications of bending-active structural principles have facilitated the development of unique, material and energy efficient, free-form lightweight systems. The systems are realized through the application of an interdisciplinary design, computational fabrication, exclusive assembly techniques and construction. These aspects are directly linked to the form-finding process through the bending-active members’ activation. A number of design and construction parameters necessary for the morphological objectives succession, as well as the consideration of the deformation behavior of the systems, have raised the challenge of associating generative configuration parameters with their respective post-formed load-deformation behavior. Along these lines, the present paper examines the design of a planar hybrid bending-active system that consists of a single elastic member interconnected with cable elements at equal length intervals of 1 m. The three-stage development of the system consists of its assembly in planar arrangement (i) and erection (ii) following an initial uniform cables’ length reduction, in connection with the appropriate kinematic constraints of the ground supports. In a consecutive post-tensioning stage (iii), the supports are fixed and the cables’ length is further reduced to provide higher system prestress conditions and a differentiated span to height ratio. In a preliminary stage, the system load-deformation behavior under uniformly distributed vertical load is investigated at the end of its erection (ii&Q) and post-tensioning stage (iii&Q). The analysis examines seven system configurations with increasing number of cable segments, from two to eight. For the eight cable segments system, fourteen alternative post-tensioned configurations, emerging from individual, or group, cable activation, are investigated in their load-deformation behavior. The analysis provides insights into the configurability of the hybrid systems and their load-deformation behavior. In conclusion, the paper discusses design aspects that contribute towards structurally efficient configurations of the hybrid system series.

Simple formulas for the natural frequencies of non-uniform cables and beams

The asymptotic development method is used to obtain approximate analytical expressions for the natural frequencies of non-uniform cables and beams. By manipulating the first-order terms, we obtain the mechanical properties (mass, stiffness, etc.) of the equivalent uniform cables and beams having the same (up to the first order) frequencies of the non-uniform one. The second order terms provide an error estimation for the previous expressions. Some examples are reported to illustrate the effectiveness and simplicity of the proposed formulas.

A continuum approach to model neurites/dendrites with emerging subtrees

Neuronal morphology plays an important role in the processing of spatiotemporal synaptic input patterns. We formulate a new cable theoretic model to study the output in a dendritic cable with many subtrees, both analytically and computationally. The model is an extension of the continuum spine model derived by Baer and Rinzel [1] and like that model, there is no direct interaction between branches. Instead, all interactions occur through the primary dendrite. The continuum branch formulation provides a link between analytical and computational approaches and allows for detailed models of structural plasticity with the advantage that parameters like branch density can be varied dynamically. This is in contrast to multicompartment modeling approaches where different models, each having a static morphology, must be used. A multicompartment model with equally spaced discrete branches implemented in NEURON [2] is used to validate the continuum branch model. Then we demonstrate the approach using Drosophila Motoneuron 5 (MN5), a monopolar neuron, where soma and axon are connected via a long primary neurite from which dendritic subtrees emerge. Parameters for the model are based on 3D reconstructions [3] of that neuron and the subtrees are reduced to uniform cables. For a passive membrane and uniformly distributed branches, this formulation provides analytic estimates of electrical parameters, such as the input resistance. Transforming the equations to the frequency domain, we examine the steady state response properties for periodic forcing, where the impact of structural properties on transfer properties and the phase shift at different locations are calculated directly. Based on calculations of the voltage response along the primary neurite, the continuum formulation performs much better than a simple cable as an approximation of the morphologically realistic model. Simulations of the continuum model are in good agreement with the realistic model for frequencies up to 1000 Hz. In insects neurons the spike initiation zone (SIZ) is usually located far away from the recording site. We use this model to investigate the impact of the location of the SIZ and morphology on spike initiation and spike shape at the recording site as well as on activation and inactivation curves of ion channels obtained by voltage clamp recordings. Also we investigate how structural properties impact the results found in a point model of MN5, where variations of ion channel densities in physiological ranges lead to different observed firing properties [4].

Development of Cable Reel for Spherical Trailer – Uniform Cable Winding

Cabled communication is considered useful for rescue robots in post-disaster environments because the cable provides good signal communication and assists in retrieving the robot. Having said that, however, the cable could also hinder robot mobility and smaller robots lack payload capacity for reels. The spherical trailer cable reel we developed consists of a spherical trailer and a cable reel with a cable oscillator to oscillate the cable over the reel. Through experiments and studies, we identified a problem with the cable oscillator that prevented the cable from being wound uniformly over the reel. We propose three improvements to solve this problem involving optimization of the spatial cam structure. This paper describes the cable reel, improved mechanisms, and experiments to test their performances.

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.

