Ординатура / Офтальмология / Английские материалы / Artificial Sight Basic Research, Biomedical Engineering, and Clinical Advances_Humayun, Weiland, Chader_2007

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Figure 14.1. Schematic representation of a cell in a dipole electric field. Cell of the width L positioned at distance Y from the surface of an electrode with radius ro. The cross-cell voltage is U . Surface at 0 potential is the return electrode located at the center of the dipole – at distance d/2 from the center of the electrode.

(220 Ohm cm [22]), and g. is the resistivity of the extracellular medium (100 Ohm cm [18]). For a cell soma of L = 10 m in width the polarization time is very short: tp ≈ 130 ns. However, it is significantly higher in the distributed structure of narrow neural processes having significant internal resistance [23].

Typical retinal neural cells extend their processes over several tens and sometimes even hundreds of microns, thus greatly exceeding the dimensions of the electrodes in a high-density implant (20 m pixel spacing is required for maximal visual acuity of 20/80). The dipole electric potential is reciprocal to the square of distance and thus is negligible at distances much larger than the size of the dipole. So the cross-cellular potential of large cells in the dipole field is practically determined by the potential on their proximal membrane. Assuming the dipole having a length d and a potential of U0 on its electrode of radius r0

where k = p for a sphere, p/2 for a hemisphere and 1 for a disk electrode, the current will be

Figure 14.2. Threshold current (in A) required for generation of a 5 mV cross-membrane voltage drop on a proximal surface of a large cell, plotted as a function of distance between the cell and the electrode surface. Calculated for electrodes of 5, 15, and 50 m in radius.

From the experimental values of the threshold current required for retinal neural cell stimulation – Ith = 0 4–3 A (at pulse duration 1 ms)[24] measured with a disk electrode of r0 = 62 5 m in diameter in a very close proximity to cells Y ≈ 0 and having a remote return electrode d >> r0 – we can deduce the

Umem = Ith · g/4r0 = 1 6–12 mV. The current required for depolarization of the cell membrane by Umem rapidly increases with the separation of a cell from

the electrodes Y, asymptotically reaching quadratic dependence, as shown in Figure 14.2. If this separation varies in different parts of the array, the stimulation threshold (and the visual outcome) will vary accordingly. Close and stable proximity of cells to the electrodes is thus an important issue in the design of a high-resolution retinal implant.

Tissue Heating

Electric current in a conductive medium generates Joule heat. Since the threshold voltage and current strongly depend on distance between electrodes and cells so will the heating. For single pulses at the threshold of neural stimulation this temperature rise is negligible – below 10−2 C. However, with application of repetitive pulses to a large array of electrodes heat might accumulate, and thus a regime of chronic stimulation requires careful consideration. Average power

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dissipation can be estimated as P = U · Ie · N · · , where U is the voltage applied to the implant electrodes, Ie is a current from one electrode, N is number of electrodes on the implant, is pulse duration, and is a pulse repetition rate. The total voltage step U is composed of three principal parts: (1) resistive loss in the solution Rs, described above, (2) pseudocapacitive voltage step in the solution, and (3) “serial resistance” of the electrode composed of resistance of charge transfer and of the metal oxide layer.

“Pseudocapacitive” behavior of the electrochemical reduction–oxidation reactions on IrOx and Pt electrodes [25, 26] is due to electrochemical storage of charge at the surface of the electrode during each phase of the pulse. An upper estimate of the energy losses can be given assuming that there is no energy “recycling”, i.e. all the energy stored during each phase of the bi-phasic pulse is converted into heat during the opposite phase. In reality, some part of the stored energy is “recycled”, but it is quite difficult to accurately estimate the reversible component of these rather complex electrochemical processes. Pseudo-

This value is close to the ratio of the maximal charge density qmax to the corresponding maximal voltage U allowed for reversible electrochemical reactions

on IrOx: qmax = 4 mC/cm2 U = 0 8 V [26], thus cp = 5 mF/cm2. For Platinum (Pt), qmax = 0 4 mC/cm2 [27], and at similar voltage cp = 0 5 mF/cm2.

The charge transfer resistance and the resistance of the oxide layer for uniformly accessible hemispherical electrode are reciprocal to the electrode surface area [28], i.e. Rser scales with the electrode radius ro as Rser 1/ro2, but for the disk electrode, where current density might be distributed non-uniformly, the scaling law might be more complex [29]. For IrOx electrodes 36 m in radius, Rser = 3 1 kOhm (estimated from the data in [26]).

The number of electrodes, N , on a 3 mm diameter implant can be estimated assuming that a pixel width is four times the radius of electrode. In this case, N ≈ 17 500, 1900, and 170 for electrodes of 5, 15, and 50 m in radius, respectively. Assuming an average current on each electrode corresponding to the results of the appropriate electrode size as plotted in Figure 14.3, the pulse duration being = 1 ms (0.5 ms per phase), and repetition rate = 25 Hz, the average power dissipation from the implant with IrOx electrodes is plotted in Figure 14.4.

