Report 2

# Purpose

To model some aspect of the vertebrate visual pathway onto the SpiNNaker system a firm understanding of the human visual system must first be grasped. This paper will provide a clear understanding of the human visual system. An important question must be answered: is one trying to create a plausible scheme which can handle coding neurons, be they biological, or abstract, or is one trying to understand how the human mind codes its neurons. In the former case, one may be led astray by finding a perfectly acceptable coding scheme which has nothing to do with the human brain, however, in the latter case, one may get lost in the sea of incomplete information on the human brain. In order to be able to make such a complicated decision, it would be nice to have a comparison of the two views, which is what this paper will set out to achieve.

# Retina

Light is concentrated from the eye and passes across these layers (from left to right) to hit the photoreceptors (right layer). This elicits chemical transformation mediating a propagation of signal to the bipolar and horizontal cells (middle yellow layer). The signal is then propagated to the amacrine and ganglion cells. (Modified from a drawing by Ramón y Cajal.)

The retina is primary location of light processing by the rods and the cones. It has 6 groups of neurons, roughly 55 types of neurons and 10 layers, from outermost to innermost, the important 3 are:

1. Photoreceptor layer - Rods / Cones
2. Inner nuclear layer Bipolar Cells,Horizontal Cells,Amacrine Cells
3. Ganglion cell layer - Ganglion Cells (gives rise to optic nerve fibers).

Although all three layers are composed of neurons, only the amacrine cells and the ganglion cells fire action potentials, the photoreceptors, bipolar cells and horizontal cells generate local graded potentials. The process of generating graded potentials will be discussed in the next section

## Photoreceptors

The photoreceptor has three segments: an outer segment, and inner segment, and a synaptic ending.

1. The outer segment absorbs light by visual pigments which are arranged into disks.
2. The inner segment contains the nucleus, ion pumps, transporters, ribosomes, mitochondria, and endoplasmic reticulum
3. the synaptic terminal releases glutamate and recieves synaptic inputs.

The process whereby light shining onto the retina is used to change a membrane potential, and generates local graded potentials, is called phototransduction and it proceeds as follows

1. Inactivated (in the dark) sodium ions move into the cell and depolarize it to about -40 mV (from -65 mV)
2. In the presence of light, opsin on the outer segment of the photoreceptor absorbs a photon
3. This leads to several intermediary steps, and the sodium gates are closed
4. In the absence of sodium the photoreceptor hyperpolarizess
5. Hyperpolarization ensures less relase of neurotransmitter glutamate

The inhibition of glutamate, which can either excite or inhibit postsynaptic bipolar cells, ensures that there are now a pool of bipolar cells that are either hyperpolarized or depolarized. It is interesting to note that the presence of light actually reduces the photoreceptors response rate. Also as a note, photoreceptors do not signal colour or light intensity, only the presence of light.

There are two types of photoreceptors; rods are found in the periphery of the retina and are primarily used at night, and they outnumber cones twenty to one, whereas cones are primarily found in the centre of the retina (fovea) and act to distinguish light and other features present under normal lighting conditions. As would be expected, there are three different types of cones; short cones react best to blue colours, medium cones react best to green colours, and long cones react best to red colours. Rod Photoreceptors on the other hand, exist in only one form, and they drive onle a single type of bipolar cell, and they furthermore synapse only to a special type of amacrine cell (AII).

## Amacrine, Horizontal and Bipolar Cells

Although the connections in the retina are complicated, they follow this general layout:

• Photoreceptors are connected to bipolar cells
• Horizontal cells connect photoreceptors
• Bipolar cells connect to ganglion cells
• Amacrine cells connect bipolar cells together

Bipolar cells receive their input from either rods or cones, but not both, and they are called rod bipolar cells, or cone bipolar cells, respectively. The mamallian retina has about 12 (Masland) different types of cone bipolar cells. It should be noted that photoreceptors are not dedicated to either rod bipolar cells or cone bipolar cells, instead they are tapped by a large number of rod bipolar and/or cone bipolar cells. Hyperpolarizing bipolar cells (ones which hyperpolarize with reduction of glutamate) have an off-centre receptive field (since shining a light on its receptive field causes it to hyperpolarize). Depolarizing bipolar cells (ones which depolarize with reduction of glutamate) have an on-centre receptive field (since shining a light on its receptive field causes it to depolarize). The h bipolar cells and the d bipolar cells are further broken down into subgroups, based on the frequency of information. Also, h bipolar cells and d bipolar cells are about equal in numbers, and, like amacrine cells, outnumber ganglion cells five to one.

