AC impedance of the perineurium of the frog sciatic nerve

NRV: An open framework for in silico evaluation of peripheral nerve electrical stimulation strategies

Electrical stimulation of peripheral nerves has been used in various pathological contexts for rehabilitation purposes or to alleviate the symptoms of neuropathologies, thus improving the overall quality of life of patients. However, the development of novel therapeutic strategies is still a challenging issue requiring extensive in vivo experimental campaigns and technical development. To facilitate the design of new stimulation strategies, we provide a fully open source and self-contained software framework for the in silico evaluation of peripheral nerve electrical stimulation. Our modeling approach, developed in the popular and well-established Python language, uses an object-oriented paradigm to map the physiological and electrical context. The framework is designed to facilitate multi-scale analysis, from single fiber stimulation to whole multifascicular nerves. It also allows the simulation of complex strategies such as multiple electrode combinations and waveforms ranging from conventional biphasic pulses to more complex modulated kHz stimuli. In addition, we provide automated support for stimulation strategy optimization and handle the computational backend transparently to the user. Our framework has been extensively tested and validated with several existing results in the literature.

Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters

BACKGROUND

Peripheral nerve recordings can enhance the efficacy of neurostimulation therapies by providing a feedback signal to adjust stimulation settings for greater efficacy or reduced side effects. Computational models can accelerate the development of interfaces with high signal-to-noise ratio and selective recording. However, validation and tuning of model outputs against in vivo recordings remains computationally prohibitive due to the large number of fibers in a nerve.

METHODS

We designed and implemented highly efficient modeling methods for simulating electrically evoked compound nerve action potential (CNAP) signals. The method simulated a subset of fiber diameters present in the nerve using NEURON, interpolated action potential templates across fiber diameters, and filtered the templates with a weighting function derived from fiber-specific conduction velocity and electromagnetic reciprocity outputs of a volume conductor model. We applied the methods to simulate CNAPs from rat cervical vagus nerve.

RESULTS

Brute force simulation of a rat vagal CNAP with all 1,759 myelinated and 13,283 unmyelinated fibers in NEURON required 286 and 15,860 CPU hours, respectively, while filtering interpolated templates required 30 and 38 seconds on a desktop computer while maintaining accuracy. Modeled CNAP amplitude could vary by over two orders of magnitude depending on tissue conductivities and cuff opening within experimentally relevant ranges. Conduction distance and fiber diameter distribution also strongly influenced the modeled CNAP amplitude, shape, and latency. Modeled and in vivo signals had comparable shape, amplitude, and latency for myelinated fibers but not for unmyelinated fibers.

CONCLUSIONS

Highly efficient methods of modeling neural recordings quantified the large impact that tissue properties, conduction distance, and nerve fiber parameters have on CNAPs. These methods expand the computational accessibility of neural recording models, enable efficient model tuning for validation, and facilitate the design of novel recording interfaces for neurostimulation feedback and understanding physiological systems.

Validated computational models predict vagus nerve stimulation thresholds in preclinical animals and humans

Objective.We demonstrated how automated simulations to characterize electrical nerve thresholds, a recently published open-source software for modeling stimulation of peripheral nerves, can be applied to simulate accurately nerve responses to electrical stimulation.Approach.We simulated vagus nerve stimulation (VNS) for humans, pigs, and rats. We informed our models using histology from sample-specific or representative nerves, device design features (i.e. cuff, waveform), published material and tissue conductivities, and realistic fiber models.Main results.Despite large differences in nerve size, cuff geometry, and stimulation waveform, the models predicted accurate activation thresholds across species and myelinated fiber types. However, our C fiber model thresholds overestimated thresholds across pulse widths, suggesting that improved models of unmyelinated nerve fibers are needed. Our models of human VNS yielded accurate thresholds to activate laryngeal motor fibers and captured the inter-individual variability for both acute and chronic implants. For B fibers, our small-diameter fiber model underestimated threshold and saturation for pulse widths >0.25 ms. Our models of pig VNS consistently captured the range ofin vivothresholds across all measured nerve and physiological responses (i.e. heart rate, Aδ/B fibers, Aγfibers, electromyography, and Aαfibers). In rats, our smallest diameter myelinated fibers accurately predicted fast fiber thresholds across short and intermediate pulse widths; slow unmyelinated fiber thresholds overestimated thresholds across shorter pulse widths, but there was overlap for pulse widths >0.3 ms.Significance.We elevated standards for models of peripheral nerve stimulation in populations of models across species, which enabled us to model accurately nerve responses, demonstrate that individual-specific differences in nerve morphology produce variability in neural and physiological responses, and predict mechanisms of VNS therapeutic and side effects.

Fibers in smaller fascicles have lower activation thresholds with cuff electrodes due to thinner perineurium and smaller cross-sectional area

Objective. In nerve stimulation therapies, fibers in larger fascicles generally have higher activation thresholds, but the mechanisms are not well understood. We implemented and analyzed computational models to uncover the effects of morphological parameters on activation thresholds.Approach. We implemented finite element models of human vagus nerve stimulation to quantify the effects of morphological parameters on thresholds in realistic nerves. We also implemented simplified models to isolate effects of perineurium thickness, endoneurium diameter, fiber diameter, and fascicle location on current density, potential distributions (Ve), and activation thresholds across cuff geometries and stimulation waveforms. UsingVefrom each finite element model, we simulated activation thresholds in biophysical cable models of mammalian axons.Main results. Perineurium thickness increases with fascicle diameter, and both thicker perineurium and larger endoneurial diameter contributed to higher activation thresholds via lower peak and broader longitudinal potentials. Thicker perineurium caused less current to enter the fascicle transversely, decreasing peakVe. Thicker perineurium also inhibited current from leaving the fascicle, causing more constant longitudinal current density, broadeningVe. With increasing endoneurial diameter, intrafascicular volume increased faster than surface area, thereby decreasing intrafascicular current density and peakVe. Additionally, larger fascicles have greater cross-sectional area, thereby facilitating longitudinal intrafascicular current flow and broadeningVe. A large neighboring fascicle could increase activation thresholds, and for a given fascicle, fiber diameter had the greatest effect on thresholds, followed by fascicle diameter, and lastly, fascicle location within the epineurium. The circumneural cuff elicited robust activation across the nerve, whereas a bipolar transverse cuff with small contacts delivering a pseudo-monophasic waveform enabled more selective activation across fiber diameters and locations.Significance. Our computational studies provide mechanistic understanding of neural responses across relevant morphological parameters of peripheral nerves, thereby informing rational design of effective therapies.

Characterization of the electrical properties of mammalian peripheral nerve laminae

BACKGROUND AND OBJECTIVE

The intrinsic electrical material properties of the laminar components of the mammalian peripheral nerve bundle are important parameters necessary for the accurate simulation of the electrical interaction between nerve fibers and neural interfaces. Improvements in the accuracy of these parameters improve the realism of the simulation and enables realistic screening of novel devices used for extracellular recording and stimulation of mammalian peripheral nerves. This work aims to characterize these properties for mammalian peripheral nerves to build upon the resistive parameter set established by Weerasuriya et al. in 1984 for amphibian somatic peripheral nerves (frog sciatic nerve) that is currently used ubiquitously in the in-silico peripheral nerve modeling community.