Propagation on a central fiber surrounded by inactive fibers in a multifibered bundle model

We studied uniform propagation on a central active fiber surrounded by inactive fibers in a multifibered bundle model lying in a large volume conductor. The behavior of a fully active bundle is considered in a companion paper. The bundle is formed by concentric layers of small cylindrical fibers (radius 5 microns), with a uniform minimum distance (d) between any two adjacent fibers, to yield a bundle radius of about 72 microns. Individual fibers are identical continuous cables of excitable membrane based on a modified Beeler-Reuter model. The intracellular volume fraction (fi) increases to a maximum of about 90% as d is reduced and remains unchanged for d < 0.01 micron. In the range of d < 0.01 micron, the central fiber is effectively shielded from external effects by the first concentric layer of inactive fibers, and a large capacitive load current flows across the surrounding inactive membranes. In addition, the fiber proximity produces a circumferentially nonuniform current density (proximity effect) that is equivalent to an increased average longitudinal interstitial resistance. The conduction velocity is reduced as d becomes smaller in the range of d < 0.1 micron, the interstitial potential becomes larger, and both the maximum rate of rise and time constant of the foot of the upstroke are increased. On the other hand, for d > 0.1 micron, there are negligible changes in the shape of the upstroke, and the behavior of the central fiber is close to that of a uniform cable in a restricted volume conductor. For d larger than about 1.2 microns, the active fiber environment is close to an unbounded isotropic volume conductor.

Simulation of two-dimensional anisotropic cardiac reentry: effects of the wavelength on the reentry characteristics.

A two-dimensional sheet model was used to study the dynamics of reentry around a zone of functional block. The sheet is a set of parallel, continuous, and uniform cables, transversely interconnected by a brick-wall arrangement of fixed resistors. In accord with experimental observations on cardiac tissue, longitudinal propagation is continuous, whereas transverse propagation exhibits discontinuous features. The width and length of the sheet are 1.5 and 5 cm, respectively, and the anisotropy ratio is fixed at approximately 4:1. The membrane model is a modified Beeler-Reuter formulation incorporating faster sodium current dynamics. We fixed the basic wavelength and action potential duration of the propagating impulse by dividing the time constants of the secondary inward current by an integer K. Reentry was initiated by a standard cross-shock protocol, and the rotating activity appeared as curling patterns around the point of junction (the q-point) of the activation (A) and recovery (R) fronts. The curling R front always precedes the A front and is separated from it by the excitable gap. In addition, the R front is occasionally shifted abruptly through a merging with a slow-moving triggered secondary recovery front that is dissociated from the A front and q-point. Sustained irregular reentry associated with substantial excitable gap variations was simulated with short wavelengths (K = 8 and K = 4). Unsustained reentry was obtained with a longer wavelength (K = 2), leading to a breakup of the q-point locus and the triggering of new activation fronts.

The Theory of Uniform Cables-Part I: Calculation of Propagation Parameters

An algorithm for computing the electromagnetic propagation modes and their associated propagation constants (i.e., the loss and phase shift per length) is rigorously developed for uniform cables. The conductors (including the shield, if present) are assumed to have circular cross sections and to be covered by two layers of dielectric insulation. By means of the algorithm, it is now possible to compute the propagation parameters of uniform cables for all frequencies below the microwave range. The algorithm consists of calculating the eigenvectors and eigenvalues of a certain matrix, which are the set of conductor voltages of the modes and the associated propagation constants, respectively. The matrix in question is computed by methods developed in a companion paper on charge densities.

The Theory of Uniform Cables-Part II: Calculation of Charge Components

The analysis of electromagnetic propagation over uniform cables depends on the calculation of the charge densities on the conductors, relative to a potential function that is not necessarily constant on the conductors. By considering such a potential function as the real part of an analytic function, two Laurent series are derived, one of which involves the Fourier components of the potential function and its associated charge densities on the conductors. The second series accounts for the relative location of the conductors. The two series are equated to give a system of linear equations that can be solved for the charge components. The results obtained, which apply to uniform cables whose conductors (including the shield, if present) have circular cross sections and are covered with two layers of dielectric insulation, can be used to calculate the propagation modes and propagation constants of the cable.

Experimental Test of Propagation-Parameter Calculations for Shielded Balanced Pair Cables

Experimental verification is presented for a recently developed method for calculating propagation parameters, such as loss and phase-shift per length, of uniform cables. For the shielded balanced pair (sbp), a computer program has been written to carry out the calculations. In this paper, these calculations are compared with measurements of three different cables that can be modeled as sbps. Agreement between calculation and measurement was within 3.3 percent over the frequency range 50 Hz to 10 MHz. The greatest deviation occurred in a cable with substantial air space in the interstitial dielectric; for the other two cables agreement was within 2 percent.