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

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Introduction

Retinitis Pigmentosa (RP) and Age-related Macular Degeneration (AMD) are retinal diseases that cause a slowly progressing loss of vision due to a degeneration of the light sensitive cells (rods and cones) in the retina. In the end state, RP and AMD can lead to complete blindness due to the loss of photoreceptors, while the connected ganglion and bipolar cells in the retina as well as the optical nerve remain largely intact. The aim of a number of retinal prostheses efforts is to partially restore vision to patients with severe cases of RP and AMD by stimulating the ganglion cells with electrical pulses emitted through an array of electrodes attached to the retina. Various clinical trials have already demonstrated the stimulation of visual sensation using single electrodes and electrode arrays. In light of these successful results, research is focused on increasing the number of electrodes in the array, which is likely to increase the capability to perform useful tasks for patients receiving the implant.

While a number of efforts toward the realization of a retinal prosthesis are ongoing [1–3], we will focus on a dual-unit prosthesis approach consisting of an external unit, with a camera and wireless transmitter, and a unit implanted in the eye consisting of a wireless receiver, implanted microelectronics, and a stimulating electrode array [4, 5]. The wireless transmission of data and power to a chronically implanted prosthesis is necessary to avoid percutaneous wire connections. Biocompatibility and safe operation of the prosthesis components has to be maintained with minimal deposition of electromagnetic power and heat, setting stringent design conditions.

This chapter is organized in three sections, respectively addressing aspects of the inductively coupled telemetry link, the thermal heat simulations of the retinal prosthesis components, and simulations of the retinal electrode array.

Inductively Coupled Links for a Dual-Unit

Retinal Prosthesis

In the dual-unit retinal prosthesis under consideration here, like in numerous other biomedical applications, inductive coupling is the preferred method for transcutaneous power transfer. Inductive links can carry data to and from implanted biomedical devices without the need of wires piercing the skin, therefore reducing the risk of infection. The effectiveness of the inductive link and compliance with safety standards are of critical importance for these applications. In general, skin mobility and variations in the thickness of subcutaneous fatty tissue can cause misalignment of the coils, leading to a change of transmission characteristics. In the retinal prosthesis, eye movement can obviously cause substantial changes in the relative positions of external and internal coils. Thus, numerical studies are necessary to assess the performance of the coupling between external and internal coils in advance to clinical trials. Different coil geometries are considered

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In the PIM, the integral along the complete paths of wire loops, dli and dlj , respectively, is partitioned into linear wire segments as shown in Figure 15.1. Thus, the inductance of Eq. (1) can be written as a sum of partial inductances

The partial inductance integral Lpkm can be calculated in a closed form for the self-inductance of a cylindrical wire segment (where k = m) [14], as

where l is the wire segment length and r is the wire radius. The mutual inductance between two cylindrical wire segments k m is approximated as the mutual coupling of two filamentary currents flowing along the longitudinal axis of cylindrical wires segments. The equation for the mutual coupling of two straight filaments placed in any desired position can be found, for example, in [13]. The equations for the selfand mutual inductances of wire segments can be evaluated very efficiently, and in this fashion the total loop inductance can be computed very quickly even for a large number of wire segments.

Coil Models and Coupling Computation

For an optimal coupling efficiency, the external telemetry and power transfer coil for the retinal prosthesis considered here must be placed very close to the eye, as illustrated in Figure 15.2. Further, the axis of external and internal coils should be aligned. As an example, Figure 15.3 shows the geometry of external and internal coils that can be used for a retinal prosthesis. The smaller internal coil has two layers, each having 9 turns of 40/44 copper litz wire. The larger external coils also has two layers, each having 10 turns of 165/46 copper litz wire.

Using the PIM, the mutual coupling of the coils shown in Figure 15.3 was computed as a function of the distance between the two. In Figure 15.4 the quasistatic results, obtained with the PIM, are compared with coupling measurements at 1 MHz, obtained using a vector network analyzer. The figure demonstrates that there is good agreement between the results obtained from the PIM and the measurements at low frequencies.

In another set of PIM simulations, shown in Figure 15.5, the mutual coupling for two different external coils are compared. Here, the external coils both have a total number of 20 turns; the coil used in Figure 15.5(a) has only one layer of 20 turns, while the coil used in Figure 15.5(b) has two layers of 10 turns each. The internal coil considered here only has 10 turns on one layer. The figures show the mutual coupling between external and internal coils for a range of distances between them and a range of angles of rotation of the eyeball that causes a misalignment of the axes of the coils. The figures illustrate that the external coil only has one layer, but the same number of turns has nearly 50% better coupling

Figure 15.2. Illustration of the human head model and placement of the external telemetry coil.

over the two-layer coil at the same distance and coaxial alignment = 0 . The

two-layer coil, however, is less sensitive to misalignment due to eye rotation

= 0 .

