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Objective Kalman filtering has previously been applied to track neural model states and parameters, particularly at the scale relevant to electroencephalography (EEG). However, this approach lacks a reliable method to determine the initial filter conditions and assumes that the distribution of states remains Gaussian. This study presents an alternative, data-driven method to track the states and parameters of neural mass models (NMMs) from EEG recordings using deep learning techniques, specifically a Long Short-Term Memory (LSTM) neural network. Approach An LSTM filter was trained on simulated EEG data generated by a neural mass model using a wide range of parameters. With an appopriately customised loss function, the LSTM filter can learn the behaviour of NMMs. As a result, it can output the state vector and parameters of NMMs given observation data as the input. Main Results Test results using simulated data yielded correlations with R squared of around 0.99 and verified that the method is robust to noise and can be more accurate than a nonlinear Kalman filter when the initial conditions of the Kalman filter are not accurate. As an example of real-world application, the LSTM filter was also applied to real EEG data that included epileptic seizures, and revealed changes in connectivity strength parameters at the beginnings of seizures. Significance Tracking the state vector and parameters of mathematical brain models is of great importance in the area of brain modelling, monitoring, imaging and control. This approach has no need to specify the initial state vector and parameters, which is very difficult to do in practice because many of the variables being estimated cannot be measured directly in physiological experiments. This method may be applied using any neural mass model and, therefore, provides a general, novel, efficient approach to estimate brain model variables that are often difficult to measure.

Objective. Optogenetic stimulation of the auditory nerve offers the ability to overcome the limitations of cochlear implants through spatially precise stimulation, but cannot achieve the temporal precision nor temporal fidelity required for good hearing outcomes. Auditory midbrain recordings have indicated a combined (hybrid) stimulation approach may permit improvements in the temporal precision without sacrificing spatial precision by facilitating electrical activation thresholds. However, previous research has been conducted in undeafened or acutely deafened animal models, and the impact of chronic deafness remains unclear. Our study aims to compare the temporal precision of auditory nerve responses to optogenetic, electrical, and combined stimulation in acutely and chronically deafened animals. Methods. We directly compare the temporal fidelity (measured as percentage of elicited responses) and precision (i.e. stability of response size and timing) of electrical, optogenetic, and hybrid stimulation (varying sub-threshold or supra-threshold optogenetic power levels combined with electrical stimuli) through compound action potential and single-unit recordings of the auditory nerve in transgenic mice expressing the opsin ChR2-H134R in auditory neurons. Recordings were conducted immediately or 2–3 weeks following aminoglycoside deafening when there was evidence of auditory nerve degeneration. Main results. Results showed that responses to electrical stimulation had significantly greater temporal precision than optogenetic stimulation (p < 0.001 for measures of response size and timing). This temporal precision could be maintained with hybrid stimulation, but only when the optogenetic stimulation power used was below or near activation threshold and worsened with increasing optical power. Chronically deafened mice showed poorer facilitation of electrical activation thresholds with concurrent optogenetic stimulation than acutely deafened mice. Additionally, responses in chronically deafened mice showed poorer temporal fidelity, but improved temporal precision to optogenetic and hybrid stimulation compared to acutely deafened mice. Significance. These findings show that the improvement to temporal fidelity and temporal precision provided by a hybrid stimulation paradigm can also be achieved in chronically deafened animals, albeit at higher levels of concurrent optogenetic stimulation levels.

Objective. The common spatial patterns (CSP) algorithm is an effective method to extract discriminatory features from electroencephalography (EEG) to be used by a brain–computer interface (BCI). However, informed selection of CSP filters typically requires oversight from a BCI expert to accept or reject filters based on the neurophysiological plausibility of their activation patterns. Our goal was to identify, analyze and automatically classify prototypical CSP patterns to enhance the prediction of motor imagery states in a BCI. Approach. A data-driven approach that used four publicly available EEG datasets was adopted. Cluster analysis revealed recurring, visually similar CSP patterns and a convolutional neural network was developed to distinguish between established CSP pattern classes. Furthermore, adaptive spatial filtering schemes that utilize the categorization of CSP patterns were proposed and evaluated. Main results. Classes of common neurophysiologically probable and improbable CSP patterns were established. Analysis of the relationship between these categories of CSP patterns and classification performance revealed discarding neurophysiologically improbable filters can decrease decoder performance. Further analysis revealed that the spatial orientation of EEG modulations can evolve over time, and that the features extracted from the original CSP filters can become inseparable. Importantly, it was shown through a novel adaptive CSP technique that adaptation in response to these emerging patterns can restore feature separability. Significance. These findings highlight the importance of considering and reporting on spatial filter activation patterns in both online and offline studies. They also emphasize to researchers in the field the importance of spatial filter adaptation in BCI decoder design, particularly for online studies with a focus on training users to develop stable and suitable brain patterns.

