neural modelling of congenitally abnormal visual pathways

Neural Modelling of Congenitally Abnormal

Visual Pathways

Annabelle GeeT

HE

U N I V E RS

IT

Y

OF

ED I N B U

RG

H

Master of Science

Cognitive Science and Natural Language Processing

School of Informatics

University of Edinburgh

2014

Abstract

Albinism and achiasma are congenital conditions severely affecting the normal rout-

ing of input through the visual pathways. However, these conditions do not have the

profound deleterious effects on perception that would be expected from their impact

on visual pathway structure. Evidence in human experiments suggests that in both

conditions, these aberrant inputs are mapped onto the primary visual cortex (V1) in

superimposed visual hemifield representations. This leads to the hypothesis that in-

tracortical interactions drive the development of hemifield dominance-driven feature

preference maps, to make these representations available to be perceived relatively

normally. However, current experimental protocols limit the possibility of directly ob-

serving this putative arrangement. In this thesis, computational modelling based on

input-driven visual development was used to observe the likely map organization of

V1 in these conditions, using a two-eyed ocular dominance model of GCAL, a self-

organizing map-based model of the primary visual cortex. When the misrouting of

inputs was simulated in the model, the resulting receptive fields and orientation map

organization supported the theory that V1 rearranges into an interdigitating pattern

dominated by hemifield dominance columns.

i

Acknowledgements

I would like to express my sincere gratitude to my supervisor, Jim Bednar, for his

kind and encouraging guidance. Thanks also to Dr Michael Hoffmann from Otto von

Guericke University Magdeburg, whose research in albinism and achiasma in human

subjects provides the motivation for this modelling project, and whose visit to Edin-

burgh in April was highly informative and inspiring. Many thanks to Jean-Luc Stevens

and Philipp Rudiger, and to my fellow MSc students, Giacomo Spigler and Tobias Fis-

cher, all of whom have been extremely helpful during the project, providing advice as

well as technical help.

ii

Declaration

I declare that this thesis was composed by myself, that the work contained herein is

my own except where explicitly stated otherwise in the text, and that this work has not

been submitted for any other degree or professional qualification except as specified.

(Annabelle Gee)

iii

Table of Contents

1 Introduction and Background 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Biological Background . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Organization of the early visual system . . . . . . . . . . . . 2

1.2.2 The primary visual cortex . . . . . . . . . . . . . . . . . . . 3

1.2.3 Albinism and achiasma . . . . . . . . . . . . . . . . . . . . . 6

1.2.4 Limitations in research . . . . . . . . . . . . . . . . . . . . . 10

1.3 Computational Modelling of V1 . . . . . . . . . . . . . . . . . . . . 10

1.3.1 Modelling of V1 development . . . . . . . . . . . . . . . . . 10

1.3.2 Models of joint OR/OD development . . . . . . . . . . . . . 11

1.3.3 LISSOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4 Modelling aims and motivation . . . . . . . . . . . . . . . . . . . . . 12

2 Methodology 142.1 The GCAL model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.1 Architecture of GCAL . . . . . . . . . . . . . . . . . . . . . 14

2.1.2 An ocular dominance model of GCAL . . . . . . . . . . . . . 16

2.1.3 Input patterns . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Modelling misrouting using GCAL . . . . . . . . . . . . . . . . . . . 17

2.2.1 A model for both conditions . . . . . . . . . . . . . . . . . . 17

2.2.2 Changes to the input stream in model training . . . . . . . . . 19

2.2.3 Mirror reversal . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Results 223.1 Setting the control (normal) condition . . . . . . . . . . . . . . . . . 22

3.1.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1.2 Adding dimming and disparity . . . . . . . . . . . . . . . . . 22

iv

3.2 The misrouted model for albinism and achiasma . . . . . . . . . . . . 25

3.2.1 Orientation maps and receptive fields . . . . . . . . . . . . . 25

3.2.2 Ocular/Hemifield dominance map organization . . . . . . . . 27

3.2.3 Joint OR/OD relationship . . . . . . . . . . . . . . . . . . . 30

4 Discussion and Conclusion 324.1 Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.2 Limitations and future improvements . . . . . . . . . . . . . . . . . . 35

4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

Bibliography 39

v

Chapter 1

Introduction and Background

1.1 Introduction

Experimental neuroscience often lends itself to generate predictions of neural organi-

zation and function, but in many cases technological improvements and advances are

required before these hypotheses can be judged confirmed or rejected. Computational

approaches can help to bridge the gap and refine predictions made by theory, and pro-

vide suggestions for new avenues of investigation, by exploring the possible outcomes

of a hypothesis within the parameters of a model.

This project aims to explore the likely primary visual cortex (V1) organization arising

in the case of two congenital conditions that affect the routing of visual pathways at

the optic chiasm, albinism and achiasma.

Although experimental data exists for the functional outcomes of both conditions, the

structural organization at the level of cortical patterns is not currently observable by

the experimental means available, especially not in humans. However, the outcomes

of these conditions can be theoretically observed within computational models that

have been demonstrated to produce biologically realistic maps of V1 through self-

organization of neuron-like units, given a set of simulated visual inputs. Under a

paradigm uniting the two conditions in a single model, this project will set out to sim-

ulate the resulting abnormal organization using GCAL, a self-organizing map model

of V1 development.

This first chapter will cover background and related work, in two parts: firstly, the

biological background for visual processing will be covered, including an introduction

to the albinotic and achiasmatic conditions and their properties. Secondly, the com-

putational approach to primary visual cortex development that will be the basis for

1

Chapter 1. Introduction and Background 2

modelling these conditions will be addressed. In the second chapter, first the archi-

tecture of the GCAL model and its two-eyed version will be described, and then the

proposed method of simulating the albinotic/achiasmatic conditions. The third chapter

will cover results and observations from the simulations of the model, and the fourth

chapter will be dedicated to discussion.

1.2 Biological Background

1.2.1 Organization of the early visual system

The processing of sensory input is necessary aspect of mammalian survival, and for

humans vision in particular is of crucial importance. Input from the visual environ-

ment is received in the form of light at the photoreceptors present in the retina. The

visual field is the space available for visual perception by the eyes. Mammals with

forward-facing eyes, such as humans, receive a large part of the visual field in stereo.

This input is processed by retinal ganglion cells, which have centre-surround receptive

fields (ON-centre OFF-surround and vice versa), then projected to the lateral genicu-

late nucleus. From there, afferent projections carry the visual information to the oc-

cipital lobe into the first area of cortical processing, V1, and then on to higher cortical

areas such as V2 and MT. Before reaching the lateral geniculate nucleus, there is a

structure known as the optic chiasm, where optic fibres cross to partially project the

input from one eye to the other side of the brain; this crossing is referred to as decus-sation. In humans with normal visual pathways, the line of decussation conforms to

the vertical meridian that passes through the middle of the retina, through the fovea

(a small pit in the retina responsible for high-acuity central vision). This means that

the entire half of the visual field on one side of the line of decussation projects to the

opposite hemisphere of the brain.


Figure 1.1: Illustration of the visual pathway from the visual field and retina, through the

subcortical structures and to the primary visual cortex. Note the crossing at the optic

chiasm. Reproduced from Hannula et al. (2005).

Therefore, each hemispheric half of V1 receives input from the contralateral side of

the visual field, which is transmitted from both the temporal hemiretina (half-retina on

either side of the vertical meridian) of the ipsilateral eye and at the nasal hemiretina of

the contralateral eye. The projections from the ipsilateral temporal hemiretina do not

cross over at the optic chiasm, while those from the contralateral nasal retina do; the

left side of the brain therefore receives extremely similar input from two eyes for the

same side of the visual field, with some discrepancy owing to the horizontal distance

between the eyes (disparity). Integration of these dual inputs in V1 neurons enables

binocular vision.

