Creation of topographical maps and modeling of brain plasticity.

1
Creation of topographical maps and modeling of
brain plasticity.
Wlodzislaw DuchDepartment of Computer
MethodsNicholas Copernicus UniversityTorun,
PolandGoogle W. Duch
2
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

3
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
• retinal projection on LGN of the thalamus
• retinotopic maps in V1
• SC multimodal maps

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Somatosensory maps

• SI cortex touch, pain, vibration, temperature.
• Somatosensory and motor maps Woolsey (1949),
  Penfield (1959), motor and sensory homunculus.
• Some examples of homunculi

Note representation of face is separate from the
rest of the body. Molecular basis ephrin-A5 ?
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Model of self-organization
SOMF, Self-Organized Feature Mapping, or Kohonen
map. Simplest model of topographic
self-organization via competitive Hebbian
activity-dependent learning.
Signal X activates most strongly a neuron with
synapses W they become more similar to X and
also neurons in the vicinity of W become more
similar to X. Receptive fields of neurons that
are close on the 2D map 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. toes3rd 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 maps

• Evidence 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
• Reorganization is a common feature of topographic
  sensory cortical maps.
• Demonstrated in visual, somatosensory and
  auditory cortex.
• Plasticity extends to higher cortical areas.
• Many processes contribute to functional
  reorganization, different temporally and
  physiological dynamics.
• Changes in receptive field size and location -
  minutes after lesions reorganization of other
  systems - days to weeks (Kossut, 1988).
• 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 to the region at the
  physiological level leads to
• Fast unmasking of existing connections which
  were normally ineffective, ex. unmasking via
  release of inhibition. Thalamic afferents may
  reach 10 columns blocking cortical inhibition
  increases receptive fields.
• 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.
• Longer time scales sprouting of terminals from
  new sources. Demonstrated in the spinal cord.

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Experimental facts

• Optical recordings from large surfaces of macaque
  visual systems.
• High resolution but only superficial layers.
• Elements of orientation selectivity patterns
• Linear zones with iso-orientation contours, 0.5-1
  mm
• Singularities - 180 degree change, clockwise or
  anticlockwise.
• Saddle points - almost constant orientation.
• Fractures - rapid change across a line.
• Characterize various features of such maps in
  statistical way.
• Find theoretical model at mesoscopic level,
  matching the level of experimental observations.

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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.
• Differences between preferred orientations and
  the direction of gradient of preferred
  orientations.
• Distribution of 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
• Continuity - nearby columns react to stimuli with
  similar features - choice of similarity affects
  patterns.
• Diversity - whole feature space should be
  covered.
• 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
• Structural models, assuming specific projections
  due to thalamic organization.
• Spectral Models, filters in Fourier space.
• Correlation-based learning, linear intra-cortical
  interactions with Hebbian learning.
• Competitive Hebbian models, non-linear lateral
  interactions.
• Mixed models and untypical models.

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Structural models

• 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 Götz 1987 Baxter 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 Schwartz 1990
Niebur and Wörgötter 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(n) Ocular
dominance z(r) obtained from convolution of n(r)
and h(r) Orientation map u grad z(r)
Orientation preference qu Rojer,
Swindale wrong predictions of correlations
between orientation preferences and cortical
locations, since all closed integrals vanish.
Iterative models (Swindale map1 and map2)
F(t1) F(t) a (F(t)h(r)) f(F(t)) 0ltalt1
f(F(t)) (1-F(t)) introduces correlation
of select/dominance
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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(t1) Fi (t) aA(r,x)
I(r,r)C0(x,x)Fi(t)I(r,r)C1(x,x)F1-i(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. Ft1(r) Ft (r) a
H(r,r)Vt1-Fi(t) Stimulus V is chosen at
random, the neighborhood H(r,r) is Gaussian
around the winner r using Euclidean
distance. High-dimensional (SOM-h) Ft1(r)
Wi(r) normalized weights, i.e. Ft1(r) (Ft
(r) a H(r,r)Vt1)/(Ft (r) a
H(r,r)Vt1) and correlation distance function
d(V,W)1-V?W
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Elastic Net
Elastic net (Durbin and Wilshaw 1987) Similar to
SOM, adds elastic term Ft1(r) Ft (r) a
H(r,r)Vt1-Fi(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.
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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 in some 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.