Importance of soft tissue inhomogeneity in magnetic peripheral nerve stimulation

Repetitive Peripheral Magnetic Nerve Stimulation (rPMS) as Adjuvant Therapy Reduces Skeletal Muscle Reflex Activity

Background: The reduction of muscle hypertonia and spasticity, as well as an increase in mobility, is an essential prerequisite for the amelioration of physiotherapeutical treatments. Repetitive peripheral magnetic nerve stimulation (rPMS) is a putative adjuvant therapy that improves the mobility of patients, but the underlying mechanism is not entirely clear.

Methods: Thirty-eight participants underwent either an rPMS treatment (N = 19) with a 5 Hz stimulation protocol in the posterior tibial nerve or sham stimulation (N = 19). The stimulation took place over 5 min. The study was conducted in a pre-test post-test design with matched groups. Outcome measures were taken at the baseline and after following intervention.

Results: The primary outcome was a significant reduction of the reflex activity of the soleus muscle, triggered by a computer-aided tendon-reflex impact. The pre-post differences of the tendon reflex response activity were −23.7% (P < 0.001) for the treatment group. No significant effects showed in the sham stimulation group.

Conclusion: Low-frequency magnetic stimulation (5 Hz rPMS) shows a substantial reduction of the tendon reflex amplitude. It seems to be an effective procedure to reduce muscular stiffness, increase mobility, and thus, makes the therapeutic effect of neuro-rehabilitation more effective. For this reason, the 5 Hz rPMS treatment might have the potential to be used as an adjuvant therapy in the rehabilitation of gait and posture control in patients suffering from limited mobility due to spasticity. The effect observed in this study should be investigated conjoined with the presented method in patients with impaired mobility due to spasticity.

Determining which mechanisms lead to activation in the motor cortex: a modeling study of transcranial magnetic stimulation using realistic stimulus waveforms and sulcal geometry

OBJECTIVE

To determine which mechanisms lead to activation of neurons in the motor cortex during transcranial magnetic stimulation (TMS) with different current directions and pulse waveforms.

METHODS

The total electric field induced in a simplified model of a cortical sulcus by a figure-eight coil was calculated using the finite element method (FEM). This electric field was then used as the input to determine the response of compartmental models of several types of neurons.

RESULTS

The modeled neurons were stimulated at different sites: fiber bends for pyramidal tract neurons, axonal terminations for cortical interneurons and axon collaterals, and a combination of both for pyramidal association fibers. All neurons were more easily stimulated by a PA - directed electric field, except association fibers. Additionally, the second phase of a biphasic pulse was found to be more efficient than the first phase of either monophasic or biphasic pulses.

CONCLUSIONS

The stimulation threshold for different types of neurons depends on the pulse waveform and relative current direction. The reported results might account for the range of responses obtained in TMS of the motor cortex when using different stimulation parameters.

SIGNIFICANCE

Modeling studies combining electric field calculations and neuronal models may lead to a deeper understanding of the effect of the TMS-induced electric field on cortical tissue, and may be used to improve TMS coil and waveform design.

Influence of coil current configuration in magnetic stimulation of a nerve fiber in inhomogeneous and anisotropic conducting media

In this study, we used a computer simulation to investigate the effects of the coil current waveform and direction on the excitation processes of the nerve axon in inhomogeneous and anisotropic conducting media in magnetic stimulation. We assumed that the nerve axon was located in the media with 2 regions having different conductivities or electrical anisotropy that simulate different tissue types. The distribution of induced electric fields was calculated with the finite element method (FEM). The nerve fiber was modeled after equivalent electrical circuits having active nodes of Ranvier. The direction of the coil current at the intersection of a figure-eight coil was assumed to flow perpendicular to the nerve axon. We observed the excitation threshold when the coil current waveform and direction are changed with varying the electrical properties such as tissue electrical conductivity and anisotropy. The simulation results show that the threshold decreases with the increase of conductivity ratio between 2 regions and it also depends on the coil current waveform and direction. Biphasic coil current has lower threshold than monophasic one when the current direction is the same in both waveforms. The results also suggest that the tissue anisotropy strongly affects the excitation threshold. The threshold increases with the increase of tissue anisotropic ratio of longitudinal direction to the transverse one respect to the nerve axon. The results in this study give useful information to explain the experimental results of the magnetic stimulation of human peripheral nervous systems and the theoretical model is applicable to understand the characteristics in magnetic stimulation of both peripheral and central nervous systems.

