Electrostimulation by time-varying magnetic fields

Influence of peripheral axon geometry and local anatomy on magnetostimulation chronaxie

Objective.Rapid switching of magnetic resonance imaging (MRI) gradient fields induces electric fields that can cause peripheral nerve stimulation (PNS) and so accurate characterization of PNS is required to maintain patient safety and comfort while maximizing MRI performance. The minimum magnetic gradient amplitude that causes stimulation, the PNS threshold, depends on intrinsic axon properties and the spatial and temporal properties of the induced electric field. The PNS strength-duration curve is widely used to characterize simulation thresholds for periodic waveforms and is parameterized by the chronaxie and rheobase. Safety limits to avoid unwanted PNS in MRI rely on a single chronaxie value to characterize the response of all nerves. However, experimental magnetostimulation peripheral nerve chronaxie values vary by an order of magnitude. Given the diverse range of chronaxies observed and the importance of this number in MRI safety models, we seek a deeper understanding of the mechanisms contributing to chronaxie variability.Approach.We use a coupled electromagnetic-neurodynamic PNS model to assess geometric sources of chronaxie variability. We study the impact of the position of the stimulating magnetic field coil relative to the body, along with the effect of local anatomical features and nerve trajectories on the driving function and the resulting chronaxie.Main results.We find realistic variation of local axon and tissue geometry can modulate a given axon's chronaxie by up to two-fold. Our results identify the temporal rate of charge redistribution as the underlying determinant of the chronaxie.Significance.This charge distribution is a function of both intrinsic axon properties and the spatial stimulus along the nerve; thus, examination of the local tissue topology, which shapes the electric fields, as well as the nerve trajectory, are critical for better understanding chronaxie variations and defining more biologically informed MRI safety guidelines.

Prediction of experimental cardiac magnetostimulation thresholds using pig-specific body models

PURPOSE

Modern high-amplitude gradient systems can be limited by the International Electrotechnical Commission 60601-2-33 cardiac stimulation (CS) limit, which was set in a conservative manner based on electrode experiments and E-field simulations in uniform ellipsoidal body models. Here, we show that coupled electromagnetic-electrophysiological modeling in detailed body and heart models can predict CS thresholds, suggesting that such modeling might lead to more detailed threshold estimates in humans. Specifically, we compare measured and predicted CS thresholds in eight pigs.

METHODS

We created individualized porcine body models using MRI (Dixon for the whole body, CINE for the heart) that replicate the anatomy and posture of the animals used in our previous experimental CS study. We model the electric fields induced along cardiac Purkinje and ventricular muscle fibers and predict the electrophysiological response of these fibers, yielding CS threshold predictions in absolute units for each animal. Additionally, we assess the total modeling uncertainty through a variability analysis of the 25 main model parameters.

RESULTS

Predicted and experimental CS thresholds agree within 19% on average (normalized RMS error), which is smaller than the 27% modeling uncertainty. No significant difference was found between the modeling predictions and experiments (p < 0.05, paired t-test).

CONCLUSION

Predicted thresholds matched the experimental data within the modeling uncertainty, supporting the model validity. We believe that our modeling approach can be applied to study CS thresholds in humans for various gradient coils, body shapes/postures, and waveforms, which is difficult to do experimentally.

Measurement of magnetostimulation thresholds in the porcine heart

PURPOSE

Powerful MRI gradient systems can surpass the International Electrotechnical Commission (IEC) 60601-2-33 limit for cardiac stimulation (CS), which was determined by simple electromagnetic simulations and electrode stimulation experiments. Only a few canine studies measured magnetically induced CS thresholds in vivo and extrapolating them to human safety limits can be challenging.

METHODS

We measured cardiac magnetostimulation thresholds in 10 healthy, anesthetized pigs using capacitors discharged into a flat spiral coil to produce damped sinusoidal waveforms with effective stimulus duration ts,eff  = 0.45 ms. Electrocardiography (ECG), blood pressure, and peripheral oximetry signals were recorded to determine threshold coil currents yielding cardiac capture. Dixon and CINE MR volumes from each animal were segmented to generate porcine-specific electromagnetic models to calculate dB/dt and E-field values in the porcine heart at threshold. For comparison, we also simulated maximum dB/dt and E-field values created by three MRI gradient systems in the heart of a human body model.

