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Influence of a constant magnetic field on action potential generation in neurons.

INTRODUCTION

In spite of increasing public concern about the impact of magnetic fields on health, use of magnetic devices in the practice of clinical medicine is on the rise. Examples include magnetic resonance imaging of body structures [1], the use of SQUID (semi-conducting quantum interference device) probes to detect magnetic fields produced by cardiac [2],[3] and neural tissue [4],[5] and the use of pulsed magnetic fields to enhance bone healing [6]. However, the understanding of the influence of magnetic fields at the cellular level is still limited. Theoretical studies suggest that constant magnetic flux densities in the range of 25-100 Tesla would be required to affect ionic currents of nerve processes [7],[8]. Experimental studies also indicate that electrically stimulated action potentials of adult mouse sensory neurons in cell culture are blocked to a large extent when the neuron was positioned in a static magnetic field of 11 milliTesla [9]. Furthermore, according to a recent experimental study, magnetic flux densities as low as 0.2 microTesla raise the excitation threshold and decrease the amplitude of the action potentials in the isolated frog sciatic nerve [10]. In this work a physical model for the reduced excitability in neurons exposed to a constant magnetic field is presented. The proposed explanation is based on the well-known Hall Effect, which is a direct consequence of the force exerted on charged carriers moving in a magnetic field. The plausibility of the proposed model is assessed in light of the Hodgkin and Huxley's model for action potential generation in neurons. In addition, in order to verify the validity of the proposed model simulations based on the Hodgkin and Huxley model have been performed using a public-domain software.

I. Physical Model:

A. Excitation Threshold as a Function of Depolarizing Current:

The reduced excitability of neurons exposed to a constant magnetic field manifests as an increase in the excitation threshold. The excitability of neuron is determined by the passive response, also known as the electrotonic response of the plasma membrane. This response can be modeled based on the equivalent circuit of Fig. 1. This equivalent circuit includes an electromotive force, [E.sub.r], which represents the resting membrane potential, the electrical

Resistance of the membrane, [R.sub.m], and the capacitance per unit area of the membrane, [C.sub.m]. In response to a depolarizing step current density [J.sub.Stim] as the source of excitation, the membrane capacitance is discharged giving rise to a rate of change of transmembrane potential, [V.sub.m], given by

d[V.sub.m]/dt = [J.sub.Stim]/[C.sub.m] (1)

The typical value of the neuron excitation threshold, i.e. the required depolarization of the membrane potential for initiation of the action potential, is approximately 15mV, which occurs over a typical time interval of 2msec. Therefore, considering the typical value of 1[micro]F / [cm.sup.2] for the membrane capacitance, the discharging current density for generation of action potential can be estimated as follows:

[J.sub.Stim] = C d[V.sub.m]/dt [congruent to] C[DELTA][V.sub.m]/[DELTA]t = 1 [micro]F/[cm.sup.2] x 15mV/2m sec = 7.5 [micro]A/[cm.sup.2] (2)

For current densities higher than the typical value estimated above, the voltage-dependent sodium channels in the plasma membrane become activated leading to further depolarization of the membrane and initiation of the action potential. Action potential is equivalent to the active response of the neuron, which can be modeled based on the Hodgkin-Huxley equivalent circuit model using variable resistors representing voltage-dependent ion channels. In general, the excitability of neuron can be characterized by the magnitude of the depolarizing current necessary to bring the membrane potential to the threshold leading to initiation of the action potential.

B. Reduced Nerve Cell Excitability in presence of a Constant Magnetic Field

Considering the interior of the neuron as a conductor, the Hall Effect can provide a plausible explanation for the reduced nerve cell excitability in presence of a constant magnetic field. According to Lorentz law, when exposed to a magnetic field, moving charged particles experience a force proportional to the product of their velocity and the magnetic flux density. The influence of a magnetic field on the function of neuron can be explained based on the Lorentz force acting on the ions present in the intracellular and extracellular environment. The source of ionic motion is the local electric field resulting from the electrical stimulation of neuron, which leads to flow of a drift current. In presence of a magnetic field these ions will also be subject to an induced electric field known as the Hall electric field. In particular, the slight redistribution of charge associated with the Lorentz magnetic force exerted on moving intracellular ions leads to formation of an induced Hall electric field in a direction perpendicular to that of action potential transmission along the axon. Therefore, as shown in Fig. 2 with a normal magnetic field [B.sub.z], under the conditions of electrical excitation, the transient ionic current density [J.sub.x], which is available for discharging the membrane capacitance, is reduced due to partial drift of ions along the direction of the Hall electric field (i.e. out of the page along the +y direction in Fig. 2). Consider the expression for the drift current given below