3D modeling of the total electric field induced by transcranial magnetic stimulation using the boundary element method

Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.

Elucidating the mechanisms and loci of neuronal excitation by transcranial magnetic stimulation using a finite element model of a cortical sulcus

OBJECTIVE

This work aims to elucidate by what physical mechanisms and where stimulation occurs in the brain during transcranial magnetic stimulation (TMS), taking into account cortical geometry and tissue heterogeneity.

METHODS

An idealized computer model of TMS was developed, comprising a stimulation coil, a cortical sulcus, and surrounding tissues. The distribution of the induced electric field was computed, and estimates of the relevant parameters were generated to predict the locus and type of neurons stimulated during TMS, assuming three different stimulation mechanisms.

RESULTS

Tissue heterogeneity strongly affects the spatial distribution of the induced electric field and hence which stimulation mechanism is dominant and where it acts. Stimulation of neurons may occur in the gyrus, in the lip of the gyrus, and in the walls of the sulcus. The stimulated cells can be either pyramidal cells having medium to large caliber axons, or intracortical fibers of medium caliber.

CONCLUSIONS

The results highlight the influence of cortical folding on the action of magnetic and electric fields on cortical tissue.

SIGNIFICANCE

Tissue geometry and heterogeneity in electrical conductivity both must be taken into account to predict accurately stimulation loci and mechanism in TMS.

Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields

We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m(-1) to 0.333 S m(-1), simulating a white-matter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic 'far-field' stimulation.

Electric fields induced in the human body by time-varying magnetic field gradients in MRI: numerical calculations and correlation analysis

The spatial distributions of the electric fields induced in the human body by switched magnetic field gradients in MRI have been calculated numerically using the commercial software package, MAFIA, and the three-dimensional, HUGO body model that comprises 31 different tissue types. The variation of |J|, |E| and |B| resulting from exposure of the body model to magnetic fields generated by typical whole-body x-, y- and z-gradient coils has been analysed for three different body positions (head-, heart- and hips-centred). The magnetic field varied at 1 kHz, so as to produce a rate of change of gradient of 100 T m(-1) s(-1) at the centre of each coil. A highly heterogeneous pattern of induced electric field and current density was found to result from the smoothly varying magnetic field in all cases, with the largest induced electric fields resulting from application of the y-gradient, in agreement with previous studies. By applying simple statistical analysis to electromagnetic quantities within axial planes of the body model, it is shown that the induced electric field is strongly correlated to the local value of resistivity, and the induced current density exhibits even stronger correlation with the local conductivity. The local values of the switched magnetic field are however shown to bear little relation to the local values of the induced electric field or current density.

The effects of pulse configuration on magnetic stimulation

A study is presented in which the authors have examined the effects of pulse configuration, stimulation intensity, and coil current direction during magnetic stimulation. Using figure-8 and circular coils, the median nerve was stimulated at the cubital fossa and at the wrist of 10 healthy volunteers, and the response amplitude and site of stimulation were determined. The key findings of this study are in agreement with other researchers' findings and confirm that biphasic stimulating pulses produce significantly higher M-wave amplitudes than monophasic stimulating pulses for the same stimulus intensity. Mean response amplitudes for biphasic stimuli applied by both coils at the elbow and wrist are consistently higher for the normal current direction. Mean response amplitudes for monophasic pulses are almost always higher for reversed currents. The site for effective stimulation (the position of the virtual cathode) cannot be defined within a fixed distance from the center of the coil (3 to 4 cm), as has been suggested by other researchers, but was found to vary depending on the coil current amplitude and direction as well as the degree of inhomogeneity of the tissues surrounding the nerve. There is a statistically significant relationship between virtual cathode shift and stimulus intensity for biphasic and monophasic pulses. Reversing the coil current direction has no statistically significant effect on the virtual cathode position. Virtual cathode shifts can be measured for biphasic and monophasic stimulations using a figure-8 coil at the wrist and the elbow. However, such a shift is difficult to determine with a circular coil.

