Shielding effects of myelin sheath on axolemma depolarization under transverse electric field stimulation

Axonal stimulation with electric currents is an effective method for controlling neural activity. An electric field parallel to the axon is widely accepted as the predominant component in the activation of an axon. However, recent studies indicate that the transverse component to the axolemma is also effective in depolarizing the axon. To quantitatively investigate the amount of axolemma polarization induced by a transverse electric field, we computed the transmembrane potential (Vm) for a conductive body that represents an unmyelinated axon (or the bare axon between the myelin sheath in a myelinated axon). We also computed the transmembrane potential of the sheath-covered axonal segment in a myelinated axon. We then systematically analyzed the biophysical factors that affect axonal polarization under transverse electric stimulation for both the bare and sheath-covered axons. Geometrical patterns of polarization of both axon types were dependent on field properties (magnitude and field orientation to the axon). Polarization of both axons was also dependent on their axolemma radii and electrical conductivities. The myelin provided a significant “shielding effect” against the transverse electric fields, preventing excessive axolemma depolarization. Demyelination could allow for prominent axolemma depolarization in the transverse electric field, via a significant increase in myelin conductivity. This shifts the voltage drop of the myelin sheath to the axolemma. Pathological changes at a cellular level should be considered when electric fields are used for the treatment of demyelination diseases. The calculated term for membrane polarization (Vm) could be used to modify the current cable equation that describes axon excitation by an external electric field to account for the activating effects of both parallel and transverse fields surrounding the target axon

Mechanic Stress Generated by a Time-Varying Electromagnetic Field on Bone Surface

Bone cells sense mechanical load, which is essential for bone growth and remodeling. In a fracture, this mechanism is compromised. Electromagnetic stimulation has been widely used to assist in bone healing, but the underlying mechanisms are largely unknown. A recent hypothesis suggests that electromagnetic stimulation could influence tissue biomechanics; however, a detailed quantitative understanding of EM-induced biomechanical changes in the bone is unavailable. This paper used a muscle/bone model to study the biomechanics of the bone under EM exposure. Due to the dielectric properties of the muscle/bone interface, a time-varying magnetic field can generate both compressing and shear stresses on the bone surface, where many mechanical sensing cells are available for cellular mechanotransduction. I calculated these stresses and found that the shear stress is significantly greater than the compressing stress. Detailed parametric analysis suggests that both the compressing and shear stresses are dependent on the geometrical and electrical properties of the muscle and the bone. These stresses are also functions of the orientation of the coil and the frequency of the magnetic field. It is speculated that the EM field could apply biomechanical influence to fractured bone, through the fine-tuning of the controllable field parameters

Vesicle Biomechanics in a Time-Varying Magnetic Field

Background Cells exhibit distortion when exposed to a strong electric field, suggesting that the field imposes control over cellular biomechanics. Closed pure lipid bilayer membranes (vesicles) have been widely used for the experimental and theoretical studies of cellular biomechanics under this electrodeformation. An alternative method used to generate an electric field is by electromagnetic induction with a time-varying magnetic field. References reporting the magnetic control of cellular mechanics have recently emerged. However, theoretical analysis of the cellular mechanics under a time-varying magnetic field is inadequate. We developed an analytical theory to investigate the biomechanics of a modeled vesicle under a time-varying magnetic field. Following previous publications and to simplify the calculation, this model treated the inner and suspending media as lossy dielectrics, the membrane thickness set at zero, and the electric resistance of the membrane assumed to be negligible. This work provided the first analytical solutions for the surface charges, electric field, radial pressure, overall translational forces, and rotational torques introduced on a vesicle by the time-varying magnetic field. Frequency responses of these measures were analyzed, particularly the frequency used clinically by transcranial magnetic stimulation (TMS). Results The induced surface charges interacted with the electric field to produce a biomechanical impact upon the vesicle. The distribution of the induced surface charges depended on the orientation of the coil and field frequency. The densities of these charges were trivial at low frequency ranges, but significant at high frequency ranges. The direction of the radial force on the vesicle was dependent on the conductivity ratio between the vesicle and the medium. At relatively low frequencies (\u3c200 \u3eKHz), including the frequency used in TMS, the computed radial pressure and translational forces on the vesicle were both negligible. Conclusions This work provides an analytical framework and insight into factors affecting cellular biomechanics under a time-varying magnetic field. Biological effects of clinical TMS are not likely to occur via alteration of the biomechanics of brain cells

