Voltage Attenuation Research Articles

Neuron Morphology Influences Axon Initial Segment Plasticity.

In most vertebrate neurons, action potentials are initiated in the axon initial segment (AIS), a specialized region of the axon containing a high density of voltage-gated sodium and potassium channels. It has recently been proposed that neurons use plasticity of AIS length and/or location to regulate their intrinsic excitability. Here we quantify the impact of neuron morphology on AIS plasticity using computational models of simplified and realistic somatodendritic morphologies. In small neurons (e.g., dentate granule neurons), excitability was highest when the AIS was of intermediate length and located adjacent to the soma. Conversely, neurons having larger dendritic trees (e.g., pyramidal neurons) were most excitable when the AIS was longer and/or located away from the soma. For any given somatodendritic morphology, increasing dendritic membrane capacitance and/or conductance favored a longer and more distally located AIS. Overall, changes to AIS length, with corresponding changes in total sodium conductance, were far more effective in regulating neuron excitability than were changes in AIS location, while dendritic capacitance had a larger impact on AIS performance than did dendritic conductance. The somatodendritic influence on AIS performance reflects modest soma-to-AIS voltage attenuation combined with neuron size-dependent changes in AIS input resistance, effective membrane time constant, and isolation from somatodendritic capacitance. We conclude that the impact of AIS plasticity on neuron excitability will depend largely on somatodendritic morphology, and that, in some neurons, a shorter or more distally located AIS may promote, rather than limit, action potential generation.

Data for spatial characterization of AC signal propagation over primary neuron dendrites.

Action potentials generated near the soma propagate not only into the axonal nerve connecting to the adjacent neurons but also into the dendrites interacting with a diversity of synaptic inputs as well as voltage gated ion channels. Measuring voltage attenuation factors between the soma and all single points of the dendrites in the anatomically reconstructed primary neurons with the same cable properties, we report the signal propagation data showing how the alternating current (AC) signal such as action potentials back-propagates over the dendrites among different types of primary neurons. Fitting equations and their parameter values for the data are also presented to quantitatively capture the spatial profile of AC signal propagation from the soma to the dendrites in primary neurons. Our data is supplemental to our original study for the dependency of dendritic signal propagation and excitability, and their relationship on the cell type-specific structure in primary neurons (DOI: 10.1016/j.neulet.2015.10.017 [1]).

An asymptotic approximation to the cable equation for arbitrary diameter taper

Somatic integration of synaptic inputs relies on the propagation of currents arising from sources across the dendritic tree. Whilst active processes strongly contribute to current flow in most neurons, understanding the passive backbone to transmission allows a better intuitive grasp of dendritic function; the results of Rall in highlighting the properties of cylindrical dendrites[1] are of foundational importance in compartmental modelling and computational neuroscience. Dendrites are, however, not generally cylindrical, they tend to taper in a way that contributes to the normalisation of input currents towards the soma[2]. We have derived an asymptotic approximation to the voltage in dendrites with an arbitrary taper profile using the insight that voltage attenuation is substantially faster than radius change in realistic morphologies (Figure ​(Figure1A).1A). This result allows faster computation and greater insight than standard approaches using large numbers of cylinders or frusta to numerically compute voltage profiles. In addition, it provides easy generalisations of the standard results of cable theory involving transients and branches. Figure 1 Asymptotic approximations reveal fundamental properties of voltage flow in tapering dendrites. A Comparison of numerical (blue) and first-order asymptotic (black dashed) methods for determining the steady-state voltage in a quadratically tapering dendritic ... A particularly interesting implication of these results is that the optimal taper profile to proximally transmit maximum voltages can be found by variational calculus, matching results from non-parametric numerical optimisation which predicted a quadratic form for the diameter taper (Figure ​(Figure1B)1B) [3].