RESULTS

The average dB/dt threshold estimated in the porcine heart was 1.66 ± 0.23 kT/s, which is 11-fold greater than the IEC dB/dt limit at ts,eff  = 0.45 ms, and 31-fold greater than the maximum value created by the investigated MRI gradients in the human heart. The average E-field threshold estimated in the porcine heart was 92.9 ± 13.5 V/m, which is 6-fold greater than the IEC E-field limit at ts,eff  = 0.45 ms and 37-fold greater than the maximum gradient-induced E-field in the human heart.

CONCLUSION

This first measurement of cardiac magnetostimulation thresholds in pigs indicates that the IEC cardiac safety limit is conservative for the investigated stimulus duration (ts,eff  = 0.45 ms).

A Huygens' surface approach to rapid characterization of peripheral nerve stimulation

PURPOSE

Peripheral nerve stimulation (PNS) modeling has a potential role in designing and operating MRI gradient coils but requires computationally demanding simulations of electromagnetic fields and neural responses. We demonstrate compression of an electromagnetic and neurodynamic model into a single versatile PNS matrix (P-matrix) defined on an intermediary Huygens' surface to allow fast PNS characterization of arbitrary coil geometries and body positions.

METHODS

The Huygens' surface approach divides PNS prediction into an extensive pre-computation phase of the electromagnetic and neurodynamic responses, which is independent of coil geometry and patient position, and a fast coil-specific linear projection step connecting this information to a specific coil geometry. We validate the Huygens' approach by performing PNS characterizations for 21 body and head gradients and comparing them with full electromagnetic-neurodynamic modeling. We demonstrate the value of Huygens' surface-based PNS modeling by characterizing PNS-optimized coil windings for a wide range of patient positions and poses in two body models.

RESULTS

The PNS prediction using the Huygens' P-matrix takes less than a minute (instead of hours to days) without compromising numerical accuracy (error ≤ 0.1%) compared to the full simulation. Using this tool, we demonstrate that coils optimized for PNS at the brain landmark using a male model can also improve PNS for other imaging applications (cardiac, abdominal, pelvic, and knee imaging) in both male and female models.

CONCLUSION

Representing PNS information on a Huygens' surface extended the approach's ability to assess PNS across body positions and models and test the robustness of PNS optimization in gradient design.

A Physical Perspective to the Inductive Function of Myelin-A Missing Piece of Neuroscience

Starting from the inductance in neurons, two physical origins are discussed, which are the coil inductance of myelin and the piezoelectric effect of the cell membrane. The direct evidence of the coil inductance of myelin is the opposite spiraling phenomenon between adjacent myelin sheaths confirmed by previous studies. As for the piezoelectric effect of the cell membrane, which has been well-known in physics, the direct evidence is the mechanical wave accompany with action potential. Therefore, a more complete physical nature of neural signals is provided. In conventional neuroscience, the neural signal is a pure electrical signal. In our new theory, the neural signal is an energy pulse containing electrical, magnetic, and mechanical components. Such a physical understanding of the neural signal and neural systems significantly improve the knowledge of the neurons. On the one hand, we achieve a corrected neural circuit of an inductor-capacitor-capacitor (LCC) form, whose frequency response and electrical characteristics have been validated by previous studies and the modeling fitting of artifacts in our experiments. On the other hand, a number of phenomena observed in neural experiments are explained. In particular, they are the mechanism of magnetic nerve stimulations and ultrasound nerve stimulations, the MRI image contrast issue and Anode Break Excitation. At last, the biological function of myelin is summarized. It is to provide inductance in the process of neural signal, which can enhance the signal speed in peripheral nervous systems and provide frequency modulation function in central nervous systems.

Optimization of MRI Gradient Coils With Explicit Peripheral Nerve Stimulation Constraints

Peripheral Nerve Stimulation (PNS) limits the acquisition rate of Magnetic Resonance Imaging data for fast sequences employing powerful gradient systems. The PNS characteristics are currently assessed after the coil design phase in experimental stimulation studies using constructed coil prototypes. This makes it difficult to find design modifications that can reduce PNS. Here, we demonstrate a direct approach for incorporation of PNS effects into the coil optimization process. Knowledge about the interactions between the applied magnetic fields and peripheral nerves allows the optimizer to identify coil solutions that minimize PNS while satisfying the traditional engineering constraints. We compare the simulated thresholds of PNS-optimized body and head gradients to conventional designs, and find an up to 2-fold reduction in PNS propensity with moderate penalties in coil inductance and field linearity, potentially doubling the image encoding performance that can be safely used in humans. The same framework may be useful in designing and operating magneto- and electro-stimulation devices.