Objective Retinal prostheses provide visual perception via electrical stimulation of the retina using an implanted array of electrodes. The retinal activation resulting from each electrode is not point-like; instead each electrode introduces a spread of retinal activation that may overlap with activations from other electrodes. With most conventional stimulation strategies this overlap leads to image blur. Here we propose a 'shaping' algorithm that uses multiple electrodes to manipulate the current between electrodes in a desired way. Approach We assume a forward model for the conversion of electrode strengths to retinal activation. Three alternative global shaping algorithms are developed by calculating reverse models under different assumptions: linear inversion using singular value decomposition to produce the pseudoinverse, a linearly constrained quadratic program, and a binary quadratic program to partition the target pattern. The algorithms were assessed using both the mean squared error between the resulting images and desired images, as well as their adherence to the maximum allowed electrode currents. Main results Under wide activation spreads the linear inversion algorithm gave improved solutions but faced two limitations: under low-noise conditions the electrode amplitudes exceeded their set limit; the set of solutions did not include the possibility of using negative local currents to induce retinal activation. The linearly constrained quadratic program and binary quadratic program respectively addressed these problems, but required much greater computation time. Significance This provides a framework for improving the resolution of future retinal implants, especially those with high density electrode arrays.

Brain-machine interfaces directly communicate between the brain and external devices. An effective trade-off between signal quality and safety required for successful clinical translation has yet to be achieved, and represents a great challenge for engineers, neuroscientists, and clinicians. The StentrodeTM, an endovascular neural interface that allows neural signals to be recorded from within a cortical vessel, has demonstrated feasibility with safety for up to six months in a large animal model. Easily-obtained electrophysiological signals to evaluate the effect of implant duration on recording performance are essential for ongoing evaluation of the device. In this work, we demonstrate that a non-invasive and quick visual stimulation technique can be used to assess chronic signal quality of an endovascular neural interface in awake freely moving animals. Visual stimulation requires little or no training to elicit a large, consistent, and well-characterized response. We report the stability of recording quality with the Stentrode over 30 days using voltage measures of signal-to-noise ratio (18.78 ± 1.92 dB, mean ± std) and peak-to-peak voltages (56.07 ± 9.56 μV) computed on visual evoked responses. Signal amplitude and electrochemical impedance spectroscopy suggest that stabilization of the electrode-tissue interface occurred over the first 20 days. However, during this stabilization period, recording quality was minimally impacted.

Objective Different frequency bands of the local field potential (LFP) have been shown to reflect neuronal activity occurring at varying cortical scales. As such, recordings of the LFP may offer a novel way to test the efficacy of neural prostheses and allow improvement of stimulation strategies via neural feedback. Here we use LFP measurements from visual cortex to characterize neural responses to electrical stimulation of the retina. We aim to show that the LFP is a viable signal that contains sufficient information to optimize the performance of sensory neural prostheses. Approach Clinically relevant electrode arrays were implanted in the suprachoroidal space of one eye in four felines. LFPs were simultaneously recorded in response to stimulation of individual electrodes using penetrating microelectrode arrays from the visual cortex. The frequency response of each electrode was extracted using multi-taper spectral analysis and the uniqueness of the responses was determined via a linear decoder. Main results We found that cortical LFPs are reliably modulated by electrical stimulation of the retina and that the responses are spatially localized. We further characterized the spectral distribution of responses, with maximum information being contained in the low and high gamma bands. Finally, we found that LFP responses are unique to a large range of stimulus parameters (∼40) with a maximum conveyable information rate of 6.1 bits. Significance These results show that the LFP can be used to validate responses to electrical stimulation of the retina and we provide the first steps towards using these responses to provide more efficacious stimulation strategies.

Objective. ON and OFF retinal ganglion cells (RGCs) are known to have non-monotonic responses to increasing amplitudes of high frequency (2 kHz) biphasic electrical stimulation. That is, an increase in stimulation amplitude causes an increase in the cell's spike rate up to a peak value above which further increases in stimulation amplitude cause the cell to decrease its activity. The peak response for ON and OFF cells occurs at different stimulation amplitudes, which allows differential stimulation of these functional cell types. In this study, we investigate the mechanisms underlying the non-monotonic responses of ON and OFF brisk-transient RGCs and the mechanisms underlying their differential responses. Approach. Using in vitro patch-clamp recordings from rat RGCs, together with simulations of single and multiple compartment Hodgkin–Huxley models, we show that the non-monotonic response to increasing amplitudes of stimulation is due to depolarization block, a change in the membrane potential that prevents the cell from generating action potentials. Main results. We show that the onset for depolarization block depends on the amplitude and frequency of stimulation and reveal the biophysical mechanisms that lead to depolarization block during high frequency stimulation. Our results indicate that differences in transmembrane potassium conductance lead to shifts of the stimulus currents that generate peak spike rates, suggesting that the differential responses of ON and OFF cells may be due to differences in the expression of this current type. We also show that the length of the axon's high sodium channel band (SOCB) affects non-monotonic responses and the stimulation amplitude that leads to the peak spike rate, suggesting that the length of the SOCB is shorter in ON cells. Significance. This may have important implications for stimulation strategies in visual prostheses.