Abstract 16363: The Association Between Cerebral Oxygenation and Brain Waves Measured by Cerebral Oximetry and Electroencephalography (EEG) During Cardiopulmonary Resuscitation (CPR): A Feasibility Study

Background: Cerebral ischemia following cardiac arrest (CA) is associated with significant morbidity and mortality. A major hurdle to improving CA outcomes has been the lack of a real-time detection system capable of identifying cerebral ischemia/oxygenation as well as brain function during CPR as markers of global ischemia. In particular no studies have examined the feasibility of real-time EEG and cerebral oximetry monitoring during CPR to evaluate for these parameters. Methods: This was a single center study using a convenience sample of CA patients enrolled between 03/2014 and 03/2015. Inclusion criteria: In/out of hospital CA, age ≥ 18 years. Portable EEG (Masimo) and cerebral oximetry (Nonin) were used during CPR cases lasting >10 minutes. Raw EEG data were captured as consecutive images (1/second) during each pause in CPR (10 seconds), while oximetry was captured continuously. Results: 16 patients were recruited; mean age = 70±13 years; 11 males and 5 females. All subjects exhibited interpretable EEG patterns, while 50% (n=8/16) had >1 interpretable pattern. There were 428 EEG images. 40.7% (n=174/428) were artifactual due to electrical interference, poor electrode adhesion or movement. 59.3% (n=254/428) were interpretable with seven distinct patterns identified: marked voltage attenuation (MVA) (78%), theta (8%), delta (5%), diffuse quasi-periodic discharge (4%), burst suppression (2%), spike/wave (2%), generalized rhythmic delta activity (1%). Based on known neurological associations, these patterns were further categorized as a) favorable (theta/delta) or b) unfavorable (the remaining patterns). No significant association was observed between cerebral oxygenation (rSO2) and favorable vs. unfavorable EEG patterns (median rSO2 (IQR) = 43.8% (39-48%) vs. 47.5% (42-52%) respectively). Conclusions: Real-time monitoring of cerebral oxygenation and function during CA is feasible. While MVA is the commonest EEG pattern, other distinct patterns also exist. Further studies are needed to explore the association between cerebral oxygenation and EEG patterns during CA as well as to identify intra-CA EEG and oximetry thresholds as markers for therapeutic interventions aimed at ameliorating cerebral ischemia during CA in real-time.

Epileptic spasms in clusters without hypsarrhythmia

Here we present an update of the electroclinical features and evolution of patients with epileptic spasms (ES) in clusters without hypsarrhythmia, with or without focal or generalized paroxysmal discharges on the interictal electroencephalography (EEG). Between February 1990 and July 2012, 26 patients met the electroclinical diagnostic criteria of ES in clusters without hypsarrhythmia. The etiology of the ES was unknown in 15 patients and structural in 11. Age at onset of the ES was between 2 and 32 mo, with a mean age of 9 mo. Fifteen patients had seizures before the onset of ES. Focal spikes were observed in 12 patients, bilateral spikes and spikes and waves in nine, multifocal spikes in three, and two patients had a normal EEG. The ictal EEG recording showed diffuse high-amplitude slow waves in 15 patients, diffuse slow waves followed by voltage attenuation in six patients, and diffuse fast rhythms in five. ES resolved in six patients after a mean follow-up of 9 yr. Neuropsychological development has been normal in these six patients. Twenty patients continue with seizures refractory to antiepileptic drugs after a mean follow-up of 13 yr. Two of them were operated; they are seizure free, with a normal neuropsychological development. Of the 18 remaining patients, 10 have severe mental retardation, five have moderate mental retardation, and three have mild mental retardation. All but 14 of them show behavioral disturbances. Our patients represent an epileptic encephalopathy that may be considered a distinct epileptic syndrome rather than a variant of West syndrome.

Wideband Modeling, Field Measurement, and Simulation of a 420-kV Variable Shunt Reactor

A 420-kV gapped-core five-legged variable shunt reactor is modeled in the frequency range 5 Hz-10 MHz based on frequency sweep measurements and curve fitting using rational functions. Comparison with time-domain measurements at reduced voltage shows that the model can accurately predict the transient behavior of the shunt reactor, both for impinging overvoltages and circuit-breaker transient recovery voltages. Among the observations is that mutual coupling between the phases leads to a beat phenomenon in the reactor voltage following disconnection. Representing the shunt reactor by an LC parallel circuit leads to unrealistic results for steep-fronted incoming waves and high-frequency oscillating overvoltages, and for the attenuation of the transient recovery voltage following disconnection.

