Transcript Computational model of the brain stem functions

Computational model of the
brain stem functions
Włodzisław Duch,
Krzysztof Dobosz, Grzegorz Osiński
Department of Informatics/Physics
Nicolaus Copernicus University, Toruń, Poland
Google: W. Duch
Neuromath, Rome, Dec. 2007
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!
Brain Stroke
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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.
Spirography data examples
Better: monitor lower/upper lung muscles + air flow.
Samples obtained from M. Świerkocka-Miastowska, Medical Academy of
Gdańsk, Poland
Spirography analysis
Example of a pathological signal analysis
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.
Neural Respiratory Rhythm
Generator
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Parametric neural network model, three populations of
spiking neurons: beaters (200 in the model), bursters
(50) and followers (50), Butera et. al. 1999.
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Reconstructing dynamics of stem structures responsible
for rhythm generation and upper and lower lung muscles
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First calibration with respect to control grup data analysis
(first look at different breathing patterns generated by
respiratory center)
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Second calibration with respect to stroke grup data
analysis (simulation of changes in breathing patterns as
a result of specific neuroanatomical and
neuropathological lesions)
First model of the
Respiratory Rhythm Generator
Fuzzy Symbolic Dynamics (FSD)
Trajectory of dynamical system (neural activities, av. rates):
1.. N
{xi (t )}it 1..
n
1. Normalize in every dimension
2. Find cluster centers (e.g. by k-means algorithm): R1, R2 ...
3. Transform to 2D:
y1 (t ) 
y2 ( t ) 
 || x(t )  R1 || 
exp  
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2
2
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2
1
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1
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 || x(t )  R2 || 
exp  
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2
2
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2
2
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1
2
FSD example
Example generated from 2346 vectors, each containing membrane
potentials of 50 follower cells from the Respiratory Rhythm Generator.
More detailed views
Same 50-D example, focusing on 3 clusters representing different
attractors.
FSD development
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Optimization of cluster centers and standard deviations
of Gaussian functions to see more structure.
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Supervised clustering, characterization of basins of
attractors, transition probabilities, types of oscillations
around each attractor.
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Multiple observations of trajectories in (yi,yj) coordinates
for pairs of attractors.
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Visualization in 3D and higher (lattice projections etc).
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More tests on real data.
Future plans
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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.