Investigating cardiac stimulation limits of MRI gradient coils using electromagnetic and electrophysiological simulations in human and canine body models

Purpose:

Cardiac stimulation (CS) limits to gradient coil switching speed are difficult to measure in humans; instead, current regulatory guidelines (IEC 60601–2-33) are based on animal experiments and electric field–to-dB/dt conversion factors computed for a simple, homogeneous body model. We propose improvement to this methodology by using more detailed CS modeling based on realistic body models and electrophysiological models of excitable cardiac fibers.

Methods:

We compute electric fields induced by a solenoid, coplanar loops, and a commercial gradient coil in two human body models and a canine model. The canine simulations mimic previously published experiments. We generate realistic fiber topologies for the cardiac Purkinje and ventricular muscle fiber networks using rule-based algorithms, and evaluate CS thresholds using validated electrodynamic models of these fibers.

Results:

We were able to reproduce the average measured canine CS thresholds within 5%. In all simulations, the Purkinje fibers were stimulated before the ventricular fibers, and therefore set the effective CS threshold. For the investigated gradient coil, simulated CS thresholds for the x-, y-, and z-axis were at least one order of magnitude greater than the International Electrotechnical Commission limit.

Conclusion:

We demonstrate an approach to simulate gradient-induced CS using a combination of electromagnetic and electrophysiological modeling. Pending additional validation, these simulations could guide the assessment of CS limits to MRI gradient coil switching speed. Such an approach may lead to less conservative, but still safe, operation limits, enabling the use of the maximum gradient amplitude versus slew rate parameter space of recent, powerful gradient systems.

Trajectory analysis for field free line magnetic particle imaging

PURPOSE

Magnetic particle imaging (MPI) is a relatively new method to image the spatial distribution of magnetic nanoparticle (MNP) tracers administered to the body with high spatial and temporal resolution using an inhomogeneous magnetic field. The spatial information of the MNP's is encoded using a field free point (FFP), or a field free line (FFL), in which the magnetic field vanishes at a point, or on a line, respectively. FFL scanning has the advantage of improved sensitivity compared to FFP scanning as a result of higher signal-to-noise ratio. The trajectory traversed by the FFL or FFP is an important parameter of the MPI system and should be selected to achieve the best imaging quality in minimum scan time, while considering hardware constraints and patient safety. In this study, we analyzed the image quality of different FFL trajectories for a large field of view (FOV) using simulations, to provide a baseline information for FFL scanning MPI system design.

METHODS

We simulated a human-sized FFL scanning MPI configuration to image a circular FOV with 160 mm diameter, and compared Radial, Spiral, Uniform Spiral, Flower, and Lissajous trajectories with different trajectory densities scanned by the FFL for constant scan time. We analyzed the system matrices of the trajectories in terms of mutual coherence and homogeneity of the spatial sensitivity. We calculated the maximum electric fields induced on a homogeneous conductive body by the selection field (SF) and the focus field (FF) to compare the trajectories based on the nerve stimulation threshold. The images were obtained using the system matrix reconstruction approach with two different image reconstruction methods. In the first one, we used the conventional image reconstruction method, algebraic reconstruction technique (ART), which gives a regularized least-squares solution. In the second one, we used the state-of-the-art alternating direction method of multipliers (ADMM), which minimizes a weighted sum of the l₁ -norm and the total variation (TV) of the images.

RESULTS

The Radial and Spiral trajectories resulted in a poor imaging performance at low trajectory densities due to relatively high coherency and poor sensitivity of the measurements, respectively. For ART reconstruction, the highest image quality with the lowest trajectory density was achieved with the Uniform Spiral trajectory. Uniform Spiral, Flower, and Lissajous trajectories yielded comparable performance with ADMM reconstruction. The rotating SF induced higher electric field amplitude compared to the FF. Consequently, maximum allowable gradient at the same trajectory density was greater for the Radial trajectory compared to the other trajectories.