A Fault-Tolerant Three-Phase Adjustable Speed Drive Topology With Active Common-Mode Voltage Suppression

A fault-tolerant adjustable speed drive (ASD) topology is introduced in this paper. A conventional ASD topology is modified to address: 1) drive vulnerability to semiconductor device faults; 2) input voltage sags; 3) motor vulnerability to effects of long leads; and 4) minimization of common-mode (CM) voltage applied to the motor terminals. These objectives are attained by inclusion of an auxiliary IGBT inverter leg, three auxiliary diodes, and isolation-reconfiguration circuit. The design and operation of the proposed topology modifications are described for different modes: 1) fault mode, 2) active CM suppression mode, and 3) auxiliary sag compensation (ASC) mode. In case of fault and sag, the isolation and hardware reconfiguration are performed in a controlled manner using triacs/antiparallel thyristors. In normal operation, the auxiliary leg is controlled to actively suppress CM voltage. For inverter IGBT failures (short circuit and open circuit), the auxiliary leg is used as a redundant leg. During voltage sags, the auxiliary leg, along with auxiliary diodes, is operated as a boost converter. A current-shaping control strategy is proposed for the ASC mode. A detailed analysis of CM performance of the proposed topology is provided, and a new figure of merit, CM distortion ratio (CMDR), is introduced to compare the attenuation of CM voltage with that of a conventional ASD topology. The output filter design procedure is outlined. A design example is presented for an 80 kW ASD system, and simulation results validate the proposed auxiliary leg based fault-tolerant scheme. Experimental results from a scaled prototype rated at 1 hp are discussed in this paper.

Transient QRS amplitude attenuation is associated with clinical recovery in patients with takotsubo cardiomyopathy

Background/objectivesLow voltage QRS complexes (LQRSV) and amplitude attenuation of QRS voltage (AAQRS) have been described in takotsubo (TC) patients, and postulated as valuable pre-angiographic markers. The aim of this observational study is to evaluate potential diagnostic and prognostic features of QRS amplitude in TC and acute coronary syndrome (ACS) patients. MethodsFifty-eight patients with TC were matched with 58 patients with ACS according to age, gender, and presence or absence of ST elevation at hospital admission. A 12-lead ECG was recorded within 12h after symptoms onset, the day after coronary angiography (CA) and before hospital discharge. When available, ECGs prior and subsequent to the acute event were also collected. ResultsQRS amplitude showed a time related trend, with a first phase characterized by an initial decrease in amplitude in both groups and a second phase, with a progressive recovery of QRS amplitude in TC patients up to pre-event levels, while QRS amplitude in ACS patients remained substantially unchanged from admission onwards. Rise in AAQRS during hospitalization showed a positive linear association with systolic function recovery and both troponin I and CK-MB decrease (all p<0.01) in TC patients. A 20% increase of mean AAQRS from admission is able to predict LVEF recovery and troponin I and CK-MB normalization in TC patients with good sensitivity and specificity. ConclusionsLQRSV and AAQRS are not reliable in differentiating ACS from TC. However, QRS amplitude attenuation in TC is transient, and is linearly associated with systolic function recovery and cardiac biomarkers normalization.

Axon-somatic back-propagation in detailed models of spinal alpha motoneurons.

Antidromic action potentials following distal stimulation of motor axons occasionally fail to invade the soma of alpha motoneurons in spinal cord, due to their passing through regions of high non-uniformity. Morphologically detailed conductance-based models of cat spinal alpha motoneurons have been developed, with the aim to reproduce and clarify some aspects of the electrophysiological behavior of the antidromic axon-somatic spike propagation. Fourteen 3D morphologically detailed somata and dendrites of cat spinal alpha motoneurons have been imported from an open-access web-based database of neuronal morphologies, NeuroMorpho.org, and instantiated in neurocomputational models. An axon hillock, an axonal initial segment and a myelinated axon are added to each model. By sweeping the diameter of the axonal initial segment (AIS) and the axon hillock, as well as the maximal conductances of sodium channels at the AIS and at the soma, the developed models are able to show the relationships between different geometric and electrophysiological configurations and the voltage attenuation of the antidromically traveling wave. In particular, a greater than usually admitted sodium conductance at AIS is necessary and sufficient to overcome the dramatic voltage attenuation occurring during antidromic spike propagation both at the myelinated axon-AIS and at the AIS-soma transitions.