Disruption to parts of the pathway may lead to abnormal input representations arriving

at the LGN and being transmitted to V1, such as in strabismus (misalignment of the

eyes), or in albinism and achiasma - which will be described in section 1.2.3.

1.2.2 The primary visual cortex

Area V1 is a region at the back of the occipital lobe in both hemispheres of the brain

serving as the first point of cortical processing of incoming visual information. Like


the rest of the neocortex this region is divided into 6 horizontal layers of neurons, with

the afferent inputs from the retina and RGCs relayed by the LGN terminating in layer

4.

All of the visual input originating from the retina is mapped onto area V1, covering the

entire visual field. This mapping is retinotopic, meaning that adjacent cells in V1 are

activated by adjacent cells on the retina. The mapping is true to the visual field except

for some global distortions, like magnification - most of the V1 area is dedicated to a

small area of the central visual field, the extent of the inhomogenous allocation being

dependent on the species (Sereno et al., 1995; Tootell et al., 1988).

The receptive fields of neurons correspond to the stimulus or set of stimuli that will

trigger their firing, which for vision was first described by Hubel and Wiesel as ”a

restricted area in the retina in which firing could be influenced by light” (Hubel and

Wiesel, 1959). This definition extended from the concept applied previously to gan-

glion cells, where receptive fields are either ON-surround or OFF-surround - denoting

a preference for light spots surrounded by dark, or vice versa.

Neurons in V1 can be classified as simple or complex depending on the structure of

their receptive fields: simple cells have receptive fields with distinct excitatory and

inhibitory regions (-ON and -OFF subregions), while in complex cells such regions

overlap, resulting in a phase invariance property (Hubel and Wiesel, 1962).

Unlike retinal ganglion cells (and lateral geniculate nucleus cells) visual cortical neu-

rons are also selective for additional dimensions of stimulus features, described below.

1.2.2.1 Selectivity for stimulus features

Cells in V1 show selectivity for certain stimulus features, including orientation, direc-

tion of movement, phase, and eye preference, among others. Because of its location

in the brain, V1 is readily accessible for optical imaging or electrophysiological ex-

perimentation in animals, and thus these various selectivities have been extensively

studied.

Orientation Preference. Selectivity for specific stimulus orientations was first dis-

covered by Hubel and Wiesel (Hubel and Wiesel, 1959) in a study of the receptive

fields of cat cortical neurons, by taking extracellular recordings of V1 cell responses to

a range of light stimuli projected on a screen. Cells were classified by their responses

to oriented gratings or bars, which will stimulate neurons with receptive fields whose

arrangement of excitatory and inhibitory subregions will correspond to the same ori-


Figure 1.2: Schematic of an orientation column. A recording electrode inserted verti-

cally will reveal neurons with the same orientation selectivity; at a tangential angle, the

selectivities will vary over the full range of orientation angles. Figure reproduced from

Purves et al. (2001)

entation in visual space. The orientation selectivity of a neuron depends on the shape

of its receptive field, for example, a cell with an elongated receptive field angled at 45

degrees with adjacent inhibitory and excitatory regions will respond most strongly to

a bar of light oriented by 45 degrees. The tuning curve for the response of a neuron

to different orientations can be described in terms of preference and selectivity: the

preference of a cell is the orientation to which it will respond maximally; its selectivity

is the rate at which its response to other orientations drops (Blasdel, 1992b).

Neurons of all orientation selectivities group together into orientation columns (Fig-

ure 1.2), perpendicular to the surface of the brain. If an electrode is inserted into an

orientation column parallel to the cortical surface, and the receptive fields recorded in

sequence, the full range of orientation preferences will be exhibited.

The topographic arrangement of orientation columns in V1 can be visualized as an ori-

entation map (Figure 1.3), in which different colours represent preference according to

the histogram. Some features of orientation maps occur across species: iso-orientation

domains are regions of the same colour, which tend to occur periodically across the

orientation map. These domains also tend to arrange around a singularity, in features

known as pinwheels (Bonhoeffer et al., 1991).

Ocular dominance. Hubel and Wiesel also demonstrated the existence of ocular

dominance columns, in monkeys (Hubel and Wiesel, 1969). V1 neurons also show

selectivity for whether a stimulus arrives from the ipsilateral or the contralateral eye.

Histological staining with radiographic methods reveals a repeating pattern of regu-


Figure 1.3: An orientation map measured from the macaque visual cortex. Colour

patches represent neurons with similar orientation preferences. Figure reproduced from

Blasdel et al. (1986).

larly alternating, fingerprint-like bands (Figure 1.4). Most neurons are more selective

for inputs arriving from one eye (monocular) while some are less selective and respond

to input presented to both eyes (binocular) - the latter tend to fall between the stripes

of ocular dominance.

The spacing and width between bands depends on the species, and may even vary be-

tween individuals; in fact some species do not exhibit ocular dominance columns at

all. Whether ocular dominance columns play a functional role in the cortex or arise as

a non-functional by-product of cortical development is still a matter of debate.

Orientation maps and ocular dominance maps share certain joint features in animals,

as revealed by experimental observation. The boundaries of ocular dominance columns

tend to approach iso-orientation region fractures at an orthogonal angle. In addition,

pinwheel centers tend to be located in the midline of ocular dominance columns ( 80%)

with the remainder generally being located at the boundary (Bartfeld and Grinvald,

1992; Obermayer and Blasdel, 1993).

1.2.3 Albinism and achiasma

1.2.3.1 Albinism

Albinism is a congenital condition resulting in a deficit of melanin synthesis, affecting

one in 17,000 people in the UK. There are cutaneous (affecting the skin), oculocuta-

neous (skin and eyes) and ocular variants of albinism; the latter two impact on visual


Figure 1.4: Ocular dominance bands in macaque monkey revealed by injection of triti-

ated proline tracer in one eye. Reproduced from Hubel et al. (1978).

function in several ways. These types of albinos commonly experience symptoms such

as reduced binocular vision, reduced acuity, nystagmus, and foveal hypoplasia (a less

pronounced fovea). Ocular albinism tends to occur more in the male population (Na-

tional Health Service, 2014).

One particular feature of this condition in all mammals is the excessive crossing at the

optic chiasm of nerve fibres carrying visual information (Lund, 1965). The physiolog-

ical consequences of this misrouting vary depending on the species under considera-

tion. Some albino ferrets (Akerman et al., 2003; Huang and Guillery, 1985) and some

Siamese cats (Weber et al., 1978; Hubel and Wiesel, 1971) show reordering of the

geniculostriate projections, so that the aberrant projections terminate in their own area

of V1 adjacent to the one receiving normal inputs (the ’Boston’ pattern (Shatz, 1977)).

An alternative pattern that may emerge is one of suppression of the incongruous cor-

tical inputs (’Midwestern’ pattern), found in other Siamese cats (Kaas and Guillery,

1973) and albino ferrets (Huang and Guillery, 1985), and most studied hypopigmented

minks (Guillery et al., 1979).

There is another type of pattern, not seen in these species. Guillery et al. (1984) investi-

gated the visual pathways of an albino green monkey; electrophysiological recordings

of receptive fields revealed no apparent suppression of the abnormal inputs, instead

finding overlapping superimposed mirror-image representations of visual field input.