Objective. The objective of this paper is to present a concrete application of the cellular composite model for calculating the membrane potential, described in an accompanying paper. Approach. A composite model that is used to determine the membrane potential for both longitudinal and transverse modes of stimulation is demonstrated. Main results. Two extreme limits of the model, near-field and far-field for an electrode close to or distant from a neuron, respectively, are derived in this paper. Results for typical neural tissue are compared using the composite, near-field and far-field models as well as the standard isotropic volume conductor model. The self-consistency of the composite model, its spatial profile response and the extracellular potential time behaviour are presented. The magnitudes of the longitudinal and transverse components for different values of electrode-neurite separations are compared. Significance. The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

Objective. A common approach in modelling extracellular electrical stimulation is to represent neural tissue by a volume conductor when calculating the activating function as the driving term in a cable equation for the membrane potential. This approach ignores the cellular composition of tissue, including the neurites and their combined effect on the extracellular potential. This has a number of undesirable consequences. First, the two natural and equally valid choices of boundary conditions for the cable equation (i.e. using either voltage or current) lead to two mutually inconsistent predictions of the membrane potential. Second, the spatio-temporal distribution of the extracellular potential can be strongly affected by the combined cellular composition of the tissue. In this paper, we develop a mean field volume conductor theory to overcome these shortcomings of available models. Approach. This method connects the microscopic properties of the constituent fibres to the macroscopic electrical properties of the tissue by introducing an admittivity kernel for the neural tissue that is non-local, non-instantaneous and anisotropic. This generalizes the usual tissue conductivity. A class of bidomain models that is mathematically equivalent to this class of self-consistent volume conductor models is also presented. The bidomain models are computationally convenient for simulating the activation map of neural tissue using numerical methods such as finite element analysis. Main results. The theory is first developed for tissue composed of identical, parallel fibres and then extended to general neural tissues composed of mixtures of neurites with different and arbitrary orientations, arrangements and properties. Equations describing the extracellular and membrane potential for the longitudinal and transverse modes of stimulation are derived. Significance. The theory complements our earlier work, which developed extensions to cable theory for the micro-scale equations of neural stimulation that apply to individual fibres. The modelling framework provides a number of advantages over other approaches currently adopted in the literature and, therefore, can be used to accurately estimate the membrane potential generated by extracellular electrical stimulation.

Objective. Stimulation strategies for retinal prostheses predominately seek to directly encode image brightness values rather than edge orientations. Recent work suggests that the generation of oriented elliptical phosphenes may be possible by controlling interactions between neighboring electrodes. Based on this, we propose a novel stimulation strategy for prosthetic vision that extracts edge orientation information from the intensity image and encodes it as oriented elliptical phosphenes. We test the hypothesis that encoding edge orientation via oriented elliptical phosphenes leads to better alphabetic letter recognition than standard intensity-based encoding. Approach. We conduct a psychophysical study with simulated phosphene vision with 12 normal-sighted volunteers. The two stimulation strategies were compared with variations of letter size, electrode drop-out and spatial offsets of phosphenes. Main results. Mean letter recognition accuracy was significantly better with the new proposed stimulation strategy (65%) compared to direct grayscale encoding (47%). All examined parameters-stimulus size, phosphene dropout, and location shift-were found to influence the performance, with significant two-way interactions between phosphene dropout and stimulus size as well as between phosphene dropout and phosphene location shift. The analysis delivers a model of perception performance. Significance. Displaying available directional information to an implant user may improve their visual performance. We present a model for designing a stimulation strategy under the constraints of existing retinal prostheses that can be exploited by retinal implant developers to strategically employ oriented phosphenes.

The validity of approximate equations describing the membrane potential under extracellular electrical stimulation (Meffin et al 2012 J. Neural Eng. 9 065005) is investigated through finite element analysis in this paper. To this end, the finite element method is used to simulate a cylindrical neurite under extracellular stimulation. Laplace's equations with appropriate boundary conditions are solved numerically in three dimensions and the results are compared to the approximate analytic solutions. Simulation results are in agreement with the approximate analytic expressions for longitudinal and transverse modes of stimulation. The range of validity of the equations describing the membrane potential for different values of stimulation and neurite parameters are presented as well. The results indicate that the analytic approach can be used to model extracellular electrical stimulation for realistic physiological parameters with a high level of accuracy.

Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

The ability to electrically stimulate neural and other excitable tissues in behaving experimental animals is invaluable for both the development of neural prostheses and basic neurological research. We developed a fully implantable neural stimulator that is able to deliver two channels of intra-cochlear electrical stimulation in the rat. It is powered via a novel omni-directional inductive link and includes an on-board microcontroller with integrated radio link, programmable current sources and switching circuitry to generate charge-balanced biphasic stimulation. We tested the implant in vivo and were able to elicit both neural and behavioural responses. The implants continued to function for up to five months in vivo. While targeted to cochlear stimulation, with appropriate electrode arrays the stimulator is well suited to stimulating other neurons within the peripheral or central nervous systems. Moreover, it includes significant on-board data acquisition and processing capabilities, which could potentially make it a useful platform for telemetry applications, where there is a need to chronically monitor physiological variables in unrestrained animals.