Amacrine cells make inhibitory synapses on the axon terminals of bipolar cells, thus controlling their output to ganglion cells. Furthermore, amacrine cells outnumber horizontal cells four to ten times over, they make up 40 percent of all neurons in the inner nucleus layer and they display the most diversity of the retinal cells, existing in around 30 forms (Masland). Amacrine cells also seem to account for the corelated firing amongst ganglion cells, and it has been suggested (Masland) that the amacrine cells are responsible for distinguishing object motion from background motion. Amacrine cell types play much more specific roles then horizontal cells (the other intermediary retinal cell) since they connect certain types of bipolar cells (for example the ON signal of a rod H bipolar cell) to a certain type of ganglion cell.

Horizontal cells are like H bipolar cells in that they hyperpolarize in the presence of glutamate, and they are the least diverse of the retinal cells existing in one of only 2 (Masland) forms. When this happens, horizontal cells reduce the release of GABA, which has an inhibitory affect on the photoreceptors. This reduction of inhibition leads to a depolarization of the photoreceptors. We therefore have the following negative feedback

Illumination${\displaystyle \to }$photoreceptor hyperpolarization${\displaystyle \to }$horizontal cell hyperpolarization${\displaystyle \to }$photoreceptor depolarization

One proposed theory for facilitation by the horizontal cells proceeds as follows. Assume we have 11 photoreceptors, one H bipolar cell, and one horizontal cell. All ten photoreceptors connect to the horizontal cell, and the middle photoreceptor (${\displaystyle P_{m}}$) connects to the bipolar cell. The surrounding cells, which represent the outer receptive field, will be designated ${\displaystyle P_{o}}$ Then we can explain an off-centre arrangement as follows. If light is shown onto the ${\displaystyle P_{m}}$ then

1. ${\displaystyle P_{m}}$ is activated by light and therefore hyperpolarizes
2. ${\displaystyle P_{m}}$ reduces release of glutamate
3. Reduction of glutamate hyperpolarizes the H bipolar cell
4. Reduction of glutamate hyperpolarizes the horizontal cell and it reduces release of GABA
5. Since ${\displaystyle P_{o}}$is still releasing glutamate, reduction in GABA is marginal

If the light is shown onto the surrounding area then

1. ${\displaystyle P_{o}}$ is activated and therefore hyperpolarizes
2. ${\displaystyle P_{o}}$ reduce release of glutamate
3. Reduction of glutamate hyperpolarizes the horizontal cell
4. Horizontal cell reduces release of GABA
5. Reduction of GABA depolarizes photoreceptors
6. ${\displaystyle P_{o}}$ not affected since they are strongly being hyperpolarized by activation
7. ${\displaystyle P_{m}}$ is affected and therefore depolarizes
8. ${\displaystyle P_{m}}$ releases glutamate
9. H Bipolar cell is depolarized

To explain diffuse light, then we consider both cases together, and as it turns out, the two effects cancel each other out, and we get little to no affects

## Ganglion Cells

The left receptive field of the ganglion cell shows that it will be activated if the light is concentrated on its center, and it will be inhibited by light shining on its outer receptive field. The right image show the opposite case

The last layer in the retina, which collects to form the optic nerve is the ganglion cell layer. There are about 12 (Masland) different types of ganglion cells, and a total of 100 million photoreceptors converge to only 1 million of them, therefore, a good deal of encoding has taken place. When one looks at the receptive field of a ganglion cell, the area of the retina from which a ganglion cell’s activity can be influenced by light, it becomes apparent that it is more sensitive to differences within the receptive field than light intensity. On-centre ganglion cells will become excited if light is shone onto the centre of their receptive fields, and likewise off-centre ganglion cells will become excited when light is shone onto the outside of their receptive fields.