CONCLUSIONS

For a large FOV coverage, the Uniform Spiral trajectory offers a good compromise between image quality and imaging time, taking safety and hardware limitations into account. The Radial trajectory, especially using l₁ -norm and TV priors in the reconstruction, may be favorable in case the SF induced electric field is higher than that of the FF at the same frequency (e.g., relatively small FOV coverage). In general, ADMM reconstruction resulted in higher contrast and resolution compared to ART, leading to lighter requirements on the density of the trajectory.

Magnetostimulation limits in magnetic particle imaging

For magnetic particle imaging (MPI), specific absorption rate (SAR) and more critically magnetostimulation (i.e., dB/dt) safety limits will determine the optimal scan parameters, such as the drive field strength and frequency. These parameters will impact the scanning speed, field-of-view (FOV) and signal-to-noise ratio in MPI. Understanding the potential safety hazards of the drive field is critical for scaling MPI for human use. In this work, we demonstrate that magnetostimulation is the primary magnetic safety consideration in MPI, and we describe the first human-subject magnetostimulation threshold experiments for MPI using homogeneous coils. Our experiments, performed on the arm and leg, indicate that magnetostimulation thresholds monotonically decrease with increasing frequency. Additionally, we show for the first time that a strong inverse correlation exists between the threshold and the body part size. The chronaxie time, on the other hand, did not vary with body part size. We conclude with an estimation of the magnetostimulation thresholds for a full-body MPI scanner: a mean asymptotic threshold of 14.3 mT-pp (peak-to-peak) with a mean chronaxie time of 289 μs, which correspond to a magnetostimulation threshold of about 15 mT-pp for frequencies between 25 and 50 kHz. These findings will have a great impact on the optimization of MPI parameters, especially in determining the number of partial FOVs required to cover a region of interest.

A realistic model for the analysis of heart magnetic stimulation

The aim of the paper is the development of an accurate numerical model to compute the current density flowing through the heart of a virtual human body, and induced by an external electric or magnetic excitation. The model has been experimentally validated and then applied to investigate the main characteristics of the heart magnetic stimulation. This has been carried out by comparing the current density induced in the cardiac region by an external magnetic pulse with the corresponding quantity due to the more traditional electric source. Magnetic stimulation is studied because it offers some advantages: in fact, compared with the electrical stimulation, this technique is contactless and might allow the stimulation of a dressed patient. The design constraint of the whole system is represented by the current density, whose waveform and intensity are a compromise between the strength of the magnetic induction field and the pulse rise time.

Stimulation threshold comparison of time-varying magnetic pulses with different waveforms

PURPOSE

To clarify whether sinusoidal pulses possess lower thresholds than rectangular ones at perception threshold, a statement often made that contradicts the theory of stimulation.

MATERIALS AND METHODS

The results of a nerve stimulation study with 65 volunteers and with trapezoidal and sinusoidal gradient pulses were used to apply the combination of the electric field, induced in the tissue of the human body, with the "Fundamental Law of Electrostimulation." This law claims that the waveshape of a pulse is not essential as long as the amplitude of the pulse does not decrease below rheobase (rheobase condition).

RESULTS

If the rheobase condition is applied to sinusoidal waveforms and the pulse duration and amplitude is corrected accordingly, both trapezoidal and sinusoidal gradient pulses have identical threshold amplitudes as a function of pulse duration.

CONCLUSION

The "Fundamental Law of Electrostimulation," including the "rheobase condition," proved to be a good basis for describing magnetic field stimulation (magnetostimulation) and that application of it to magnetostimulation is suitable as the basis for describing magnetic field stimulation with various waveforms. For nonrectangular pulses, pulse durations and pulse amplitudes must be corrected according to the "rheobase condition." The exponential Blair Equation is less suited to be applied in magnetostimulation.

Increased Time Rate of Change of Gradient Fields: Effect on Peripheral Nerve Stimulation at Clinical MR Imaging

PURPOSE

To increase gradient stimulation from 100% to a fixed 120% level and to assess patient acceptance of the degree of peripheral nerve stimulation (PNS) at magnetic resonance (MR) imaging.

