Computational model of the brain stem functions

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Computational model of the brain stem functions

• Wlodzislaw Duch, Krzysztof Dobosz, Grzegorz
  Osinski
• Department of Informatics/Physics
• Nicolaus Copernicus University, Torun, Poland
• Google W. Duch
• Neuromath, Rome, Dec. 2007

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Brain stem

• Most important but least understood brain
  structure, integrative center for regulation of
  respiration, muscle tone, cardiovascular
  function, level of consciousness, motor responses
  to sensory stimuli, homeostasis.
• The reticular formation is a poorly understood,
  complex network of neurons required for
  maintenance of wakefulness and alertness.
• Receives huge number of ascending and descending
  inputs.

Not much progress since Mcculloch Kilmer 1969
model!
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Brain Stroke

• A major cause of physical social impairment,
  3rd cause of death in Europe.
• Brain stem stroke is particularly damaging to
  basic physiological functions, including
  breathing.
• Many types of breathing patterns have been
  recorded using brain spirographic techniques.
• Neurologists have no clue how to interpret these
  patterns we need analysis/parametric model to do
  it.
• Non-linear analysis techniques have been used
  (return maps, fractal dimensions, ICA, etc) with
  limited success.
• New techniques based on fuzzy symbolic dynamics
  are being developed.

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Spirography data examples
Better monitor lower/upper lung muscles air
flow. Samples obtained from M. Swierkocka-Miastows
ka, Medical Academy of Gdansk, Poland
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Spirography analysis
Example of a pathological signal analysis
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Levels of control of breathing
Simplified schematic presentation of levels of
control of breathing PRG Pontine Respiratory
Group, VRG Ventral Respiratory Group, DRG
Dorsal Respiratory Group.
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Neural Respiratory Rhythm Generator

• Parametric neural network model, three
  populations of spiking neurons beaters (200 in
  the model), bursters (50) and followers (50),
  Butera et. al. 1999.
• Reconstructing dynamics of stem structures
  responsible for rhythm generation and upper and
  lower lung muscles
• First calibration with respect to control grup
  data analysis (first look at different breathing
  patterns generated by respiratory center)
• Second calibration with respect to stroke grup
  data analysis (simulation of changes in breathing
  patterns as a result of specific neuroanatomical
  and neuropathological lesions)

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First model of the Respiratory Rhythm Generator
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Fuzzy Symbolic Dynamics (FSD)

• Trajectory of dynamical system (neural
  activities, av. rates)

1. Normalize in every dimension 2. Find cluster
centers (e.g. by k-means algorithm) R1, R2
... 3. Transform to 2D
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FSD example
Example generated from 2346 vectors, each
containing membrane potentials of 50 follower
cells from the Respiratory Rhythm Generator.
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More detailed views
Same 50-D example, focusing on 3 clusters
representing different attractors.
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FSD development

• Optimization of cluster centers and standard
  deviations of Gaussian functions to see more
  structure.
• Supervised clustering, characterization of basins
  of attractors, transition probabilities, types of
  oscillations around each attractor.
• Multiple observations of trajectories in (yi,yj)
  coordinates for pairs of attractors.
• Visualization in 3D and higher (lattice
  projections etc).
• More tests on real data.

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Future plans

• Time to pay more attention to the brain stem!
• Analysis of types of behavior of the model.
• Lesion studies.
• Parametric fits to real breathing patterns.
• Connection to the simulated model of lungs,
  feedback.
• Extension to other major areas of the brain stem.
• Correlation of the brain stem activity (reticular
  formation) with other brain areas.
• Brain stem as global controller of the cortex,
  transition to coma and persistent vegetative
  state.
• EU Project Poland, Denmark, Italy, UK, Japan.