Action Potential Blocking and Directional Firing by Electrical Field Induction, Modeling and Discussion

Many invasive and non-invasive methods have been proposed to excite a neuron in the nerves system. For non-invasive methods like Transcranial Magnetic Stimulation (TMS) there is few investigation on the shape and property of the induced electrical field and its interaction with a neuron to directionally fire or block an action potential. In this article, E-fields are generated by two capacitive plates as a source. E-fields are modified in MATLAB and induced on a pyramidal neuron to study the effect of E-field on a neuron. A method is proposed to block action potential (AP) or fire and direct it into the desired direction by a non-invasive method. Blocking AP can be useful for pain reduction or anesthesia in a desired region of the body. A full modeling investigation on required form of E-field, Hyper-polarization and depolarization values in membrane potential and induction time to directionally fire or block AP have been discussed for various dendrite diameters and channel densities in one-dimensional and two-dimensional pyramidal neurons

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

The Fascicle Undulation Effect on the Activating Function in Magnetic Stimulation of Peripheral Nerves with Transverse and Longitudinal Fields

Analysis of activating function for a long, myelinated nerve fiber with undulating path in transverse and longitudinal induced electric fields was performed. The induced electric field was computed using a finite element model composed by a round coil beneath a bath with saline solution. Longitudinal and transverse components of the induced electric field were computed along two axes, one tangential and the other axial to the coil. The influence of a transverse field on the modified activating function was analyzed when the fiber path was determined by the fascicle undulation, and by the fascicle undulation plus the fiber undulation inside the fascicle. For the first path type, undulation wavelength of 40 to 90 mm and 0.8 mm amplitude determined a classic activating function with: (a) multiple virtual cathodes that could generate two or three stimulation sites for axially oriented coil, and (b) virtual cathode with distorted shape in amplitude up to 35% and location up to 67% for tangentially oriented coil. For axially oriented coil, the transverse field term of the modified activating function was comparable in amplitude with the classic activating function, however significant attenuation could occur due to perineurium. For the second path type with wavelength of tenths of millimeters and amplitudes of a quarter of the wavelength, the classic activating function had such a dramatic increase in the spatial frequency that could not predict the stimulation site with the usual interpretation of the virtual cathode. Similarity between the results obtained with the first path type and the ones obtained in a previous in-vitro experiment suggests that the undulating fascicles within the nerve trunk can be responsible for stimulation with transverse fields

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

An Asymptotic Model of Electroporation-Mediated Molecular Delivery in Skeletal Muscle Tissue

<p>Electroporation is a biological cell's natural reaction to strong electric fields, where transient pores are created in the cell membrane. While electroporation holds promise of being a safe and effective tool for enhancing molecular delivery in numerous medical applications, it remains largely confined to preclinical research and clinical trials due to an incomplete understanding of the exact mechanisms involved. Muscle fibers are an important delivery target, but traditional theoretical studies of electroporation ignore the individual fiber geometry, making it impossible to study the unique transverse and longitudinal effects from the pulse stimulus. In these long, thin muscle fibers, the total reaction of the fiber to the electric field is due to fundamentally different effects from the constituent longitudinal and transverse components of the electric field generated by the pulse stimulus. While effects from the transverse component have been studied to some degree, the effects from the longitudinal component have not been considered. </p><p>This study develops a model of electroporation and delivery of small molecules in muscle tissue that includes effects from both the transverse and longitudinal components of the electric field. First, an asymptotic model of electric potential in an individual muscle fiber is derived that separates the full 3D boundary value problem into transverse and a longitudinal problems. The transverse and longitudinal problems each have their own respective source functions: the new "transverse activating function" and the well known longitudinal activating function (AF). This separation enhances analysis of the different effects from these two AFs and drastically reduces computational intensity. Electroporation is added to the asymptotic fiber model, and simplified two-compartment mass transport equations are derived from the full 3D conservation of mass equations to allow simulation of molecular uptake due to diffusion and the electric field. Special emphasis is placed on choosing model geometry, electrical, and pulsing parameters that are in accordance with experiments that study electroporation-mediated delivery of small molecules in the skeletal muscle of small mammals.</p><p>Simulations reveal that for fibers close to the electrodes the transverse AF dominates, but for fibers far from the electrodes the longitudinal AF enhances uptake by as much as 2000%. However, on the macroscopic tissue level, the increase in uptake from the longitudinal AF is no more than 10%, given that fibers far from the electrodes contribute so little to the total uptake in the tissue. The mechanism underlying the smaller effect from the longitudinal AF is found to be unique to the process of electroporation itself. Electroporation occurs on the short time scale of polarization via the transverse AF, drastically increases membrane conductance, and effectively precludes further creation of pores from charging of the membrane via the longitudinal AF. The exact value of enhancement in uptake from the longitudinal AF is shown to depend on pulsing, membrane, and tissue parameters. Finally, simulation results reproduce qualitative, and in some cases quantitative, behavior of uptake observed in experiments.</p><p>Overall, percent increase in total tissue uptake from the longitudinal AF is on the order of experimental variability, and this study corroborates previous theoretical models that neglect the effects from the longitudinal AF. However, previous models neglect the longitudinal AF without explanation, while the asymptotic fiber model is able to detail the mechanisms involved. Mechanisms revealed by the model offer insight into interpreting experimental results and increasing efficiency of delivery protocols. The model also rigorously derives a new transverse AF based on individual fiber geometry, which affects the spatial distribution of uptake in tissue differently than predicting uptake based on the magnitude of the electric field, as used in many published models. Results of this study are strictly valid for transport of small molecules through small non-growing pores. For gene therapy applications the model must be extended to transport of large DNA molecules through large pores, which may alter the importance of the longitudinal AF. In broader terms, the asymptotic model also provides a new, computationally efficient tool that may be used in studying the effect of transverse and longitudinal components of the field for other types of membrane dynamics in muscle and nerves.</p>Dissertatio