The electric field induced in the brain by magnetic stimulation: a 3-D finite-element analysis of the effect of tissue heterogeneity and anisotropy

We investigate the effect of tissue heterogeneity and anisotropy on the electric field and current density distribution induced in the brain during magnetic stimulation. Validation of the finite-element (FE) calculations in a homogeneous isotropic sphere showed that the magnitude of the total electric field can be calculated to within an error of approximately 5% in the region of interest, even in the presence of a significant surface charge contribution. We used a high conductivity inclusion within a sphere of lower conductivity to simulate a lesion due to an infarct. Its effect is to increase the electric field induced in the surrounding low conductivity region. This boost is greatest in the vicinity of interfaces that lie perpendicular to the current flow. For physiological values of the conductivity distribution, it can reach a factor of 1.6 and extend many millimeters from the interface. We also show that anisotropy can significantly alter the electric field and current density distributions. Either heterogeneity or anisotropy can introduce a radial electric field component, not present in a homogeneous isotropic conductor. Heterogeneity and anisotropy are predicted to significantly affect the distribution of the electric field induced in the brain. It is, therefore, expected that anatomically faithful FE models of individual brains which incorporate conductivity tensor data derived from diffusion tensor measurements, will provide a better understanding of the location of possible stimulation sites in the brain.

New currents in electrical stimulation of excitable tissues

Electric fields can stimulate excitable tissue by a number of mechanisms. A uniform long, straight peripheral axon is activated by the gradient of the electric field that is oriented parallel to the fiber axis. Cortical neurons in the brain are excited when the electric field, which is applied along the axon-dendrite axis, reaches a particular threshold value. Cardiac tissue is thought to be depolarized in a uniform electric field by the curved trajectories of its fiber tracts. The bidomain model provides a coherent conceptual framework for analyzing and understanding these apparently disparate phenomena. Concepts such as the activating function and virtual anode and cathode, as well as anode and cathode break and make stimulation, are presented to help explain these excitation events in a unified manner. This modeling approach can also be used to describe the response of excitable tissues to electric fields that arise from charge redistribution (electrical stimulation) and from time-varying magnetic fields (magnetic stimulation) in a self-consistent manner. It has also proved useful to predict the behavior of excitable tissues, to test hypotheses about possible excitation mechanisms, to design novel electrophysiological experiments, and to interpret their findings.

Evaluation of the cable model for electrical stimulation of unmyelinated nerve fibers

The cable model, used to calculate the membrane potential of an unmyelinated nerve fiber due to electrical stimulation, is reexamined under passive steady-state conditions. The validity of two of the assumptions of the cable model are evaluated, namely that the membrane potential be a function of the axial coordinate only and that the extracellular potential due to the presence of the nerve fiber be negligible. The membrane potential calculated from the passive steady-state cable model is compared with the membrane potential obtained from an analytical three-dimensional (3-D) volume conductor model of a nerve fiber. It is shown that for very small electrode-fiber distances (of only a few fiber radii), both assumptions are violated and the two models give quite different results. Over a wide range of the electrode-fiber distance (about 0.1 mm to 1 cm), both assumptions are fulfilled and the two models give approximately the same results. For very large distances (more than 10 cm, independent of fiber diameter) only the second assumption is satisfied, but a modification of the activating function of the cable model allows to calculate the membrane potential in agreement with the 3-D model.

Current orientation induced by magnetic stimulation influences a cognitive task

The direction of the current induced by transcranial magnetic stimulation (TMS) over the motor cortex has been observed to influence the threshold and latency of evoked muscle responses. This study investigates the effect of TMS-induced current orientation (ICO) over the prefrontal cortex, on a specific cognitive task (memory-guided saccade). TMS was applied with a figure-of-eight coil, placed at one of eight different orientations over the prefrontal cortex. The most effective ICO was antero-lateral, which is a different optimal ICO from that seen over the hand area of the motor cortex. This demonstrates that ICO can alter the effect of TMS on cognitive functions and that ICO is an independent variable that should not be ignored when designing TMS studies.