Autoradiographic methods (using 3-H proline labelling) showed a lack of ocular pref-

erence column formation in the affected area but normal columns in the peripheral


visual field areas (where no aberrant inputs terminate). Although hemifield dominance

columns would not appear in staining for ocular preference staining, electrophysiology

revealed segregation between normal and abnormal afferent inputs, with virtually no

recording sites activated by both hemifields. This pattern is referred to as True Albino.

In human albinos, experiments have also demonstrated no geniculostriate reordering or

suppression of the erroneously routed inputs, as determined by studying receptive field

locations using fMRI. Instead, the aberrant input from the other hemifield of vision ar-

rives at V1 superimposed over the normal representation (Hoffmann et al., 2003), as in

the 1984 green monkey study. Albino humans therefore also express the True Albino

pattern.

1.2.3.2 Achiasma

Achiasma - also referred as non-decussating retino-fugal fibre syndrome in the litera-

ture (Apkarian et al., 1994, 1995) is a rare condition in which the nerve fibres fail to de-

cussate at the optic chiasm, resulting in the afferent fibres from each hemiretina of the

same eye projecting to the ipsilateral side of the visual cortex.

Figure 1.5: Schematic of the aberrant

wiring in achiasma. Reproduced from

Sinha and Meng (2012).

Achiasma in humans generally occurs in

isolation, usually signalled by the pres-

ence of see-saw nystagmus (Korff et al.,

2003), but can sometimes occur as part of

the VACTERL association, a condition

which affects multiple systems including

the heart, the digestive system, the renal

system, and vertebral and limb forma-

tion (Prakash et al., 2010). Again, how-

ever, despite the gross misrouting of vi-

sual inputs, achiasmatic individuals have

relatively normal visual function (Victor

et al., 2000).

The misrouting characterized in achi-

asma can be thought of as counterpart to

albinism, as instead of excessive decus-

sation there is none - resulting in the same mirror-reversed hemifield overlap of repre-

sentations described above, but in the other (ipsilateral) cerebral hemisphere. Evidence

for the projections being conserved beyond the LGN (like those of the True Albino pat-


Figure 1.6: Illustration of the retinal inputs to V1 cortices in the normal, albino and the

achiasmatic brains. Reproduced from Apkarian et al. (1999).

tern) has been found in the only animal model (the Belgian sheepdog) (Williams et al.,

1994).

Therefore in achiasma, the end result of the decussation(for the most part) can be seen

as counterpart to albinism, as instead of excessive decussation there is none - resulting

in the same mirror-reversed hemifield overlap of representations described above, but

in the other (ipsilateral) cerebral hemisphere; uncorrelated inputs arrive at V1 neurons,

as illustrated in Figure 1.5. In the case of achiasma, neuroimaging studies such as

fMRI-based hemifield mapping in humans has demonstrated that the aberrantly pro-

jected portion of visual field is retinotopically overlaid onto the normal representation

in a mirror-symmetric manner (Davies-Thompson et al., 2012). In addition, popula-

tion receptive field mapping has demonstrated bilateral pRFs in the V1 of achiasmatic

(pRFs respond to inputs from both visual hemifields, when in a cortex receiving con-

gruous inputs from one visual hemifield it would be unilateral) (Sinha and Meng, 2012;

Hoffmann et al., 2012).

Therefore, the erroneous projections supply the visual cortex with conflicting informa-

tion from different visual hemifields, leading to a similar situation as seen in a large

non-peripheral portion of the V1 region in the True Albino pattern ( Figure 1.6). As

a result, similar questions are raised and not yet fully answered in achiasma as in al-

binism; how does V1 organization change in response to the misrouting?


1.2.4 Limitations in research

In animal data, most species studied did not exhibit the True Albino pattern seen in

humans; the Guillery et al. (1984) study remains the only insight into possible intra-

cortical arrangements in the face of albinotic misrouting, but not with direct visual

observation. Regarding achiasma the Williams et al. (1994) study did not extend to the

organization in V1.

In addition to the limited animal data for the True Albino pattern and achiasma, the

invasive nature of experimental techniques available for use in animals such as cats

and monkeys means that there is a lack of human data on V1 organization as a conse-

quence of either of these conditions, and the only study to date on an individual mon-

key exhibiting the True Albino pattern was subject to experimental limitations when it

came to showing histological evidence of hemifield dominance columns. Some fMRI-

based studies in humans allow researchers to establish the findings described earlier,

but imaging resolution is not currently high enough to directly observe the pattern of

organization arising from these conditions.

Therefore, computational approaches may serve as a useful way to predict V1 organi-

zation in humans, ahead of experimental advances, based on the physiological param-

eters of the misrouting as determined by current studies on albinism and achiasma.

1.3 Computational Modelling of V1

1.3.1 Modelling of V1 development

A key consideration when thinking about computational models of neural function is

the level of abstraction at which to operate. Depending on the mechanisms of inter-

est, the appropriate level of detail will dictate how useful the model is to describe a

particular phenomenon. When high-level processing is being considered, a high-level

abstraction of the activities of individual units is more computationally efficient and

informative over a range of individuals than attempting to emulate every minute detail

of the system in question.

In the case of this project, the organization at the level of feature preference maps in V1

precludes the need for modelling individual neurons in detail or compartments of neu-

rons. A high-level abstraction of neurons as units yielding a single variable in response

to activation is sufficient for investigating patterns of connections between them, and

how they change based on activity.


1.3.2 Models of joint OR/OD development

There exists a variety of models of V1 development that are able to account for the

formation of orientation preference and ocular dominance maps in response to input

activity. Models based on map representations vary in type along several axes, includ-

ing the level of abstraction and implementation.

Non-incremental models. Some models use abstract processes to form visual maps

(non-incremental models), such as correlation-based models, which use functions to

represent long-term correlations in inputs to the visual network. CBL models assume

linearity in the visual system and fixed lateral connections, and are able to form realistic

separate OR and OD maps (Miller et al., 1989; Miller, 1994; Erwin et al., 1995), but

not joint ones (Piepenbrock et al., 1997; Erwin et al., 1995).

Incremental models. Other models might learn a structure from the repeated pre-

sentation of images, termed ’incremental’ models. Lateral connections in these models

can be fixed (Obermayer et al., 1995; Riesenhuber et al., 1998; Shouval et al., 1997)

or modifiable (Burger and Lang, 1999; Alexander et al., 2004). Incremental models

include SOM-based models, discussed next.

SOM-based models. The self-organizing map (SOM), invented by Teuvo Kohonen

(Kohonen, 1982) is a type of unsupervised neural network algorithm, producing maps

in a one- or two-dimensional representation of the statistical features of an input space,

while preserving its topology and relationships between neighbouring units.

Research groups have implemented high-dimensional and low-dimensional SOMs as

V1 cortical sheets to model OR and OD development, some yielding results for joint

maps mostly consistent with experimental observations, with some exceptions such as

a slightly unrealistic OR organization pattern (Riesenhuber et al., 1998).

1.3.3 LISSOM

The LISSOM (laterally-interconnected synergetically self-organizing map) family of

models Miikkulainen et al. (2005) extend from the SOM models to define a high-

level model of visual cortical development, based on the principle of input-driven self-

organization. These models have the advantage over their predecessors of being able

to combine multiple feature dimensions. Eschewing the modelling of individual neu-


ronal function, the biological units of the V1 representation within these models are

best thought of as vertical columns of neurons acting feature detectors, with the same

set of stimulus preferences over multiple dimensions (e.g. orientation, ocular prefer-

ence).