A compact theory of magnetic nerve stimulation: predicting how to aim

Background: A compact theory that predicts quantitatively when and where magnetic neurostimulation will occur is needed as a guide to therapy, ideally providing a single equation that defines the target volume of tissue excited by single or dual coils. Methods: A first-principles analysis of magnetic stimulation incorporating a simplified description of electromagnetic fields and a simplified cable theory of the axon yields a mathematical synthesis predicting how to aim. Results: Nerve stimulation produced by a single circular coil having one or more closely packed turns occurs in donut shaped volume of tissue beneath the coil. Axons spanning several millimeters are the sites of magnetic stimulation. The sites of maximal transmembrane depolarization in nerve fibers correspond to points where the axons enter or exit this volume of magnetically induced voltage and current. The axonal membrane at one end is depolarized locally during the rising phase of current in the coil. The axonal membrane at the opposite end is depolarized locally during the falling phase of current in the coil. Penetration depths of several centimeters from the skin surface or approximately one to two coil radii are practical. With two coils placed in a figure-of-eight configuration the separate clockwise and counterclockwise currents generate magnetic fields that add, producing maximal stimulation of a spindle shaped volume, centered at a depth of one-third to one-half coil radius from the body surface. Conclusions: This condensed synthesis of electromagnetic theory and cable theories of axon physiology provides a partial solution to the targeting problem in peripheral and in transcranial magnetic stimulatio

Transmembrane potential induced on the internal organelle by a time-varying magnetic field: a model study

<p>Abstract</p> <p>Background</p> <p>When a cell is exposed to a time-varying magnetic field, this leads to an induced voltage on the cytoplasmic membrane, as well as on the membranes of the internal organelles, such as mitochondria. These potential changes in the organelles could have a significant impact on their functionality. However, a quantitative analysis on the magnetically-induced membrane potential on the internal organelles has not been performed.</p> <p>Methods</p> <p>Using a two-shell model, we provided the first analytical solution for the transmembrane potential in the organelle membrane induced by a time-varying magnetic field. We then analyzed factors that impact on the polarization of the organelle, including the frequency of the magnetic field, the presence of the outer cytoplasmic membrane, and electrical and geometrical parameters of the cytoplasmic membrane and the organelle membrane.</p> <p>Results</p> <p>The amount of polarization in the organelle was less than its counterpart in the cytoplasmic membrane. This was largely due to the presence of the cell membrane, which "shielded" the internal organelle from excessive polarization by the field. Organelle polarization was largely dependent on the frequency of the magnetic field, and its polarization was not significant under the low frequency band used for transcranial magnetic stimulation (TMS). Both the properties of the cytoplasmic and the organelle membranes affect the polarization of the internal organelle in a frequency-dependent manner.</p> <p>Conclusions</p> <p>The work provided a theoretical framework and insights into factors affecting mitochondrial function under time-varying magnetic stimulation, and provided evidence that TMS does not affect normal mitochondrial functionality by altering its membrane potential.</p

Neuromodulation with Electromagnetic Stimulation for Seizure Suppression: From Electrode to Magnetic Coil