J = qn[v.sub.d] = q[bar.[mu]]nE (3)

Where q, [bar.[mu]], n, and E represent the electronic charge, the average ionic mobility, the density of the given ion, and the electric field respectively, and [v.sub.d] = [bar.[mu]]E denotes the drift velocity. Based on the above expression, and using the expression for the Lorentz force [F.sub.M] = q[v.sub.d]B it can be shown that the ratio [J.sub.y]/[J.sub.x] of the transient current density in the direction perpendicular to action potential transmission, [J.sub.y], relative to the depolarizing transient current density [J.sub.x] flowing parallel to the transmission direction is given by [11]

[J.sub.y]/[J.sub.x] [bar.[mu]][B.sub.z] (4)

II. Model Verification based on Simulation:

A. Simulation Methodology:

The validity of the model for the influence of a constant magnetic field on the excitation threshold of neuron can be demonstrated based on simulation. In particular, simulation of the response of a neuron to a depolarizing current in presence of a magnetic field must be in agreement with empirical results presented above indicating a decrease in the excitation threshold. The reduction in the neuronal excitation threshold is basically equivalent to a decrease in the amplitude of the depolarizing current. Specifically, based on the proposed model (equation 4) it is expected that the amplitude of the stimulating current is reduced in proportion to the magnitude of the applied magnetic flux density.

By implementing the Hodgkin-Huxley model equations in MATLAB[TM], the public-domain software HHSim allows the behavior of the neuronal membrane to be simulated in response to a variety of stimuli. This graphical simulator, which provides full access to the Hodgkin-Huxley model parameters, permits application of a depolarizing current to a segment of the axon, which can be specified through the STIM option.

B. Simulation Results:

Fig. 3 shows the transmembrane potential of a neuronal segment in response to two depolarizing current stimuli, which has been simulated using the HHSim software. In this simulation using the STIM option, first a depolarizing current with an amplitude of [I.sub.stim1] = 3.8 nA, and then a depolarizing current with an amplitude of [I.sub.stim2] = 3 6 nA representing a 5.3% decrease in magnitude of the stimulating current are applied. As is evident, while the first stimulus generates an action potential, the 5.3% reduction in the magnitude of the stimulating current leads to suppression of the action potential as the membrane potential is not sufficiently depolarized to reach the critical threshold level. The 5.3% reduction in the magnitude of the stimulus current necessary to suppress the action potential was estimated based on equation (4) to simulate the effect of the magnetic field. Based on experimental observations [9] a magnetic field of 11 milliTesla is sufficient to block action potential generation. Assuming an

Average ionic mobility of [bar.[mu]] = 5 [m.sup.2][V.sup.-1] [sec.sup.-1], from equation (4) the ratio of the current associated with the induced Hall electric field to the depolarizing current stimulus, namely the product [bar.[mu]][B.sub.z], will be equal to 0.055. Therefore, a 5.5% reduction (5.3% applied in the simulation) in the depolarizing current resulting from exposure of moving ions to an induced electric field originating from the magnetic field is sufficient to suppress the action potential. Note that given the typical value of 7.5[micro]A/[cm.sup.2] for the stimulating current density leading to generation of an action potential estimated from equation (2), the values used for the stimulus current in the simulation correspond to a section of the neuronal membrane with an area of roughly 0.05[mm.sup.2].