Thermal Modeling

One of the key requirements to prevent potential tissue damage caused by an electronic implant – such as the retinal prosthesis – is to limit the thermal elevation induced in the human body due to the operation of the implant itself. While the extra-ocular components of the retinal prosthesis are not expected to have any direct thermal effects on the tissues of the eye, the intra-ocular components will cause temperature increase due to power dissipation. Further, the wireless telemetry link between the external (primary) coil and the internal (secondary) coil will cause electromagnetic power deposition in the tissues, which in turn could lead to temperature increase. While sources of heat cannot

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Figure 15.3. An example of internal and external coil geometries for a dual-unit retinal prosthesis.

be removed completely, measures can be taken to minimize the heat due to a biomimetic device such as the retinal prosthesis.

Bio-Heat Equation Formulation

In general, the temperature variation in a generic body can be described by a partial differential equation (PDE) of conduction, given by C Tt = ·K T±S,

tissues in the human body and the regulating action of blood, Pennes incorporated terms to describe the warming effect of the basal metabolism and the regulatory

Figure 15.4. Simulated and measured results for the mutual coupling between the two coils in Figure 15.3.

influence of blood on tissue temperatures [15]. Pennes’ basic Bio-Heat Equation (BHE) can therefore be written as

where A is the rate of heat production due to metabolic processes per unit volume, B is the blood perfusion constant, and Tb is the temperature of blood (assumed constant at Tb = 37 0 C). As can be seen from Eq. (4), the temperature variation with respect to time depends on a number of tissue properties, which would lead to wide varying temperatures within the human body. Also, while the metabolic rate is a source of heat, the blood perfusion constant B is a measure of how well a particular tissue is permeated with blood, which is reflected in its temperature. The term B T − Tb acts as a source of heat if T > Tb, and as a sink if T < Tb.

Electromagnetic Deposition

If a biological object is exposed to RF energy (e.g. the wireless telemetry system), E- and H-fields penetrate the tissues leading to power deposition. This power deposition leads to temperature increase per unit time given by Tt = SARC , where SAR is the Specific Absorption Rate [16]. The SAR is defined as the time rate

of incremental energy SAR = d dW , dissipated in a material incremental mass

dt dm

dm, contained in a volume element dV of given mass density , i.e. dm = dV . The SAR is related to magnitude E of the electric field by SAR = E 2, whereis the electrical conductivity of the tissue. Thus, once we know the E-field distribution in the tissues, we can obtain the SAR, from which we can obtain

the heat generated per unit volume per unit time, which can be incorporated in the BHE as a source.

Joule Heating

When considering electronic implants within the tissue, power dissipation within the electronic circuits has to be considered. Assuming the heat dissipation per unit volume of an implant is Pi, it can be incorporated in the BHE as a source. Thus, the complete BHE governing heat conduction within a body volume under RF exposure and with internal electronic components can be expressed as

Computational Method

The BHE given in Eq. (5) is a PDE and can be solved using a variety of computational methods. An efficient computational solution of Eq. (5) can be obtained by means of 3D finite difference methods, such as that in [17], which is based on the conservation of thermal energy Qi j k within a cell at the 3D coordinates (i, j, k). Heat generated by the sources is added algebraically

For simplicity, the cells have been assumed to be cubes of size . The flow of heat into the cell via conduction is calculated using the analogy of heat flow to current flow where the equivalent of Ohm’s Law V = IR is Fourier’s Law T = Q Rth . Here, Q is the rate of heat transfer and Rth is the thermal resistance. For the derivation of this analogy, the reader is referred to [18].

Let Ki±1 j k Ki j±1 k, and Ki j k±1 be the thermal conductivity of the tissue cells adjacent to cells Ki j k. The series thermal resistance between point Ki j k

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Similarly, conduction heat contributions from the other five adjacent cells are

added to obtain the total heat energy increment, Qtotal = QC + QG. The temperature increment from time tn = n · t to tn+1 = n + 1 · t is then given by

Thus, with the knowledge of boundary values, initial conditions, and properties of the tissues, we can use an explicit finite difference method to solve the BHE (5).

