The extracellular potential field of the single active nerve fiber in a volume conductor

The potential field of an active fiber in a uniform medium of infinite extent and within a nerve trunk is calculated from transmembrane potential data. The resulting distributions are given quantitatively. A comparison of both magnitude and field pattern in the nerve trunk and infinite medium environments is made and the effect of interstitial conductivity and nerve trunk diameter on potential magnitudes is considered.     

On Bioelectric Potentials in an Inhomogeneous Volume Conductor

Green's theorem is used to derive two sets of expressions for the quasi-static potential distribution in an inhomogeneous volume conductor. The current density in passive regions is assumed to be linearly related instantaneously to the electric field. Two equations are derived relating potentials to an arbitrary distribution of impressed currents. In one, surfaces of discontinuity in electrical conductivity are replaced by double layers and in the other, by surface charges. A multipole equivalent generator is defined and related both to the potential distribution on the outer surface of the volume conductor and to the current sources. An alternative result involves the electric field at the outer surface rather than the potential. Finally, the impressed currents are related to electrical activity at the membranes of active cells. The normal component of membrane current density is assumed to be equal at both membrane surfaces. One expression is obtained involving the potentials at the inner and outer surfaces of the membrane. A second expression involves the transmembrane potential and the normal component of membrane current.     

Electric Field-Induced Transmembrane Potential Depends on Cell Density and Organizatio

Electrochemotherapy is a novel technique to enhance the delivery of chemotherapeutic drugs into tumor cells. In this procedure, electric pulses are delivered to cancerous cells, which induce membrane permeabilization, to facilitate the passage of cytotoxic drugs through the cell membrane. This study examines how electric fields interact with and polarize a system of cells. Specifically, we consider how cell density and organization impact on induced cell transmembrane potential due to an external electric field. First, in an infinite volume of spherical cells, we examined how cell packing density impacts on induced transmembrane potential. With high cell density, we found that maximum induced transmembrane potential is suppressed and that the transmembrane potential distribution is altered. Second, we considered how orientation of cell sheets and strands, relative to the applied field, affects induced transmembrane potential. Cells that are parallel to the field direction suppress induced transmembrane potential, and those that lie perpendicular to the applied field potentiate its effect. Generally, we found that both cell density and cell organization are very important in determining the induced transmembrane potential resulting from an applied electric field.     

A calculation of the magnetic field of a nerve action potential.

The magnetic field outside an isolated axon is calculated using transmembrane potential data to specify the boundary conditions to a solution of Laplace's equation. It is shown that the contribution to the magnetic field from the current inside the membrane is two orders of magnitude larger than that from the external current. The contribution from current within the membrane is negligible. Comparisons are made between waveforms calculated for a crayfish lateral axon and those measured for a frog sciatic nerve. This calculation suggests that the magnetic field measured outside nerves can be used to determine their internal current without puncturing the nerve membrane.     

Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment

The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.     

The magnetic field of a single axon. A comparison of theory and experiment.

The magnetic field and the transmembrane action potential of a single nerve axon were measured simultaneously. The volume conductor model was used to calculate the magnetic field from the measured action potential, allowing comparison of the model predictions with the experimental data. After analyzing the experiment for all systematic errors, we conclude that the shape of the magnetic field can be accurately predicted from the transmembrane potential and, more importantly, the shape of the transmembrane potential can be calculated from the magnetic field. The data are used to determine ri, the internal resistance per unit length of the axon, to be 19.3 +/- 1.9 k omega mm-1, implying a value for the internal conductivity of 1.44 +/- 0.33 omega -1 m-1. Magnetic measurements are compared with standard bioelectric techniques for studying nerve axons.     