Depolarizing on centre cone bipolar cells connect with corresponding on centre ganglion cells. Also, hyperpolarizing off centre cone bipolar cells connect with corresponding off centre ganglion cells. Consequently, a change in membrane potential of the bipolar cell, causes a change in the membrane potential of its ganglion cell in the same direction. Surprisingly, rods and cones of the same area of the retina, supply the same ganglion cell but by different means. The rods generally connect onto rod bipolar cells, which then connect to amacrine cells, which finally connect to the ganglion cells. Although all ganglion cells recieve input from cone bipolar cells, most of their inputs come from amacrine cells (50-75%)

The ganglion cells can be loosely grouped into P and M categories. The P ganglion cells project to the four dorsal layers of the LGN, and they have small receptive field centres, high spatial resolution, are sensitive to colour, and provide information about fine detail at high contrast. The M ganglion cells project to the larger cells in the two ventral layers of the LGN, have larger receptive fields, are more sensitive to small differences in contrast and to movement, they fire at higher frequencies, and conduct impulses more rapidly along their larger diameter axons.

Amazingly, the ganglion cells neglect almost ninety-nine percent of the information presented to them by the photoreceptors. They do not convey absolute levels of illumination, because they behave the same at different background levels of light, it appears that they measure differences between their receptive fields by comparing the degree of illumination between the centre and the surround of their receptive fields.

# Lateral Geniculate Nucleus

Green represents input from the left eye, and red represents input from the right eye. It is interesting to note that the layers don't completely interweave, one proposed reason is the different functions of the layers.

The optic nerve projects onto a structure called the Lateral Geniculate Nucleus. The LGN is structured such that it has a left and a right hemisphere, within which there are six distinct layers of the LGN. The receptive fields of adjacent neurons overlap since neighbouring regions of the retina make connections with neighbouring geniculate cells. This overlap means that the receptive field of the LGN is even more scrutinous when it comes to diffuse light than is the ganglion receptive field. Therefore, whereas the ganglion receptive field does somewhat respond to diffuse light, the LGN receptive field is very poor at responding to diffuse light.

Historically the layers are numbered from the bottom up, and layers 1 and 2 have the larger, and much faster cells. These M cells work much faster, however, they do not process as much information. The P cells on the other hand, which are found in layers 3 to 6, are much smaller and slower, but come with the added advantage that they can do complex calculations such as colour detection. Between each of the M and P layers lies a zone of very small cells, the K cells. Layers 2, 3 and 5 receive their inputs from the ipsilateral eye (w.r.t the left or right hemisphere) whereas layers 1, 4 and 6 receive their inputs from the contralateral eye (w.r.t. the left or the right hemisphere). There are roughly 1 million cells in the LGN, however, the optic nerve fibres each connect to multiple LGN cells, as opposed to a simple one to one mapping. Not only are the cells topographically ordered (neighbouring photoreceptors project to neighbouring cells) but they are retinotopically registered along the different levels. Therefore, if a sample rod is taken from layer 1 to layer 6, then (for each eye) those appropriate cells will have the same receptive fields.

# Visual Cortex

One proposed situation for simple cells. The three overlapping cells from the LGN are only activated when a bar of a certain size and orientation hits that particular receptive field

The LGN eventually projects onto one of the six layers of the primary visual cortex (aka V1), but mostly onto layer 4. From here information is passed onto V2, V4 and MT, and finally Inferotemporal and Parietal 7. It is important to note that both hemispheres of the visual cortex are symmetric, and they simply receive their inputs from the respective LGN hemisphere. As is the case for the other areas of the cortex, the visual cortex has 6 distinct layers. The visual cortex is much more complicated than the LGN or the retina because it has many more cells, many more horizontal connections, and although it has all of its inputs feeding in from the LGN, it is difficult to predict where that information streams out to, therefore it has, as present, an unknown bandwidth. It is known, however, that only twenty percent of the neurons are intrinsic (accept incoming info?), the other eighty percent project to other parts of the brain, possibly within the neocortex. Conservative estimates place the number of different types of neurons in the cortex at around 1000 (Masland)

