Ординатура / Офтальмология / Английские материалы / Artificial Sight Basic Research, Biomedical Engineering, and Clinical Advances_Humayun, Weiland, Chader_2007
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Figure 15.6. (a) Location of stimulator ASIC (chip) in eyeball. (b) Cross section of a 0.25 mm resolution model. A graded-K coating arrangement is shown in the figure.
tissue types. The dotted line indicates the axis along which the thermal profiles for different insulator configurations are shown in Figure 15.7.
Figure 15.7 gives the temperature profile parallel to the axis of the eye, through the insulator. All the simulations were performed for 22 minutes of real-world time, during which the temperatures obtain their steady-state values.
As expected, the maximum temperature rise T = 1 657 C) within the
chip/insulator package takes place for configuration with uniform KINSULATOR = 0 2 W/m C, while the minimum rise T = 0 986 C) takes place for uniform
KINSULATOR = 30 W/m C. The graded coating configuration partially restricted
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Figure 15.7. Profiles of the temperature increase along the axis of the eye going through the chip. (I) Only one insulator coating of K = 0 2 W/m C; (II) Graded insulator coating,
KINNER = 0 2 W/m C; KOUTER = 30 W/m C; (III) Graded insulator coating, KINNER = 30 W/m C; KOUTER = 0 2 W/m C; (IV) Single Uniform coating, K = 30 W/m C.
the flow of heat from the chip, leading to intermediate temperature increments in the chip/insulator region and the surrounding parts. For high-K insulator, heat flows freely outward from the chip. Consequently, the temperature rise in the chip is lower, and the tissues at far away points have higher thermal increment. For low-K insulator, the restricted heat induces comparatively higher temperature rise within the chip/insulator region, and the relatively faraway tissues are almost unaffected.
Implanted Coil
The heat dissipated by the receiving coil for the telemetry system in the retinal prosthesis can contribute to the thermal increase in the surrounding tissues. As an example, we have considered the effect of two possible locations of the receiving coil: (1) outside the eye, surrounding the eyeball, and (2) implanted in the eye, in place of the lens. In both cases, the axis of the coil is identical to the axis of the eyeball. Figure 15.8 illustrates the position of the coils relative to the eyeball.
The power dissipated in the coil was calculated using the total resistance of the coil and the current that is assumed to flow in the coil itself. Table 15.1 compares
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Figure 15.8. The location of the two receiving-coil positions considered for thermal simulations. Note that both have been assumed to be tightly wound four-turn coils.
Table 15.1. Maximum temperature increase in various tissues of the human body due to the power dissipation of the receiving coil for the wireless telemetry. “Anterior” indicates the results with the receiving coil implanted in place of the lens, while “Surrounding” implies that the receiving coil is of 25 mm diameter and surrounds the eyeball.
Tissue |
Maximum temperature rise C |
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Anterior |
Surrounding |
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Retina |
0.025 |
0.358 |
Skin |
0.089 |
1.433 |
Fat |
0.152 |
1.222 |
Muscle |
0.409 |
1.045 |
Cornea |
0.240 |
0.105 |
Vitreous Humor |
0.415 |
0.314 |
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the maximum temperature increments caused by the two considered coil configurations on some of the tissues, for a given power dissipation 546 W . Further details can be found in [30].
Electrode Array
The effect of the power dissipation of the electrode array can also be quantified. Figure 15.9a and 15.9b are horizontal and vertical cross sections, respectively, showing the position on the retina, at the back of the eyeball, of an 8 × 8 stimulating electrode array, in a 0.125 mm resolution head model. This model was extracted from the larger, lower resolution (0.25 mm) eye model shown in Figure 15.6b.
The current injected in each electrode is biphasic in nature, with a pulse that for illustrative purposes can be assumed of equal width for the cathodic and anodic phase. Figure 15.10 shows the power dissipation pattern in each electrode for two different current waveforms.
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Figure 15.9. Cross section of the thermal model showing configuration of the electrode array on the retina. (a) Perpendicular to electrode array. (b) Parallel to electrode array.
For the given current injection values and periodicity, the temperature increment due to the power dissipated in the electrode array is lower than 0.01 C. The low thermal elevation is expected since the power dissipation per unit volume 158 Watts/m3 is extremely small and zero most of the time. The
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Figure 15.10. Power dissipation by a single platinum electrode for an injected current of617 A at pulse width = (a) 1ms, (b) 3 ms; and pulse repetition rates of 50 Hertz.
temperature increase in the tissue due to the flow of the current can be calculated in a similar fashion, and it is currently under consideration.
Computation of Electric Current Densities in the Retina
When designing the stimulating electrode array, it is useful to predict the electric current densities and potentials induced in the various retinal layers by the stimulating electrodes. Determination of currents and potentials is important for achieving optimal stimulation while avoiding risks of tissue damage due to excessive current [31].
Current density simulations can answer questions regarding:
•optimal electrode geometry and current return placement
•safe maximum amount of current to inject for a given configuration
•efficiency of current injection for particular setting
•aspects of safety of implanted device for particular configurations, related to current circulation through living tissue.