不同时变磁场对神经纤维的诱导刺激作用的仿真研究

利用神经纤维的无源电缆模型描述神经纤维在磁刺激下的阈下行为,通过数字仿真得出了神经纤维在不同频率的磁刺激感应电场作用下阈下膜电位的时间特征包括波形和幅度,发现高频的感应电场诱导作用下得到的膜电位幅值小于低频电场的性质。同时采用积分变换频域分析的方法,得出了在不同空间分布的感应电场诱导刺激作用下神经纤维的响应特性,发现和低频比较,高频的空间分布函数频率成分的感应电场诱导得到的膜电位幅值较低。计算出在刺激线圈中采用典型刺激电流作用下在神经纤维响应得到的膜电位的特征。从时空两域阐述神经纤维对不同时变磁场诱导作用下的阈下响应行为,对磁刺激仪中刺激线圈的刺激电流的选择和线圈尺寸的设计都具有指导意义。     

Electrostatic modeling of ion pores. Energy barriers and electric field profiles

This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied. The method used is one introduced by Levitt (1978, Biophys. J. 22:209), who solved an equivalent problem, in which a surface charge density is placed at the dielectric boundary. It is shown that there are singularities in this surface charge density if the model system has sharp corners. Numerically accurate calculations require exact treatment of these singularities. The major result of this paper is the development of a projection method that explicitly accounts for this behavior. It is shown how this technique can be used to compute, both reliably and efficiently, the electrical potential within a model pore in response to any electrical source. As the length of a channel with fixed radius is increased, the peak in the image potential approaches that of an infinitely long channel more rapidly than previously believed. When a transmembrane potential is applied the electric field within a pore is constant over most of its length. Unless the channel is much longer than its radius, the field extends well into the aqueous domain. For sufficiently dissimilar dielectrics the calculated values for the peak in the image potential and for the field well within the pore can be summarized by simple empirical expressions that are accurate to within 5%.     

An analytical model for the calculation of the change in transmembrane potential produced by an ultrawideband electromagnetic pulse

The electric field pulse shape and change in transmembrane potential produced at various points within a sphere by an intense, ultrawideband pulse are calculated in a four stage, analytical procedure. Spheres of two sizes are used to represent the head of a human and the head of a rat. In the first stage, the pulse is decomposed into its Fourier components. In the second stage, Mie scattering analysis (MSA) is performed for a particular point in the sphere on each of the Fourier components, and the resulting electric field pulse shape is obtained for that point. In the third stage, the long wavelength approximation (LWA) is used to obtain the change in transmembrane potential in a cell at that point. In the final stage, an energy analysis is performed. These calculations are performed at 45 points within each sphere. Large electric fields and transmembrane potential changes on the order of a millivolt are produced within the brain, but on a time scale on the order of nanoseconds. The pulse shape within the brain differs considerably from that of the incident pulse. Comparison of the results for spheres of different sizes indicates that scaling of such pulses across species is complicated.     

Non-uniform Distribution of Outer Hair Cell Transmembrane Potential Induced by Extracellular Electric Field

Intracochlear electric fields arising out of sound-induced receptor currents, silent currents, or electrical current injected into the cochlea induce transmembrane potential along the outer hair cell (OHC) but its distribution along the cells is unknown. In this study, we investigated the distribution of OHC transmembrane potential induced along the cell perimeter and its sensitivity to the direction of the extracellular electric field (EEF) on isolated OHCs at a low frequency using the fast voltage-sensitive dye ANNINE-6plus. We calibrated the potentiometric sensitivity of the dye by applying known voltage steps to cells by simultaneous whole-cell voltage clamp. The OHC transmembrane potential induced by the EEF is shown to be highly nonuniform along the cell perimeter and strongly dependent on the direction of the electrical field. Unlike in many other cells, the EEF induces a field-direction-dependent intracellular potential in the cylindrical OHC. We predict that without this induced intracellular potential, EEF would not generate somatic electromotility in OHCs. In conjunction with the known heterogeneity of OHC membrane microdomains, voltage-gated ion channels, charge, and capacitance, the EEF-induced nonuniform transmembrane potential measured in this study suggests that the EEF would impact the cochlear amplification and electropermeability of molecules across the cell.     