METHODS

A custom designed characterization chamber was implemented and used to measure the radial and longitudinal impedance between 10 mHz and 50 kHz of freshly excised canine vagus nerves using four-point impedance spectroscopy. The impedance spectra were parametrically fitted to an equivalent circuit model to decompose and estimate the components of the various laminae. Histological sections of the electrically characterized nerves were then made to quantify the geometry and laminae thicknesses of the perineurium and epineurium. These measured values were then used to calculate the estimated intrinsic electrical properties, resistivity and permittivity, from the decomposed resistances and reactances. Finally, the estimated intrinsic electrical properties were used in a finite element method (FEM) model of the nerve characterization setup to evaluate the realism of the model.

RESULTS

The geometric measurements were as follows: nerve bundle (1.6 ± 0.6 mm), major nerve fascicle diameter (1.3 ± 0.23 mm), and perineurium thickness (13.8 ± 2.1 μm). The longitudinal resistivity of the endoneurium was estimated to be 0.97 ± 0.05 Ωm. The relative permittivity and resistivity of the perineurium were estimated to be 2018 ± 391 and 3.75 kΩm ± 981 Ωm, respectively. The relative permittivity and resistivity of the epineurium were found to be 9.4 × 106  ± 8.2 × 106 and 55.0 ± 24.4 Ωm, respectively. The root mean squared (RMS) error of the experimentally obtained values when used in the equivalent circuit model to determine goodness of fit against the measured impedance spectra was found to be 13.0 ± 10.7 Ω, 2.4° ± 1.3°. The corner frequency of the perineurium and epineurium were found to be 2.6 ± 1.0 kHz and 368.5 ± 761.9 Hz, respectively. A comparison between the FEM model in-silico impedance experiment against the ex-vivo methods had a RMS error of 159.0 ± 95.4 Ω, 20.7° ± 9.8°.

CONCLUSION

Although the resistive values measured in the mammalian nerve are similar to those of the amphibian model, the relative permittivity of the laminae bring new information about the reactance and the corner frequency (frequency at peak reactance) of the peripheral nerve. The measured and estimated corner frequency are well within the range of most bioelectric signals, and are important to take into account when modeling the nerve and neural interfaces.

Measuring and modeling the effects of vagus nerve stimulation on heart rate and laryngeal muscles

BACKGROUND

Reduced heart rate (HR) during vagus nerve stimulation (VNS) is associated with therapy for heart failure, but stimulation frequency and amplitude are limited by patient tolerance. An understanding of physiological responses to parameter adjustments would allow differential control of therapeutic and side effects. To investigate selective modulation of the physiological responses to VNS, we quantified the effects and interactions of parameter selection on two physiological outcomes: one related to therapy (reduced HR) and one related to side effects (laryngeal muscle EMG).

METHODS

We applied a broad range of stimulation parameters (mean pulse rates (MPR), intra-burst frequencies, and amplitudes) to the vagus nerve of anesthetized mice. We leveraged the in vivo recordings to parameterize and validate computational models of HR and laryngeal muscle activity across amplitudes and temporal patterns of VNS. We constructed a finite element model of excitation of fibers within the mouse cervical vagus nerve.

RESULTS

HR decreased with increased amplitude, increased MPR, and decreased intra-burst frequency. EMG increased with increased MPR. Preferential HR effects over laryngeal EMG effects required combined adjustments of amplitude and MPR. The model of HR responses highlighted contributions of ganglionic filtering to VNS-evoked changes in HR at high stimulation frequencies. Overlap in activation thresholds between small and large modeled fibers was consistent with the overlap in dynamic ranges of related physiological measures (HR and EMG).

CONCLUSION

The present study provides insights into physiological responses to VNS required for informed parameter adjustment to modulate selectively therapeutic effects and side effects.

A Highly Miniaturized, Chronically Implanted ASIC for Electrical Nerve Stimulation

We present a wireless, fully implantable device for electrical stimulation of peripheral nerves consisting of a powering coil, a tuning network, a Zener diode, selectable stimulation parameters, and a stimulator IC, all encapsulated in biocompatible silicone. A wireless RF signal at 13.56 MHz powers the implant through the on-chip rectifier. The ASIC, designed in TSMC's 180 nm MS RF G process, occupies an area of less than 1.2 mm². The IC enables externally selectable current-controlled stimulation through an on-chip read-only memory with a wide range of 32 stimulation parameters (90-750 µA amplitude, 100 µs or 1 ms pulse width, 15 or 50 Hz frequency). The IC generates the constant current waveform using an 8-bit binary weighted DAC and an H-Bridge. At the most power-hungry stimulation parameter, the average power consumption during a stimulus pulse is 2.6 mW with a power transfer efficiency of ∼5.2%. In addition to benchtop and acute testing, we chronically implanted two versions of the device (a design with leads and a leadless design) on two rats' sciatic nerves to verify the long-term efficacy of the IC and the full system. The leadless device had the following dimensions: height of 0.45 cm, major axis of 1.85 cm, and minor axis of 1.34 cm, with similar dimensions for the device with leads. Both devices were implanted and worked for experiments lasting from 21-90 days. To the best of our knowledge, the fabricated IC is the smallest constant-current stimulator that has been tested chronically.

Stretchable gold nanowire-based cuff electrodes for low-voltage peripheral nerve stimulation

Objective. Electrical stimulation of the peripheral nervous system (PNS) can treat various diseases and disorders, including the healing process after nerve injury. A major challenge when designing electrodes for PNS stimulation is the mechanical mismatch between the nerve and the device, which can lead to non-conformal contact, tissue damage and inefficient stimulation due to current leakage. Soft and stretchable cuff electrodes promise to tackle these challenges but often have limited performance and rely on unconventional materials. The aim of this study is to develop a high performance soft and stretchable cuff electrode based on inert materials for low-voltage nerve stimulation.Approach. We developed 50µm thick stretchable cuff electrodes based on silicone rubber, gold nanowire conductors and platinum coated nanowire electrodes. The electrode performance was characterized under strain cycling to assess the durability of the electrodes. The stimulation capability of the cuff electrodes was evaluated in anin vivosciatic nerve rat model by measuring the electromyography response to various stimulation pulses.Main results. The stretchable cuff electrodes showed excellent stability for 50% strain cycling and one million stimulation pulses. Saturated homogeneous stimulation of the sciatic nerve was achieved at only 200 mV due to the excellent conformability of the electrodes, the low conductor resistance (0.3 Ohm sq^-1), and the low electrode impedance.Significance. The developed stretchable cuff electrode combines favourable mechanical properties and good electrode performance with inert and stable materials, making it ideal for low power supply applications within bioelectronic medicine.

