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

Minimizing electric fields and increasing peripheral nerve stimulation thresholds using a body gradient array coil

PURPOSE

To demonstrate the performance of gradient array coils in minimizing switched-gradient-induced electric fields (E-fields) and improving peripheral nerve stimulation (PNS) thresholds while generating gradient fields with adjustable linearity across customizable regions of linearity (ROLs).

METHODS

A body gradient array coil is used to reduce the induced E-fields on the surface of a body model by modulating applied currents. This is achieved by performing an optimization problem with the peak E-field as the objective function and current amplitudes as unknown variables. Coil dimensions and winding patterns are fixed throughout the optimization, whereas other engineering metrics remain adjustable. Various scenarios are explored by manipulating adjustable parameters.

RESULTS

The array design consistently yields lower E-fields and higher PNS thresholds across all scenarios compared with a conventional coil. When the gradient array coil generates target gradient fields within a 44-cm-diameter spherical ROL, the maximum E-field is reduced by 10%, 18%, and 61% for the X, Y, and Z gradients, respectively. Transitioning to a smaller ROL (24 cm) and relaxing the gradient linearity error results in further E-field reductions. In oblique gradients, the array coil demonstrates the most substantial reduction of 40% in the Z-Y direction. Among the investigated scenarios, the most significant increase of 4.3-fold is observed in the PNS thresholds.

CONCLUSION

Our study demonstrated that gradient array coils offer a promising pathway toward achieving high-performance gradient coils regarding gradient strength, slew rate, and PNS thresholds, especially in scenarios in which linear magnetic fields are required within specific target regions.

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.

Experimental validation of a PNS-optimized whole-body gradient coil

PURPOSE

Peripheral nerve stimulation (PNS) limits the usability of state-of-the-art whole-body and head-only MRI gradient coils. We used detailed electromagnetic and neurodynamic modeling to set an explicit PNS constraint during the design of a whole-body gradient coil and constructed it to compare the predicted and experimentally measured PNS thresholds to those of a matched design without PNS constraints.

METHODS

We designed, constructed, and tested two actively shielded whole-body Y-axis gradient coil winding patterns: YG1 is a conventional symmetric design without PNS-optimization, whereas YG2's design used an additional constraint on the allowable PNS threshold in the head-imaging landmark, yielding an asymmetric winding pattern. We measured PNS thresholds in 18 healthy subjects at five landmark positions (head, cardiac, abdominal, pelvic, and knee).

RESULTS

The PNS-optimized design YG2 achieved 46% higher average experimental thresholds for a head-imaging landmark than YG1 while incurring a 15% inductance penalty. For cardiac, pelvic, and knee imaging landmarks, the PNS thresholds increased between +22% and +35%. For abdominal imaging, PNS thresholds did not change significantly between YG1 and YG2 (-3.6%). The agreement between predicted and experimental PNS thresholds was within 11.4% normalized root mean square error for both coils and all landmarks. The PNS model also produced plausible predictions of the stimulation sites when compared to the sites of perception reported by the subjects.

CONCLUSION

The PNS-optimization improved the PNS thresholds for the target scan landmark as well as most other studied landmarks, potentially yielding a significant improvement in image encoding performance that can be safely used in humans.

Peripheral nerve stimulation informed design of a high-performance asymmetric head gradient coil

PURPOSE

Peripheral nerve stimulation (PNS) limits the image encoding performance of both body gradient coils and the latest generation of head gradients. We analyze a variety of head gradient design aspects using a detailed PNS model to guide the design process of a new high-performance asymmetric head gradient to raise PNS thresholds and maximize the usable image-encoding performance.

METHODS

A novel three-layer coil design underwent PNS optimization involving PNS predictions of a series of candidate designs. The PNS-informed design process sought to maximize the usable parameter space of a coil with <10% nonlinearity in a 22 cm region of linearity, a relatively large inner diameter (44 cm), maximum gradient amplitude of 200 mT/m, and a high slew rate of 900 T/m/s. PNS modeling allowed identification and iterative adjustment of coil features with beneficial impact on PNS such as the number of winding layers, shoulder accommodation strategy, and level of asymmetry. PNS predictions for the final design were compared to measured thresholds in a constructed prototype.

RESULTS

The final head gradient achieved up to 2-fold higher PNS thresholds than the initial design without PNS optimization and compared to existing head gradients with similar design characteristics. The inclusion of a third intermediate winding layer provided the additional degrees of freedom necessary to improve PNS thresholds without significant sacrifices to the other design metrics.

CONCLUSION

Augmenting the design phase of a new high-performance head gradient coil by PNS modeling dramatically improved the usable image-encoding performance by raising PNS thresholds.