## Simple Cells & Complex Cells

There are three subgroups of cells within the cortex: Simple cells, complex cells, and complex cells with end inhibition. The simple cells respond only to a bar of a certain size, and oriented at a certain angle. The complex cells on the other hand can detect edges of any size and/or orientation. Complex cells can also detect corners, in which case we label them with end inhibition. It may be the case that an array of simple cells could connect to a complex cell to give rise to its behaviour. To illustrate this point, consider the case where a complex cell has a receptive field of that of 100 simple cells (10x10 plane) and for each 'cell' it has four simple cells oriented at 90 degrees to each other. Then with 400 simple cells, the complex cells can react to a whole host of bars, in one of four positions, anywhere along its receptive field. If we consider a complex cell with 3600 simple cells, then it can distinguish bars of any orientation every ten degrees. Throughout the entire mammalian visual stream, one will find that there is a great deal of hierarchies and precise stratification, the visual cortex is no exception.

Proposed diagrom for complex cells, through use of simple cells. As is clear, a complex cell can distinguish between edges anywhere on its visual field, and generally of any size. By extending the same arguement, one can show how the complex cells can detect edges.

## Ocular Dominance Columns

An interesting formation within the visual cortex is that of Ocular Dominance Columns (ODCs). Horizontally along the layers of the cortex, there exist strips which are entirely controlled by one eye or the other, but not both. It has been suggested that activity dependent competition causes the formation of ocular dominance columns. The columns are 250 to 500 ${\displaystyle \mu m}$ wide, and taking the soma to be from 4 to 100 ${\displaystyle \mu m}$ wide, that means that every column has about 5 to 75 neurons.

## Orientation Columns

Not suprisingly, if one samples the cortex perpindicular to its surface, one we encounter similar orientation preferences amongst the neurons. The columns here are much more percise than ODCs as these are on average only 20 to 50 ${\displaystyle \mu m}$ wide, which means that there are less than a dozen neurons in each column. When the a map of the OCs are superimposed with a map of the ODCs it can be seen that where the ODCs meet, OCs cross perpindicular to the two ODCs. This makes sense since the neurons for both eyes in that area should have the same orientation preference.

# Visual pathway

Because of the complex nature of the visual system, and the burden of pure parallel processing, it is quite difficult to trace the exact pathways in the visual system.

# Miscl

## Spike Time Dependent Plasticity

Simply the plasticity that arises from the precise timing of the pre and post synaptic potential, generally following this pattern

1. Pre-synaptic neuron fires (Cue Millenium Falcon blasters)
2. Post-synaptic neuron fires shortly afterwards (cue pinball machine)

The short window which the post-synaptic neuron has to wait before firing probably has to do with the propogation delay of the pre-synaptic neuron. This has been believed to exist ever since Hebb first proposed it in 1949, and the first experiments of the timing of pre and postsynaptic firings was done by Markran in 1994 .

## Rate based plasticity

Rate based plasticity does not contradict STDP, it can in fact work alongside STDP, however, it proposes that the firing rate of neurons, and not just their percise timing window, also contributes towards neuronal plasticity. Therefore, the faster a pre-synaptic neuron fires off towards its target, the more excited it will become. One problem presented by this model, is its lack of biological plausability. In the human visual system, images are percieved within 100 msec, and there are a minimum of 10 stages for the neurons to propagate, and each neuron takes an average of 10 msec. Using this information it is not hard to see that each neuron will only be able to fire once. This information, although does not directly contradict rate based plasticity, it does somewhat undermine it.

## Rate Coding

With rate coding, the rate of fire is itself a form of information, for example the following case could be one interpretation:

• 1 spike each second = wind brushing against hair
• 2 spikes each second = mosquito on skin
• 3 spikes each second = girl slapping you in the face
• 4 spikes each second = having arm jammed in a revolving door

The problem with this scheme is the biological constraint of 100 spikes per second imposed earlier. Furthermore, any computer scientist will be quick to point out that this is a simple unary coding system which poses no compression whatsoever. One could argue that computation continues even after the stimulus has been removed, and the fact that only ten percent of the brains neurons are firing at any given time implies that the other neurons may be 'dormant' processing the previous stimuli

## Feed Forward Arguements

There are a few reasons why people would support feed forward architectures

1. Ease of design
2. Less energy consumption
3. Time constraints (especially with the visual stream)

The arguements against feed forward only systems focus on the fact that the human brain clearly has feed back connections, as is evident in the visual cortex feeding back into the LGN.

