Channel – Rhodopsin
Based Vision Prosthesis Model
Elena Kaye
Maryam Etezadi – Amoli
Sharareh Noorbaloochi
Khuram Zia
Psychology 221
Winter, 2007
Introduction
Motivation
Many diseases, such as retinitis
pigmentosa and age-related macular degeneration, cause blindness by damaging
the photoreceptors, but leave the retinal ganglion cells unharmed. Retinitis pigmentosa involves the
degeneration of photoreceptors and affects 70,000 people in the
Current retinal prostheses can be divided into two categories: epiretinal and subretinal.
Figure 1: Epiretinal and
subretinal implants (from Zrenner, 2002)
Subretinal devices consist of light-sensitive micro-photodiodes that are implanted between the pigment epithelium layer and the outer layer of the retina where the photoreceptors are normally located. These devices replace the rods and cones with photodiodes. Light falling on the photodiodes activates the attached electrodes, which then activate the remaining retinal cells. An advantage of subretinal implants is that by replacing only the damaged photoreceptors, the rest of the retinal pathway and natural neural network of the eye is preserved, thus maintaining proper spatial encoding [11].
Epiretinal devices are implanted on the top layer of the retina, where the retinal ganglion cells are located. These devices receive electrical signals from a distant camera and processing unit and directly stimulate the ganglion cells that form the optic nerve. Epiretinal devices bypass the processing network of the retina completely, and thus the camera and processing system must do the proper image encoding so that the signal transmitted to the optic nerve will be properly decoded by the visual cortex [11].
The purpose of this project is to investigate a totally different type of retinal prosthesis based on channelrhodopsin.
Rhodopsin
Channelrhodopsin-2 (ChR2) is a photopigment that can be embedded in the membranes of specific neurons using viral delivery. ChR2 induces light-gated channels, so once the pigment is in place, light pulses can be used to activate these channels, triggering the neurons to fire on a millisecond-timescale [2]. Bi et al. took this further by embedding rhodopsin in the membranes of retinal ganglion cells of mice. By shining light on the cells, they were able to induce the cells to fire and transmit a signal to the visual cortex. Thus ChR2 introduces a new paradigm in visual prostheses, where surviving retinal ganglion cells serve as the replacement for damaged photoreceptors [1].
Theoretically, with the proper sequence of light pulses, ganglion cells can be triggered to mimic their natural firing patterns, thus inducing vision. The purpose of this project is to investigate the different aspects and challenges involved in using ChR2 as a visual prosthesis.
Receptive Fields
The pathway in the retina from the rods and cones to the ganglion cells involves complex processing from many different cell types. Since the ChR2 prosthesis method involves bypassing this processing system and directly stimulating the ganglion cells (similar to epiretinal devices), we must first understand the nature of this processing so that we can hope to accurately mimic it. Figure 2 from [8] shows the many layers involved in processing the rod and cone outputs.
Figure 2. Multilayer cell.
This complexity can be modeled using the concept of a receptive field. The receptive field of a ganglion cell is the region in the retina where light influences the response of that ganglion cell. There are several different types of receptive field architectures, but in this project, we will consider only the center-surround architecture. There are two classes of center-surround receptive fields: on-center, off surround, and off-center, on-surround. Cells modeled by an on-center receptive field respond by increasing their firing rate above the baseline spontaneous firing rate when light falls on the center of their receptive field. Light falling on the surround area of the field causes a decrease from the baseline spontaneous firing rate. Off-center cells respond in the opposite way: light falling on the center decreases the firing rate from baseline, and light falling on the surround increases the rate. [10]
A common way to model the center-on receptive field is by using a function created from the difference of two Gaussians:
where σcen is the standard deviation of the Gaussian representing the receptive field center and σsur is the standard deviation of the Gaussian representing the surround.
Figure 3 shows the creation of an on-center receptive field using this model.
Figure 3. Difference of Gaussians model.
With the receptive field concept, we can model the ganglion cell response using a linear relationship. The change in firing rate from baseline (Δr) can be found using the following relation:
where G(x,y) represents the receptive field and I(x,y) represents the stimulus (image) intensity at position (x,y). Thus finding the response of a ganglion cell (the change in firing rate from baseline) to a contrast pattern involves taking a weighted sum of the intensity values, where the weighting is determined by the receptive field of the ganglion cell.
Methods
Block diagram of overall
system
Block Diagram of the
Processing Steps
Figure 4. Block
diagram of the processing algorit
Description of components in processing scheme
Stimulus
The stimulus for our system is a still input image of size 256 x 256 pixels. We are assuming that the entire input image spans 5 degrees of visual angle, centered on the fovea. Using the conversion factor of 1 degree = 300 um, each pixel in image space corresponds to 0.0195 degrees of visual angle or 5.86 um on the retina.
Linear
The linear portion of our system involves determining the change in spike rate for the ganglion cells due to the input image. As previously described, this involves doing an element-wise multiplication of the receptive field with patches of the image. With a circularly-symmetric receptive field, as we are using, this operation is equivalent to convolving the input image with the receptive field function. Since convolution is easily implemented in Matlab using the conv2 command, viewing this calculation as convolution greatly simplifies this step of the procedure. We used the ‘same’ flag for the conv2 operation so that our resulting image would not change in size, but this choice means that the edges of the resulting image contain some artifacts that do not directly correspond to the desired operation of pointwise-multiplication of the receptive field with individual patches of the image.