Advancements in Gradient System Performance for Clinical and Research MRI

In magnetic resonance imaging (MRI), spatial field gradients are applied along each axis to encode the location of the nuclear spin in the frequency domain. During recent years, the development of new gradient technologies has been focused on the generation of stronger and faster gradient fields for imaging with higher spatial and temporal resolution. This benefits imaging methods, such as brain diffusion and functional MRI, and enables human imaging at ultra-high field MRI. In addition to improving gradient performance, new technologies have been presented to minimize peripheral nerve stimulation and gradient-related acoustic noise, both generated by the rapid switching of strong gradient fields. This review will provide a general background on the gradient system and update on the state-of-the-art gradient technology. EVIDENCE LEVEL: 5 TECHNICAL EFFICACY: Stage 1.

Physiological effects of human body imaging with 300 mT/m gradients

PURPOSE

The use of high-performance gradient systems (i.e., high gradient strength and/or high slew rate) for human MRI is limited by physiological effects (including the elicitation of magnetophosphenes and peripheral nerve stimulation (PNS)). These effects, in turn, depend on the interaction between time-varying magnetic fields and the body, and thus on the participant's position with respect to the scanner's isocenter. This study investigated the occurrence of magnetophosphenes and PNS when scanning participants on a high-gradient (300 mT/m) system, for different gradient amplitudes, ramp times, and participant positions.

METHODS

Using a whole-body 300 mT/m gradient MRI system, a cohort of participants was scanned with the head, heart, and prostate at magnet isocenter and a train of trapezoidal bipolar gradient pulses, with ramp times from 0.88 to 4.20 ms and gradient amplitudes from 60 to 300 mT/m. Reports of magnetophosphenes and incidental reports of PNS were obtained. A questionnaire was used to record any additional subjective effects.

RESULTS

Magnetophosphenes were strongly dependent on participant position in the scanner. 87% of participants reported the effect with the heart at isocenter, 33% with the head at isocenter, and only 7% with the prostate at isocenter. PNS was most widely reported by participants for the vertical gradient axis (67% of participants), and was the dominant physiological effect for ramp times below 2 ms.

CONCLUSION

This study evaluates the probability of eliciting magnetophosphenes during whole-body imaging using an ultra-strong gradient MRI system. It provides empirical guidance on the use of high-performance gradient systems for whole-body human MRI.

Magneto-stimulation limits in medical imaging applications with rapid field dynamics

Objective. The goal of this work is to extend previous peripheral nerve stimulation (PNS) studies to scenarios relevant to magnetic particle imaging (MPI) and low-field magnetic resonance imaging (MRI), where field dynamics can evolve at kilo-hertz frequencies. Approach. We have constructed an apparatus for PNS threshold determination on a subject’s limb, capable of narrow and broad-band magnetic stimulation with pulse characteristic times down to 40 μs. Main result. From a first set of measurements on 51 volunteers, we conclude that the PNS dependence on pulse frequency/rise-time is compatible with traditional stimulation models where nervous responses are characterized by a rheobase and a chronaxie. Additionally, we have extended pulse length studies to these fast timescales and confirm thresholds increase significantly as trains transition from tens to a few pulses. We also look at the influence of field spatial distribution on PNS effects, and find that thresholds are higher in an approximately linearly inhomogeneous field (relevant to MRI) than in a rather homogeneous distribution (as in MPI). Significance. PNS constrains the clinical performance of MRI and MPI systems. Extensive magneto-stimulation studies have been carried out recently in the field of MPI, where typical operation frequencies range from single to tens of kilo-hertz. However, PNS literature is scarce for MRI in this fast regime, relevant to small (low inductance) dedicated MRI setups, and where the resonant character of MPI coils prevents studies of broad-band stimulation pulses. This work advances in this direction.

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.

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.

Prediction of peripheral nerve stimulation thresholds of MRI gradient coils using coupled electromagnetic and neurodynamic simulations

PURPOSE

As gradient performance increases, peripheral nerve stimulation (PNS) is becoming a significant constraint for fast MRI. Despite its impact, PNS is not directly included in the coil design process. Instead, the PNS characteristics of a gradient are assessed on healthy subjects after prototype construction. We attempt to develop a tool to inform coil design by predicting the PNS thresholds and activation locations in the human body using electromagnetic field simulations coupled to a neurodynamic model. We validate the approach by comparing simulated and experimentally determined thresholds for 3 gradient coils.

METHODS

We first compute the electric field induced by the switching fields within a detailed electromagnetic body model, which includes a detailed atlas of peripheral nerves. We then calculate potential changes along the nerves and evaluate their response using a neurodynamic model. Both a male and female body model are used to study 2 body gradients and 1 head gradient.

RESULTS

There was good agreement between the average simulated thresholds of the male and female models with the experimental average (normalized root-mean-square error: <10% and <5% in most cases). The simulation could also interrogate thresholds above those accessible by the experimental setup and allowed identification of the site of stimulation.

