Investigation of assumptions underlying current safety guidelines on EM-induced nerve stimulation

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.

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.

Evaluation of Peripheral Electrostimulation Thresholds in Human Model for Uniform Magnetic Field Exposure

The external field strength according to the international guidelines and standards for human protection are derived to prevent peripheral nerve system pain at frequencies from 300-750 Hz to 1 MHz. In this frequency range, the stimulation is attributable to axon electrostimulation. One limitation in the current international guidelines is the lack of respective stimulation thresholds in the brain and peripheral nervous system from in vivo human measurements over a wide frequency range. This study investigates peripheral stimulation thresholds using a multi-scale computation based on a human anatomical model for uniform exposure. The nerve parameters are first adjusted from the measured data to fit the peripheral nerve in the trunk. From the parameters, the external magnetic field strength to stimulate the nerve was estimated. Here, the conservativeness of protection limits of the international guidelines and standards for peripheral stimulation was confirmed. The results showed a margin factor of 4-6 and 10-24 times between internal and external protection limits of Institute of Electrical and Electronics Engineers standard (IEEE C95.1) and International Commission on Non-Ionizing Radiation Protection guidelines, with the computed pain thresholds.

Electric field calculation and peripheral nerve stimulation prediction for head and body gradient coils

PURPOSE

To demonstrate and validate electric field (E-field) calculation and peripheral nerve stimulation (PNS) prediction methods that are accurate, computationally efficient, and that could be used to inform regulatory standards.

METHODS

We describe a simplified method for calculating the spatial distribution of induced E-field over the volume of a body model given a gradient coil vector potential field. The method is easily programmed without finite element or finite difference software, allowing for straightforward and computationally efficient E-field evaluation. Using these E-field calculations and a range of body models, population-weighted PNS thresholds are determined using established methods and compared against published experimental PNS data for two head gradient coils and one body gradient coil.

RESULTS

A head-gradient-appropriate chronaxie value of 669 µs was determined by meta-analysis. Prediction errors between our calculated PNS parameters and the corresponding experimentally measured values were ~5% for the body gradient and ~20% for the symmetric head gradient. Our calculated PNS parameters matched experimental measurements to within experimental uncertainty for 73% of ∆G_min estimates and 80% of SR_min estimates. Computation time is seconds for initial E-field maps and milliseconds for E-field updates for different gradient designs, allowing for highly efficient iterative optimization of gradient designs and enabling new dimensions in PNS-optimal gradient design.

CONCLUSIONS

We have developed accurate and computationally efficient methods for prospectively determining PNS limits, with specific application to head gradient coils.

Neuroman: Voxel Phantoms from Surface Models of 300 Head Structures Including 12 Pairs of Cranial Nerves

For a precise simulation of electromagnetic radiation effects, voxel phantoms require detailed structures to approximate humans. The phantoms currently used still do not have sophisticated structures. This paper presents voxel and surface models of 300 head structures with cranial nerves and reports on a technique for voxel reconstruction of the cranial nerves having very thin and small structures. In real-color sectioned images of the head (voxel size: 0.1 mm), 300 structures were segmented using Photoshop. A surface reconstruction was performed automatically on Mimics. Voxel conversion was run on Voxel Studio. The abnormal shapes of the voxel models were found and classified into three types: thin cord, thin layers, and thin parts in the structures. The abnormal voxel models were amended using extended, filled, and manual voxelization methods devised for this study. Surface models in STL format and as PDF files of the 300 head structures were produced. The STL format has good scalability, so it can be used in most three-dimensional surface model software. The PDF file is very user friendly for students and researchers who want to learn the head anatomy. Voxel models of 300 head structures were produced (TXT format), and their voxel quantity and weight were measured. A voxel model is difficult to handle, and the surface model cannot use the radiation simulation. Consequently, the best method for making precise phantoms is one in which the flaws of the voxel and surface models complement each other, as in the present study.

Optimizing selective stimulation of peripheral nerves with arrays of coils or surface electrodes using a linear peripheral nerve stimulation metric

OBJECTIVE

We present a PNS oracle, which solves these computation time and linearity problems and is, therefore, well-suited for fast optimization of voltage distributions in contact electrode arrays and current drive patterns in non-contact magnetic coil arrays.

APPROACH

The PNS oracle metric for a nerve fiber is computed from an electric field map using only linear operations (projection, differentiation, convolution, scaling). Due to its linearity, this PNS metric can be precomputed for a set of coil or electrode segments, allowing rapid PNS prediction and comparison of any possible coil or electrode stimulation configuration constructed from this set. The PNS oracle is closely related to the classical activating function and modified driving functions but is adjusted to better correlate with full neurodynamic modeling of myelinated mammalian nerves.

MAIN RESULTS

We validated the PNS oracle in three MRI gradient coils and two body models and found good correlation between the PNS oracle and the full neurodynamic modeling approach (R ²  >  0.995). Finally, we demonstrated its potential utility by optimizing the driving currents and voltages of arrays of 108 magnetic coils or 108 contact electrodes to selectively stimulate target nerves in the lower leg.

