Computational model of the Computational model of the brain stem functionsbrain stem functions

Włodzisław DuchWłodzisław Duch, , Krzysztof Dobosz, Grzegorz OsińskiKrzysztof Dobosz, Grzegorz Osiński

Department of InformaticsDepartment of Informatics/Physics/PhysicsNicolaus Copernicus UniversityNicolaus Copernicus University, , Toruń, PolandToruń, Poland

Google: W. DuchGoogle: W. Duch

Neuromath, Rome, Dec. 2007Neuromath, Rome, Dec. 2007

Brain stemBrain stemMost important but least understood Most important but least understood brain structure, integrative center for brain structure, integrative center for regulation of respiration, muscle regulation of respiration, muscle tone, cardiovascular function, level tone, cardiovascular function, level of consciousness, motor responses of consciousness, motor responses to sensory stimuli, homeostasis. to sensory stimuli, homeostasis.

The reticular formation is a poorly The reticular formation is a poorly understood, complex network of understood, complex network of neurons required for maintenance of neurons required for maintenance of wakefulness and alertness.wakefulness and alertness.

Receives huge number of ascending Receives huge number of ascending and descending inputs.and descending inputs.

Not much progress since Mcculloch & Kilmer 1969 model!Not much progress since Mcculloch & Kilmer 1969 model!

Brain StrokeBrain Stroke A major cause of physical & social impairment, 3A major cause of physical & social impairment, 3rdrd cause cause

of death in Europe.of death in Europe. Brain stem stroke is particularly damaging to basic Brain stem stroke is particularly damaging to basic

physiological functions, including breathing.physiological functions, including breathing. Many types of breathing patterns have been recorded Many types of breathing patterns have been recorded

using brain spirographic techniques.using brain spirographic techniques. Neurologists have no clue how to interpret these Neurologists have no clue how to interpret these

patterns; we need analysis/parametric model to do it.patterns; we need analysis/parametric model to do it. Non-linear analysis techniques have been used (return Non-linear analysis techniques have been used (return

maps, fractal dimensions, ICA, etc) with limited success.maps, fractal dimensions, ICA, etc) with limited success. New techniques based on fuzzy symbolic dynamics are New techniques based on fuzzy symbolic dynamics are

being developed. being developed.

Spirography data examplesSpirography data examples

Better: monitor lower/upper lung muscles + air flow.Samples obtained from M. Świerkocka-Miastowska, Medical Academy of Gdańsk, Poland

Spirography analysisSpirography analysis

Example of a pathological signal analysisExample of a pathological signal analysis

SSimplified schematic presentation of levels of control of implified schematic presentation of levels of control of breathing; PRG – Pontine Respiratory Group, VRG – Ventral breathing; PRG – Pontine Respiratory Group, VRG – Ventral Respiratory Group, DRG – Dorsal Respiratory Group.Respiratory Group, DRG – Dorsal Respiratory Group.

Levels of control of breathingLevels of control of breathing

Neural Respiratory Rhythm Neural Respiratory Rhythm GeneratorGenerator

Parametric neural network model, three populations of Parametric neural network model, three populations of spiking neurons: beaters (200 in the model), bursters spiking neurons: beaters (200 in the model), bursters (50) and followers (50), Butera et. al. 1999.(50) and followers (50), Butera et. al. 1999.

Reconstructing dynamics of stem structures responsible Reconstructing dynamics of stem structures responsible for rhythm generation and upper and lower lung musclesfor rhythm generation and upper and lower lung muscles

First calibration with respect to control grup data analysis First calibration with respect to control grup data analysis (first look at different breathing patterns generated by (first look at different breathing patterns generated by respiratory center)respiratory center)

Second calibration with respect to stroke grup data Second calibration with respect to stroke grup data analysis (simulation of changes in breathing patterns as analysis (simulation of changes in breathing patterns as a result of specific neuroanatomical and a result of specific neuroanatomical and neuropathological lesions)neuropathological lesions)

First model of the First model of the Respiratory Rhythm GeneratorRespiratory Rhythm Generator

Fuzzy Symbolic Dynamics (FSD)Fuzzy Symbolic Dynamics (FSD)

Trajectory of dynamical Trajectory of dynamical systemsystem (neural activities, av. rates): (neural activities, av. rates):

1..1..{ ( )}t N

i i nx t

1. Normalize in every dimension1. Normalize in every dimension

2. Find cluster centers (e.g. by k-means algorithm): 2. Find cluster centers (e.g. by k-means algorithm): RR11, , RR2 2 ......

3. Transform to 2D:3. Transform to 2D:

11 2

11

|| ( ) ||1( ) exp

22

x t Ry t

22 2

22

|| ( ) ||1( ) exp

22

x t Ry t

FSD exampleFSD example

Example generated from 2346 vectors, each containing membrane Example generated from 2346 vectors, each containing membrane potentials of 50 follower cells from the Respiratory Rhythm Generator.potentials of 50 follower cells from the Respiratory Rhythm Generator.

More detailed viewsMore detailed views

Same 50-D example, focusing on 3 clusters representing different Same 50-D example, focusing on 3 clusters representing different attractors.attractors.

FSD developmentFSD development

Optimization of cluster centers and standard deviations Optimization of cluster centers and standard deviations of Gaussian functions to see more structure.of Gaussian functions to see more structure.

Supervised clustering, characterization of basins of Supervised clustering, characterization of basins of attractors, transition probabilities, types of oscillations attractors, transition probabilities, types of oscillations around each attractor.around each attractor.

Multiple observations of trajectories in (Multiple observations of trajectories in (yyii,,yyjj) coordinates ) coordinates

for pairs of attractors.for pairs of attractors.

Visualization in 3D and higher (lattice projections etc).Visualization in 3D and higher (lattice projections etc).

More tests on real data. More tests on real data.

Future plansFuture plans

Time to pay more attention to the brain stem!Time to pay more attention to the brain stem! Analysis of types of behavior of the model.Analysis of types of behavior of the model. Lesion studies.Lesion studies. Parametric fits to real breathing patterns.Parametric fits to real breathing patterns. Connection to the simulated model of lungs, feedback.Connection to the simulated model of lungs, feedback. Extension to other major areas of the brain stem.Extension to other major areas of the brain stem. Correlation of the brain stem activity (reticular formation) Correlation of the brain stem activity (reticular formation)

with other brain areas. with other brain areas. Brain stem as global controller of the cortex, transition to Brain stem as global controller of the cortex, transition to

coma and persistent vegetative state. coma and persistent vegetative state. EU Project: Poland, Denmark, Italy, UK, Japan.EU Project: Poland, Denmark, Italy, UK, Japan.