The development of biologically realistic maps using this architecture is enabled by the

inclusion of Hebbian learning in lateral connections to the V1 units, in addition to the

afferent connections emanating from lower layers in the hierarchy. Hebb (Hebb, 1949)

postulated that correlated activity between two neurons would increase their connec-

tion strength (”cells that fire together wire together”), enabling correlations in input

data to be encoded into the activity of the network: the excitatory connections acti-

vate nearby neurons and inhibitory connections dampen further neurons, resulting in

activity bubbles in response to inputs stimuli. With repeated stimulation this Hebbian

learning leads to organized stimulus preferences in the V1 units.

Given a set of input stimuli, the V1 sheet of the model will develop a topographic map

representation of the input space fed to the photoreceptor layer. As a result, the input

statistics of the visual inputs will be reflected in this representation: for example, ex-

posing the network to repeated iterations of natural scenes with trees and landscapes

tends to result in higher proportions of vertical and horizontal orientation representa-

tions, as these tend to be common in those types of scenes.

GCAL (Law et al., 2011; Stevens et al., 2013) is a version of LISSOM which includes

contrast gain control and homeostatic adaptation in V1, making it more biologically

realistic and stable. This model will be used in this thesis to simulate the congenital

misrouting in albinism and achiasma, and will be defined in further detail within the

methodology section.

The self-organizing map models of V1 development are written and run using Topo-

graphica, an open-source neural map simulator, written in Python (freely available at

topographica.org).

1.4 Modelling aims and motivation

Despite the aberrant inputs into V1, relatively normal visual function is preserved in

achiasmatic and albinotic individuals (Hoffmann et al., 2007, 2003; Victor et al., 2000;

Apkarian et al., 1994, 1995). Given that in humans the True Albino pattern precludes

reorganization at the subcortical levels, the hypothesis is that intracortical interactions

adapt to make the inputs available for normal perception, and that this adaptation is

topographica.org


dominated by hemifield dominance columns.

Computational modelling allows the opportunity to predict the organization in the area

of V1 innervated by conflicting inputs. Hypotheses about the predicted consequences

of this misrouting include:

• Orientation map organization will be impacted by the interdigitation of hemifield

preference maps.

• The joint orientation and hemifield dominance maps will show a different rela-

tionship between their selectivity gradients relative to the normal orientation/oc-

ular preference joint maps.

• Hemifield dominance maps will resemble the ocular dominance maps seen in

strabismus, a condition where the inputs arriving at V1 are uncorrelated (but

arrive from different eyes, rather than the same eye), including strong monoc-

ularity and a lack of lateral inhibitory interaction between cells with different

hemifield preferences.

In the following section, the methods used to carry out this modelling will be described,

followed by results, analysis and discussion.

Chapter 2

Methodology

2.1 The GCAL model

2.1.1 Architecture of GCAL

GCAL (gain-control, adaptive, laterally-interconected) is organized into three inter-

connected levels (or stages) of sheets of units (Figure 2.1). Units of the photoreceptor

layer project to ”LGN-ON” and ”LGN-OFF” sheets. LGN sheets are suffixed with

ON or OFF depending on whether the receptive fields of their constituent units are

on-center or off-center (respond most strongly to a light spot surrounded by dark,

or vice-versa). In actual fact, the LGN layer can be thought of as representative of

the processing that occurs in both the retinal ganglion cells (RGC) and the LGN.

Figure 2.1: Architecture of the GCAL

model, including photoreceptor, LGN

and V1 layers. Reproduced from

Stevens et al. (2013)

LGN units project to V1, the simulated pri-

mary visual cortex; units in V1 also receive

lateral connections from other units in V1,

both excitatory and inhibitory.

In the V1 sheet, units represent vertical

columns of neurons sharing stimulus feature

preferences rather than single neurons. The

projections from the photoreceptor sheet to

the LGN sheet and then to V1 are retinotopic

in nature, meaning that the center of the con-

nection field for the units in V1 and LGN lay-

ers are mapped onto the equivalent sheet co-

ordinate positions in the lower sheets.

14

Chapter 2. Methodology 15

Input stimuli. Inputs to the network are simulated by changing the activation levels

of the units of the photoreceptor sheet(s). The activation value ψ of a given unit i is the

grayscale value of that point in the stimulus image. Images that can used for stimuli

include noisy disks, elongated Gaussians, and samples from natural images (patches)

of the same size as the photoreceptor sheet: all have been used to successfully form

realistic feature preference maps.

LGN activity. In the LGN sheets, the units have receptive fields that are either on-

center or off-center, determined by a Difference-of-Gaussians kernel applied to con-

nection weights ωi j from photoreceptor unit i to LGN-ON or LGN-OFF unit j. The

activation of a unit in the LGN sheet layers at time t + δt is then given by Equation

2.1, where gain control is applied in the form of divisive inhibition, making the model

robust to differences in contrast.

η j,O(t +δt) = f

(γO ∑i∈Fj,p ψi(t)ωi, j

k+ γS ∑ i ∈ Fj,sηi,O(t)ψi j,S

)(2.1)

V1 Activity. Each unit in V1 receives input from three sources: the afferent connec-

tions from the LGN ON/OFF sheets, lateral inhibitory connections and lateral excita-

tory connections. For each unit j, each projection type p has a contribution value C j,p

given by:

C j,p(t +δt) = ∑i∈Fj,p

ηi,p(t)ωi j,p (2.2)

The three contributions (p = A for Afferent, I for Inhibitory and E for Excitatory) are

then jointly computed using the following equation to give the activation level of unit

j at time t:

η j,v(t) = f

(∑p

γpC jp(t)

)(2.3)

Adaptation in the V1 layer. On every iteration of the simulation, the threshold of

activation of a V1 unit (θ) is updated, using a specified homeostatic learning rate (λ),

to bring the average V1 activity to a target level (µ=0.024 in these models), keeping a

stable overall level of actvity.

θ(t) = θ(t−1)+λ(η̄ j(t)−µ) (2.4)

...where η̄ j is the smoothed exponential average of that particular unit’s activity, given

by:

η̄ j = (1−β)η j(t)+βη̄ j(t−1) (2.5)


2.1.1.0.1 Learning. Connection weights are randomly initialized before training.

Then at each iteration, Hebbian learning is applied to update the connection weights

of the afferents from the LGN -ON and OFF layers to V1 (ψi j,A), simulating changes

in connections occurring from correlation between the presynaptic activity and postsy-

naptic response in the V1 units, constrained by divisive weight normalization:

ωi j,p(t) =ωi j,p(t−1)+αη jηi

∑k(ωk j,p(t−1)+αη jηk)(2.6)

As a result, connection strengths change and adapt depending on the inputs, and sur-

rounding neurons influence each other with lateral connections.

All equations are from Stevens et al. (2013).

2.1.2 An ocular dominance model of GCAL

Ocular dominance and disparity are stimulus dimensions that depend on input arriving

from two eyes. The GCAL model (described in Stevens et al. (2013)) comprises a

single photoreceptor sheet; in this case, the model has one photoreceptor sheet added,

along with an additional LGN-On and LGN-Off sheet.

Figure 2.2: Two-eyed adaptation of the GCAL model described in Stevens et al. (2013).

In this schematic the inputs are slightly dimmed and offset for disparity, generating maps

of ocular dominance. Images on the photoreceptor layers sourced from Shouval et al.

(1996).


This altered GCAL architecture is illustrated in Figure 2.2. Although they are

named as such, the model is agnostic to the notion of ’right’ and ’left’ sheets, so the

naming of the photoreceptor sheets and LGN sheets is arbitrary.