SIGNIFICANCE

Peripheral nerve stimulation (PNS) by electromagnetic fields can be accurately simulated using coupled electromagnetic and neurodynamic modeling. Such simulations are slow and non-linear in the electric field, which makes it difficult to iteratively optimize coil and electrode configurations or drive patterns aiming to avoid PNS or to initiate it for therapeutic purposes.

Sensitivity analysis of neurodynamic and electromagnetic simulation parameters for robust prediction of peripheral nerve stimulation

Peripheral nerve stimulation (PNS) has become an important limitation for fast MR imaging using the latest gradient hardware. We have recently developed a simulation framework to predict PNS thresholds and stimulation locations in the body for arbitrary coil geometries to inform the gradient coil optimization process. Our approach couples electromagnetic field simulations in realistic body models to a neurodynamic model of peripheral nerve fibers. In this work, we systematically analyze the impact of key parameters on the predicted PNS thresholds to assess the robustness of the simulation results. We analyze the sensitivity of the simulated thresholds to variations of the most important simulation parameters, including parameters of the electromagnetic field simulations (dielectric tissue properties, body model size, position, spatial resolution, and coil model discretization) and parameters of the neurodynamic simulation (length of the simulated nerves, position of the nerve model relative to the extracellular potential, temporal resolution of the nerve membrane dynamics). We found that for the investigated setup, the subject-dependent parameters (e.g. tissue properties or body size) can affect PNS prediction by up to ~26% when varied in a natural range. This is in accordance with the standard deviation of ~30% reported in human subject studies. Parameters related to numerical aspects can cause significant simulation errors (>30%), if not chosen cautiously. However, these perturbations can be controlled to yield errors below 5% for all investigated parameters without an excessive increase in computation time. Our sensitivity analysis shows that patient-specific parameter fluctuations yield PNS threshold variations similar to the variations observed in experimental PNS studies. This may become useful to estimate population-average PNS thresholds and understand their standard deviation. Our analysis indicates that the simulated PNS thresholds are numerically robust, which is important for ranking different MRI gradient coil designs or assessing different PNS mitigation strategies.

Functionalized Anatomical Models for Computational Life Sciences

The advent of detailed computational anatomical models has opened new avenues for computational life sciences (CLS). To date, static models representing the anatomical environment have been used in many applications but are insufficient when the dynamics of the body prevents separation of anatomical geometrical variability from physics and physiology. Obvious examples include the assessment of thermal risks in magnetic resonance imaging and planning for radiofrequency and acoustic cancer treatment, where posture and physiology-related changes in shape (e.g., breathing) or tissue behavior (e.g., thermoregulation) affect the impact. Advanced functionalized anatomical models can overcome these limitations and dramatically broaden the applicability of CLS in basic research, the development of novel devices/therapies, and the assessment of their safety and efficacy. Various forms of functionalization are discussed in this paper: (i) shape parametrization (e.g., heartbeat, population variability), (ii) physical property distributions (e.g., image-based inhomogeneity), (iii) physiological dynamics (e.g., tissue and organ behavior), and (iv) integration of simulation/measurement data (e.g., exposure conditions, “validation evidence” supporting model tuning and validation). Although current model functionalization may only represent a small part of the physiology, it already facilitates the next level of realism by (i) driving consistency among anatomy and different functionalization layers and highlighting dependencies, (ii) enabling third-party use of validated functionalization layers as established simulation tools, and (iii) therefore facilitating their application as building blocks in network or multi-scale computational models. Integration in functionalized anatomical models thus leverages and potentiates the value of sub-models and simulation/measurement data toward ever-increasing simulation realism. In our o²S²PARC platform, we propose to expand the concept of functionalized anatomical models to establish an integration and sharing service for heterogeneous computational models, ranging from the molecular to the organ level. The objective of o²S²PARC is to integrate all models developed within the National Institutes of Health SPARC initiative in a unified anatomical and computational environment, to study the role of the peripheral nervous system in controlling organ physiology. The functionalization concept, as outlined for the o²S²PARC platform, could form the basis for many other application areas of CLS. The relationship to other ongoing initiatives, such as the Physiome Project, is also presented.

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.

Functionalized anatomical models for EM-neuron Interaction modeling

The understanding of interactions between electromagnetic (EM) fields and nerves are crucial in contexts ranging from therapeutic neurostimulation to low frequency EM exposure safety. To properly consider the impact of in vivo induced field inhomogeneity on non-linear neuronal dynamics, coupled EM-neuronal dynamics modeling is required. For that purpose, novel functionalized computable human phantoms have been developed. Their implementation and the systematic verification of the integrated anisotropic quasi-static EM solver and neuronal dynamics modeling functionality, based on the method of manufactured solutions and numerical reference data, is described. Electric and magnetic stimulation of the ulnar and sciatic nerve were modeled to help understanding a range of controversial issues related to the magnitude and optimal determination of strength-duration (SD) time constants. The results indicate the importance of considering the stimulation-specific inhomogeneous field distributions (especially at tissue interfaces), realistic models of non-linear neuronal dynamics, very short pulses, and suitable SD extrapolation models. These results and the functionalized computable phantom will influence and support the development of safe and effective neuroprosthetic devices and novel electroceuticals. Furthermore they will assist the evaluation of existing low frequency exposure standards for the entire population under all exposure conditions.