MATERIALS AND METHODS

Two hundred ten patients underwent MR imaging of various body regions according to clinical indications. An additional three-dimensional fast low-angle shot sequence with the 120% stimulation level was performed. A patient questionnaire was distributed after MR imaging to document the presence, degree, and location of PNS. Degree was measured with an 11-point scale (score range, 0-10). Age was analyzed between the sexes for significant statistical differences. Furthermore, correlation between location of examination and location and degree of stimulation was performed. To determine stimulation discomfort relative to other factors typically present at MR imaging, the degree of discomfort due to room temperature, size of magnet bore, acoustic noise, examination time, and heating sensation was determined for comparison, as well.

RESULTS

Thirty-five (16.7%) patients reported a stimulation sensation during imaging in one or more locations, while six (2.9%) felt very uncomfortable local stimulation (score of 8-10). No significant difference between male and female patients regarding age, sex, and appearance or degree of stimulation sensation could be detected. No significant correlation between location of examination and location and degree of stimulation was recorded. Compared with other side effects, PNS was considered relatively unimportant.

CONCLUSION

The 120% gradient stimulation level seems acceptable for routine clinical imaging with this gradient system, since only 2.9% of patients experienced very uncomfortable local stimulation.

Peripheral nerve stimulation properties of head and body gradient coils of various sizes

Peripheral nerve stimulation (PNS) caused by time-varying magnetic fields has been studied both theoretically and experimentally. A human volunteer study performed on three different body-size gradient coils and one head-size gradient coil is presented in this work. The experimental results were used to generate average PNS threshold parameters for the tested gradient systems. It was found that the average stimulation threshold increases while gradient-region-of-uniformity size decreases. In addition, linear relationships between PNS parameters and diameter of homogeneous gradient spherical volume (DSV) were discovered: SR(min) and DeltaG(min) both vary inverse linearly with DSV. More importantly, the chronaxie value was found to vary inversely linearly with the DSV. This finding indicates that, contrary to the general understanding, the parameter "chronaxie" in the commonly accepted simple stimulation models cannot be considered to be a single-value, nerve-specific constant. A modified linear model for gradient-induced PNS based on these results was developed, which may permit, for the first time, the general prediction of nerve stimulation properties for gradient coils of arbitrary linear region dimension.

Gradient system providing continuously variable field characteristics

Peripheral nerve stimulation limits the use of whole-body gradient systems capable of slew rates > 80 T/m/s and gradient strengths > 25 mT/m. The stimulation threshold depends mainly on the amplitude of the induced electric field in the patient's body, and thus can be influenced by changing the total magnetic flux of the gradient coil. A gradient system was built which allows continuous variation of the field characteristics in order to permit the use of full gradient performance without stimulation (slew rate 190-210 T/m/s, G(max) 32-40 mT/m). The system consists of a modular six-channel gradient coil designed with a modified target field method, two three-channel amplifiers, and a six-channel gradient controller. It is demonstrated that two coils on one gradient axis can be driven by two amplifiers in parallel, without significant changes in image quality. Scaling of the field properties and stimulation threshold according to the current polarity and ratio of both coil sets was verified in both phantom and volunteer studies.

Review of patient safety in time-varying gradient fields

In magnetic resonance, time-varying gradient magnetic fields (dB/dt) may stimulate nerves or muscles by inducing electric fields in patients. Models predicted mean peripheral nerve and cardiac stimulation thresholds. For gradient ramp durations of less than a few milliseconds, mean peripheral nerve stimulation is a safe indicator of high dB/dt. At sufficient amplitudes, peripheral nerve stimulation is perceptible (i.e., tingling or tapping sensations). Magnetic fields from simultaneous gradient axes combine almost as a vector sum to produce stimulation. Patients may become uncomfortable at amplitudes 50%-100% above perception thresholds. In dogs, respiratory stimulation has been induced at about 300% of mean peripheral nerve thresholds. Cardiac stimulation has been induced in dogs by small gradient coils at thresholds near Reilly's predictions. Cardiac stimulation required nearly 80 times the energy needed to produce nerve stimulation in dogs. Nerve and cardiac stimulation thresholds for dogs were unaffected by 1.5-T magnetic fields.