Non-uniform Distribution of Outer Hair Cell Transmembrane Potential Induced by Extracellular Electric Field

Intracochlear electric fields arising out of sound-induced receptor currents, silent currents, or electrical current injected into the cochlea induce transmembrane potential along the outer hair cell (OHC) but its distribution along the cells is unknown. In this study, we investigated the distribution of OHC transmembrane potential induced along the cell perimeter and its sensitivity to the direction of the extracellular electric field (EEF) on isolated OHCs at a low frequency using the fast voltage-sensitive dye ANNINE-6plus. We calibrated the potentiometric sensitivity of the dye by applying known voltage steps to cells by simultaneous whole-cell voltage clamp. The OHC transmembrane potential induced by the EEF is shown to be highly nonuniform along the cell perimeter and strongly dependent on the direction of the electrical field. Unlike in many other cells, the EEF induces a field-direction-dependent intracellular potential in the cylindrical OHC. We predict that without this induced intracellular potential, EEF would not generate somatic electromotility in OHCs. In conjunction with the known heterogeneity of OHC membrane microdomains, voltage-gated ion channels, charge, and capacitance, the EEF-induced nonuniform transmembrane potential measured in this study suggests that the EEF would impact the cochlear amplification and electropermeability of molecules across the cell.     

The relationship between sensitivity to 60-Hz electric fields and induced transmembrane potentials in plants root cells

Summary Growth rates and cell diameters were determined from 12 species of plant roots exposed to a 60-Hertz (Hz) electric field of 360 Volts per meter (V/m) in an aqueous inorganic nutrient medium [conductivity: 0.07–0.09 Siemens per meter (S/m)]. The degree of growth depression ranged from zero to nearly 100 percent of control. Cell diameters ranged from 13.5 to 31.8 µm as an averaged value for procambial, cortical, and meristem cells. Sensitivity to the electric field as determined by root growth rate reduction increased with increasing cell size. Sensitivity also increased with increase in 60 Hz induced transmembrane potentials; the transmembrane potential threshold for growth reduction was about 6.0 mV and the potential for near-complete cessation of growth was about 10–11 mV.Two different hypothetical mechanisms of action by which applied electric fields induce biological effects at the cellular level were tested. The two mechanisms pertain to different possible modes of action of applied electric fields: one mechanism postulates the involvement of the transmembrane field, the other mechanism postulates the tangential electric field as the important factor for inducing biological effects. The data support the transmembrane and not the tangential field mechanism. It is concluded that the effects observed are consistent with a membrane related mechanism and that there is a narrow range (a few mV) between threshold and debilitating induced membrane potentials.     

Extracellular currents and potentials of the active myelinated nerve fiber.

This paper is concerned with the accurate and rapid calculation of extracellular potentials and currents from an active myelinated nerve fiber in a volume conductor, under conditions of normal and abnormal conduction. The neuroelectric source for the problem is characterized mathematically by using a modified version of the distributed parameter model of L. Goldman and J. S. Albus (1968, Biophys. J., 8:596-607) for the myelinated nerve fiber. Solution of the partial differential equation associated with the model provides a waveform for the spatial distribution of the transmembrane potential V(z). This model-generated waveform is then used as input to a second model that is based on the principles of electromagnetic field theory, and allows one to calculate easily the spatial distribution for the potential everywhere in the surrounding volume conductor for the nerve fiber. In addition, the field theoretic model may be used to calculate the total longitudinal current in the extracellular medium (I0L(z)) and the transmembrane current per unit length (im(z)); both of these quantities are defined in connection with the well-known core conductor model and associated cable equations in electrophysiology. These potential and current quantities may also be calculated as functions of time and as such, are useful in interpreting measured I0L(t) and im(t) data waveforms. An analysis of the accuracy of conventionally used measurement techniques to determine I0L(t) and im(t) is performed, particularly with regard to the effect of electrode separation distance and size of the volume conductor on these measurements. Also, a simulation of paranodal demyelination at a single node of Ranvier is made and its effects on potential and current waveforms as well as on the conduction process are determined. In particular, our field theoretic model is used to predict the temporal waveshape of the field potentials from the active, non-uniformly conducting nerve fiber in a finite volume conductor.     