Influence of unfused cranial bones on magnetoencephalography signals in human infants

OBJECTIVE

To clarify the effects of unfused cranial bones on magnetoencephalography (MEG) signals during early development.

METHODS

In a simulation study, we compared the MEG signals over a spherical head model with a circular hole mimicking the anterior fontanel to those over the same head model without the fontanel for different head and fontanel sizes with varying skull thickness and conductivity.

RESULTS

The fontanel had small effects according to three indices. The sum of differences in signal over a sensor array due to a fontanel, for example, was < 6% of the sum without the fontanel. However, the fontanel effects were extensive for dipole sources deep in the brain or outside the fontanel for larger fontanels. The effects were comparable in magnitude for tangential and radial sources. Skull thickness significantly increased the effect, while skull conductivity had minor effects.

CONCLUSION

MEG signal is weakly affected by a fontanel. However, the effects can be extensive and significant for radial sources, thicker skull and large fontanels. The fontanel effects can be intuitively explained by the concept of secondary sources at the fontanel wall.

SIGNIFICANCE

The minor influence of unfused cranial bones simplifies MEG analysis, but it should be considered for quantitative analysis.

Quantified Morphology of the Cervical and Subdiaphragmatic Vagus Nerves of Human, Pig, and Rat

It is necessary to understand the morphology of the vagus nerve (VN) to design and deliver effective and selective vagus nerve stimulation (VNS) because nerve morphology influences fiber responses to electrical stimulation. Specifically, nerve diameter (and thus, electrode-fiber distance), fascicle diameter, fascicular organization, and perineurium thickness all significantly affect the responses of nerve fibers to electrical signals delivered through a cuff electrode. We quantified the morphology of cervical and subdiaphragmatic VNs in humans, pigs, and rats: effective nerve diameter, number of fascicles, effective fascicle diameters, proportions of endoneurial, perineurial, and epineurial tissues, and perineurium thickness. The human and pig VNs were comparable sizes (∼2 mm cervically; ∼1.6 mm subdiaphragmatically), while the rat nerves were ten times smaller. The pig nerves had ten times more fascicles-and the fascicles were smaller-than in human nerves (47 vs. 7 fascicles cervically; 38 vs. 5 fascicles subdiaphragmatically). Comparing the cervical to the subdiaphragmatic VNs, the nerves and fascicles were larger at the cervical level for all species and there were more fascicles for pigs. Human morphology generally exhibited greater variability across samples than pigs and rats. A prior study of human somatic nerves indicated that the ratio of perineurium thickness to fascicle diameter was approximately constant across fascicle diameters. However, our data found thicker human and pig VN perineurium than those prior data: the VNs had thicker perineurium for larger fascicles and thicker perineurium normalized by fascicle diameter for smaller fascicles. Understanding these differences in VN morphology between preclinical models and the clinical target, as well as the variability across individuals of a species, is essential for designing suitable cuff electrodes and stimulation parameters and for informing translation of preclinical results to clinical application to advance the therapeutic efficacy of VNS.

Quantitative comparisons of block thresholds and onset responses for charge-balanced kilohertz frequency waveforms

OBJECTIVE

There is growing interest in delivering kilohertz frequency (KHF) electrical signals to block conduction in peripheral nerves for treatment of various diseases. Previous studies used different KHF waveforms to achieve block, and it remains unclear how waveform affects nerve block parameters.

APPROACH

We quantified the effects of waveform on KHF block of the rat tibial nerve in vivo and in computational models. We compared block thresholds and onset responses across current-controlled sinusoids and charge-balanced rectangular waveforms with different asymmetries and duty cycles.

MAIN RESULTS

Sine waves had higher block thresholds than square waves, but used less power at block threshold. Block threshold had an inverse relationship with duty cycle of rectangular waveforms irrespective of waveform asymmetry. Computational model results were consistent with relationships measured in vivo, although the models underestimated the effect of duty cycle on increasing thresholds. The axonal membrane substantially filtered waveforms, the filter transfer function was strikingly similar across waveforms, and filtering resulted in post-filtered rms block thresholds that were approximately constant across waveforms in silico and in vivo. Onset response was not consistently affected by waveform shape, but onset response was smaller at amplitudes well above block threshold. Therefore, waveforms with lower block thresholds (e.g. sine waves or square waves) could be more readily increased to higher amplitudes relative to block threshold to reduce onset response. We also observed a reduction in onset responses across consecutive trials after initial application of supra-block threshold amplitudes.

SIGNIFICANCE

Waveform had substantial effects on block thresholds, and the amplitude relative to block threshold had substantial effects on onset response. These data inform choice of waveform in subsequent studies and clinical applications, enhance effective use of block in therapeutic applications, and facilitate the design of parameters that achieve block with minimal onset responses.

Implantable Neural Interfaces and Wearable Tactile Systems for Bidirectional Neuroprosthetics Systems

Neuroprosthetics and neuromodulation represent a promising field for several related applications in the central and peripheral nervous system, such as the treatment of neurological disorders, the control of external robotic devices, and the restoration of lost tactile functions. These actions are allowed by the neural interface, a miniaturized implantable device that most commonly exploits electrical energy to fulfill these operations. A neural interface must be biocompatible, stable over time, low invasive, and highly selective; the challenge is to develop a safe, compact, and reliable tool for clinical applications. In case of anatomical impairments, neuroprosthetics is bound to the need of exploring the surrounding environment by fast-responsive and highly sensitive artificial tactile sensors that mimic the natural sense of touch. Tactile sensors and neural interfaces are closely interconnected since the readouts from the first are required to convey information to the neural implantable apparatus. The role of these devices is pivotal hence technical improvements are essential to ensure a secure system to be eventually adopted in daily life. This review highlights the fundamental criteria for the design and microfabrication of neural interfaces and artificial tactile sensors, their use in clinical applications, and future enhancements for the release of a second generation of devices.

Long-Term Functionality of Transversal Intraneural Electrodes Is Improved By Dexamethasone Treatment

Neuroprostheses aimed to restore lost functions after a limb amputation are based on the interaction with the nervous system by means of neural interfaces. Among the different designs, intraneural electrodes implanted in peripheral nerves represent a good strategy to stimulate nerve fibers to send sensory feedback and to record nerve signals to control the prosthetic limb. However, intraneural electrodes, as any device implanted in the body, induce a foreign body reaction (FBR) that results in the tissue encapsulation of the device. The FBR causes a progressive decline of the electrode functionality over time due to the physical separation between the electrode active sites and the axons to interface. Modulation of the inflammatory response has arisen as a good strategy to reduce the FBR and maintain electrode functionality. In this study transversal intraneural multi-channel electrodes (TIMEs) were implanted in the rat sciatic nerve and tested for 3 months to evaluate stimulation and recording capabilities under chronic administration of dexamethasone. Dexamethasone treatment significantly reduced the threshold for evoking muscle responses during the follow-up compared to saline-treated animals, without affecting the selectivity of stimulation. However, dexamethasone treatment did not improve the signal-to-noise ratio of the recorded neural signals. Dexamethasone treatment allowed to maintain more working active sites along time than saline treatment. Thus, systemic administration of dexamethasone appears as a useful treatment in chronically implanted animals with neural electrodes as it increases the number of functioning contacts of the implanted TIME and reduces the intensity needed to stimulate the nerve.