Electromyography in MRI--first recordings of peripheral nerve activation caused by fast magnetic field gradients

Prior studies on the evaluation of stimulation by MRI were based on the subjective feeling of the volunteers. A wide variety of stimulation thresholds between the subjects was observed. In order to exclude subjective perception levels as a cause of this variation, we developed a method to investigate the activation of peripheral nerves after gradient switching by electromyography (EMG) within the MR-imager. Five healthy volunteers were positioned in the MR-scanner with the bridge of the nose at isocenter. The amplitude of sinusoidal pulse trains of the anterior-posterior gradient (rise-times: 200 or 300 micros, various numbers of oscillations) was increased stepwise. Four surface electrodes were placed on the region where a muscle-twitch was reported. Electric activity of the muscle during stimulation experiments was recorded with an MR-compatible electro-physiologic amplifier. Stimulation thresholds were defined by the appearance of an EMG-signal. Thresholds were sharp and consistent with the report of the subjects.

Paradigm shift in lead design

During the past 30 years there has been a tremendous development in electrode technology from bulky (90 mm2) to pin-sized (1.0 mm2) electrodes. Simultaneously, impedance has increased from 110 Ohms to >1 kOhms, which has been termed a "paradigm shift" in lead design. If current is responsible for stimulation, why is its impedance a key factor in saving energy? Further, what mechanism is behind this development based on experimental findings and what conclusion can be drawn from it to optimize electrode size? If it is assumed that there is always a layer of nonexcitable tissue between the electrode surface and excitable myocardium and that the electric field (potential gradient) produced by the electrode at this boundary is reaching threshold level, then a formula can be derived for the voltage threshold that completely describes the electrophysiology and electrophysics of a hemispherical electrode. Assuming that the mean chronic threshold for porous steroid-eluting electrodes is 0.6 V with 0.5-ms pulse duration, thickness of nonexcitable tissue can be estimated to be 1.5 mm. Taking into account this measure and the relationship between chronaxie and electrode area, voltage threshold, impedance, and energy as a function of surface area can be calculated. The lowest voltage for 0.5-ms pulse duration is reached with r(o) = 0.5 d, yielding a surface area of 4 mm2 and a voltage threshold of 0.62 V, an impedance of 1 kOhms, and an energy level of 197 nJ. It can be deduced from our findings that a further reduction of surface areas below 1.6 mm2 will not diminish energy threshold substantially, if pulse duration remains at 0.5 ms. Lowest energy is reached with t = chronaxie, yielding an energy level <100 nJ with surface areas < or =1.5 mm2. It is striking to see how well the theoretically derived results correspond to the experimental findings. It is also surprising that the hemispheric model so accurately approximates experimental results with differently shaped electrodes that it can be concluded that electrode shape seems to play a minor role in electrode efficiency. Further energy reduction can only be achieved by reducing the pulse duration to chronaxie. A real paradigm shift will occur only if the fundamentals of electrostimulation in combination with electrophysics are accepted by the pacing community.

Reduced circular field-of-view imaging

A rapid dynamic imaging technique based on polar k-space sampling is presented. A gain in temporal resolution is achieved by angular undersampling. A detailed analysis of the point spread function of angular undersampled polar imaging reveals a reduced diameter of the corresponding circular field of view. Under the assumption that dynamic changes are restricted to a local circular field of view, angular undersampled dynamic imaging allows the recording of rapid changes at high temporal and spatial resolution. The theoretical and experimental details of the technique are presented.

Magnetostimulation in MRI

In national and international bodies, there is active discussion of appropriate safety regulations of levels of magnetic field strength in MRI. Present limits are usually expressed in terms of the switching rate dB/dt, but the validity of this is open to debate. Application of the fundamental law of electrostimulation is well-established, both on theoretical and experimental grounds. Application of this law, in combination with Maxwell's law, yields a very simple equation that we call the fundamental law of magnetostimulation. This law has the hyperbolic form of a strength-duration curve and allows an estimation of the lowest possible value of the magnetic flux density capable of stimulating nerves and muscles. Calculations prove that the threshold for heart excitation is much higher than those for nerve and muscle stimulations. Experimental results from us and other authors confirm the correctness of the derived laws for magnetostimulation. In light of these findings, proposed safety limits should be reconsidered.