Steady-state point-source stimulation of a nerve containing axons with an arbitrary distribution of diameters

Can high-field MREIT be used to directly detect neural activity? Theoretical considerations

We sought to determine the feasibility of directly studying neural tissue activity by analysis of differential phase shifts in MRI signals that occurred when trickle currents were applied to a bath containing active or resting neural tissue. We developed a finite element bidomain model of an aplysia abdominal ganglion in order to estimate the sensitivity of this contrast mechanism to changes in cell membrane conductance occurring during a gill-withdrawal reflex. We used our model to determine both current density and magnetic potential distributions within a sample chamber containing an isolated ganglion when it was illuminated with current injected synchronously with the MR imaging sequence and predicted the resulting changes in MRI phase images. This study provides the groundwork for attempts to image neural function using Magnetic Resonance Electrical Impedance Tomography (MREIT). We found that phase noise in a candidate 17.6 T MRI system should be sufficiently low to detect phase signal differences between active and resting membrane states at resolutions around 1 mm(3). We further delineate the broad dependencies of signal-to-noise ratio on activity frequency, current application time and active tissue fractions and outline strategies that can be used to lower phase noise below that presently observed in conventional MREIT techniques. We also propose the idea of using MREIT as an alternative means of studying neuromodulation.

Conductivity tensor mapping of the human brain using diffusion tensor MRI

Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity tensor of tissue can be quantitatively inferred from the water self-diffusion tensor as measured by diffusion tensor magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion tensor eigenvalues (respectively, final sigma and d) in agreement with theoretical bounds and experimental measurements presented here (final sigma/d approximately 0.844 +/- 0.0545 S small middle dots/mm(3), r(2) = 0.945). The extension to other biological transport phenomena is also discussed.

Selectivity of multiple-contact nerve cuff electrodes: a simulation analysis

Advances in functional neuromuscular stimulation (FNS) have increased the need for nerve cuff designs that can control multiple motor functions through selective stimulation of selected populations of axons. This selectivity has proved to be difficult to achieve. Recent experiments suggest that it is possible to slowly reshape peripheral nerve without affecting its physiological function. Using computer simulations we have tested the hypothesis that changing the cross section of a nerve from a round to a flat configuration can significantly improve the selectivity of a nerve cuff. We introduce a new index to estimate selectivity to evaluate the various designs. This index is based on the ability of a nerve electrode to stimulate a target axon without stimulating any other axons. The calculations involve a three-dimensional finite element model to represent the electrical properties of the nerve and cuff and the determination of the firing properties of individual axons. The selectivity rating was found to be significantly higher for the Flat Cuff than the Round Cuff. The result was valid with uniform or random distribution of axons and with a random distribution of fascicles diameters. Flattening of individual fascicles also improved the selectivity of the Flat Cuff but only when the number of contacts used was increased to maintain uniform contact density. Therefore, cuff designs that can reshape the nerve into flatter configurations should yield better cuff performance than the cylindrical cuffs but will require higher contact density.

Theoretical study of magnetic field of current monopoles in special volume conductor using symmetry analysis

We derive a formula for the magnetic field outside volume conductors having axial symmetry with radial and axial symmetrically distributed source currents. The magnetic field is shown to have components only along the cylindrical polar angle direction and its magnitude to depend only on the topological structure of the volume conductor and the location of the source current. With this formula, the magnetic field generated by the volume current of a current monopole within and on the symmetrical axis of several volume conductors (such as semi-infinite volume, infinite slab, sphere, infinite cylinder, semi-infinite cylinder, finite cylinder, prolate spheroid, and oblate spheroid) is shown to be equivalent to the magnetic field generated by a line current calculated using the Biot-Savart's law. In the first three volume conductors, the monopole solution of the magnetic field allows the calculation of magnetic fields generated by arbitrarily distributed (and balanced for finite volume conductors) current monopoles.

A generalized cable equation for magnetic stimulation of axons

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

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

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

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

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