2.1.3 Input patterns

Input types. The GCAL network has been shown to develop realistically when trained

on a variety of inputs, developing preferences for any feature dimensions represented

in the inputs; for example, if there are elongated, oriented edges, the network will de-

velop a preference map for the different orientations.

To train the model on natural images, a dataset is specified for the simulation, and for

each iteration the pattern generator chooses an image. The image is then randomly ori-

ented and a random set of coordinates selected (within specified parameters), at which

location on the image a small ’patch’ is sampled and presented to the input sheet. the

size of the patch selected depends on the resolution and size of the image.

Ocular preference and selectivity. To simulate ocular preference, a dimming factor

is included to create an asymmetry in the activation levels ψ of photoreceptor sheet

units. In the case of Gaussian inputs, this factor dims each Gaussian relative to the one

in the other photoreceptor sheet, in such a way that their total brightness always sums

to the same value. For natural image inputs, one image patch is dimmed relative to

the other. The spatial correlation remains identical (if no disparity has been included)

but the difference in scale between the inputs results in ocular selectivity developing.

Adding disparity to one of the input images affects the spatial correlation between the

photoreceptor sheets, leading to increased ocular selectivity.

2.2 Modelling misrouting using GCAL

2.2.1 A model for both conditions

In the context of albinism and achiasma, some simplifying assumptions can be made to

model the V1 organization properties that might arise for both cases in a single model.

In both conditions input from the opposite hemifield is erroneously routed, and the net

result is that V1 receives inputs from the ipsilateral visual hemifield along with the

normal contralateral hemifield input, rather than a set of inputs in stereo from only the


contralateral hemifield.

Figure 2.3: Schematic diagram illustrating the principle behind the misrouting in al-

binism and achiasma, and how both conditions can be modelled in this case using the

same paradigm. The point of fixation denotes the centre of the visual field, and the

patches of images with blue and red backgrounds are transmitted to V1 through the

blue and red projections respectively after arriving at the contralateral hemiretina. Note

that the portion of ipsilateral inputs that correctly arrive at V1 in albinism are deliberately

ignored for simplification (see text). In the achiasma case as well as the albinism case,

the aberrant inputs arrive at V1 in the same mirror-flipped, overlapped configuation, but

on opposite sides of the brain.

In the albinism case, there are some inputs that are still normally routed, that con-

tribute to the representation of the periphery. For the purposes of this study, the pe-

ripheral sections of the visual field that are represented normally will be excluded from

modelling as a simplification. For both models the region of V1 that will be represented

will be parafoveal (the region surrounding the fovea).

Theoretically, the consequences of both types of misrouting on V1 organization can

be simulated by changing the input pattern specifications and one set of connections

between the LGN and V1 sheets, as will be described next.


2.2.2 Changes to the input stream in model training

In the normal case these photoreceptor sheets are representative of the two hemireti-

nae that receive the contralateral side of the visual field. If the left hemisphere V1 is

being considered, then the left hemiretinae of the left and right eyes contribute to the

right field of vision, which in normal physiology is routed to the left side of the brain

(contralateral to the visual hemifield).

In both the achiasmatic and albinotic conditions, the misrouting of nerves leads to in-

puts from both hemiretinae of the same eye terminating on the same side of the visual

cortex (whether it is ipsilateral for the achiasma case, or contralateral for the albino

case). Therefore, in the model this can be emulated by presenting inputs from those

two hemiretinae, and identifying the ’left’ and ’right’ photoreceptor sheets as the left

and right ’hemiretinae’ contributing to the visual field. The photoreceptor sheets do

not represent a full hemiretina, but the parafoveal area described before: the area of V1

that will be simulated will therefore be the V1 region that the parafovea retinotopically

maps onto. We will be observing the effects on V1 organization for this misrouting

paradigm applied to idealized inputs (elongated, oriented Gaussian patterns) and natu-

ral images of foliage scenes (image obtained from the McGill Calibrated Colour Image

Database (Olmos et al., 2003)).

Figure 2.4: Idealized elongated Gaussian

inputs for training the normal and misrouted

conditions, with dimming between the eyes

and added disparity to one of the patterns.

For the Gaussian inputs protocol, the

misrouted condition model will be

trained on inputs as shown in Figure 2.4.

The normal inputs have Gaussian pat-

terns in stereo, with some dimming be-

tween eyes, and some disparity between

them. Photoreceptor sheets in the mis-

routed model are presented with random

positions and orientations of Gaussians

for each eye, resulting in a lack of spa-

tial correlation between the eyes. In the

normal case, this input is from the same

visual field for both photoreceptor sheets,

aside from some offset and some dim-

ming added to simulate disparity and oc-

ular dominance, leading to units develop-


ing preferences for the source of the incoming connections (the ’left’ or the ’right’

photoreceptor sheet).

Figure 2.5: Top: the original natural image input (From McGill (Olmos et al., 2003)).

Middle and bottom: The two patches for each case represent the input that will be

presented to the photoreceptor sheets, whose units will be activated by the level of

grayscale in the image.

In the case of albinism and achiasma, to simulate the inputs arriving from hemireti-

nae of the same eye in the natural image protocol, the parafoveal patch presented origi-

nates from a separate location along the y-axis. A patch of the image will be presented

to one photoreceptor sheet, and the input to the other eye will be a patch of the same

size from the other side of the visual field. A minimum distance is specified so as to

ensure the image is completely spatially uncorrelated with the one presented to the first

photoreceptor sheet (Figure 2.5).


2.2.3 Mirror reversal

In addition to arriving from the opposite visual hemifield, the misrouted portion of the

visual field is mirror flipped along the midline, so that its retinotopic representation in

V1 is inverted (Sinha and Meng, 2012) (see Figure 2.3).

This property can be emulated in the model by adding an offset to the projections from

one of the LGN sheets to V1, so that the activated units are in fact at the equivalent

position on V1 but across the midline.

Figure 2.6: 10x10 projection of afferent inputs to the V1 sheet: afferent weights are

in their initial randomized, untrained state. The afferent projections depicted here ar-

rive from the ’RightLGNOn’ and ’LeftLGNOn’ layers of the model; the projections are

then situated with respect to the retinal area they are connected to. The left LGN-ON

projections are reflected across the midline relative to the right ones. The same flip-

ping principle applied to the right LGN-ON afferent projections is applied to the right

LGN-OFF afferent projections.

The implementation of this mirror flipping can be verified by observing projection

plots of the connection fields of the afferent connections from the LGN to V1 sheet.

The plots in Figure 2.6 represent the connection weights of every 10th neuron of the

V1 layer - representing projections incoming from the LGN-ON afferent layer. In these

plots the projections are situated with respect to the region of the LGN layer they are

arriving from. The same flipping step is applied to the ’Left’ LGN-OFF layer, so that

all input coming from the ’Left’ photoreceptor sheet arrives mirrored at the LGN.

Chapter 3

Results

3.1 Setting the control (normal) condition

Before observing the effects of applying the alterations to the two-eyed GCAL model

described in the previous section, a control condition must be established for com-

parison between the normal and misrouted visual pathways. The parameters for the

control condition are set based on the realism of the trained model with respect to

existing animal data.

3.1.1 Parameters

The V1 area was simulated with a 96 x 96 sheet of units. All four LGN -ON and -OFF

sheets were 24x24 units in size and both retina input (photoreceptor) sheets were also

24x24. Natural images used are photographs of foliage and trees with a resolution

of 768x576 pixels, from the McGill Calibrated Colour Image Database (Olmos et al.,

2003). The model was allowed to self-organize for 10,000 iterations.