Evidence for GABAergic fibers entering the superior cervical ganglion of rat from the preganglionic nerve trunk

The origin of gamma-aminobutyric acid immunoreactive (GABA-IR) nerve fibers present in the superior cervical ganglion (SCG) of rat was investigated. With immunocytochemical techniques many nerve fibers showed GABA-like positivity in the cervical sympathetic trunk, whereas similar staining could not be revealed in the internal carotid nerve or in the external carotid nerve. Ligation of the cervical sympathetic trunk for 24 h resulted a dramatic reduction in the staining density in the ganglion and in the cervical sympathetic trunk distal to the ligature. After transection of the preganglionic nerve fibers for eleven days or more, very few fibers staining for GABA were seen in the ganglion. The immunohistochemical results suggest that a major source of GABA within the SCG is a population of GABAergic axons entering from the preganglionic trunk.     

Evidence for GABAergic fibers entering the superior cervical ganglion of rat from the preganglionic nerve trunk

Summary The origin of gamma-aminobutyric acid immunoreactive (GABA-IR) nerve fibers present in the superior cervical ganglion (SCG) of rat was investigated. With immunocytochemical techniques many nerve fibers showed GABA-like positivity in the cervical sympathetic trunk, whereas similar staining could not be revealed in the internal carotid nerve or in the external carotid nerve. Ligation of the cervical sympathetic trunk for 24 h resulted a dramatic reduction in the staining density in the ganglion and in the cervical sympathetic trunk distal to the ligature. After transection of the preganglionic nerve fibers for eleven days or more, very few fibers staining for GABA were seen in the ganglion. The immunohistochemical results suggest that a major source of GABA within the SCG is a population of GABAergic axons entering from the preganglionic trunk.     

Induction of action potentials in fish red muscle by denervation

The effects of denervation on the electrical membrane properties of fish red muscle were investigated. Forty to fifty hours after denervation, miniature endplate potentials disappeared abruptly and field stimulation of the nerve within the muscle failed to evoke endplate potentials, indicating that transmission failure occurred at this time. The membrane resistance of the red muscle fibre increased after denervation. Normally innervated fish red muscles do not generate action potentials in response to either nerve or direct muscle stimulation. However, approximately 3 weeks after nerve sectioning, action potentials could be induced in the muscles. The action potential was sodium-dependent, and was sensitive to tetrodotoxin. Actinomycin D injected in the early phase after operation suppressed the induction of the action potential. These results indicate that RNA synthesis is preliminary to the induction of the action potential mechanism, and that this mechanism is under neural control.     

Effect of pore structure on energy barriers and applied voltage profiles. I. Symmetrical channels.

This paper presents calculations of the image potential for an ion in an aqueous pore spanning a lipid membrane and for the electric field produced in such a pore when a transmembrane potential is applied. The pore diameter may be variable. As long as the length-to-radius ratio in the narrow portion of a channel is large enough, the image potential for an ion in or near the mouth of a channel is determined by the geometry of the mouth. Within the constriction, the image potential of the ion-pore system may be reasonably approximated by constructing an "equivalent pore" of uniform diameter spanning a somewhat thinner membrane. When a transmembrane potential is applied the electric field within a constricted, constant radius, section of the model pore is constant. If the length-to-radius ratio of the narrow part of the channel is not too large or the channel ensemble has wide mouths, the field extends a significant distance into the aqueous region. The method is used to model features of the gramicidin A channel. The energy barrier for hydration (for exiting the channel) is identified with the activation energy for gramicidin conductance (Bamberg and Läuger, 1974, Biochim. Biophys. Acta. 367:127).     