Sophisticated behavioral responses can often be generated only a few hundred milli seconds after a change in the environment. Since neurons can only generate spikes at about one every 5 milli seconds, even when firing maximally, Feldman concluded that this puts a limit of roughly 100 computational steps between input and output.

## Feed Back Arguements

It is clearly obvious that the human brain has feed back connections, therefore, scientists have tried to model them, as is the case with back propogation networks such as Hoppfield. Recurrent networks make coding schemes much more complex, and computationally less tractable. One arguement is that feeback is constrained to a purely local basis, and that the feedback is used for learning more than signal propogation, which then would not slow down signal transmission time.

## Temporal Order Coding

Temporal coding tries to include compression by doing way with the arcane unary system imposed by rate coding. The basic premise is that neurons will become sensitive to the timing of the incoming spikes, such that we have the following cases:

• A>B>C means the person is hungry
• B>A>C means the person is sleepy
• C>A>B means the person is horny
• C>B>A means the person is looking around the house for the his keys, but little does he know, they are in his hands.

and all of this information was transmitted in only one time quantum (10 msec). The promising aspect of this scheme is that it provides one possible mechanism for memories, since with 10 billion neurons, one could have a near infinite memory capacity with this scheme. Unfortunately, there is very little biological evidence to substantiate this scheme, there have not been enough biophysical studies in the dependence of order amongst spiking neurons.

## Polychronization

Polychronization is another very promising coding scheme which could explain the near infinite memory capacity of the brain, however, lacks much biological support. This scheme purports that groups of neurons that arrive at the same time (at the target neuron) each convery meaning. It is biologically plausable since it relies on the different propogation delays of nerons to ensure asynchrony, however, there is very little evidence to suggest that in vivo neurons polychronize. There is, however, evidence that in vivo neurons do sometimes work in groups, but as of yet, it is not known whether this is an inherent condition of the system, or a stochastic manifestation...in an otherwise unjust world.

## Dendritic Coding

Read the paper nad comment on this

## Lateral Inhibition

This happens a lot in the retina and the geniculocortical pathway. Read some papers and comment on this

# Occular Dominance Columns

In the cortex, and to a certain degree in the LGN there exists an interworking of areas of localization. These are either controlled by the left eye or the right, however, never by both. Many models have been presented for the formation of these columns, most notably by Elliot and Shadbolt. Read some more technical info on this.

# References

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Masland, Richard H (2001). "The Fundamental Plan of the Retina". Nature Neuroscience 4 (9).

Masland, Richard H (23 May 2003). "The Retina's Fancy Tricks". Nature 423: 387–388.

Masland, Richard H (2004). "Neuronal Cell Types". Current Biology 14: R497–R500.

DeVries, Steven H (December 2000). "Bipolar Cells Use Kainate and AMPA Receptors to Filter Visual Information into Separate Channels". Neuron 28: 847–856.

Boycott, Brian; Wassle, Heinz (June 1999). "Parallel Proccessing in the Mammalian Retina". Ivestigative Opthalmology & Visual Science 40: 1313–1327.

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Becker, Suzanna (2005). "A Computational Principle for Hippocampal Learning adn Neurogenesis". Hippocampus 15: 722–738.

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Shors, Tracey J; David A Townsend, Mingrui Zhao, Yevgenia Kozorovitsky, Elizabeth Gould (2002). "Neurogenesis May Relate to Some but not all Types of Hippocampal-Dependent Learning". Hippocampus 12: 578–584. Cite uses deprecated parameter |coauthors= (help)

Aimone, James B; Janet Wiles, Fred H Gage (2006). "Potential Role for adult neurogenesis in the encoding of time in new memories". Nature Neuroscience 9 (6): 723–726. Cite uses deprecated parameter |coauthors= (help)