On the parameters used in finite element modeling of compound peripheral nerves

OBJECTIVE

Computational modeling is an important tool for developing and optimizing implantable neural stimulation devices, but requires accurate electrical and geometrical parameter values to improve predictive value. We quantified the effects of perineurial (resistive sheath around each fascicle) and endoneurial (within each fascicle) parameter values for modeling peripheral nerve stimulation.

APPROACH

We implemented 3D finite element models of compound peripheral nerves and cuff electrodes to quantify activation and block thresholds of model axons. We also implemented a 2D finite element model of a bundle of axons to estimate the bulk transverse endoneurial resistivity; we compared numerical estimates to an analytical solution.

MAIN RESULTS

Since the perineurium is highly resistive, potentials were approximately constant over the cross section of a fascicle, and the perineurium resistivity, longitudinal endoneurial resistivity, and fascicle diameter had important effects on thresholds. Activation thresholds increased up to ~130% for higher perineurium resistivity (~400 versus 2200 Ω m) and by ~35%-250% for lower longitudinal endoneurial resistivity (3.5 versus 0.75 Ω m), with larger increases for smaller diameter axons and for axons in larger fascicles. Further, thresholds increased by ~30%-180% for larger fascicle radii, yielding a larger increase with higher perineurium resistivity. Thresholds were largely insensitive to the transverse endoneurial resistivity, but estimates of the bulk resistivity increased with extracellular resistivity and axonal area fraction; the numerical and analytical estimates were in strong agreement except at high axonal area fractions, where structured axon placements that achieved tighter packing produced electric field inhomogeneities.

SIGNIFICANCE

We performed a systematic investigation of the effects of values and methods for modeling the perineurium and endoneurium on thresholds for neural stimulation and block. These results provide guidance for future modeling studies, including parameter selection, data interpretation, and comparison to experimental results.

A model of motor and sensory axon activation in the median nerve using surface electrical stimulation

Surface electrical stimulation has the potential to be a powerful and non-invasive treatment for a variety of medical conditions but currently it is difficult to obtain consistent evoked responses. A viable clinical system must be able to adapt to variations in individuals to produce repeatable results. To more fully study the effect of these variations without performing exhaustive testing on human subjects, a system of computer models was created to predict motor and sensory axon activation in the median nerve due to surface electrical stimulation at the elbow. An anatomically-based finite element model of the arm was built to accurately predict voltages resulting from surface electrical stimulation. In addition, two axon models were developed based on previously published models to incorporate physiological differences between sensory and motor axons. This resulted in axon models that could reproduce experimental results for conduction velocity, strength-duration curves and activation threshold. Differences in experimentally obtained action potential shape between the motor and sensory axons were reflected in the models. The models predicted a lower threshold for sensory axons than motor axons of the same diameter, allowing a range of sensory axons to be activated before any motor axons. This system of models will be a useful tool for development of surface electrical stimulation as a method to target specific neural functions.

Simulation of effects of the electrode structure and material in the density measuring system of the peripheral nerve based on micro-electrical impedance tomography

The electrode structure in micro-electrical impedance tomography (MEIT) highly influences the measurement sensitivity and therefore the reconstructed image quality. Hence, optimizing the electrode structure leads to the improvement of image quality in the reconstruction procedure. Although there have been many investigations on electrical impedance tomography (EIT) electrodes, there is no comprehensive study on their influence on images of the peripheral nerve. In this paper, we present a simulation method to study the effects of the electrode structure in the density measurement system of the peripheral nerve based on MEIT. The influence of the electrode structure such as dimensions, material and the number of electrodes and also the recognition feature of different radii of fascicle and different locations of fascicles has been studied. Data were reconstructed from the real and imaginary parts of complex conductivity data, respectively. It has been shown that the material of the electrodes had no effect on the reconstructed images, while the dimensions of the electrodes significantly affected the image sensitivity and thus the image quality. An increase in the number of electrodes increased the amount of data and information content. However, as the number of electrodes increased due to the given perimeter of the peripheral nerve, the area of the electrodes was reduced. This reduction affects the reconstructed image quality. The real and imaginary parts of the data were separately reconstructed for each case. Although, in real EIT systems, the reconstructed images using the real part of the signal have a better signal-to-noise ratio (SNR), this study proved that for a density measuring system of the peripheral nerve, the reconstructed images using the imaginary part of the signal had better quality. This simulation study proposes the effects of the electrode size and material and obtained spatial resolution that was high enough to reconstruct fascicles in a peripheral nerve.

Chronic interfacing with the autonomic nervous system using carbon nanotube (CNT) yarn electrodes

The ability to reliably and safely communicate chronically with small diameter (100–300 µm) autonomic nerves could have a significant impact in fundamental biomedical research and clinical applications. However, this ability has remained elusive with existing neural interface technologies. Here we show a new chronic nerve interface using highly flexible materials with axon-like dimensions. The interface was implemented with carbon nanotube (CNT) yarn electrodes to chronically record neural activity from two separate autonomic nerves: the glossopharyngeal and vagus nerves. The recorded neural signals maintain a high signal-to-noise ratio (>10 dB) in chronic implant models. We further demonstrate the ability to process the neural activity to detect hypoxic and gastric extension events from the glossopharyngeal and vagus nerves, respectively. These results establish a novel, chronic platform neural interfacing technique with the autonomic nervous system and demonstrate the possibility of regulating internal organ function, leading to new bioelectronic therapies and patient health monitoring.

Modeling the response of small myelinated axons in a compound nerve to kilohertz frequency signals

OBJECTIVE

There is growing interest in electrical neuromodulation of peripheral nerves, particularly autonomic nerves, to treat various diseases. Electrical signals in the kilohertz frequency (KHF) range can produce different responses, including conduction block. For example, EnteroMedics' vBloc® therapy for obesity delivers 5 kHz stimulation to block the abdominal vagus nerves, but the mechanisms of action are unclear.

APPROACH

We developed a two-part computational model, coupling a 3D finite element model of a cuff electrode around the human abdominal vagus nerve with biophysically-realistic electrical circuit equivalent (cable) model axons (1, 2, and 5.7 µm in diameter). We developed an automated algorithm to classify conduction responses as subthreshold (transmission), KHF-evoked activity (excitation), or block. We quantified neural responses across kilohertz frequencies (5-20 kHz), amplitudes (1-8 mA), and electrode designs.