An Electrical Inspection of the Subsurface Cisternae of the Outer Hair Cell

The cylindrical outer hair cell (OHC) of Corti’s organ drives cochlear amplification by a voltage-dependent activation of the molecular motor, prestin (SLC26a5), in the cell’s lateral membrane. The voltage-dependent nature of this process leads to the troublesome observation that the membrane resistor-capacitor filter could limit high-frequency acoustic activation of the motor. Based on cable theory, the unique 30 nm width compartment (the extracisternal space, ECS) formed between the cell’s lateral membrane and adjacent subsurface cisternae (SSC) could further limit the influence of receptor currents on lateral membrane voltage. Here, we use dual perforated/whole-cell and loose patch clamp on isolated OHCs to sequentially record currents resulting from excitation at apical, middle, and basal loose patch sites before and after perforated patch rupture. We find that timing of currents is fast and uniform before whole-cell pipette washout, suggesting little voltage attenuation along the length of the lateral membrane. Prior treatment with salicylate, a disrupter of the SSC, confirms the influence of the SSC on current spread. Finally, a cable model of the OHC, which can match our data, indicates that the SSC poses a minimal barrier to current flow across it, thereby facilitating rapid delivery of voltage excitation to the prestin-embedded lateral membrane.

Chapter 21 - Electrophysiologic recordings in traumatic brain injury

Following a traumatic brain injury (TBI), the brain undergoes numerous electrophysiologic changes. The most common techniques used to evaluate these changes include electroencepalography (EEG) and evoked potentials. In animals, EEGs immediately following TBI can show either diffuse slowing or voltage attenuation, or high voltage spiking. Following a TBI, many animals display evidence of hippocampal excitability and a reduced seizure threshold. Some mice subjected to severe TBI via a fluid percussion injury will eventually develop seizures, which provides a useful potential model for studying the neurophysiology of epileptogenesis. In humans, the EEG changes associated with mild TBI are relatively subtle and may be challenging to distinguish from EEG changes seen in other conditions. Quantitative EEG (QEEG) may enhance the ability to detect post-traumatic electrophysiologic changes following a mild TBI. Some types of evoked potential (EP) and event related potential (ERP) can also be used to detect post-traumatic changes following a mild TBI. Continuous EEG monitoring (cEEG) following moderate and severe TBI is useful in detecting the presence of seizures and status epilepticus acutely following an injury, although some seizures may only be detectable using intracranial monitoring. CEEG can also be helpful for assessing prognosis after moderate or severe TBI. EPs, particularly somatosensory evoked potentials, can also be useful in assessing prognosis following severe TBI. The role for newer technologies such as magnetoencephalography and bispectral analysis (BIS) in the evaluation of patients with TBI remains unclear.

Input integration around the dendritic branches in hippocampal dentate granule cells.

Recent studies have shown that the dendrites of several neurons are not simple translators but are crucial facilitators of excitatory postsynaptic potential (EPSP) propagation and summation of synaptic inputs to compensate for inherent voltage attenuation. Granule cells (GCs)are located at the gateway for valuable information arriving at the hippocampus from the entorhinal cortex. However, the underlying mechanisms of information integration along the dendrites of GCs in the hippocampus are still unclear. In this study, we investigated the input integration around dendritic branches of GCs in the rat hippocampus. We applied differential spatiotemporal stimulations to the dendrites using a high-speed glutamate-uncaging laser. Our results showed that when two sites close to and equidistant from a branching point were simultaneously stimulated, a nonlinear summation of EPSPs was observed at the soma. In addition, nonlinear summation (facilitation) depended on the stimulus location and was significantly blocked by the application of a voltage-dependent Ca(2+) channel antagonist. These findings suggest that the nonlinear summation of EPSPs around the dendritic branches of hippocampal GCs is a result of voltage-dependent Ca(2+) channel activation and may play a crucial role in the integration of input information.

