On the computation of a retina resistivity profile for applications in multi-scale modeling of electrical stimulation and absorption.

This study proposes a methodology for computationally estimating resistive properties of tissue in multi-scale computational models, used for studying the interaction of electromagnetic fields with neural tissue, with applications to both dosimetry and neuroprosthetics. Traditionally, models at bulk tissue- and cellular-level scales are solved independently, linking resulting voltage from existing resistive tissue-scale models as extracellular sources to cellular models. This allows for solving the effects that external electric fields have on cellular activity. There are two major limitations to this approach: first, the resistive properties of the tissue need to be chosen, of which there are contradicting measurements in literature; second, the measurements of resistivity themselves may be inaccurate, leading to the mentioned contradicting results found across different studies. Our proposed methodology allows for constructing computed resistivity profiles using knowledge of only the neural morphology within the multi-scale model, resulting in a practical implementation of the effective medium theory; this bypasses concerns regarding the choice of resistive properties and accuracy of measurement setups. A multi-scale model of retina is constructed with an external electrode to serve as a test bench for analyzing existing and resulting resistivity profiles, and validation is presented through the reconstruction of a published resistivity profile of retina tissue. Results include a computed resistivity profile of retina tissue for use with a retina multi-scale model used to analyze effects of external electric fields on neural activity.

In Vivo Magnetic Stimulation of Rat Sciatic Nerve With Centimeter- and Millimeter-Scale Solenoid Coils.

Previous reports of magnetic stimulation of the peripheral nervous system (PNS) used various coil geometries, all with outer diameters larger than 35 mm, and stimulation energies in the 50 J range to evoke neural excitation. Recent reports of central nervous system (CNS) activation used sub-mm-scale solenoid coils with mJ energy levels. The goal of this study was to translate the lower energy levels from the CNS to the PNS via using smaller coils placed in closer proximity to the neural tissue. Such a performance improvement would advance the state of the art of magnetic stimulation and provide a path towards new neuroprosthetic devices. Primarily, we investigated the range of coil outer diameters from 25 mm down to 5 mm to better understand the dependence of coil diameter on energy required for PNS activation. Nine cm- and mm-scale copper solenoid coils, with various resistances, inductances, inner and outer diameters, and heights were compared by quantizing neuromuscular responses to magnetic stimulation via capacitive discharge excitation of rat sciatic nerves in vivo. Additionally, the effects of stimulus duration and coil position were investigated. As opposed to prior work, this study compares a subset of stimulation parameters in an intact nerve preparation, and shows that magnetic stimulation with coils that abut the nerve is a reliable, effective method of neuromuscular stimulation. Although we observed different energies required for neuromuscular activation depending on the coil and excitation parameters used, for the experimental configuration, devices, and stimulus waveform shapes presented in this manuscript, no systematic dependence of PNS activation on coil diameter was found, even for the mm-scale coils investigated herein. However, there was a clear relationship between discharge circuit capacitance and energy required to evoke a neuromuscular response. Coils approximately 12 mm in outer diameter and larger consistently evoked responses, whereas coils 5 mm in outer diameter did not. Furthermore, we observed meaningful neuromuscular excitation when stimulating with energies as low as 20 J. Although this is an improvement over prior work, it is still orders of magnitude greater than the energy required for conventional electrical stimulation, suggesting that these devices are presently not suitable for use in an application requiring continued pulsed stimulation. Nevertheless, these devices are suitable for basic research and as clinical tools that infrequently stimulate, such as in diagnostic applications.

A µm-Scale Computational Model of Magnetic Neural Stimulation in Multifascicular Peripheral Nerves.

There has been recurring interest in using magnetic neural stimulation for implantable localized stimulation. However, the large stimulation voltages and energies necessary to evoke neuronal activity have tempered this interest. To investigate the potential of magnetic stimulation as a viable methodology and to provide the ability to investigate novel coil designs that can result in lower stimulation threshold voltages and energies, there is a need for a model that accurately predicts the magnetic field-tissue interaction that results in neuronal stimulation. In this study, we provide a computational framework to accurately estimate the stimulation threshold and have validated the model with in vivo magnetic stimulation experiments. To make such predictions, we developed a micrometer-resolution anatomically driven computational model of rat sciatic nerve and quantified the effect of tissue heterogeneity (i.e., fascicular organization, axon distribution, and density) and axonal membrane capacitance on the resulting threshold. Using the multiresolution impedance method, we computed the spatial-temporal distribution of the induced electric field in the nerve and applied this field to a Frankenhaeuser-Huxley axon model in NEURON to simulate the nonlinear mechanisms of the membrane channels. The computational model developed predicts the stimulation thresholds for four magnetic coil designs with different geometrical parameters within the 95% confidence interval (experiments count = 4) of measured in vivo stimulation thresholds for the rat sciatic nerve.