MAIN RESULTS

We found heterogeneous conduction responses across the modeled nerve trunk, both for a given parameter set and across parameter sets, although most suprathreshold responses were excitation, rather than block. The firing patterns were irregular near transmission and block boundaries, but otherwise regular, and mean firing rates varied with electrode-fibre distance. Further, we identified excitation responses at amplitudes above block threshold, termed 're-excitation', arising from action potentials initiated at virtual cathodes. Excitation and block thresholds decreased with smaller electrode-fibre distances, larger fibre diameters, and lower kilohertz frequencies. A point source model predicted a larger fraction of blocked fibres and greater change of threshold with distance as compared to the realistic cuff and nerve model.

SIGNIFICANCE

Our findings of widespread asynchronous KHF-evoked activity suggest that conduction block in the abdominal vagus nerves is unlikely with current clinical parameters. Our results indicate that compound neural or downstream muscle force recordings may be unreliable as quantitative measures of neural activity for in vivo studies or as biomarkers in closed-loop clinical devices.

Influence of Anatomical Detail and Tissue Conductivity Variations in Simulations of Multi-Contact Nerve Cuff Recordings

Accurate simulations of peripheral nerve recordings are needed to develop improved neuroprostheses. Previous models of peripheral nerves contained simplifications whose effects have not been investigated. We created a novel detailed finite element (FE) model of a peripheral nerve, and used it to carry out a sensitivity analysis of several model parameters. To construct the model, in vivo recordings were obtained in a rat sciatic nerve using an 8-channel nerve cuff electrode, after which the nerve was imaged using magnetic resonance imaging (MRI). The FE model was constructed based on the MRI data, and included progressive branching of the fascicles. Neural pathways were defined in the model for the tibial, peroneal and sural fascicles. The locations of these pathways were selected so as to maximize the correlations between the simulated and in vivo recordings. The sensitivity analysis showed that varying the conductivities of neural tissues had little influence on the ability of the model to reproduce the recording patterns obtained experimentally. On the other hand, the increased anatomical detail did substantially alter the recording patterns observed, demonstrating that incorporating fascicular branching is an important consideration in models of nerve cuff recordings. The model used in this study constitutes an improved simulation tool and can be used in the design of neural interfaces.

Intraneural stimulation elicits discrimination of textural features by artificial fingertip in intact and amputee humans

Restoration of touch after hand amputation is a desirable feature of ideal prostheses. Here, we show that texture discrimination can be artificially provided in human subjects by implementing a neuromorphic real-time mechano-neuro-transduction (MNT), which emulates to some extent the firing dynamics of SA1 cutaneous afferents. The MNT process was used to modulate the temporal pattern of electrical spikes delivered to the human median nerve via percutaneous microstimulation in four intact subjects and via implanted intrafascicular stimulation in one transradial amputee. Both approaches allowed the subjects to reliably discriminate spatial coarseness of surfaces as confirmed also by a hybrid neural model of the median nerve. Moreover, MNT-evoked EEG activity showed physiologically plausible responses that were superimposable in time and topography to the ones elicited by a natural mechanical tactile stimulation. These findings can open up novel opportunities for sensory restoration in the next generation of neuro-prosthetic hands.

DOI:http://dx.doi.org/10.7554/eLife.09148.001

Our hands provide us with a wide variety of information about our surroundings, enabling us to detect pain, temperature and pressure. Our sense of touch also allows us to interact with objects by feeling their texture and solidity. However, completely reproducing a sense of touch in artificial or prosthetic hands has proven challenging. While commercial prostheses can mimic the range of movements of natural limbs, even the latest experimental prostheses have only a limited ability to ‘feel’ the objects being manipulated. Oddo, Raspopovic et al. have now brought this ability a step closer by exploiting an artificial fingertip and appropriate neural interfaces through which different textures can be identified.

The initial experiments were performed in four healthy volunteers with intact limbs. Oddo, Raspopovic et al. connected the artificial fingertip to the volunteers via an electrode inserted into a nerve in the arm. When moved over a rough surface, sensors in the fingertip produced patterns of electrical pulses that stimulated the nerve, causing the volunteers to feel like they were touching the surface. The volunteers were even able to tell the difference between the different surface textures the artificial fingertip moved across.

The temporary electrodes used in this group of volunteers are unsuitable for use with prosthetic limbs because they can easily be knocked out of position. Therefore, in a further experiment involving a volunteer who had undergone an arm amputation a number of years previously, Oddo, Raspopovic et al. tested an implanted electrode array that could, in principle, remain in place long-term. This volunteer could also identify the different textures the artificial fingertip touched, with a slightly higher degree of accuracy than the previous group of intact volunteers. Further studies are now required to explore the potential of this approach in larger groups of volunteers.

DOI:http://dx.doi.org/10.7554/eLife.09148.002

In situ measurement of tissue impedance using an inductive coupling interface circuit

In this work, a method of an inductive coupling impedance measurement (ICIM) is proposed for measuring the nerve impedance of a dorsal root ganglion (DRG) under PRF stimulation. ICIM provides a contactless interface for measuring the reflected impedance by an impedance analyzer with a low excitation voltage of 7 mV. The paper develops a calibration procedure involving a 50-Ω reference resistor to calibrate the reflected resistance for measuring resistance of the nerve in the test. A de-embedding technique to build the equivalent transformer circuit model for the ICIM circuit is also presented. A batteryless PRF stimulator with ICIM circuit demonstrated good accuracy for the acute measurement of DRG impedance both in situ and in vivo. Besides, an in vivo animal experiment was conducted to show that the effectiveness of pulsed radiofrequency (PRF) stimulation in relieving pain gradually declined as the impedance of the stimulated nerve increased. The experiment also revealed that the excitation voltage for measuring impedance below 25 mV can prevent the excitation of a nonlinear response of DRG.

Model-based analysis and design of nerve cuff electrodes for restoring bladder function by selective stimulation of the pudendal nerve

OBJECTIVE

Electrical stimulation of the pudendal nerve (PN) is being developed as a means to restore bladder function in persons with spinal cord injury. A single nerve cuff electrode placed on the proximal PN trunk may enable selective stimulation of distinct fascicles to maintain continence or evoke micturition. The objective of this study was to design a nerve cuff that enabled selective stimulation of the PN.

APPROACH

We evaluated the performance of both flat interface nerve electrode (FINE) cuff and round cuff designs, with a range of FINE cuff heights and number of contacts, as well as multiple contact orientations. This analysis was performed using a computational model, in which the nerve and fascicle cross-sectional positions from five human PN trunks were systematically reshaped within the nerve cuff. These cross-sections were used to create finite element models, with electric potentials calculated and applied to a cable model of a myelinated axon to evaluate stimulation selectivity for different PN targets. Subsequently, the model was coupled to a genetic algorithm (GA) to identify solutions that used multiple contact activation to maximize selectivity and minimize total stimulation voltage.

MAIN RESULTS

Simulations did not identify any significant differences in selectivity between FINE and round cuffs, although the latter required smaller stimulation voltages for target activation due to preserved localization of targeted fascicle groups. Further, it was found that a ten contact nerve cuff generated sufficient selectivity for all PN targets, with the degree of selectivity dependent on the relative position of the target within the nerve. The GA identified solutions that increased fitness by 0.7-45.5% over single contact activation by decreasing stimulation of non-targeted fascicles.