Non-invasive brain tissue stimulation with a magnetic coil provides several irreplaceable advantages over that with an implanted electrode, in altering neural activities under pathological situations. We reviewed clinical cases that utilized time-varying magnetic fields for the treatment of epilepsy, and the safety issues related to this practice. Animal models have been developed to foster understanding of the cellular/molecular mechanisms underlying magnetic control of epileptic activity. These mechanisms include (but are not limited to) (1) direct membrane polarization by the magnetic field, (2) depolarization blockade by the deactivation of ion channels, (3) alteration in synaptic transmission, and (4) interruption of ephaptic interaction and cellular synchronization. Clinical translation of this technology could be improved through the advancement of magnetic design, optimization of stimulation protocols, and evaluation of the long-term safety. Cellular and molecular studies focusing on the mechanisms of magnetic stimulation are of great value in facilitating this translation

Electric and magnetic fields inside neurons and their impact upon the cytoskeletal microtubules

If we want to better understand how the microtubules can translate and input the information carried by the electrophysiologic impulses that enter the brain cortex, a detailed investigation of the local electromagnetic field structure is needed. In this paper are assessed the electric and the magnetic field strengths in different neuronal compartments. The calculated results are verified via experimental data comparison. It is shown that the magnetic field is too weak to input information to microtubules and no Hall effect, respectively QHE is realistic. Local magnetic flux density is less than 1/300 of the Earth’s magnetic field that’s why any magnetic signal will be suffocated by the surrounding noise. In contrast the electric field carries biologically important information and acts upon voltage-gated transmembrane ion channels that control the neuronal action potential. If mind is linked to subneuronal processing of information in the brain microtubules then microtubule interaction with the local electric field, as input source of information is crucial. The intensity of the electric field is estimated to be 10V/m inside the neuronal cytoplasm however the details of the tubulin-electric field interaction are still unknown. A novel hypothesis stressing on the tubulin C-termini intraneuronal function is presented replacing the current flawed models (Tuszynski 2003, Mershin 2003, Hameroff 2003, Porter 2003) presented at the Quantum Mind II Conference held at Tucson, Arizona, 15-19 March 2003, that are shown in this presentation to be biologically and physically inconsistent

Doctor of Philosophy

dissertationMagnetic fields are permeable to the biological tissues and can induce electric field in the conductive structures. Some medical devices take advantage of this ability to transfer energy from the source to the receiving site without direct contact. Prosthetic devices such as retinal implants use time-varying magnetic field to achieve wireless power transfer to the implanted magnetic coil. However, devices such as magnetic stimulators use the induction principle to create an electric field at the stimulation site. Efficiency of these devices is primarily dependent on the design of the magnetic coils. Therefore, in this work, we designed and validated efficient magnetic coils for wireless power transfer to implanted devices and magnetic stimulation of the peripheral nerves. Typical wireless power transfer (WPT) systems uses two-coil based design to achieve contactless power transfer to the implanted electronics. These systems achieve low power transfer efficiency (< 30%) and frequency bandwidth. Moreover, efficient wireless system requires high coupling and load variation tolerance during device operation. To design an electromagnetic safe WPT system, the power absorbed by the tissue and radiated field due to the proximal magnetic coils needs to be minimized. In this work, we proposed a multi-coil power transfer system which solves some of the current challenges. The proposed multi-coil WPT system achieves more than twice the power transfer efficiency, controllable voltage gain, wider frequency bandwidth, higher tolerance to coupling and load variations, lower absorbed power in the tissue and lower radiated field from the magnetic coil than a comparable two-coil system. In this work, we have developed analytic models of the multi-coil WPT system and validated the accuracy of the solutions using experiments. Magnetic coils play an important role in controlling the distribution of induced electric field inside the nerve during magnetic stimulation. In the past, homogeneous models were used to estimate the field profile inside conductive tissue due to the time varying current in the magnetic coil. Moreover, the effect of the surrounding media and stimulation mechanisms was understudied, which limits the optimization accuracy of the magnetic coils. In this work, we developed anatomically correct tissue models to study the effect of tissue heterogeneity and the surrounding media on the induced electric field. We also developed an optimization algorithm for designing energy efficient cm-size magnetic coils, that were then used for ex-vivo magnetic stimulation of the frog's sciatic nerve