When a continuous train of pulses is applied, the heat diffusion into the surrounding liquid creates a steady distribution of temperature. Under the steadystate conditions in the spherically symmetric case the temperature decreases reciprocal with the distance, i.e. it drops by 50% at the distance similar to the radius of the array. Thus for practical purposes the cells within a few hundred microns of an implant will be subject to temperatures similar to those at its surface. The power dissipation from the disk-shaped array of electrodes of diameter D surrounded by liquid with thermal conductivity having the ambient

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needed for cellular stimulation. Materials with high surface area, such as carbon black [31] or TiN [26, 32] can, in principle, strongly increase capacitance of the double layer—up to 0 95 mF/cm2 [26], but may have a slow dynamic response.

Faradaic process can provide higher charge values. However, for chronic stimulation the electrochemical reactions should (a) not cause noticeable decomposition of the electrode material, and (b) its products should not be cytotoxic. Oxidation/reduction of Iridium (Ir) oxide on the surface of an Ir electrode satisfies both criteria, and such electrodes have been extensively discussed in literature [26, 33–35]. The Pt electrodes have also been used for cell stimulation [3, 27]. The iridium oxide injects charge by a fast, reversible faradaic reaction involving reduction and oxidation between the Ir3+ and Ir4+ states of the oxide, with the exchange of charge balancing counter-ions with the electrolyte [33]. Unlike Pt, these redox reactions are confined to the oxide film, with no generation of soluble species required to transfer charge. Accordingly the maximum amount of charge per unit area that can be passed without corrosion and gas formation for IrOx electrodes is 4 mC/cm2 [26, 35], while for Pt it is much lower: 0 4 mC/cm2 [27, 36]. Some studies suggest even more conservative limit of 0 15 mC/cm2 [37].

distance from surface, m

Figure 14.4. Threshold charge density on electrode with a pulse duration of 0.5 ms/phase, plotted as a function of distance between the cell and the electrode surface. Calculated for electrodes of 5, 15, and 50 m in radius. Maximal safe charge densities for Pt, TiN, and IrOx electrodes are shown as horizontal lines.

Current density on the surface of the electrode is

It is limited by the electrochemical tolerance of the electrode material. As shown in Figure 14.4 (for a Umem = 5 mV), this limits the distance between electrodes and cells as a function of the electrode size and material. For example, the Pt electrodes of 10 m in diameter can only be used at distances up to about 15 m from the cells. IrOx electrodes of the same size can operate safely at distances up to 70 m. Larger electrodes are less restricted by electrochemical safety.

Divergence of Electric Field

Electric fields (and the associated electric currents) emanating from the stimulating electrodes diverge, i.e. they spread with the distance. Thus the dynamic range of targeted stimulation, i.e. the ratio of the electric field in front on an electrode to electric field produced by the neighboring electrodes, decreases with the distance from the array, as illustrated in Figure 14.5a. Electric potential of a spherical electric field, characteristic for a monopolar electrode having a return electrode at infinity, can be described as following:

The width of its normalized lateral distribution (along the x axis) increases linearly with the distance z from the plane of the array√ . For example, the full width at half maximum of this distribution: X = 2 3 · z ≈ 3 46z, i.e. the electric potential at a distance of X = 3 46z is half of the maximum value. A dipole electric field, approximating a coaxial pair of electrodes located in

diverges linearly with√ the distance z. The full width at half maximum of this distribution, X =√2 22/3 − 1 · z ≈ 1 53z, while the full width at 1/10th of the maximum, X = 2 102/3 − 1 · z ≈ 3 81z; i.e. cells located at distance z in front of one electrode will be affected by the neighboring electrode by 1/10th of its maximal value if the electrodes are separated by the distance X/2. Divergence of the electric field increases the area affected by each electrode and thus reduces the maximal achievable resolution. This effect, analogous to out- of-focus imaging, filters out the higher spatial frequencies in the stimulation pattern thus limiting the spatial resolution, as shown in Figure 14.5b, c. The lower the level of tolerable interference from neighboring electrodes (determining the dynamic range of targeted stimulation), the wider should be the pixel spacing, effectively lowering the resolution. For example, to resolve spatial frequency of 25 lines/mm (geometrically corresponding to maximal visual

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under the prosthesis), we explored the placement of perforated membranes with a basal seal to prevent growth out the bottom. These experiments were performed in vitro with cultured rat retinas and in vivo with the RCS rat retinas. In the experiment illustrated in Figure 14.7, the 10 and 20 m perforations lay atop the 40 m chambers, with their bottoms sealed with a membrane. When retinas

A B

C

Figure 14.7. (a) Schematic of a 3-layered membrane with entry channels on top, wider inner chambers, and a closed at the bottom. Voltage can be applied between the inner electrode (1) and the common return electrode (2). (b) View from below at the lithographically fabricated chamber array with the entrance apertures of 10 and 20 m in width and chambers of 40 m in width. (c) RCS rat retina grown into the chamber array 15 days after the implantation. Retinal tissue migrated through the holes into the chambers of 40 m in width. This way the apertures achieve very close proximity to the cells in the Inner Nuclear Layer. The amount of tissue migrating into the chambers can be adjusted by controlling the depth of the chambers.