The rapidly pulsed magnetic gradient fields used in magnetic resonance imaging (MRI) studies generate electric fields in the body. As the induced electric field (E) is proportional to the rate of change of the pulsed magnetic field (B), pairs of positive and negative E pulses are produced with a duration t_r equal to the rise and fall times of the trapezoidal B pulses and separated by a delay t_d arising from the plateau of the trapezoid. The effects of these electric fields have long been a matter of concern, and have been addressed with many modeling studies and experiments on human subjects. Previous studies on the effects of electromagnetic fields on the nervous system have generally focussed on unwanted peripheral nerve stimulation (PNS) during full-body MRI, or on intended electromagnetic stimulation of cortical areas by coils placed on the scalp.
Modeling studies have shown how the E field can generate action potentials (APs) in axons near the surface of the body. Generally, the fields used in a typical MRI experiment are below the levels for generation of APs, and the fields generated by the head coils used in functional MRI (fMRI) experiments are of even lower levels. However, it is widely recognized that very small stimuli can have significant effects on the behavior of cortical networks, even when far below the threshold for creating APs. If fMRI pulsed B fields could produce a significant disruption of the behavior of these networks, they could cause artifacts in the measured neural activity. To our knowledge, this study is the only attempt to analyze the effect of these fields on a model of a neocortical network that contains morphologically detailed and realistically firing pyramidal cells.
Previous studies have used modified Hodgkin-Huxley cable equation or compartmental models of myelinated axons that contain additional terms representing the effect of the induced electric. Two mechanisms can lead to changes in membrane potential that can affect neuronal or axonal firing: (1) E fields that are longitudinal to the cell membrane surface generate transmembrane currents that are proportional to the gradient of the field along the surface. (2) E fields that are transverse to the cell membrane can produce shifts in the intracellular membrane potential that are proportional to the field strength. In the context of PNS and generation of APs in axons, (1) has generally been shown to have the greatest effect, although (2) cannot be ignored.
The object of the present study was to use an existing GENESIS (see genesis-sim.org) simulation of the thalamorecipient layer of primary auditory cortex (Beeman 2013), and apply typical fMRI-generated E-fields to a network of 2304 pyramidal cells coupled to 576 inhibitory basket cells. The effects and thresholds for both mechanisms (1) and (2) were studied using trapezoidal B pulses that have durations t_d and rise times t_r typical of those used in echo planar imaging (EPI) fMRI experiments. We found that the thresholds for the E field and gradients that have a noticeable effect on single cell firing were comparable for mechanisms (1) and (2). E field thresholds were about 50 V/m, at least an order of magnitude greater than those estimated to occur at the location of the auditory cortex. However, they are close enough to be an issue with higher levels of B-field strength that may be used the future.
Cortical geometry does not lend itself to the production of longitudinal E fields, because the long axes of the pyramidal cells of the auditory and visual cortices are oriented perpendicularly to the cortical surface, transverse to the induced electric fields. Therefore network simulations were performed primarily with the more likely transverse orientation. When E field stimuli at the level of the single cell thresholds were applied to cells in a network undergoing normal background activity in the absence of auditory stimulus, the effects on average firing rate and the spectral components of the summed excitatory synaptic currents were very large. This would be expected from the stochastic resonance properties of a weak coherent signal (the E field pulses applied to every pyramidal cell) and the ongoing activity of the individual cells. Thresholds for producing APs in the absence of ongoing cortical activity were more than twice as high.
For a typical t_r of 0.2 msec with long intervals between pairs of a positive E pulse followed by a negative pulse, the effect is maximal for t_d > 5 msec, and becomes vanishingly small by t_d = 0.1 msec. For B pulses of the opposite polarity, the hyperpolarizing negative E pulses precede the positive ones. In this case the effect is far less and is greatest for large values of t_d that span the width of an AP.
These results may be understood in terms of the differences between the dynamics of the channels found in neocortical neurons and in this model, and the Hodgkin-Huxley Na and K channnels that are found in axons. Axons have the function of reliably delivering APs, with minimal disruptions of their timing. For the pyramidal cell model, as in simpler Hodgkin_Huxley axon models, APs are generated from the interplay of fast Na channels and the hyperpolarizing K channels. However, Ca channels and Ca concentration dependent K channels with slower dynamics act to prolong the hyperpolarized period following an AP, contributing to spike frequency adaptation and causing a greater sensitivity to inputs that occur when the cell is near threshold for firing. The time constants near threshold for Na inactivation and K activation are in the range 4-5 msec for both squid axon and cortical neuron channels. However, the Na activation time constant for cortical cells is about 4 times shorter (0.1 msec) than for axons. These characteristics are responsible for the different sensitivity of the models to perturbations and the effect of t_r and t_d.
Continuing work will model in detail the E fields that would be expected at the auditory and visual cortices during typical EPI fMRI gradient pulse sequences. Further details and simulation scripts may be obtained from http://genesis-sim.org/GENESIS/fMRInet