For the model trained on Gaussian inputs, the dimming factor was set to 0.8 and dis-

parity to 3.0. For the model trained on the Foliage inputs, dimming was set to 0.48 and

disparity also to 3.0. These parameter settings were chosen for the control conditions

as they yielded realistic, organized orientation and ocular dominance patterns, with

interactions between them as described in experimental literature (Blasdel, 1992a).

3.1.2 Adding dimming and disparity

Figures 3.2a and 3.2b demonstrate how the added dimensions of ocular dominance and

disparity affect the map organization and interactions. After training, the orientation

22

Chapter 3. Results 23

maps, ocular dominance maps and two-dimensional Fourier spectra were measured.

The training pattern used has an impact on the spatial frequency of the orientation pref-

erence patches, represented in the Fourier spectrum (FFT) plots, as the type of input

(be it idealized gaussian images, or foliage images) results in differently organized ori-

entation maps, reflecting the statistics of the inputs to the network. The V1 area trained

on Gaussian inputs produces an FFT with clear ring form that is preserved when dim-

ming and disparity are added. In the model trained on Foliage inputs, the FFT plot is

noisier and less well-defined but a ring structure is visible. The ring-shaped appear-

ance of the Fourier power spectrum (FFT) of the orientation map conveys the regular

repetition of patches of all orientations across the V1 map, in all directions, consistent

with animal data (Obermayer and Blasdel, 1993).

Ocular dominance. When adding dimming, OD maps form, showing a clear pres-

ence of bands of ocular dominance, with smooth transitions between eye preferences.

Units that are black or white in the map respond more strongly to inputs from one

eye or the other (monocular), while units in the middle range of selectivities are more

binocular. Adding disparity sharpens the edges of the ocular dominance bands, reflect-

ing more accurately the stripe-like pattern seen in animal data (Figure 3.1), with most

neurons still remaining binocular (refer to Figure 3.6b).

Figure 3.1: Bands of ocular preference measured using optical imaging, from Blasdel

(1992a) A: Ocular dominance bands. B: Ocular dominance bands outlined with the

transition boundaries between them.


(a) Results for model trained on Gaussian inputs.

(b) Results for model trained on Foliage inputs.

Figure 3.2: Feature preference map results for the control condition of the model,

trained on two different types of inputs. OR: Orientation maps showing the preferred

orientation of V1 units, colour-coded by orientation. OD: (Ocular Dominance) Ocular

preference maps where the preference of the neurons for one eye or the other is repre-

sented by its scale of white or black colouring; in the gray range, units are less selective

for which eye the inputs are arriving from. FFT: Fourier spectrum of the orientation

plots.


3.2 The misrouted model for albinism and achiasma

The misrouted model was run using the same parameters for dimming and disparity as

those used to generate the orientation and ocular preference maps in Figure 3.2.

3.2.1 Orientation maps and receptive fields

Orientation maps. Like in the control condition, the model was trained on two dif-

ferent types of inputs: idealized Gaussians and natural images of foliage scenes. For

the Gaussians case, the inputs were set to the completely spatially uncorrelated Gaus-

sians, seeded independently in each eye, while in the Foliage case the patch input

approach described was used.

Orientation maps are measured at the final state of the model after training, using

repeated presentations of sine gratings over a range of phases and orientations, and

colour-coding the units by the orientations that elicit the maximal response.

Normally formed orientation maps exhibit recognizable features, which are highlighted

in Figure 3.3.

Figure 3.3: Orientation maps for the normal and misrouted conditions, for Gaussian

and Foliage inputs. Features highlighted using the shape outlines include saddle

points(white diamonds), linear zones(black lines) and fractures(white circles).

Saddle points are areas where one orientation patch is mostly crossed by another;


linear zones can be described as a region where along one axis the preferred orientation

varies continuously; and fractures describe a sudden transition from one iso-orientation

domain to another with a very different orientation preference. Pinwheels have been

mentioned in the introduction as singularities around which iso-orientation domains

converge; they are shown in Figures 3.8a and 3.8b, where their relation to ocular/hemi-

field dominance boundaries is also observed.

When the misrouting is applied to the model, the orientation map organization is no-

ticeably different from the control case, for both types of inputs. The features described

above can still be found in the misrouted maps, but misrouting appears to have an im-

pact on the regular organization of these features across the map.

Receptive fields. Connection Fields (CFs) represent the incoming weights to a given

unit; by substracting the -OFF component of the connection field from the -ON com-

ponent yields an approximation of the receptive field of that neuron.

(a) Trained on Gaussian inputs. (b) Trained on Foliage inputs.

Figure 3.4: Receptive fields of every 10th neuron in V1 as represented by the con-

nection fields (CFs) from left and right afferent inputs from LGN sheets, with the -OFF

component subtracted from the ON component.

The profiles of the receptive fields differ in the control cases for both Gaussian

and Foliage inputs, but both exhibit distinct -ON and -OFF regions. In the Gaussian

case due to the inputs being oriented lines that are brighter than their background the

receptive fields tend to have an ON-center and two surrounding OFF-lobes, while the


Figure 3.5: Hemifield dominance maps in the misrouted model: preference for either

hemifield is represented on a scale from black (for the left hemifield) to white (for the

right hemifield).

Foliage case shows a wider variety due to the different edges and forms shown to the

network in training.

In the control case, the CFs are extremely similar for inputs arriving from both eyes.

This is not the case in the misrouted condition, where receptive fields from one vi-

sual hemifield resemble those seen in the normal case, but are completely dissimilar

when coming from the other hemifield, where they appear formless and unorganized.

The connections weights therefore develop normally for one set of incoming affer-

ents but bear no correlation to the inputs arriving from the other. Eyeballing the two

projections, the pattern appears complementary between each hemifield, where those

receptive fields that are organized normally in one hemifield are not in the other.

3.2.2 Ocular/Hemifield dominance map organization

Ocularity/hemifield preference. In the misrouted condition model, for both types of

inputs, the resulting ocular preference maps show extreme selectivity for input from

one visual hemifield or the other (In this case, the maps are in fact hemifield prefer-ence maps). As a result, the maps show a stark contrast from the smoothly varying

ocular preference maps in the control model (Figure 3.2).


(a)

(b)

Figure 3.6: (a) Histograms of binocular vs monocular neurons for normal and misrouted

cases. (b) Receptive fields of monocular V1 units in the normal case and in the mis-

routed case (Left and Right ON-OFF Connection Fields).

Receptive fields of monocular neurons. To demonstrate how the lack of correla-

tion affects receptive fields of V1 units, a neuron was selected from the midline of an

ocular/hemifield dominance band, so that its selectivity for a particular eye or hemi-

field was highest.

To classify neurons as binocular or monocular (though in the misrouted case they might

be termed ’bihemifield’ or ’monohemifield’), the histogram of ocular/hemifield domi-

nance was plotted on a range from -0.2 to 1.2 and separated into 10 bins. The value of

the bins surrounding 0.0 and 1.0 were combined to estimate the proportion of monoc-

ular neurons (tuned for input from one eye/hemifield) and the remainder to estimate


the proportion of binocular neurons. Figure 3.6b shows how the monocular neurons

in the normal case have a similar profile even though the cell is strongly selective for

one of the eyes in particular; the correlation in the inputs from each eye drives a hor-

izontal correlation in the connections. However, in the misrouted case, the neuron

strongly selective for one hemifield will develop a normal receptive field appropriate

to its input type (in resemblance to those seen in the normal condition), but only in the

connections to one hemifield; the connections to the other hemifield are disorganized

and undeveloped.