Interpretation of the Low-Voltage ECG

Interpretation of the Low-Voltage ECG

Denervation-induced homeostatic dendritic plasticity in morphological granule cell models

Event Abstract Back to Event Denervation-induced homeostatic dendritic plasticity in morphological granule cell models Steffen Platschek1, Hermann Cuntz1, 2, Mario Vuksic1, 3, Thomas Deller1 and Peter Jedlicka1* 1 Goethe University, Institute of Clinical Neuroanatomy, Neuroscience Center, Germany 2 Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Germany 3 University of Zagreb, School of Medicine, Croatian Institute for Brain Research, Croatia Neuronal death and subsequent denervation of target areas are major consequences of several neurological conditions such asischemia or neurodegeneration (Alzheimer's disease). The denervation-induced axonal loss results in reorganization of the dendritic tree of denervated neurons. The dendritic reorganization has been previously studied using entorhinal cortex lesion (ECL). ECL leads to shortening and loss of dendritic segments in the denervated outer molecular layer of the dentate gyrus. However, the functional importance of these long-term dendritic alterations is not yet understood and their impact on neuronal electrical properties remains unclear. Here we analyzed what happens to the electrotonic structure and excitability of dentate granule cells after lesion-induced alterations of their dendritic morphology, assuming all other parameters remain equal. We performed comparative electrotonic analysis in anatomically and biophysically realistic compartmental models of 3D-reconstructed healthy and denervated granule cells. Using the method of morphological modeling based on optimization principles minimizing the amount of wiring and maximizing synaptic democracy, we built artificial granule cells which replicate morphological features of their real counterparts. Our results show that somatofugal and somatopetal voltage attenuation in the passive cable model are strongly reduced in denervated granule cells. In line with these predictions, the attenuation both of simulated backpropagating action potentials and forward propagating EPSPs was significantly reduced in dendrites of denervated neurons. Intriguingly, the enhancement of action potential backpropagation occurred specifically in the denervated dendritic layers. Furthermore, simulations of synaptic f-I curves revealed a homeostatic increase of excitability in denervated granule cells. In summary, our morphological and compartmental modeling indicates that unless modified by changes of passive and/or active membrane properties, the plastic remodeling of dendrites following lesion of entorhinal inputs to granule cells will boost the efficacy of action potential backpropagation significantly and maintain their firing rate. Our results suggest that in addition to synaptic and intrinsic plasticity, a novel form of homeostatic plasticity,structural plasticity due todendritic remodeling.is operating in denervated neurons. Acknowledgements Supported by NSF/BMBF (US-German Collaboration in Computational Neuroscience, No. 01GQ1203A), by Young Investigators Grant (Faculty of medicine, Goethe-University) and by DFG Keywords: electrotonic analysis, Computer Simulation, compartmental modeling, morphological modeling, voltage attenuation, backpropagating action potential, homeostatic plasticity, granule cell Conference: 4th NAMASEN Training Workshop - Dendrites 2014, Heraklion, Greece, 1 Jul - 4 Jul, 2014. Presentation Type: Poster presentation Topic: morphological and functional characterizations Citation: Platschek S, Cuntz H, Vuksic M, Deller T and Jedlicka P (2014). Denervation-induced homeostatic dendritic plasticity in morphological granule cell models. Front. Syst. Neurosci. Conference Abstract: 4th NAMASEN Training Workshop - Dendrites 2014. doi: 10.3389/conf.fnsys.2014.05.00028 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 11 Apr 2014; Published Online: 12 Jun 2014. * Correspondence: Dr. Peter Jedlicka, Goethe University, Institute of Clinical Neuroanatomy, Neuroscience Center, Frankfurt, Other, please specify, 60590, Germany, peterjedlicka@yahoo.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Steffen Platschek Hermann Cuntz Mario Vuksic Thomas Deller Peter Jedlicka Google Steffen Platschek Hermann Cuntz Mario Vuksic Thomas Deller Peter Jedlicka Google Scholar Steffen Platschek Hermann Cuntz Mario Vuksic Thomas Deller Peter Jedlicka PubMed Steffen Platschek Hermann Cuntz Mario Vuksic Thomas Deller Peter Jedlicka Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Electrocardiogram voltage attenuation and shortening of the duration of P-waves, QRS complexes, and QT intervals