Reconstruction of the Abdominal Vagus Nerve Using Sural Nerve Grafts in Canine Models

Background

Recently, vagus nerve preservation or reconstruction of vagus has received increasing attention. The present study aimed to investigate the feasibility of reconstructing the severed vagal trunk using an autologous sural nerve graft.

Methods

Ten adult Beagle dogs were randomly assigned to two groups of five, the nerve grafting group (TG) and the vagal resection group (VG). The gastric secretion and emptying functions in both groups were assessed using Hollander insulin and acetaminophen tests before surgery and three months after surgery. All dogs underwent laparotomy under general anesthesia. In TG group, latency and conduction velocity of the action potential in a vagal trunk were measured, and then nerves of 4 cm long were cut from the abdominal anterior and posterior vagal trunks. Two segments of autologous sural nerve were collected for performing end-to-end anastomoses with the cut ends of vagal trunk (8–0 nylon suture, 3 sutures for each anastomosis). Dogs in VG group only underwent partial resections of the anterior and posterior vagal trunks. Laparotomy was performed in dogs of TG group, and latency and conduction velocity of the action potential in their vagal trunks were measured. The grafted nerve segment was removed, and stained with anti-neurofilament protein and toluidine blue.

Results

Latency of the action potential in the vagal trunk was longer after surgery than before surgery in TG group, while the conduction velocity was lower after surgery. The gastric secretion and emptying functions were weaker after surgery in dogs of both groups, but in TG group they were significantly better than in VG group. Anti-neurofilament protein staining and toluidine blue staining showed there were nerve fibers crossing the anastomosis of the vagus and sural nerves in dogs of TG group.

Conclusion

Reconstruction of the vagus nerve using the sural nerve is technically feasible.     

Modelling the influence of thermal effects induced by radio frequency electric field on the dynamics of the ATPase nano-biomolecular motors

We model the dynamics of the F₀ component of the F₀F₁-ATPase mitochondrion-based nano-motor operating in a stochastically-fluctuating medium that represents the intracellular environment. The stochastic dynamics are modeled via Langevin equation of motion wherein fluctuations are treated as white noise. We have investigated the influence of an applied alternating electric field on the rotary motion of the F₀ rotor in such an environment. The exposure to the field induces a temperature rise in the mitochondrion’s membrane, within which the F₀ is embedded. The external field also induces an electric potential that promotes a change in the mitochondrion’s transmembrane potential (TMP). Both the induced temperature and the change in TMP contribute to a change in the dynamics of the F₀. We have found that for external fields in the radio frequency (RF) range, normally present in the environment and encountered by biological systems, the contribution of the induced thermal effects, relative to that of the induced TMP, to the dynamics of the F₀ is more significant. The changes in the dynamics of the F₀ part affect the frequency of the rotary motion of the F₀F₁-ATPase protein motor which, in turn, affects the production rate of the ATP molecules.     

A study of pre- and postganglionic fibres in the intestinal nerve (Remak's nerve) of the chicken

Summary The mean peak CV's of two electrophysiologically defined groups of fibres in the intestinal nerve of the chicken have been determined.One group of fibres is constituted by the processes of enteric cholinergic neurones which project along the side branches of the intestinal nerve and synapse within the nerve trunk. These preganglionic fibres have a mean peak CV (at 40 °C) of 0.31 m·s^–1.The other group is made up of fibres of postganglionic neurones which project orally along the nerve trunk. The results suggest that some postganglionic neurones project only as far as the next ganglion whilst others project beyond the next two ganglia for distances greater than 5 mm. The postganglionic fibres have a mean peak CV (at 40 °C) of 0.71 m·s^–1.These figures demonstrate that both pre- and postganglionic fibres are unmyelinated. The temperature coefficient (Q₁₀) for the CV of unmyelinated fibres in the intestinal nerve was 1.57.Abbreviations CAP compound action potential - CV conduction velocity - Q ₁₀ temperature coefficient