SIGNIFICANCE

This study suggests that using an optimal nerve cuff design and multiple contact activation could enable selective stimulation of the human PN trunk for restoration of bladder function.

Probabilistic modeling of selective stimulation of the human sciatic nerve with a flat interface nerve electrode

Ankle control is critical to both standing balance and efficient walking. The hypothesis presented in this paper is that a Flat Interface Nerve Electrode (FINE) placed around the sciatic nerve with a fixed number of contacts at predetermined locations and without a priori knowledge of the nerve's underlying neuroanatomy can selectively control each ankle motion. Models of the human sciatic nerve surrounded by a FINE of varying size were created and used to calculate the probability of selective activation of axons within any arbitrarily designated, contiguous group of fascicles. Simulations support the hypothesis and suggest that currently available implantable technology cannot selectively recruit each target plantar flexor individually but can restore plantar flexion or dorsiflexion from a site on the sciatic nerve without spillover to antagonists. Successful activation of individual ankle muscles in 90% of the population can be achieved by utilizing bipolar stimulation and/or by using a cuff with at least 20 contacts.

Electrochemical activation and inhibition of neuromuscular systems through modulation of ion concentrations with ion-selective membranes

Conventional functional electrical stimulation aims to restore functional motor activity of patients with disabilities resulting from spinal cord injury or neurological disorders. However, intervention with functional electrical stimulation in neurological diseases lacks an effective implantable method that suppresses unwanted nerve signals. We have developed an electrochemical method to activate and inhibit a nerve by electrically modulating ion concentrations in situ along the nerve. Using ion-selective membranes to achieve different excitability states of the nerve, we observe either a reduction of the electrical threshold for stimulation by up to approximately 40%, or voluntary, reversible inhibition of nerve signal propagation. This low-threshold electrochemical stimulation method is applicable in current implantable neuroprosthetic devices, whereas the on-demand nerve-blocking mechanism could offer effective clinical intervention in disease states caused by uncontrolled nerve activation, such as epilepsy and chronic pain syndromes.

In vivo impedance evaluation of Au/PI microelectrode with surface modulated by alkanethiolate self-assembled monolayers

The goal of this study was to verify that a fully implanted microelectrode with modulated surface may have a reduced rising rate of total impedance and a longer life time. In the previous work, alkanethiolate self-assembled monolayers (SAMs) surface as protein-resistant spacer or cell-repulsive dense-packed spacer has been verified from in vitro experiments. In this study, microelectrodes with the same surface modulation were implanted into the subcutaneous layers of Wistar rats. Nine rats were implanted with the microelectrodes and the total impedance data were measured every 24 h for 2 weeks after implantation. An equivalent electrical circuit model of the electrode-tissue interface was established and parameters were estimated by using an optimization algorithm. Four out of nine rats had manifested acute inflammation reaction and the rests revealed only slight tissue response. Histological examination for the inflammatory group showed fibroblasts, macrophages, and polymorphonuclear leukocytes in adjacent to the electrode contact surface. In the inflammatory group, no significantly difference in total impedance was found in both types of electrodes. However, the trend of total impedance of SAMs-treated electrodes could maintain a steady state value after 1 week. For the non-inflammatory group, both types of electrodes could reduce the impedance value within implanted days. The tissue resistance might be related to the thickness of cells adhered upon the electrode contacts.

Simulation of intra-orbital optic nerve electrical stimulation

In blind subjects who still have functional retinal ganglion cells, electrical stimuli applied to the optic nerve can produce localised visual sensations. This has been demonstrated with an intracranially implanted self-sizing spiral cuff electrode, but, to avoid skull opening, intra-orbital cuff implantation is now considered. In its orbital segment, the optic nerve is surrounded by subarachnoidal cerebrospinal fluid (CSF) and dura mater. Dura mater is a tough fibrous tissue that can impede electrical stimulation. In the study, the issue of whether or not to remove the dura mater at the implantation site was addressed using simulation on numerical models. Several volume conductor models were built representing, respectively: the cuff implanted directly around the nerve; the cuff over the nerve after connective tissue encapsulated the implant; and the cuff electrode placed around the dura mater. Stimulation-induced electric potential fields were computed for these configurations using a full 3D finite elements software. Responses of fibres within the nerve were computed. A large range of dural conductivities and several CSF thicknesses were considered. In all simulated conditions, the presence of dura mater around a layer of CSF increased excitation thresholds. Selectivity performance also decreased, but was found to be independent of the CSF thickness. However, simulations showed that, if the diameter of the cuff electrode is adapted to the target nerve, the injected charge associated with activation is limited within a reasonable range. Electrical stimulation of the optic nerve with a cuff electrode implanted around the dura mater should therefore be feasible.

Electrode Array for Reversing the Recruitment Order of Peripheral Nerve Stimulation: Experimental Studies

One of the most challenging problems in peripheral nerve stimulation is the ability to activate selectively small axons without large ones. Electrical stimulation of peripheral nerve activates large diameter fibers before small ones. Currently available techniques for selective activation of small axons without large ones require long-duration stimulation pulses (>500 micros) and large stimulation amplitude, which shorten battery life of the implanted stimulator and could lead to electrode corrosion. In the current study, the hypothesis that small axons can be recruited before large ones with narrow pulse width (50 micros) using an electrode array was tested in both simulations simulation and experiments in the cat lateral gastrocnemius (LG) model. The LG nerve innervates both LG and soleus muscle groups with axons within 10-13 and 8-12 microm diameter ranges, respectively. A finite element model of LG nerve was constructed and simulations showed that, when activating 40% of LG, a conventional tripolar electrode activated only 9% of soleus whereas the electrode arrays of 5, 7, and 11 contacts activated 39, 46, and 60% of soleus respectively, suggesting that the arrays could activate small axons before fully recruiting large axons. In animal experiments, peak twitch force of LG and soleus were plotted as a function of stimulation amplitude to indicate the recruitment curve. At 40% activation of LG, a conventional tripolar electrode activated only 7% of soleus whereas the electrode arrays of 5, 7, and 11 contacts activated 43, 48, and 72% of soleus respectively. The electrode arrays also decreased significantly the recruitment curve slopes to only 10-20% of the value obtained for the tripolar electrode in both computer simulations and experiments. In conclusion, the 5-, 7-, and 11-contact arrays can be used to reverse the recruitment order of peripheral nerve stimulation with a narrow pulse.

