Brain Maps

8/13/2019 Brain Maps

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Plan

Intro: topographical maps everywhere

Somatosensory maps

Theoretical models

What is to be explained in visual map formation?

Assumptions and types of models

Summary and conclusions


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Topographical maps

Topographic representation of spatial patterns:

key feature of visual and tactile data analysis;

used also by motor and auditory system.

Serves locomotor navigation and object recognition.Tactile and motor maps: homunculus representation, cortex and

cerebellum

Visual system - many maps of different type:

1. retinal projection on LGN of the thalamus;

2. retinotopic maps in V1

3. SC multimodal maps


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Model of self-organization

SOMF, Self-Organized Feature Mapping, or Kohonen map.

Simplest model of topographic self-organization via competitive Hebbianactivity-dependent learning.

,1 , dlai i i c it t h r r t t t i O c W W X W

SignalXactivates most

strongly a neuron with

synapses W; they become

more similar toXand also

neurons in the vicinity of W

become more similar toX.

Receptive fields of neurons

that are close on the 2Dmap are close in the input

space.

Update equation:


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Global Somatosensory Map

Data: 3D coordinates of 40 body areas,

density of points prop. to inverse resolution, 600 pointsTest points: interpolation, 160 labeled points

SOM map: long and narrow, 20x5, hexagonal neighborhoods.

Why head/neck between legs/hands, but face outside?

5. thumb, 6. 2nd finger 7. 13. face 4. leg, 9. foot, 10. toes

3rd finger 8. 4th finger 11. back, 12. chest

1. forearm 2. upper arm 3. shoulder


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Theoretical accounts

Only a few papers on somatosensory or motor maps;

no papers on global features of homunculus maps.

Few papers on Superior Colliculus maps (saccade generation).

Orientation and ocular dominance maps in V1 studied most

frequently.

Usually simulations of neural dynamics at mesoscopic level.

Few papers based on neural field approach, spin systems and

analytical considerations.

Erwin, E., Obermayer, K., and Schulten, K.J. (1995). Models of orientation

and ocular dominance columns in the visual cortex: A critical comparison.

Neural Computation, 7(3):425-468

Swindale, N.V. (1996). The development of topography in the visual cortex: A

review of models. Network 7(2):161-247.


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Stability of maps

Maps were considered static in adult animals, but:Brown, T.G, Sherrington, C.S (1912) On the instability of a cortical point.

In 'critical' period of development (6 days in rats):

Visual deprivation change physiological (Wiesel and Hubel, 1963,1970) and anatomical monocular organization of afferents into visual

cortex.

Changes in the thalamocortical projections due to damage to

peripheral nerves.Somatosensory deprivation in young animals (destroying whiskers

in a neonatal rat) leads to changes in topography of the whisker

representations (barrel field), responding to stimulation of other

body regions (Waite and Taylor, 1978).


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Plasticity of mapsEvidence for plasticity in adult animals from:

limb amputations or nerve lesions, from rodents to primates

Review: Gilbert, C.D. (1993) Rapid dynamic changes in adult cerebral cortex.

Curr. Opin. Neurobiol. 3: 100-103

1. Reorganization is a common feature of topographic sensory cortical maps.

2. Demonstrated in visual, somatosensory and auditory cortex.

3. Plasticity extends to higher cortical areas.

4. Many processes contribute to functional reorganization, different temporally

and physiological dynamics.

5. Changes in receptive field size and location - minutes after lesions;

reorganization of other systems - days to weeks (Kossut, 1988).

6. Mechanisms probably common to all cortical maps, may play a role in normal

functioning, activity-dependent mechanisms are critical for maintenance of

topographic maps.


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Mechanisms of plasticity

Loss of input, changes in intensity or pattern of the afferent drive tothe region at the physiological level leads to:

1. Fast: unmasking of existing connections which were normally

ineffective, ex. unmasking via release of inhibition.

Thalamic afferents may reach 10 columns; blocking corticalinhibition increases receptive fields.

2. Medium: activity dependence within intracortical circuits, with

Hebbian preference to the most active inputs, competition for

synaptic sites coupled with somatotopic continuity and overlap.Strengthening of polysynaptic pathways.

3. Longer time scales: sprouting of terminals from new sources.

Demonstrated in the spinal cord.


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Orientation + dominance

Contour plot: black contours - bands of eye dominance;

gray lines - isoorientation.

Singularities usually near centers of ocular dominance bands.

Saddle points also near centers.

Local orthogonality and global orthogonality.

Global disorder - autocorrelation function.

Correlation between orientation and eye dominance.

Differencesbetween preferred orientations and the direction of

gradient of preferred orientations.

Distributionof orientation specificities.

.
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Theoretical assumptions

Large 2-D grid of elements representing neural assemblies, reacting

to signals in their receptive field (spatial filters).

Feature vector representation: receptive field position, dominance,

orientation angle, orientation preference, color information

Weight vector representation: synaptic strength, high-dimensional.

3 important principles:

1. Continuity - nearby columns react to stimuli with similar

features - choice of similarity affects patterns.