Since receptive fields increase in size with distance from the fovea, we convolved the input image with Gaussians of many different sigma values so that pairs of images could later be chosen according to the desired size of the receptive field center and surround. Figure 5 shows the result of convolving the input image with Gaussians representing the center and surround responses, then taking the difference of the resulting images. The intensity of each pixel in the difference image indicates the change in spike rate for the ganglion cell whose receptive field is centered at that pixel.
Nonlinear
In order to get a reasonable spike rate value, we must perform one more processing step on the difference image. This processing step ensures that the firing rate of the ganglion cell does not drop below zero or exceed its maximum firing rate. The function we chose is based on figure 5b of Chichilnisky’s paper [3]. We first take each pixel value in the difference image and scale it to lie in the range [-0.2, 0.2], and then apply the following function (C(x) = standard normal cumulative distribution function):
The function takes the following form:
Processing the difference image resulting from the convolution with this function gives an image representing the average spike rate.
Sampling
Once we have the spike rate images of ganglion cells for different receptive field sizes, we need to sample them according to the position of the ganglion cell with respect to the center of the fovea. The dendritic field size of ganglion cells and their corresponding receptive field size increases with radial distance from the fovea (eccentricity). Hence we sample the images in a circular fashion where each circle is taken from a spike rate image for a specific receptive field size. As we increase the radius of the circle, the samples are taken from a larger receptive field. The sampling idea is depicted in Figure 6.
Figure 6: The
In Matlab this is done by using polar coordinates, where the pixel coordinates are described as x = rcos(θ) and y = rsin(θ). Since the coordinates are integer numbers, the x and y values are rounded down by using the FLOOR command. The sampling algorithm has two inputs:
- The number of circular levels
- The number of samples per circular level.
In our implementation, the images were uniformly sampled radially according to the number of sampling levels. A uniform angular sampling was adopted. Figure 7 shows the superimposed sampling pattern of all the spike rates for 7 circular levels and 20 samples per circle.
Figure 7: Radial sampling patterns. The samples on each circle will be taken from a different convolved image.
Mapping to Ganglion
Once we have the sampled average spike rates, we will need to find the coordinates of the ganglion cells that we will be stimulating with the optical stimulation device. There are two important considerations that we should take into account: First, there are no ganglion cells in the fovea and second, the ganglion cells are densely packed in multiple layers near the fovea. In the densely packed region, individual cell activation would be very difficult for the optical device because no single cell is capable of absorbing a large fraction of the incident light and effectively blocking the adjacent cells. For these two reasons, the optical stimulation technology should avoid the multilayer region in the center of the fovea. This region spans 3 mm in radius around the fovea [6].
In order to avoid these regions, we magnify the 5 degree (0.75 mm in radius) visual field to a region 20 mm in radius around the fovea. Since we need to avoid the multilayer region, we do not even bother sampling the points that will be mapped to this region. An alternative would have been to sample everywhere, but then discard any points that fall in the multilayer region. The mapping idea is depicted in Figure8.
Figure 8. Mapping.
Another fact to consider is that ganglion cell density drops exponentially as we move away from the multilayered region (Figure 9 C and D).
Figure 9. The Ganglion cell density plots [6]
In our mapping scheme, we will mimic this density distribution by using concentric circles whose radii increase as powers of 2. This results in a distribution of mapped points that is denser near the edge of the multilayer region, and sparser as we move outwards. This is shown in Figure 10.
Figure 10. The
radius of the mapped cell coordinates increase with powers of 2. The ganglion
cell coordinates are in mm.
Poisson
The output of the nonlinear processing step gives the average firing rate of the ganglion cells in spikes per second. This rate becomes the input parameter (λ) for a Poisson generator. Poisson processes are often used to model neuron firing patterns. The output of the Poisson generator is a sequence that indicates the firing pattern we need to induce on the ganglion cell in order to achieve the desired visual response to our input image. The code for the Poisson process generates spikes based on exponentially distributed interarrival times. The neuron’s refractory period of 5 ms is taken into account.
Materials
General Considerations
In this section potential materials to implement our method will be described. Our goal was to design a system that would deliver light stimuli to the ganglion cells of the retina
according to the method we developed. Various constraints were analyzed and their influence on the choice of particular devices and the design of a system as a whole was considered. The constraints were divided into three groups.
First group of constraints was related to the properties of light-evoked voltage response of ChR2-expressing neurons described in [1]. Figure11 shows the voltage responses of these neurons. The experiments showed that the threshold light intensity required for producing responses in ChR2-expressing retinas was near 1014 – 1015 photons cm-2 s-1 [1]. In addition to intensity limitations, it was found that the ganglion cells expressing ChR-2 were most sensitive to the wavelength of 460nm. The spectral sensitivity is shown in Figure 12. Given these two findings, the devices suitable for our purpose had to satisfy these spectral and intensity requirements.
The second group of constraints is imposed by the dimensions of the ganglion cells and retina, and cells density distribution. The size of the human ganglion cell soma is 4-24ms on average. To maximize the effectiveness of the vision restoration device, ideally each of the cells should be stimulated individually. Therefore it is desirable for the device to produce the light beam diameter approaching the diameter of the cell. To target each cell the number of the light sources should equal the number of the ganglion cells. Since there is about a million of the ganglion cells in the human retina, targeting each cell doesn’t appear possible at the moment. What does seem possible is distributing the light beams shining on the retina in accordance to the density distribution of the cells: decreasing from fovea to periphery of the retina. Due to complex multi layered layout of ganglion cells in the foveocentric region (of diameter ~6mm [6]) the light beams produced by the device will have to be diverged properly to avoid excitation of the cells in this region.
Finally, the ergonomics considerations were taken into account. The ideal prosthesis device has to be small and light. Lower power consumption is desirable as the space to accommodate power supply will