A 3-D admittance-level computational model of a rat hippocampus for improving prosthetic design.

Hippocampal prosthetic devices have been developed to bridge the gap between functioning portions of the hippocampus, in order to restore lost memory functionality in those suffering from brain injury or diseases. One approach taken in recent neuroprosthetic design is to use a multi-input, multi-output device that reads data from the CA3 in the hippocampus and electrically stimulates the CA1 in an attempt to mimic the appropriate firing pattern that would occur naturally between the two areas. However, further study needs to be conducted in order to optimize electrode placement, pulse magnitude, and shape for creating the appropriate firing pattern. This paper describes the creation and implementation of an anatomically correct 3D model of the hippocampus to simulate the electric field patterns and axonal activation from electrical stimulation due to an implanted electrode array. The activating function was applied to the voltage results to determine the firing patterns in possible axon locations within the CA1.

Magnetic stimulation of mammalian peripheral nerves in vivo: an alternative to functional electrical stimulation.

Functional electrical stimulation is the current gold standard for stimulating neuronal interfaces for functional neuromuscular and cortical applications, but it is not without its drawbacks. One such fault is the need to have direct electrical contact with the nerve tissue, and any side effects this causes. Functional magnetic stimulation, which works though electromagnetic induction, does not require electrical contact and may be a viable alternative to functional electrical stimulation. We are investigating the capabilities of magnetic stimulation with centimeter scale (< 2.5 cm) coils in feline and rodent sciatic nerves in vivo. We have shown that magnetic stimulation can consistently produce the same levels of neuromuscular activation as electrical stimulation. Additionally, the position of the coil relative to the nerve influences neuromuscular activation, suggesting the possibility of selective muscle activation.

A µm-resolution heterogeneous tissue model for the magnetic stimulation of multifascicular sciatic nerve.

Efficacy of magnetic stimulation of the central or peripheral nervous system depends on the spatial and temporal distribution of the induced electric field generated by the magnetic coil. Therefore, accurate estimation of the induced electric field is crucial to the design and optimization of magnetic coils, particularly as the coil dimensions are reduced. In this work, we developed a numerical model of a multifascicular sciatic nerve to study the effect of tissue heterogeneity on the induced electric field. Using a multi-resolution electric field solver, we can resolve feature sizes as small as 1µm, allowing inclusion of the nerve membrane and the myelination layer. Preliminary results indicate that fascicle distribution and axons' proximity to each other significantly affect the magnitude and distribution of the induced electric field as compared to traditional homogeneous tissue models for field simulation.

Multi-coil approach to reduce electromagnetic energy absorption for wirelessly powered implants.

Near-field inductive coupling is a commonly used technique for wireless power transfer (WPT) in biomedical implants. Owing to the close proximity of the implant coil(s) with the tissue ( ∼1 mm) and high current ( ∼100-300 mA) in the magnetic coil(s), a significant induced electric field can be generated for the operating frequency (1-20 MHz). In this Letter, a multi-coil-based WPT technique is proposed to selectively control the currents in the external and implant coils to reduce the specific absorption rate (SAR). A three-coil WPT system, that can achieve 26% reduction in peak 1-g SAR and 15% reduction in peak 10-g SAR, as compared to a two-coil WPT system with the same dimensions, is implemented and used to demonstrate the effectiveness of the proposed approach. To achieve the seamless design for the external and implant electronics, the multi-coil system achieves the same voltage gain and bandwidth as the two-coil design with 46% improvement in the power transfer efficiency.

Ferrite core non-linearity in coils for magnetic neurostimulation.

The need to correctly predict the voltage across terminals of mm-sized coils, with ferrite core, to be employed for magnetic stimulation of the peripheral neural system is the motivation for this work. In such applications, which rely on a capacitive discharge on the coil to realise a transient voltage curve of duration and strength suitable for neural stimulation, the correct modelling of the non-linearity of the ferrite core is critical. A demonstration of how a finite-difference model of the considered coils, which include a model of the current-controlled inductance in the coil, can be used to correctly predict the time-domain voltage waveforms across the terminals of a test coil is presented. Five coils of different dimensions, loaded with ferrite cores, have been fabricated and tested: the measured magnitude and width of the induced pulse are within 10% of simulated values.