David Boinagrov

Strength–Duration Relationship for Extracellular Neural Stimulation: Numerical and Analytical Models

The strength-duration relationship for extracellular stimulation is often assumed to be similar to the classical intracellular stimulation model, with a slope asymptotically approaching 1/τ at pulse durations shorter than chronaxy. We modeled extracellular neural stimulation numerically and analytically for several cell shapes and types of active membrane properties. The strength-duration relationship was found to differ significantly from classical intracellular models. At pulse durations between 4 μs and 5 ms stimulation is dominated by sodium channels, with a slope of -0.72 in log-log coordinates for the Hodgkin-Huxley ion channel model. At shorter durations potassium channels dominate and slope decreases to -0.13. Therefore the charge per phase is decreasing with decreasing stimulus duration. With pulses shorter than cell polarization time (∼0.1-1 μs), stimulation is dominated by polarization dynamics with a classical -1 slope and the charge per phase becomes constant. It is demonstrated that extracellular stimulation can have not only lower but also upper thresholds and may be impossible below certain pulse durations. In some regimes the extracellular current can hyperpolarize cells, suppressing rather than stimulating spiking behavior. Thresholds for burst stimuli can be either higher or lower than that of a single pulse, depending on pulse duration. The modeled thresholds were found to be comparable to published experimental data. Electroporation thresholds, which limit the range of safe stimulation, were found to exceed stimulation thresholds by about two orders of magnitude. These results provide a biophysical basis for understanding stimulation dynamics and guidance for optimizing the neural stimulation efficacy and safety.

Selectivity of direct and network-mediated stimulation of the retinal ganglion cells with epi-, sub- and intraretinal electrodes

OBJECTIVE Intra-retinal placement of stimulating electrodes can provide close and stable proximity to target neurons. We assessed improvement in stimulation thresholds and selectivity of the direct and network-mediated retinal stimulation with intraretinal electrodes, compared to epiretinal and subretinal placements. APPROACH Stimulation thresholds of the retinal ganglion cells (RGCs) in wild-type rat retina were measured using the patch-clamp technique. Direct and network-mediated responses were discriminated using various synaptic blockers. MAIN RESULTS Three types of RGC responses were identified: short latency (SL, τ < 5 ms) originating in RGCs, medium latency (ML, 3 < τ < 70 ms) originating in the inner nuclear layer and long latency (LL, τ > 40 ms) originating in photoreceptors. Cathodic epiretinal stimulation exhibited the lowest threshold for direct RGC response and the highest direct selectivity (network/direct thresholds ratio), exceeding a factor of 3 with pulse durations below 0.5 ms. For network-mediated stimulation, the lowest threshold was obtained with anodic pulses in OPL position, and its network selectivity (direct/network thresholds ratio) increased with pulse duration, exceeding a factor of 4 at 10 ms. Latency of all three types of responses decreased with increasing strength of the stimulus. SIGNIFICANCE These results define the optimal range of pulse durations, pulse polarities and electrode placement for the retinal prostheses aiming at direct or network-mediated stimulation of RGCs.

Upper threshold of extracellular neural stimulation.

It is well known that spiking neurons can produce action potentials in response to extracellular stimulation above certain threshold. It is widely assumed that there is no upper limit to somatic stimulation, except for cellular or electrode damage. Here we demonstrate that there is an upper stimulation threshold, above which no action potential can be elicited, and it is below the threshold of cellular damage. Existence of this upper stimulation threshold was confirmed in retinal ganglion cells (RGCs) at pulse durations ranging from 5 to 500 μs. The ratio of the upper to lower stimulation thresholds varied typically from 1.7 to 7.6, depending on pulse duration. Computational modeling of extracellular RGC stimulation explained the upper limit by sodium current reversal on the depolarized side of the cell membrane. This was further confirmed by experiments in the medium with a low concentration of sodium. The limited width of the stimulation window may have important implications in design of the electro-neural interfaces, including neural prosthetics.

Photovoltaic Pixels for Neural Stimulation: Circuit Models and Performance

Photovoltaic conversion of pulsed light into pulsed electric current enables optically-activated neural stimulation with miniature wireless implants. In photovoltaic retinal prostheses, patterns of near-infrared light projected from video goggles onto subretinal arrays of photovoltaic pixels are converted into patterns of current to stimulate the inner retinal neurons. We describe a model of these devices and evaluate the performance of photovoltaic circuits, including the electrode-electrolyte interface. Characteristics of the electrodes measured in saline with various voltages, pulse durations, and polarities were modeled as voltage-dependent capacitances and Faradaic resistances. The resulting mathematical model of the circuit yielded dynamics of the electric current generated by the photovoltaic pixels illuminated by pulsed light. Voltages measured in saline with a pipette electrode above the pixel closely matched results of the model. Using the circuit model, our pixel design was optimized for maximum charge injection under various lighting conditions and for different stimulation thresholds. To speed discharge of the electrodes between the pulses of light, a shunt resistor was introduced and optimized for high frequency stimulation.

