We modeled three types of electrodes, namely the standard tip active electrode (Figure 1B “conical electrode,” where the active area is cylindrical and located away from the tip), an electrode consisting of single active area extending as an annulus across the width of the electrode (Figure 1C “annular electrode”), and an electrode consisting of multiple separated active areas each extending as an annulus across the width of the electrode (Figure 1D, “striped electrode”)—the latter a design suggested by Wei and Grill (2005) to improve the electrode's efficiency.

The size and shape of the electrode shaft was kept constant for all three electrode types and only the area of the electrode covered with insulation was altered, to change the length and geometry of active (non-insulated) segments. Thus the shaft always had a base diameter of 125 μm, and a total length of 1902 μm (Figure 1A). The electrode had a constant length of 1550 μm, and then tapered to a point with an angle of 20°. The end of the tip was blunted so that the tip diameter was 1 μm. The electrode shaft was kept constant, so that differences in geometry would play only a small part in creating damage due to mechanical insertion and this would not need to be considered. The insulation was modeled to have similar properties as Parylene-C (σ = 1.136 × 10⁻¹⁵ S/m) and was 3-μm thick. The electrode material was taken to be Platinum/Iridium at a ratio of 80/20 (σ = 3.3 × 10⁶ S/m).

For the conical and annular electrodes we modeled five active-area heights (h in Figure 1; for the annular electrode this active area was on the shaft—Figure 1C; for the conical electrode this active area was on the pointed tip region—Figure 1B) of 5, 10, 20, 50, and 100 μm. In addition, a conical electrode with h = 125 μm was also modeled. All modeled electrodes are listed in Table 1. For the striped electrodes, annular stripes were spread out over a total height of 100 μm. (i.e., the distance between the bottom of the stripe closest to the base and the top of the stripe closest to the tip), with a combined active segment length of 72 μm. Electrodes with 2, 4, and 8 stripes were modeled; the segments were all electrically continuous under the insulation. For a cortical visual prosthesis we want to target layer 4Cb of the visual cortex (Normann, 1990), thus the height of the electrode is important so that we are not stimulating multiple cortical layers. An electrode with a smaller height would be preferred so that it is more specific in which layers are activated and hence in this study we have placed more emphasis on the height of the electrode rather than the geometrical surface area.

Axis-symmetric finite element models of the electrodes surrounded by an isotropic homogeneous medium representative of brain tissue, σ = 0.1 S/m (Gabriel et al., 1996), were developed in COMSOL Multiphysics (Version 4.0a, Comsol Inc., Stockholm, Sweden). Brain tissue was modeled as a cylinder with radius and height of 20 cm with the outer boundaries that were not touching the electrode set to ground (V = 0). This dimension was chosen so that the ground was located sufficiently far away from the electrode so that its location did not interfere with the results of the field generated from each of the electrodes. The models were partitioned into mesh elements using a fine triangular mesh. The models were created so that the same mesh was used for each electrode; the material properties of the individual elements were altered to change the insulated/non-insulating areas of the electrode geometry. This ensured the validity of comparisons made between different electrode geometries. Models were created in 2-D in order to reduce computational cost, however they are representative of a 3-D situation.

The electrode contacts were set to deliver a DC cathodic current of 25 μA (unless otherwise stated), which is close to the upper threshold for the perception of phosphenes in the human visual cortex (Schmidt et al., 1996) and similar to the threshold for activation of motor outputs with stimulation in motor cortex (Tandon et al., 2008). While the frequencies that have been used to generate phosphenes in the visual cortex range from 75 to 200 Hz (Schmidt et al., 1996) a DC current as used in this study is suitable when comparing fields across the tissue, which is resistive. This also reduces the dimensionality of the comparison by removing the capacitance of the electrode from the results. The voltages (Φ) at the nodes of the mesh elements were calculated by solving Laplace's equation ∇² Φ = 0. The current density (J) along the surface of the electrode within the mesh elements was calculated using Ohm's law J = −σ∇Φ. The maximum current density was calculated as the average current density over the 1% of the electrode surface with the greatest current density. For simplicity we modeled the brain material and ignored the surface effects of the electrode. If we consider that the electrode impedance is connected in series with the tissue resistance, then the current through both elements would be equal. The drive voltage will depend on the electrodes' capacitance and on the stimulation duration, and these have not been considered. There will also be additional currents due to parasitic capacitance of the insulated part of the electrode which also has not been considered. Tissue resistance was calculated using V = IR, where I was the current supplied to the electrode and V was the resultant voltage at the electrode surface. The capacitance due to the polarization of the electrode interface was not considered; this would roughly scale with the inverse of the surface area of the electrode (Schwan, 1968).