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Due to the very low frequencies used for the stimulation of the retina, the simulation of the resulting current densities can be approximated through static or quasi-static methods. The “Impedance Method” [32–34] or its dual, the “Admittance Method” [35, 36] are two computationally efficient methods that can be used to calculate the resulting current densities in 2D or 3D. In the Impedance Method, the anatomical model of the retina is discretized and approximated as an equivalent impedance mesh, built of lumped circuit elements. This approach reduces the problem to a solution of a linear system of equations. The final result of the simulation are the approximate current density vectors at the centers of each of the voxels forming the anatomical model, as well as the electric potential at each vertex of each voxel in reference to the model’s ground. Before applying the Impedance Method, a suitable discrete retinal model needs to be produced. For a successful simulation, the model must be anatomically correct and have a resolution that is sufficient to describe the electrical characteristics of the retinal layers. Further, the low frequency impedance of each tissue must be known if the tissue itself is to be modeled as a “bulk” material with given dielectric properties.
The following sections briefly describe some aspects of high-resolution discrete model generation, the basics of the Impedance Method, the challenges involved in such high-resolution modeling, and illustrative results.
Layered Retina Model
In order to understand the interaction of the current injected by the electrode array and the ganglion cell layer of the retina, the retinal models must be anatomically correct and sufficiently detailed. One such model is the Visible Human model, available at a resolution of 1 mm [21]., While acceptable for tissues surrounding the eye, a 1mm resolution is grossly insufficient to describe the anatomical characteristics of the retina. Thus, models of the retina with accurate descriptions of all its layers [37, 38] have been artificially generated through mathematical descriptions or obtained from anatomical atlases, and these refined models were used to replace retinal tissue in the original 1mm resolution model.
Figure 15.11 shows a 2D model of the retina and electrode array created with a software application that was written to generate discretized models of the human eye – or other anatomical structures – at arbitrary resolution starting from geometrical descriptions. In our simulations we use current sources to provide a stimulus to the retina. In addition to organic structures, the model needs to include the electrodes used for excitation, the current return, and a marker for the ground potential, as shown in Figure 15.12.
Impedance Method
The idea behind the impedance method [32] is to convert a physical system to a discretized model, and combine that information with the electrical impedance of each material to obtain an equivalent electric circuit, built of lumped circuit
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Figure 15.11. (a) Geometric model of human retina and linear electrode array. (b) 2D slice across the Z-plane of resulting model discretized at 2 m resolution.
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Figure 15.12. (a) 3D geometric retina model with array of electrodes. (b) View of matching uniformly discretized section, 10 m resolution; insulator between electrodes is not shown.
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components. This equivalent electric circuit can be represented as a linear system, and then be solved using Ohm’s Law.
Starting from the discretized model, the solution of the system will result in knowing the electric potential at each vertex of each voxel relative to the model’s ground as well as the current density vector at the center of each voxel. The method can be applied to 2D or 3D discretized models, formed of either uniform or different sized cells or voxels. The method for uniform resolution cells can be found in [32] and it will be briefly summarized here.
The first step is to convert each voxel of the model to its equivalent impedance network formed of lumped circuital elements. Since the model is linear, each of the three orthogonal directions (X, Y, and Z) is considered separately, and the final impedance network for the voxel is obtained combining all the resulting components.
Considering a single voxel of the discretized model (Figure 15.13), it is possible for example to approximate the impedance seen by a current flowing in the X direction by lumping the impedance of each of the sub-volumes into a circuit element, knowing that the equivalent resistance will be
L |
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R = W H |
(8) |
and the equivalent capacitance will be
C = |
W H |
0 r |
(9) |
L |
where 0 is the permittivity of free space. and r are the resistivity and the relative electric permittivity, respectively, of the voxel’s material along the X axis. W H, and L are the respective width, height, and length of the sub-voxel volume.
For each voxel, this process is performed in all three orthogonal axes, as shown in Figure 15.14. Then, the resulting lumped elements are combined to form the equivalent impedance network that approximates the voxel electrical
Figure 15.13. Voxel sub-volumes used to calculate lumped circuit elements in X direction. The resistor in parallel with the capacitor will represent the low-frequency impedance of one sub-volume.
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Figure 15.14. Process for generating equivalent impedance network of a voxel.
behavior. Contributions from all voxels in the model are then combined to form the equivalent impedance network that represents the entire model.
Note that the resultant electrical circuit will have nodes coinciding with the vertices of the model’s voxels. One node is assigned the ground potential. External stimuli can then be modeled as current sources, connected between two nodes, one belonging to an electrode and the other to the current return. The equivalent impedance matrix for the circuit is then built and the system solved for voltages and currents. The X, Y, and Z components of the voxels’ total current density can then be calculated by considering the area normal to the sub-volume that each lumped impedance represents. Finally, the total current density vector for each voxel is calculated by adding the contributions of all the sub-volumes in all three axes, as shown in Figure 15.15.
Figure 15.15. Current density calculation with the impedance method.