Photovoltaic Restoration of Sight with High Visual Acuity in Rats with Retinal Degeneration

Patients with retinal degeneration lose sight due to gradual demise of photoreceptors. Electrical stimulation of the surviving retinal neurons provides an alternative route for delivery of visual information. Subretinal photovoltaic arrays with 70μm pixels were used to convert pulsed near-IR light (880-915nm) into pulsed current to stimulate the nearby inner retinal neurons. Network-mediated responses of the retinal ganglion cells (RGCs) could be modulated by pulse width (1-20ms) and peak irradiance (0.5-10 mW/mm2). Similarly to normal vision, retinal response to prosthetic stimulation exhibited flicker fusion at high frequencies, adaptation to static images, and non-linear spatial summation. Spatial resolution was assessed in-vitro and in-vivo using alternating gratings with variable stripe width, projected with rapidly pulsed illumination (20-40Hz). In-vitro, average size of the electrical receptive fields in normal retina was 248±59μm – similar to their visible light RF size: 249±44μm. RGCs responded to grating stripes down to 67μm using photovoltaic stimulation in degenerate rat retina, and 28μm with visible light in normal retina. In-vivo, visual acuity in normally-sighted controls was 29±5μm/stripe, vs. 63±4μm/stripe in rats with subretinal photovoltaic arrays, corresponding to 20/250 acuity in human eye. With the enhanced acuity provided by eye movements and perceptual learning in human patients, visual acuity might exceed the 20/200 threshold of legal blindness. Ease of implantation and tiling of these wireless arrays to cover a large visual field, combined with their high resolution opens the door to highly functional restoration of sight.

Strength-duration relationship for extracellular neural stimulation

Understanding the mechanisms and dynamics of extracellular neural stimulation is very important for the development of electro-neural interfaces in general, and for the design of stimulation waveforms and electrode configurations for neural prosthetic implants, in particular. The most common type of neural stimulation is extracellular, and yet its mechanisms and dynamics have scarcely been explored and described. Its strength-duration relationship is often assumed to be similar to the classical intracellular dependence, with a slope asymptotically approaching 1/τ at pulse durations τ shorter than chronaxy. The current study explores the basic mechanisms of extracellular stimulation and derives its strength-duration curve in a wide range of stimulus durations for various waveforms and cell shapes. We used two different models of active membrane properties: the Hodgkin-Huxley model of the squid giant axon [1], and a six-channel salamander retinal ganglion cell model [2]. Three cell geometries were analyzed: an idealized planar cell with two uniformly polarized flat surfaces, and more realistic spherical and cylindrical shapes corresponding to the soma and unmyelinated axon or axon hillock. The strength-duration relationship was found to differ significantly from classical intracellular models. For the Hodgkin-Huxley model at pulse durations between 4 μs and 5 ms stimulation is dominated by sodium channels, and has a slope of approximately –0.72 in log-log coordinates. At shorter durations it is dominated by the potassium channels, and has a much lower slope of about –0.13. With pulses shorter than cell polarization time (typically about 0.1-1 μs), it is dominated by polarization dynamics, and asymptotically approaches the classical –1 slope. For retinal ganglion cells we demonstrate that extracellular stimulation can have not only lower but also upper thresholds, and may be impossible below certain pulse durations. For both cell models we have found that in some stimulation regimes the stimulus can hyperpolarize cells, suppressing rather than stimulating spiking behavior. Thresholds for burst stimuli can be either higher or lower than that of a single pulse, depending on pulse duration. The modeled thresholds were found to be comparable to published experimental data obtained with rabbit retinal ganglion cells. These results provide a biophysical basis for understanding stimulation dynamics, and guidance for optimizing the efficacy and safety of extracellular neural stimulation.

Photovoltaic restoration of high visual acuity in rats with retinal degeneration

Patients with retinal degeneration lose sight due to gradual demise of photoreceptors. Electrical stimulation of the surviving retinal neurons provides an alternative route for delivery of visual information. We developed subretinal photovoltaic arrays to convert pulsed light into bi-phasic pulses of current to stimulate the nearby inner retinal neurons. Bright pulsed illumination is provided by image projection from video goggles and avoids photophobic effects by using near-infrared (NIR, 880-915nm) light. Experiments in-vitro and in-vivo demonstrate that the network-mediated retinal stimulation preserves many features of natural vision, such as flicker fusion, adaptation to static images, and most importantly, high spatial resolution. Our implants with 70μm pixels restored visual acuity to half of the normal level in rats with retinal degeneration. Ease of implantation and tiling of these wireless arrays to cover a large visual field, combined with their high resolution opens the door to highly functional restoration of sight.

Reply to Rattay

reply: We thank Dr. Rattay (2014) for commenting on our work (Boinagrov et al. 2012) and exploring the nature of the stimulation upper limit in a multi-compartmental model of the retinal ganglion cell (RGC), and confirming the sodium current reversal as a mechanism of this effect under certain conditions. We are aware of the fact that stimulation threshold in the axonal hillock is lower than in the cell soma due to higher concentration of the sodium ion channels in that area. We have demonstrated previously that transverse cellular polarization and associated stimulation in spherical and cylindrical geometry have similar characteristics (Boinagrov et al. 2010), and therefore, stimulation upper threshold can be described using the same model, just with higher concentration of the sodium channels. On the other hand, suppression of the propagating action potential (AP) in the hyperpolarized soma is indeed beyond the single-compartment model, and was not considered in our study. As we state in the discussion, the main distinction between the roles of the sodium current reversal on depolarized membrane and the anodal surround block is that the sodium current reversal is responsible for prevention of the action potential generation in the first place, while hyperpolarization of the other compartments in the cell might prevent its propagation there. It would be interesting to check whether there are (and what are the ranges of) experimental conditions where AP is generated in axonal hillock and propagates into its axon, but is not detected in the cell soma. This can be done, for example, using electrophysiological imaging on high-density multielectrode arrays (Litke et al. 2004). An alternative way to discriminate between these phenomena is to stimulate RGCs with anodic pulses: there should still be the sodium outflow with strong stimuli, but no anodal surround block.