Figure 3.7: Lateral inhibitory connection fields of V1 units to surrounding units in the

normal and misrouted cases, situated within in the V1 layers and overlaid with the

boundaries of the ocular/hemifield dominance bands in light blue. The darker the hue,

the stronger the connections. The units in question is in the centre of their connection

field. Each alternating band contains units with a preference for either eye/hemifield.

Lateral inhibition. In Figure 3.7, the connection weights to the unit shown demon-

strate how the lateral relationship between units changes. In the normal case, the in-

hibitory connection is relatively diffuse with some stronger connections to units with

the same ocular preference. In the misrouted case there is a clear targeting to hemifield

preference bands of the same preference, with a lack of interaction with units in the

immediately adjacent band.


3.2.3 Joint OR/OD relationship

The combined relationship between OR and OD maps can be observed by overlaying

elements of the feature preference maps (Figure 3.8).

(a) Control model trained on a Gaussian input stream and on a Foliage input

stream. The white rectangles show examples of the boundaries of ocular

preference columns approaching those of the orientation preference bands

at orthogonal angles.

(b) Misrouted model trained on a Gaussian input stream and on a Foliage

input stream. The white ellipses show examples of the boundaries of oc-

ular preference columns coinciding with those of the orientation preference

bands.

Figure 3.8: Joint maps of orientation preference and ocular preference boundaries

(black lines), showing the different relationships occurring in the normal relative to the

misrouted condition. Small circles are pinhweel centers.

In resemblance to existing animal data (of animals with normally routed pathways),

in the normal case the contours of ocular preference bands tend to intersect at right an-

gles with boundaries of iso-orientation domains. Pinwheels tend to occur in the mid-


lines of ocular dominance bands, and sometimes on the ocular dominance boundaries.

(a) Trained on Gaussian inputs. (b) Trained on Foliage inputs.

Figure 3.9: Maps of orientation selectivity (OS), both alone and overlaid with ocular se-

lectivity in the normal and misrouted conditions, trained on Gaussian(a) and Foliage(b)

image inputs. Darker areas represent areas of low selectivity (such as pinwheel cen-

ters) and lighter areas areas of high selectivity

For both input stream types, in the misrouted condition the map organization shows

clear segregation along hemifield boundary lines. The white ellipses in Figure 3.8b

draw attention to areas where the boundaries of iso-orientation domains follow neatly

along the hemifield dominance line, rather than the orthogonal relationships shown in

Figure 3.8a; in the orientation map in the misrouted case, the hemifield dominance

columns are visible, even without any plotting that feature dimension on the map.

This relationship is highlighted by the orientation selectivity maps in Figure 3.9. In the

normal case, the lighter regions (where orientation selectivity is highest) sometimes

fall in regions of lower ocular preference - along the boundaries of ocular dominance

columns. Contrast with the misrouted case, where the figure illustrates how the selec-

tivity changes abruptly at hemifield preference boundaries while in the normal case the

selectivity varies smoothly across ocular dominance boundary lines. As a result, the

pattern of hemifield dominance is neatly discernible in the orientation selectivity map

as outlined in dark (less selective) regions.

Chapter 4

Discussion and Conclusion

4.1 Model results

The control (normally routed) model, with dimming and disparity included to generate

ocular dominance, exhibits features found in normal V1 orientation maps, including

saddle points, fractures, pinwheels and linear zones. The ringness of the FFT plots and

ocular dominance map pattern are similar to those seen in animal experiments (Ober-

mayer and Blasdel, 1993), with a distribution of monocular and binocular neurons also

resembling those seen in animal data (in the ratio of binocular to monocular neurons,

Figure 3.6a)(Kiorpes et al., 1998). The relationships between ocular dominance and

orientation preference are also realistic: pinwheel centers (areas of low orentation se-

lectivity) tend to fall in the center of ocular dominance columns, while areas of high

orientation selectivity tend to coincide with areas of low ocular selectivity (boundary

lines) in an orthogonal manner (Figure 3.9)(Blasdel, 1992a). Receptive fields, approx-

imated by the connection fields of units with respect to the LGN layers - are similar

between the two eyes, even with more monocular neurons. Once the misrouting is ap-

plied, the organization changes markedly, with regard to receptive fields, visual maps

and lateral connections.

Receptive fields. Figures 3.4 and 3.6b reflect the bilateral nature of the receptive

fields of the V1 area as a whole; individually it is apparent that each neuron forms

normal receptive fields (such as an ON lobe flanked by two OFF lobes in the Gaus-

sian case) for the inputs arriving from one hemifield but not the other. In Hoffmann

et al. (2012), human experiments reveal bilateral population receptive fields (receive

inputs from both ipsilateral and contralateral visual hemifields) at the level of V1 in

32

Chapter 4. Discussion and Conclusion 33

achiasma. In the 1984 Guillery study, the electrode sites recorded showed receptive

fields selective for one or the other hemifield, with one recording obtained showing

activity elicited in response to stimulation in both visual hemifields (Guillery et al.,

1984). Receptive fields for individual neurons cannot be measured in humans due to

experimental (and ethical) limitations, but in the model they can be approximated with

connection fields from the LGN layer. Results here show there is a strong separation

in the misrouted model of the projections arriving from the LGN to the V1 layer, as

the units in V1 are rarely activated by both photoreceptor sheets at the same time.

This bilateral receptive field property does not occur at the unit level, but rather at the

population level; individual units do not show strong organized connections to both

fields.

Dominance of hemifield maps. In the misrouted model, the hemifield preference

map dominates over the orientation map. The normal orientation map features are

contained within hemifield preference boundaries, but at the edges selectivity drops,

unlike in normal orientation maps where the selectivity varies smoothly across ocular

dominance boundaries. The pattern can be seen as interdigitation of two orientation

maps - one for each hemifield.

Resemblance to strabismic maps. There is no imaging data for hemifield dom-

inance on the True Albino pattern, for practical reasons: although it is possible to

image the a separate visual pathway by injecting a tracer into one eye, no such proto-

col can be applied so that it only enters half the visual pathway from one eye. Thus,

the Guillery study showed that ocular dominance bands did not form in the regions

innervated by the normal and abnormal afferents, but could not show with histological

methods the hemifield columns believed to be formed in their place, and therefore no

observations could be made of the width or spacing of ocular dominance dominance

bands. However, the nature of the misrouting lends the model to comparison with stra-

bismic results. In strabismus, the visual pathways are not inherently misrouted like in

albinism and achiasma, but the afferent inputs that arrive at V1 are uncorrelated due to

misalignment of the eyes.

The hemifield dominance maps in this study strongly resemble those in strabismic V1

organization as seen in cats (Lowel, 1994) and monkeys (Kiorpes et al., 1998). Figure

4.1a shows the ocular dominance columns as imaged in normal and strabismic cats.

The pattern change from normal to strabismic - becoming more sharply delineated - is


(a)(b)

Figure 4.1: (a) Ocular dominance columns in the normal (A) and strabismic (B) cat

cortex, revealed by intraocular tritiated proline injection into one eye (Lowel, 1994). (b)

Ocular dominance distributions in strabismic (A) vs normal (B) monkeys (Kiorpes et al.,

1998).

comparable to that seen in the results for albinism and achiasma in this model.

One of the effects of strabismus is a loss of binocular neurons, and a subsequent loss

of binocular vision, same as is seen in albinism and achiasma. The results obtained in

Figure 3.6a can be directly compared to results in macaque monkeys induced with ex-

perimental strabismus, showing a higher ratio of monocular to binocular neurons than

in the normal case (Figure 4.1b)(Kiorpes et al., 1998). In the misrouted GCAL model,

the proportion of neurons ’binocular’ for both hemifields reduced to 33% and 42% for

Gaussian and Foliage inputs respectively, in comparison to the 74% and 68% seen in

the normal case.