Magnetic and electrical stimulation of undulating nerve fibres: a simulation study

Mathematical models of myelinated nerve fibres are highly stylized abstractions of real nerve fibres. For example, nerve fibres are usually assumed to be perfectly straight. Such idealizations can cause discrepancies between theoretical predictions and experimental results. One well-known discrepancy is that the currently used models predict (contradictory to experimental findings) that an activation of nerve fibres is not possible with a pure transverse electric field. This situation occurs when a magnetic coil is placed symmetrically above a straight nerve fibre for magnetic nerve stimulation, or when an anode and a cathode are placed equidistantly on a line perpendicular to the fibre in the case of electrical stimulation. It is shown that this discrepancy does not occur if the physiological undulation of peripheral nerve fibres is included in the models. Even for small undulation amplitudes (e.g. 0.02 mm), it is possible to activate the fibre in these positions. For physiological undulations, as found in the literature, and favourable (off-centre) positions, the typical reduction of the thresholds is in a range between one and five, compared with perfectly straight fibres.

Influence of pulse sequence, polarity and amplitude on magnetic stimulation of human and porcine peripheral nerve

1. Mammalian phrenic nerve, in a trough filled with saline, was excited by magnetic coil (MC)-induced stimuli at defined stimulation sites, including the negative-going first spatial derivative of the induced electric field along a straight nerve, at a bend in the nerve, and at a cut nerve ending. At all such sites, the largest amplitude response for a given stimulator output setting was elicited by an induced damped polyphasic pulse consisting of an initial quarter-cycle hyperpolarization followed by a half-cycle depolarization compared with a predominantly 'monophasic' quarter-cycle depolarization. 2. Simulation studies demonstrated that the increased efficacy of the induced quarter-cycle hyperpolarizing-half-cycle depolarizing polyphasic pulse was mainly attributed to the greater duration of the outward membrane current phase, resulting in a greater outward charge transfer afforded by the half-cycle (i.e. quarter-cycles 2 and 3). The advantage of a fast rising initial quarter-cycle depolarization was more than offset by the slower rising, but longer duration depolarizing half-cycle. 3. Simulation further revealed that the quarter-cycle hyperpolarization-half-cycle depolarization showed only a 2.6 % lowering of peak outward current and a 3.5 % lowering of outward charge transfer at threshold, compared with a half-cycle depolarization alone. Presumably, this slight increase in efficacy reflects modest reversal of Na+ inactivation by the very brief initial hyperpolarization. 4. In vitro, at low bath temperature, the nerve response to an initial quarter-cycle depolarization declined in amplitude as the second hyperpolarizing phase progressively increased in amplitude and duration. This 'pull-down' phenomenon nearly disappeared as the bath temperature approached 37 C. Possibly, at the reduced temperature, delay in generation of the action potential permitted the hyperpolarization phase to reduce excitation. 5. Pull-down was not observed in the thenar muscle responses to median nerve stimulation in a normal human at normal temperature. However, pull-down emerged when the median nerve was cooled by placing ice over the forearm. 6. In a nerve at subnormal temperature straddled with non-conducting inhomogeneities, polyphasic pulses of either polarity elicited the largest responses. This was also seen when stimulating distal median nerve at normal temperature. These results imply excitation by hyperpolarizing-depolarizing pulse sequences at two separate sites. Similarly, polyphasic pulses elicited the largest responses from nerve roots and motor cortex. 7. The pull-down phenomenon has a possible clinical application in detecting pathologically slowed activation of Na+ channels. The current direction of the polyphasic waveform may become a significant factor with the increasing use of repetitive magnetic stimulators which, for technical reasons, induce a cosine-shaped half-cycle, preceded and followed by quarter-cycles of opposite polarity.