Changing the field generated in the tissue may alter the pattern of neural excitation. Neural excitation by extracellular sources can be predicted by the activating function (Rattay, 1986) which is proportional to the second spatial derivative of the extracellular potential f ∝ ∂²V/∂x². A positive value of the activating functions means that neurons in this region can be stimulated and the higher the value of f, the more likely it is that a neuron in this region would be activated (Rattay, 1986). A negative value of f, indicates that a neuron in this region will not be activated with the supplied pulse, but would be activated with a pulse of the opposite sign.

Distributions of f_z = ∂²V/∂z² (for activation of axons oriented parallel to the electrode surface—see Figure 2) were calculated in the tissue surrounding the electrode surface. The value of f_z was calculated along a line parallel to the electrode surface at distances (r) of 10, 60, and 500 μm. These positions were chosen to represent the near (r = 10 μm), mid (r = 60 μm) and far (r = 500 μm) fields. The step size, Δz, was equivalent to the mesh spacing, which ranged from ~1 μm at r = 10 to ~100 μm at r = 500 μm. The activating function distributions were calculated for three cases: a current-controlled mode with the electrode drive set to −25 μA; a voltage-controlled mode where the electrode drive was set to be −1 V; and a power-controlled mode where the power dissipated in the tissue was 1 μW (P = IV). The peak value and the full width at half maximum (FWHM) of the activating function distribution, f_z, was calculated in order to easily compare the different electrode types. An example distribution is shown in Figure 2D. Thus a higher peak value of f_z indicates a lower current would be required to stimulate neurons. A higher FWHM indicates a larger region of tissue would be stimulated.

When a current of 25 μA was applied, all electrode types show non-uniform current density over the active surface (Figure 3), with the conical electrodes showing the largest difference between maximum current density and average current density. All electrodes show edge effects with local peaks in current density at the electrode-insulation boundaries. The maximum current density occurs at the tip for the conical electrodes, at the electrode/insulation boundaries for the annular electrodes, and at the outermost electrode/insulation boundaries for the striped electrodes. The maximum current densities for the conical electrodes are more than 10 times larger than for the annular and striped electrodes of the same active height (Table 1). Increasing the number of striped segments on the electrode surface reduces the maximum current density for the same active height; however, the solid 100-μm annulus, which has total height equal to that of the striped electrodes, has the lowest maximum current density when supplied with the same current.

With regard to the resistances of the different electrode types (calculated by COMSOL; Figure 4), as expected, as the surface area is increased, the resistance of the electrode decreases. The electrode with striped insulation had low resistance and increasing the number of stripes reduced the resistance even more (Table 1). However, overall, the lowest resistance was found with the solid 100-μm annular electrode which has the same total height as the electrodes striped with insulation. This is as expected as this electrode has the greatest exposed surface area.

Figure 5 shows the electric potential calculated at points along the dashed line shown in Figure 1. For small area electrodes the field is very high close to the exposed part of the electrode, as expected from the Laplace equation. Away from the electrodes the field becomes independent of the configuration of the source. The electrodes striped with insulation follow a similar pattern of voltage decay as the 100-μm annulus.