The lateral inhibitory connection profile of the neurons in hemifield columns (Figure

3.7) also resembles that seen in strabismus, where connections from the neuron are

targeted only to cells with similar ocular preference (Lowel, 1994).

With a lack of spatial correlation between the input patches presented to each eye,

ocular selectivity for one or the other eye became stronger and more defined, but the

width of the hemifield dominance columns do not appear to favour one hemifield or the

other. In the model, the dimming factor between the photoreceptor sheets is not biased

towards either sheet, so units are not disproportionately activated over the course of

training by inputs arriving from one hemifield during training. As a result, note the


relatively even spacing, as seen in the ocular dominance maps from the model results

(Figure 3.5). Based on these results, it could be predicted that if hemifield dominance

stripes could be imaged in animals with the True Albino pattern, the stripes would be

of similar width, again, as is seen with strabismus Lowel (1994).

4.2 Limitations and future improvements

In addition to the results presented here, there is room for improving, exploring and

expanding the model for the misrouted conditions.

The ocular dominance model. Modelling ocular dominance in GCAL is currently

limited to dimming the inputs in one eye relative to the other, or adding slight spatial

disparity. However, the true mechanisms by which ocular dominance are formed in

animals are not fully known; the dimming paradigm in GCAL results in realistic joint

OR/OD maps, but there is no specific biological correlate to this mechanism. If a more

realistic approach to occular dominance formation is eventually developed, it would

be of interest observe the resulting patterns in the misrouted model.

Model realism. In this model the retinotopic mirror-reversal of the aberrant inputs

was simulated by specifying targets for the projections from the LGN layer to the V1

layer to arrive at mirrored location, retinotopically. The optic chiasm actually occurs

before the LGN in the visual pathway, so the addition of a retinal ganglion cell (RGC)

layer would enable this flipping to occur between the photoreceptor layer and the LGN

layer, which would be more realistic in structure. In addition, for albinism specifically,

if the correctly routed peripheral projections could be incorporated into the model,

there might be interesting dynamics to explore at the border between the overlapping

hemifield region and the normal region. Incorporating an RGC layer might also play

into exploring prenatal maps, discussed next.

Prenatal visual maps. In this thesis the maps are developed from a random initial

state. However, in reality, preference maps are present in a rudimentary adult-like state

at birth (Horton and Hocking, 1996), which experiments have revealed to be formed

due to genetically determined spontaneous neural activity stimulating V1 prenatally,

including retinal waves (Wong, 1999). An interesting research question would be to


investigate whether this segregated organization would also arise from a normal pre-

visual state. In practice, the model could be trained with a schedule of two phases of

input presentations to the photoreceptor sheets, to simulate genetically driven internal

inputs, and environmentally driven visual inputs. Orientation maps and ocular prefer-

ence maps have been shown to develop adult-like joint orientation/ocular preference

map properties, and this has been successfully modelled in the past using noisy disk

inputs to the network, in an earlier version of GCAL (Jegelka et al., 2006). However,

there is evidence of some correlation between the eyes for the spontaneous activity

(Ackman et al., 2012). If the misrouting of inputs affects this correlation, then maps

at birth might reflect this. As there is no data on prenatal achiasmatic or True Albino

cortical maps modelling this situation in GCAL would be interesting to model. Both

situations could be considered: V1 development from a normal prenatal map, and V1

development from a prenatal map presumed affected by misrouting befre visual input

even occurs.

Tilt aftereffect experiments. The tilt aftereffect (TAE) is a visual illusory phenomenon,

where subjects are presented with an oriented grating to fixate on (the adaptor), then

a new oriented grating is presented with a slight angle relative to the adaptor. At this

point, a ’tilt illusion’ occurs, where the test grating looks tilted at a stronger angle than

it is, away from the adaptor angle (direct effect). The indirect effect is the illusion

of angles that are further away appearing tilted toward the adaptor angle. The TAE

measurement is the difference between the presented and perceived angles measured

before and after adaptation over a range of orientations. The direct tilt after-effect has

been associated the lateral inhibitory connections present in V1, and has been previ-

ously simulated using the RF-LISSOM model (Bednar and Miikkulainen, 2000). The

experimental paradigm for exploring how albinism affects the direct TAE is illustrated

in Figure 4.2. Here, an adaptor stimulus is presented at both the normally routed and

misrouted locations of the visual field, and it is hypothesized that if there is no crosstalk

between the hemifield regions, the result should be similar to the control group. Oth-

erwise, if there was an effect elicited in the opposite hemifield from the misrouted

adaptor, the supposition would be that the misrouted and normal inputs arriving at V1

would end up forming neurons with dual visual fields.

In subjects with albinism, performance in the TAE experiment was the same as in con-

trol groups. The lack of inter-hemifield crosstalk in the results, in theory, support the

lack of interaction between the hemifield dominance columns that was previously vi-


Figure 4.2: Paradigm for the Tilt After Affect in albino patients. reproduced from Klemen

et al. (2012).

sualized in Figure 3.7 with the inhibitory connection fields.

To carry this out in Topographica with the two-eyed GCAL model, for the purposes of

validation against human psychophysical data, the basic method would involve:

• Presenting a series of sine gratings of varying orientations to the network.

• Measuring the response in V1.

• Presenting an adapting pattern, with plasticity enabled in V1 (when presenting

test patterns, it is generally disabled, to test the response of the settled network).

• Repeating the first two steps; the difference between the response before and

after adaptation yields the TAE.

Hypothetically, if this protocol is carried out on the trained misrouted model at the

adaptor locations, the reduced inhibitory lateral connections between hemifield columns

should lead to the same results as in Klemen et al. (2012). Note that this protocol would

not have an in-subject control, however, as the control ipsilateral and contralateral lo-

cations would not be available in the network as it is currently excluding the normal

inputs in albinism.

The inital stages of this experimentation were carried out, with the decoding accuracy

arriving below 5 degrees of error. Unfortunately, time limitations have required that an

exploration of this effect in this albinism/achiasma model be continued at a later date.


4.3 Conclusion

As predicted by several experimental studies, the misrouting paradigm for albinism and

achiasma applied to the two-eyed ocular dominance GCAL model resulted in a joint

orientation/hemifield preference map structure that differs significantly from the joint

orientation/ocular dominance relationship seen in the normal case. The organization

in V1 was dominated by hemifield preference maps, replacing the ocular dominance

maps seen in the normal case; the pattern was strongly reminiscent of strabismus, but

for hemifield rather than ocular dominance. The results reflect the observations in-

ferred from indirect experiments made in humans and the sole animal model of the

True Albino pattern (Guillery et al., 1984), but importantly also relate to results found

in strabismus, a condition with similar neural correlates.

However, there are possible alterations that might improve the realism of the model,

namely the addition of an RGC layer from which the mirror-reversal of the inputs for

each condition would realistically take place, and which could potentially be incorpo-

rated into a scenario including prenatal and postnatal phases. Exploring how prenatally

developed maps might impact on the development of these maps, with the hypothesis

that the normal joint orientation/ocular dominance relationship present at birth will

give way to a hemifield preference-dominated map, due to a rearrangement of hor-

izontal connections in response to spatially uncorrelated visual inputs. Subsequent

investigations would also be beneficial in validating the model against psychophysical

data for information on function.

In summary, this project supports the current hypothesis that the likely response of the

visual cortex to the misrouting in human albinism and achiasma is an interdigitating

arrangement of preference columns driven by hemifield dominance.

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