Extracellular voltage profile for reversing the recruitment order of peripheral nerve stimulation: a simulation study

Electrical stimulation of peripheral nerve activates large-diameter fibers before small ones. A physiological recruitment order, from small to large-diameter axons, is desirable in many applications. Previous studies using computer simulations showed that selective activation of small fibers could be achieved by reshaping the extracellular voltage profile along the nerve using an array of nine electrodes. In this study, several electrode-array configurations were tested in order to minimize the number of contacts. Electrode arrays of 5, 7, 9, and 11 contacts with 0.75 mm contact separation were performed in computer simulations of dog sacral root (S2). Electrode arrays of 5 and 7 contacts recruited 40% of small axons (<10 microm) when recruiting only 10% of larger axons. Effectiveness of 9- and 11-contact arrays decreased with the presence of epineurium and perineurium. The effectiveness of electrode arrays was independent of stimulation pulsewidth. The biphasic-pulse stimulation with the amplitude of the second phase set as low as possible should be used to prevent the excitation of large axons during the second phase and to minimize the electrode corrosion. Arrays of 5 and 7 contacts also decreased the recruitment curve slope to 26% and 51% of the tripolar electrode, respectively. This modeling study predicts that reversing the recruitment order of peripheral nerve stimulation could be achieved by reshaping the extracellular voltage using electrode arrays of 5 or 7 contacts.

Selectivity of multiple-contact nerve cuff electrodes: a simulation analysis

Advances in functional neuromuscular stimulation (FNS) have increased the need for nerve cuff designs that can control multiple motor functions through selective stimulation of selected populations of axons. This selectivity has proved to be difficult to achieve. Recent experiments suggest that it is possible to slowly reshape peripheral nerve without affecting its physiological function. Using computer simulations we have tested the hypothesis that changing the cross section of a nerve from a round to a flat configuration can significantly improve the selectivity of a nerve cuff. We introduce a new index to estimate selectivity to evaluate the various designs. This index is based on the ability of a nerve electrode to stimulate a target axon without stimulating any other axons. The calculations involve a three-dimensional finite element model to represent the electrical properties of the nerve and cuff and the determination of the firing properties of individual axons. The selectivity rating was found to be significantly higher for the Flat Cuff than the Round Cuff. The result was valid with uniform or random distribution of axons and with a random distribution of fascicles diameters. Flattening of individual fascicles also improved the selectivity of the Flat Cuff but only when the number of contacts used was increased to maintain uniform contact density. Therefore, cuff designs that can reshape the nerve into flatter configurations should yield better cuff performance than the cylindrical cuffs but will require higher contact density.

Ionic permeability of the opossum sciatic nerve perineurium, examined using electrophysiological and electron microscopic techniques

A parallel electrophysiological and electron microscopic study was used to assess the ionic permeability of the sciatic nerve perineurium of the opossum Monodelphis domestica. The electrophysiological method was used to monitor permeability to K(+), followed by combined electron microscopy and X-ray probe analysis to monitor permeability to the electron-dense tracer lanthanum. Isolated but intact nerves were mounted in a 'grease gap' chamber for extracellular measurement of DC potential and compound action potential (CAP). Challenge with 100 mM [K(+)] Ringer was used to assess the K(+) permeability of the perineurium, since a change in DC potential (DeltaDC) under these conditions reflected changes in the axonal resting membrane potential. There was no detectable change in DC potential or CAP to the first K(+) challenge (n=71 nerves) indicating negligible K(+) permeability under control conditions. The inflammatory mediators histamine 0.1-40 mg/ml (1. 3-130 mM), bradykinin (0.1-4.7 mM) and 5HT (serotonin) 0.1-5.0 mg/ml (0.5-23.5 mM) caused no measurable DeltaDC on subsequent challenge with 100 mM [K(+)] Ringer, indicating no effect on perineurial K(+) permeability. In nerves exposed to the bile salt sodium deoxycholate (DOC, 6 min, 4 mM), challenge with elevated K(+) Ringer caused a dose-dependent DeltaDC in the range 10-100 mM [K(+)] (1.67+/-0.17 mV in 100 mM [K(+)], n=20), indicating increased perineurial permeability caused by DOC, but the response was smaller than that previously reported for the frog perineurium. Lanthanum was observed in the outer layers of the perineurium, but was not seen to penetrate the endoneurium in any of the nerves examined (n=51), even after DOC application. This study shows that the combined electrophysiological and electron microscopic technique for monitoring ionic permeability can be applied to mammalian nerve, and suggests that the opossum perineurium is more resistant to tight junction opening by chemical modulators than is the frog perineurium.

Force-current relationships in intraneural stimulation: role of extraneural medium and motor fibre clustering

Animal experiments and model simulations of monopolar, intrafascicular nerve stimulation are presented to study force-current relationships (recruitment curves). The conductivity of the extraneural medium is of prime importance to the resulting recruitment cures: an insulating extraneural medium generally leads to steeper curves with lower threshold currents than a well-conducting extraneural medium. Extensive statistical comparison of experimental and model results suggests the occurrence of clustering of alpha-motoneurons within the fascicle, manifesting itself mainly by an increased spread in threshold currents, as opposed to the situation where the fibres are distributed uniformly throughout the entire fascicle.

Transverse tripolar stimulation of peripheral nerve: a modelling study of spatial selectivity

Various anode-cathode configurations in a nerve cuff are modelled to predict their spatial selectivity characteristics for functional nerve stimulation. A 3D volume conductor model of a monofascicular nerve is used for the computation of stimulation-induced field potentials, whereas a cable model of myelinated nerve fibre is used for the calculation of the excitation thresholds of fibres. As well as the usual configurations (monopole, bipole, longitudinal tripole, 'steering' anode), a transverse tripolar configuration (central cathode) is examined. It is found that the transverse tripole is the only configuration giving convex recruitment contours and therefore maximises activation selectivity for a small (cylindrical) bundle of fibres in the periphery of a monofascicular nerve trunk. As the electrode configuration is changed to achieve greater selectivity, the threshold current increases. Therefore threshold currents for fibre excitation with a transverse tripole are relatively high. Inverse recruitment is less extreme than for the other configurations. The influences of several geometrical parameters and model conductivities of the transverse tripole on selectivity and threshold current are analysed. In chronic implantation, when electrodes are encapsulated by a layer of fibrous tissue, threshold currents are low, whereas the shape of the recruitment contours in transverse tripolar stimulation does not change.