CONCLUSIONS

Our simulation framework allows accurate prediction of gradient coil PNS thresholds and provides detailed information on location and "next nerve" thresholds that are not available experimentally. As such, we hope that PNS simulations can have a potential role in the design phase of high performance MRI gradient coils.

Predicting Magnetostimulation Thresholds in the Peripheral Nervous System using Realistic Body Models

Rapid switching of applied magnetic fields in the kilohertz frequency range in the human body induces electric fields powerful enough to cause Peripheral Nerve Stimulation (PNS). PNS has become one of the main constraints on the use of high gradient fields for fast imaging with the latest MRI gradient technology. In recent MRI gradients, the applied fields are powerful enough that PNS limits their application in fast imaging sequences like echo-planar imaging. Application of Magnetic Particle Imaging (MPI) to humans is similarly PNS constrained. Despite its role as a major constraint, PNS considerations are only indirectly incorporated in the coil design process, mainly through using the size of the linear region as a proxy for PNS thresholds or by conducting human experiments after constructing coil prototypes. We present for the first time, a framework to simulate PNS thresholds for realistic coil geometries to directly address PNS in the design process. Our PNS model consists of an accurate body model for electromagnetic field simulations, an atlas of peripheral nerves, and a neurodynamic model to predict the nerve responses to imposed electric fields. With this model, we were able to reproduce measured PNS thresholds of two leg/arm solenoid coils with good agreement.

Magnetic Field Reference Levels for Arbitrary Periodic Waveforms for Prevention of Peripheral Nerve Stimulation

Guidelines for prevention of peripheral nerve stimulation from exposure to low frequency magnetic fields have been developed by standard-setting bodies. Exposure limits or reference levels (RLs) are typically set in terms of the maximum root-mean-square amplitude of a sinusoidal waveform; however, environmental flux densities are often periodic, non-sinusoidal waveforms. This work presents a procedure for deriving RLs for any generalized periodic waveform using the empirical nerve-stimulation threshold data obtained from human volunteer MRI experiments. For this purpose, the "Law of Electrostimulation" (LOE), which sets forth conditions of a waveform necessary to trigger the action potential required to depolarize cell membranes, is applied to various waveforms. The results of the LOE analysis are waveform-specific, amplitude thresholds of stimulation that are found in terms of the empirically-derived rheobase threshold time-rate-of-change flux density and chronaxie from trapezoidal pulse MRI experiments. The thresholds are converted to amplitude RLs in two asymptotic frequency regimes as per the usual practice in standard setting. The resulting RLs have the same frequency dependence as in existing standards (i.e., inverse-frequency below a transition frequency and flat above). It is shown that the transition frequency is dependent only on the shape of the waveform. Both sinusoidal and non-sinusoidal waveforms have identical peak-to-peak amplitude RLs above their respective transition frequencies. Below these frequencies, all peak-to-peak amplitude RLs have the same functional dependence on frequency when the frequency is normalized to the waveform-specific transition frequency. This results in simple criteria for testing the amplitude of any arbitrary periodic waveform against potential for stimulation. These criteria are compared to guidance given for non-sinusoidal waveforms in the ICNIRP 1 Hz-100 kHz exposure standard.

A Model of Electrostimulation Based on the Membrane Capacitance as Electromechanical Transducer for Pore Gating

BACKGROUND

Electrostimulation has gained enormous importance in modern medicine, for example, in implantable pacemakers and defibrillators, pain stimulators, and cochlear implants. Most electrostimulation macromodels use the electrical current as the primary parameter to describe the conventional strength-duration relationship of the output of a generator. These models normally assume that the stimulation pulse charges up the passive cell membrane capacitance, and then the increased (less-negative) transmembrane potential activates voltage-gated sodium channels. However, this model has mechanistic and accuracy limitations.

NOVEL CONCEPT

Our model assumes that the membrane capacitance is an electromechanical transducer and that the membrane is compressed by the endogenous electric field. The pressure is quadratically correlated with the transmembrane voltage. If the pressure is reduced by an exogenous field, the compression is released and, thus, opening the pores for Na(+) influx initiates excitation.

RESULTS

The exogenous electric field must always be equal to or greater than the rheobase field strength (rheobase condition). This concept yields a final result that the voltage-pulse-content produced by the exogenous field between the two ends of a cell is a linear function of the pulse duration at threshold level. Thus, the model yields mathematical formulations that can describe and explain the characteristic features of electrostimulation.

CONCLUSIONS

Our model of electrostimulation can describe and explain electrostimulation at cellular level. The model's predictions are consistent with published experimental studies. Practical applications in cardiology are discussed in the light of this model of electrostimulation.

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.