Multiple pathologies in concert may lead to attenuation of the electrocardiogram (ECG) voltage. A case of a patient illustrating the above is presented, who showed marked attenuation of the ECG voltage. Automated values of the amplitude of the ECG QRS complexes, P-waves, and T-waves (in mm), duration of the QRS complexes, P-waves, and QT intervals (in ms), in 2 ECGs were compared. The patient was a 64-year-old woman who developed in the setting of a fatal illness, pleural and pericardial effusions, pneumomediastinum, pneumoperitoneum, subcutaneous emphysema in the neck and chest, peripheral edema with weight gain of 43.4lbs, marked hypoalbuminemia, abnormal liver tests, and renal failure. All the above pathologies led to a marked attenuation of the ECG voltage, and shortening of the mean P-wave, QRS complexes, and QTc interval durations. The postulated mechanism of the observed ECG phenomena is discussed.

Analysis of the Dielectric Loss in the Transmission Line Based on Time Domain BLT Equation

Dielectric loss is caused due to imperfect dielectric insulation, in order to study the impact of the dielectric loss consider a uniform loss transmission line with leak conductance. The BLT equation from the frequency domain to time domain is derived to improve the time domain BLT equation, and the aim of using the time domain BLT equation to calculate load voltage of the transmission line with transient signal source, through the calculation results to analyze the impact of the dielectric loss. The results showed that the attenuation of the terminal load transient response voltage occurred when the dielectric loss exists, and this effect is nonlinear.

Data Acquisition System Connect to CMG-3T Low-Frequency Seismic Pendulum

Aiming at the low-frequency performance of the lowfrequency seismic pendulum CMG -3T, we design a data acquisition system can acquire the low-frequency seismic waves, at the same time we accomplish the process of adjusting the CMG-3T. This paper gives designing scheme include the low noise design of the power module, the design of the connector to RS232 which can send command to adjusting the mass of CMG-3T,the design of voltage attenuation network and no-source low-pass filter network of data acquisition system, the last is the design of software for adjusting the CMG-3T.

Design of a silicon Mach-Zehnder modulator with a U-type PN junction.

We have developed a silicon depletion-mode modulator featuring a novel U-type PN junction that enables a substantial improvement in electro-optical modulation efficiency. Through electrical, optical, and manufacturing process simulations, an ultralow VπL of 0.63 V·cm is exhibited with 3 V reverse bias. The high modulation efficiency enables a high extinction ratio (ER) of >17 dB with only a 1 mm phase shifter when the excess loss at the "on" state is 2 dB. The ER can maintain >12 dB at ∼28 GHz operation with a 3 V peak-to-peak voltage due to the small voltage attenuation of the short phase shifter.

Generalized cable theory for neurons in complex and heterogeneous media

Cable theory has been developed over the last decade, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion, or capacitive effects, but their impact on cable properties is not known. In this paper, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for morecomplex media, for example, in the presence of ionic diffusion, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically, always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.

The electric properties of extracellular media affect cable properties of neurons

Cable theory has been developed over the last decades, usually assuming that the extracellular space around membranes is a perfect resistor. However, extracellular media may display more complex electrical properties due to various phenomena, such as polarization, ionic diffusion or capacitive effects, but their impact on cable properties is not known. Here, we generalize cable theory for membranes embedded in arbitrarily complex extracellular media. We outline the generalized cable equations, then consider specific cases. The simplest case is a resistive medium, in which case the equations recover the traditional cable equations. We show that for more complex media, for example in the presence of ionic diffusion, or polarization, the impact on cable properties such as voltage attenuation can be significant. We illustrate this numerically always by comparing the generalized cable to the traditional cable. We conclude that the nature of intracellular and extracellular media may have a strong influence on cable filtering as well as on the passive integrative properties of neurons.