III. Discussion:

Simulation of a neuronal membrane segment in response to two depolarizing current stimuli indicated that a relatively small reduction in the amplitude of the stimulus current resulting from presence of a magnetic field may suppress action potential generation, thereby confirming the validity of the proposed model. The proposed model further suggests that in presence of a magnetic field, the equivalent circuit representing the neuronal plasma membrane may be expanded by including a magnetic-field-dependent current source whose magnitude is proportional to the magnetic flux density. Therefore, in quantitative agreement with the proposed model describing the influence of a constant magnetic field on the neuronal excitation threshold, the reduction in the stimulus current may be accounted for in the equivalent circuit model of the membrane using a hyperpolarizing dependent current source whose magnitude is proportional to [bar.[mu]][B.sub.z].

IV. Conclusion:

A physical model for reduced excitability in neurons exposed to constant magnetic field was presented. The slight redistribution of ionic charge resulting from the magnetic force acting on the mobile ions in the intracellular space was introduced as the origin of a Hall electric field in a direction perpendicular to action potential transmission along the axon. The Hall electric field, in turn, gives rise to a transient current density flowing in a direction perpendicular to the direction of the depolarizing current responsible for bringing the membrane potential to the threshold level necessary for action potential generation. The current density associated with the Hall electric field is a fraction of the total stimulating current density available for depolarizing the membrane as the ions forming this current component are set into motion as a result of electrical stimulation of the neuron. The validity of the proposed model is verified by simulations based on the Hodgkin-Huxley model for current flow through axonal membrane. A rigorous proof of the validity of the proposed model, however, requires employment of experimental neurophysiological methods for measurement of the induced electric field.

ARTICLE INFO

Article history:

Received 25 June 2014

Received in revised form 8 July 2014

Accepted 10 August May 2014

Available online 30 August 2014

REFERENCES

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[3] Wikswo Jr, J.P., J.P. Barach, 1983. Gundersen SC, "First magnetic measurements of action currents in isolated cardiac Purkinje fibers", 11 Nuovo Cimento, 2: 368-378.

[4] Wikswo Jr, JP, J.P. Barach, J.A. Freeman, 1980. "Magnetic field of a nerve impulse, First measurement", Science, 208: 53-55.

[5] Rose, D.F., P.D. Smith, S. Sato, 1987. "Magnetoencephalography and epilepsy research", Science, 238: 329.

[6] Basset, C.A.L., 1985. "The development and application of pulsed electromagnetic fields (PEMFs) for ununited fractures and arthrodeses", Clin Plast Surg, 12:159-277.

[7] Wikswo Jr., J.P., J.P. Barach, 1980. "An estimate of the steady magnetic field strength required to influence nerve conduction", IEEE Trans. on Biomedical Engineering, BME, 27: 722-723.

[8] Liboff, R.L., 1980. "Neuromagnet Thresholds", J. Theor. Biol., 83: 427-436.

[9] Cavopol, A.V., A.W. Wamil, R.R. Holcomb and M.J. McLean, 1995. "Measurement and Analysis of Static Magnetic Fields That Block Action Potentials in Cultured Neurons", Bioelectromagnetics, 16: 197-206.

[10] Shalygin, A.N., V.V. Volkov, G.V. Maksimov, S.M. Novikov, 2008. "Influence of weakend constant magnetic fields on nerve cell excitability", Biophysics, 53(3): 243-244.

[11] Jamasb, S., 2011. "Effect of a Constant Magnetic Field on Neuron Excitability", Proceedings of the 1st National Conference on Biomagnetism, Qasvin, Iran.

(1) Yaser Adinevand Ghobadi, (2) Shahriar Jamasb, (3) Iman Chaharmahali, (4) Abbas Motamed

(1) Department Of Electrical Engineering, College of Engineering, Saveh Science andResearch Branch, Islamic Azad University, Saveh, Iran

(2) Department of Biomedical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

(3) Young Researchers and Elite Club, Borujerd Branch, Islamic Azad University, Borujerd Iran

(4) Department of Electrical Engineering, college of Engineering, Borujerd Branch, Islamic Azad University, Borujerd, Iran

Corresponding Author: Yaser Adinevand Ghobadi, Influence of Constant Magnetic Field on Action Potential Generation in Neurons
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Author:Ghobadi, Yaser Adinevand; Jamasb, Shahriar; Chaharmahali, Iman; Motamed, Abbas
Publication:Advances in Environmental Biology
Article Type:Report
Date:Jun 1, 2014
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