2. Diversity- whole feature space should be covered.

3. Global disorder

Models may look quite different but are based on similar principles.
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Theoretical models

Models proposed so far belong to 5 categories:

1. Structural models, assuming specific projections due to thalamic

organization.

2. Spectral Models, filters in Fourier space.

3. Correlation-based learning, linear intra-cortical interactions with

Hebbian learning.

4. Competitive Hebbian models, non-linear lateral interactions.

5. Mixed models and untypical models.


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Structural models

1. Structural models, assuming specific projections due to thalamic

organization.

The icecube model of Hubel and Wisel (1974)

The pinwheel model of Breitenberg and Breitenberg (1979)

Extensions:

Gtz 1987Baxter and Dow 1989

Problems with: global disorder, fractures.

In a) no singularities or saddlepoints, in b) wrong singularities.


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Spectral models

Spectral Models, filters in Fourier space.Swindale 1980-92; Rojer and Schwartz1990; Niebur and Wrgtter 1993

One-step models, very few parameters:

n(r), white-noise patterns, Gaussian numbers around 0, as input

h(r), representation of a band-pass filter H()Ocular dominance z(r) obtained from convolution of n(r) and h(r)Orientation map: u= grad z(r);

Orientation preference q=||u||

Rojer, Swindale: wrong predictions of correlations between orientation

preferences and cortical locations, since all closed integrals vanish.

Iterative models (Swindale map1and map2):

F(t+1) = F(t) + a(F(t)*h(r))f(F(t)); 0


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Correlation-based models

Hebbian linear models.

Miller, Keller, Stryker 1989 high-dimensional model:x- retinal location, r- cortical.

For each eye separately Fi(t) ={Wi(t)}

Fi(t+1) = Fi(t) + aA(r,x) [I(r,r)*C0(x,x)*Fi(t)+I(r,r)*C1(x,x)*F1i(t)];

where A(r,x) describes location and size of receptive fields;

I(r,r) is intracortical interaction of the Mexican hat type;

C0 is a correlation functions for the same eye, C1 for different eyes;

Non-linearities may be added by normalization of weight vectors or limiting their

range.

Newer models (Miller et al 1990-2000): separate populations of ON and OFF-

centered cells in LGN, more compelx reccurent models.


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Competitive Hebbian models

Low dimensional(SOM-l):at least (r, q sin(2f, q cos(2f, z(r)), i.e. position r(x,y), degree of orientation

preference q, orientation angle f, dominance z.

Ft+1(r) = Ft(r) + aH(r,r)[Vt+1Fi(t)];

Stimulus V is chosen at random, the neighborhood H(r,r) is Gaussian around thewinner r using Euclidean distance.

High-dimensional (SOM-h): Ft+1(r) = {Wi(r)}

normalized weights, i.e.

Ft+1(r) = (Ft(r) + aH(r,r)Vt+1)/||(Ft(r) + aH(r,r)Vt+1)||

and correlation distance function d(V,W)=1VW
http://localhost/var/www/apps/conversion/tmp/scratch_6/SOM-low.gifhttp://localhost/var/www/apps/conversion/tmp/scratch_6/SOM-low.gif


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Elastic Net

Elastic net(Durbin and Wilshaw 1987)

Similar to SOM, adds elastic term

Ft+1(r) = Ft(r) + aH(r,r)[Vt+1Fi(t)] + bS[Ft(r) Ft(r)] ;

with summation over r units nearest to r.

Competitive Hebbian models simulate correctly strabismus and development of

maps for biased or restricted patterns.

Allow for joint pattern development of ocular dominance and orientation.

Linear zone are perhaps less prominent as they should be, but with the present

experimental data it is hard to quantify.
http://localhost/var/www/apps/conversion/tmp/scratch_6/model-elastic.gifhttp://localhost/var/www/apps/conversion/tmp/scratch_6/model-elastic.gif


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Summary of results

Linear zones: perhaps less prominent in correlation-based models and SOM-h.

Singularities: arise spontaneously in most models but missing or wrong insome structural models; saddle points wrong only in Icecube model.

Fractures: correct in most models; Miller and Linsker models predict

discontinuities but higher map resolutions are needed to resolve this.

Global disorder: missing only from structural models.

Orthogonality: local appears in most models but may be too strong in SOM-l

and EN; global may be a separate property, addressed only by Sindales model

Power spectrum: wrong in some models, low-pass instead of band-pass filters.

Distribution of feature specificities: correct in models that include them.

Anisotropies, monocular deprivation: easy to get.

Orientation deprivation, bias, joint development of occularity and orientation,

correlations of higher orientation specificity with occularity: only in

competitive Hebbian?


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Conclusions

Structural models (Hubel, Wisel, Breitenberg) do not agree with

experimental data.

Competitive Hebbian approaches have qualitative properties that

agree with almost all experimental data.

More precise data are needed to eliminate other models.

Orientation selectivity is probably activity driven but

models using recurrent lateral connections may explain it using only intra-cortical

dynamics; including contrast-invariance of orientation tuning, development of the

orientation tuning may help to answer to what degree this mechanism is sufficient.

Interplay between theory/experiment is essential to understanding

topographical maps.

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Brain Maps