An electrophysiological method for measuring the potassium permeability of the nerve perineurium

An electrophysiological method is described for measuring the potassium permeability (PK) of the perineurium of the sciatic nerve of the frog. The method is based on the principle of grease-gap recording, in which an insulating compartment separates two surface recording electrodes. The sciatic nerves of frogs Rana temporaria and R. pipiens were isolated and mounted across a five compartment chamber, with Vaseline grease seals on the partitions between compartments. Compartments #1, #2 and #5 contained frog Ringer solution, #4 was filled with Vaseline and formed the grease gap, and #3 was the test compartment in which solutions could be changed. The nerve was stimulated via platinum electrodes in compartments #1 and #2, and DC potentials and compound action potentials (CAP) were recorded between Ag/AgCl electrodes connected through Ringer-agar bridges to compartments #3 and #5. In nerves with undamaged perineurium, changing from normal Ringer to high [K+] Ringer (100 mM, KCl replacing NaCl) for 2 min caused negligible change in DC potential or CAP, indicating that raised [K+] was not reaching the axon surface, and hence that the perineurium was exerting a diffusional restriction on K+ entry. In nerves damaged by stretching or drying, K+ pulses caused a depolarising change in DC potential (delta DC), and corresponding decline in CAP amplitude, consistent with a leaky perineurium allowing K+ entry and axonal depolarisation. Ringer made hypertonic by the addition of 2.5 M sucrose or 5 M NaCl caused increased perineurial permeability to K+. The method was calibrated by measuring the delta DC in response to raised [K+] in the range 5-100 mM [K+] in desheathed nerves; from this calibration curve relating delta DC to endoneurial [K+] it was possible to calculate the change in endoneurial [K+] occurring in intact preparations. The calculations showed that the undamaged perineurium had a PK of < 6.3 x 10(-7) cm.s-1, similar to the value calculated for in situ nerves using radioisotopic techniques, but less than the value reported for isolated perineurial cylinders. The method gives real-time information on the K+ permeability of the nerve perineurium and its modulation by experimental treatments.

Selective control of muscle activation with a multipolar nerve cuff electrode

Acute experiments were performed on adult cats to study selective activation of medial gastrocnemius, soleus, tibialis anterior, and extensor digitorum longus with a cuff electrode. A spiral nerve cuff containing twelve "dot" electrodes was implanted around the sciatic nerve and evoked muscle twitch forces were recorded in six experiments. Spatially isolated "dot" electrodes in four geometries: monopolar, longitudinal tripolar, tripolar with four common anodes, and two parallel tripoles, were combined with transverse field steering current(s) from an anode(s) located 180 degrees around from the cathode(s) to activate different regions of the nerve trunk. To quantify the degree of selectivity, a selectivity index was defined as the ratio of the force in one muscle to the force in all four muscles in response to a particular stimulus. The selectivity index was used to construct recruitment curves for a muscle with the optimal degree of selectivity. Physiological responses were correlated with the anatomical structure of the sciatic nerve by identifying the nerve fascicles innervating the four muscles, and by determining the relative positions of the electrodes and the nerve fascicles. The results indicated that the use of transverse field steering current improved selectivity. We also found that tripoles with individual dot anodes were more selective than tripoles with four common dot anodes. Stimulation with two parallel tripoles was effective in activating selectively fascicles that could not be activated selectively with only a single tripole. The multipolar cuff proved an effective method to control selectively and progressively the force in muscles innervated by fascicles that were well defined at the level of the cuff.

Simulation of multipolar fiber selective neural stimulation using intrafascicular electrodes

A realistic, quantitative model is presented for the excitation of myelinated nerve fibers by intrafascicular electrodes. It predicts the stimulatory regions of any configuration of any number of electrodes, positioned anywhere inside the fascicle. The model has two parts. First, the nerve fiber is represented by a lumped electrical network and its response to an arbitrary extracellular potential field is calculated. Second, assuming a cylindrical geometry of the nerve bundle and its surroundings, an analytical expression for this field is derived. With realistic parameters, the model is applied to two cases: monopolar stimulation by a single cathode and stimulation by a specific tripolar configuration. It is shown that tripolar stimulation has the better spatial selectivity. Also tripolar stimulation is less sensitive to the conductivity of the medium surrounding the nerve and yields a more natural recruitment order.

A model for compound action potentials and currents in a nerve bundle. I: The forward calculation

We describe a model for the Compound Action Currents (CACs) and Compound Action Potentials (CAPs) produced by a peripheral nerve bundle in vitro. The Single Fiber Action Currents (SFACs) and the extracellular Single Fiber Action Potentials (SFAPs) are calculated using a generalized volume conduction model. Frequency-dependent conductivities, variations in the intracellular action potentials with recording temperature and axon conduction velocity, and the effects of axonal myelination are incorporated into the volume conduction calculation. We demonstrate how the propagation distance and the recording radius affect the simulated Compound Action Signals (CASs) of various nerve bundles. We also demonstrate how the frequency-dependent and -independent conductivities affect the CASs simulated by our model. For this simulation, some of the parameters for the nerve bundles and Conduction Velocity Distributions (CVDs) were obtained from the literature. In accompanying papers, we use the simulated CASs to investigate the effects of variations in the model parameters on the CVDs predicted by our inverse model.

Diffusion barrier properties of the perineurium: an in vivo ionic lanthanum tracer study

While the perineurium as a diffusion barrier has been extensively investigated by light and electron microscopy, such studies have been largely restricted to the use of protein tracers. In the present study the permeability of the perineurium to a physiologically more relevant ionic tracer has been assessed. In vivo the rat sural or tibial nerve was either microinjected with lanthanum nitrate solution for endoneurial application or bathed in the lanthanum solution for epineurial application. The findings generally demonstrated an effective barrier to the tracer which failed to penetrate the inner layers of the perineurium. Only at the highest lanthanum concentration and longest time intervals employed did trace quantities occasionally penetrate the barrier and then only in the presence of some cytopathological changes to the outermost perineurial cells. The usefulness of the microinjection method was limited by the slight but unavoidable trauma to the perineurium. The findings are related to those of other studies which have used electron dense tracers, also to studies using physiological including electrophysiological techniques and morphological including freeze-fracture methods.

Endoneurial capillary permeability to [14C]sucrose in frog sciatic nerve

Using an in situ perfusion technique, we measured the [14C]sucrose permeability-surface area product (PA) in endoneurial capillaries of 48 frog sciatic nerves, as 6.6 +/- 0.6 (S.E.M.) X 10(-5) s-1, and the vascular space as 1.31 +/- 0.10%. Assuming A = 30 cm2/g, P = 2.2 X 10(-6) cm/s. P for sucrose was greater than P in some barrier tissues with tight junctions, but was less than P in all capillaries examined so far except rat cerebral capillaries. These observations demonstrate that endoneurial capillaries are an effective part of the blood-nerve barrier to water-soluble non-electrolytes. The findings are consistent with capillary impermeability to microperoxidase and with capillary ultrastructure.

Morphological correlates of permeability in the frog perineurium: vesicles and "transcellular channels"

Lanthanum, applied to the outside of the fixed sciatic nerve of Rana pipiens, did not enter the endoneurium, but was halted by functionally tight junctions at the inner layers of the perineurium. This component of the blood-nerve barrier consists of several concentric layers of cells interspersed with an extracellular matrix of amorphous ground substance, collagen fibrils, and fine filaments. Numerous vesicular profiles are closely associated with the surface membranes of all the cells. The application of lanthanum to fixed tissue revealed that these profiles are attached to the cell surface by narrow necks, and open to the extracellular space. The attenuated cells are filled by the vesicular structures, which often appear to overlap. Stereoscopic electron microscopy showed that these vesicles did not fuse with each other or with the apposing cell surface to form transcellular channels. Channel formation does not appear to contribute significantly to the permeability of any of the perineurial layers.