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 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

Example of a pathological signal analysis 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 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)

First model of the Respiratory Rhythm Generator

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:

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 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.

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.