Profiles of the discrete second spatial derivatives, f_z = Δ²V_e/Δz², were plotted along a parallel line, at three electrode-to-axon distances, r, for three different electrode supply conditions; electrodes supplied with 25 μA, electrodes supplied with 1 V, and electrodes supplied with 1 μW. From these distributions the maximum value of f_z and the value of the FWHM was obtained.

With neural prostheses there are a number of factors that affect neural tissue damage but, with respect to electrical stimulation, the charge density and charge per phase have been found to be important cofactors in causing neural damage (Agnew et al., 1983). Many studies have shown that increased charge density at the tip of the electrode is associated with increased histological damage (Pollen, 1977; Yuen et al., 1981; Agnew et al., 1983; McCreery et al., 1990). Charge density is the product of current density and pulse duration. Shannon (1992) used the results collected by McCreery to develop an expression for the maximum safe level of stimulation which is log(QA)=k−log(Q) where Q is the charge per phase (μC/ph) and, A, is the surface area of the electrode (cm²). From McCreery's data on the cat cerebral cortex Shannon determined a safe, k, value of 1.5 over a charge density range of 1–1000 μC/cm². Reducing the charge density on the surface of the electrode allows for a greater charge per phase to be used before histological damage is seen.

Results of this study show that electrode size and geometry greatly affects the current density distribution on the surface. These results show that the annular electrodes distribute the current more evenly on the surface than the conical electrodes; this could reduce the likelihood for tissue damage. The maximum current density on the surface of a conical electrode with the same height as an annular electrode can be up to 10 times greater due to its smaller surface area. If electrode height is kept constant in order to target a specific cortical layer, then the annular electrode would be able to provide a greater charge per phase to the tissue before histological damage would be seen. However, histological studies will need to be performed to determine whether the maximum current density on the surface of the electrode is correlated with levels of tissue damage and these are planned in the future.

In order to reduce tissue damage, the development of electrodes with a highly uniform current density distribution on their surface has been investigated. These studies have shown that by recessing the electrode, the surface current density can be made almost uniform (Rubinstein et al., 1987; Ksienski, 1992). In this study, the annular electrodes were only recessed from the surface of the insulation by 3 μm, i.e., the insulation was 3-μm thick, thus the distance between the surface of the metal electrode and the surface of the insulating coating was 3 μm. Potentially, the current density of the annular electrodes could be made more uniform by increasing the thickness of the Parylene coating, further reducing the propensity for tissue damage.

The pattern of neural excitation was determined by calculating values of the activating function generated in the tissue for three conditions: current controlled stimulation, voltage controlled stimulation and power controlled stimulation.

The annulus design has been proposed because on insertion of the device, the active part of the electrode is away from the tip. The tip is the most fragile part of the electrode during insertion and so if the tip is damaged for the annular type electrodes the active area will remain unscathed. However, this also means that the tip of the electrode needs to extend further into the brain in order for the active part of the electrode to sit at the correct depth.

The electric fields calculated in these finite element models were based on the idealized assumption that the brain is an isotropic, homogeneous material, which is not the case (Miocinovic et al., 2009). Further, this is an electrostatic model of the field, so no frequency effects were accounted for and current distribution on the surface is assumed to be unaffected by the capacitive layer that forms between the electrode surfaces and surrounding tissue. Within these limits, this modeling study aimed to make a simple comparison between different electrode geometries, and therefore the simplified model should suffice. However, due to this simplification the power consumption will be significantly under estimated as we have not accounted for the power dissipated charging the capacitance of the tissue interface. The electrode interface impedance may be significantly higher than the tissue resistance, and this is greatly dependent on the electrode surface area (Schwan, 1968).

Neural excitation was measured by calculating values of the activating function for axons parallel to the surface of the electrode. We acknowledge that the distributions of neurons and axons in the cortex are much more complex, and so calculating the value of the activating function may not accurately reflect neuronal excitation in situ. Also if the distributions of the activating function were calculated along different lines, then the electrode most suitable for stimulation may be different. For example, for conical electrodes, the distance from the electrode tip to the neurons may be a better metric, as the tip is more likely to stimulate neurons.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.