The boundary condition between human body tissue and air is obtained by using the concept of continuity of heat flow normal to the skin surface. This is expressed as the convective boundary condition, K Tnˆ = Ha T − Ta , where nˆ signifies the unit normal to the skin surface, Ha is the convective heat coefficient of the ambient (air), and Ta is the ambient temperature. Boundaries truncating the model within the body are modeled using Dirichlet boundary conditions (boundary condition of the first kind), i.e. the temperature at the boundaries is assumed to be constant.

The electromagnetic power deposition due to the wireless link for power and data transfer can be calculated using the Finite-Difference Time-Domain (FDTD) method, as done in [19], and included if needed in Eq. (5). However, if the design of the wireless link is such that the electromagnetic absorption is within limits established by international safety standards, such as IEEE and ANSI, the influence of the SAR on the temperature increase is minor compared to the other sources of heat, and is neglected in the BHE computation.

To obtain the initial temperature values within the head, the BHE is solved

for the 3D head model without any external factors (SAR, Pimplant). In the retinal prosthesis case, for practical purposes, only the region around the eye

is needed since the temperature increase is largely confined around the region of the implant. Therefore, after the initial (basal) temperature is obtained with a large model of the human body, only a subsection of this is needed for the computation of the temperature increase due to the implant. Thus, only smaller volumes around the eye region were used, for example, in [19] to compute the thermal increase due to the retinal prosthesis implant.

Tissues Properties

For the purpose of obtaining computational results of the temperature increase due to the retinal prosthesis system, a 1mm resolution 3D head model based on the Visible Human Project of the National Library of Medicine [20, 21] was used. A number of other models derived from MRI scans of volunteers are in general widely available and can also be used for the purpose. The thermal parameters (C,K,A,B) for the tissues can be obtained as described in [16, 22], while the dielectric properties at the frequency of the telemetry system can be obtained

from [23–26]. Both the metabolic rate A and the blood perfusion constant B describe thermoregulatory mechanisms of the human tissues. The head models used have a skin–air and a cornea–air interface, each characterized by a different convection coefficient Ha Ha = 10 5 mW2 for skin–air, Ha = 20 mW2 for cornea–air). Previous simulations [19] showed that using a constant Ha = 10 5 mW2 for all tissue-to-air interfaces has a negligible effect on the accuracy.

A very important aspect of modeling the eye is the relationship between the retina and the choroid tissue. The choroid is a highly vascularized tissue, i.e. it contains a significant amount of blood vessels. Therefore, the choroid is modeled with the dielectric properties of blood. However, during simulation, the temperature of the choroid is allowed to vary, as opposed to being held constant at TB.

Extensive studies have indicated that the high blood circulation density between the choroid and the retina is responsible for the retinal temperature regulation. To this extent, the retinal tissues are assumed to be perfused with

the “choroidal blood”, i.e. instead of TB the regulating temperature is Tchoroid. To get a deeper understanding of the choroidal effects on the retina, the reader is

referred to [27–29].

Component Modeling and Thermal Elevation Results

Stimulator Chip

Gosalia et al. [19] previously obtained thermal elevation results using the explicit finite difference method to implement the BHE. Different positions (in the center of the vitreous cavity and at the anterior of the eye between the ciliary muscles) and sizes (4 × 4 × 0 5 mm and 6 × 6 × 1 mm) were considered. The chip was covered by an insulating encapsulation with a uniform thickness of 0.5 mm, and was allowed to dissipate 12.4 mW over its entire volume (excluding the insulation). The thermal conductivities of the chip and the insulation were assumed to be constant and uniform over their volume and equal to 60 J/(m.s. C) and 30 J/(m.s. C), respectively. As those simulations showed, placing the chip in the anterior region, or increasing its size, reduced the computed temperature increase in the vitreous humor and the retina. The complexity of the relation between temperature increase and physical characteristics of the implanted electronics is not limited to their position or size; for example, it can also involve the power distribution characteristics and material properties of biocompatible materials used for insulating the chip. To complement the study in [19], here we show as an example the effect on the temperature increase in the eye of the thermal conductivity K of the insulation surrounding the microchip. Four cases have been considered, representing different constant K or graded K values for the chip insulation.

Figure 15.6a gives a 3D view of the stimulator chip implanted in the eyeball. Figure 15.6b shows a horizontal cross section of the same model (at 0.25 mm resolution), with the chip located in the middle of the vitreous humor. Figure 15.6b is a tissue-rich model, with different colors indicating different