(1810 - 1896)

Zoólogo alemán. Su labor científica fue enorme en el campo de las investigaciones zoológicas. Sus aportes se plasmaron en obras sobre mamíferos, aves, insectos, reptiles y moluscos.

Biomedical Sciences

1999 | Statistical identification of non-linear dynamics of normal and epileptic brain.

Main executives entity: National Center for Scientific Research (CNIC)

Main author: Pedro Valdés Sosa.

Summary: A new methodology is developed for the study of stochastic non-linear Systems, and it consists on a synthesis of the empiric identification of the system's properties through the focus guided by data (non parametric series of time) in models, and the calculation of similarity-verisimilitude of physical models (approach guided by models).

When both focuses were applied to the evaluation of cerebral dynamics, it was demonstrated that the normal activity in rest and the existence of an epileptic crisis of wave point can be modeled respectively as physiologic and pathological Hopf bifurcations. The stochastic non-linear models used by the authors constitute a rebuttal to the chaotic theory of epilepsy, based on purely determinist models.

The work consists on 2 revision publications, 8 publications in magazines indexed in the ISI, a patent and 18 presentations in International events. Parts of the work are reflected in two doctoral thesis of Biological and Mathematical Sciences respectively.

The work starts from the premise that neuronal masses are non-linear, stochastic and non-autonomous dynamic systems, and that only convergent application of the methods guided by objects and guided by data will provide useful dynamics theory for the understanding of brain's operation through the study of the encephalogram.

These are its most important results :

- 1. It was demonstrated that normal activity at rest (alpha rhythm) can be modeled as the random fluctuation of a punctual attractor to a limit cycle (Hopf physiological bifurcation) which explains the appearance of both types of attractors in the same proportion in normal population.
- 2. The stochastic non-linear models constitute a rebuttal to chaotic epilepsy theory, because the determinist part corresponds to a limit cycle when it is taken into account the stochastic act field of tip and wave activity.
- 3. The emergence of an epileptic crisis can be modeled as a pathological Hopf bifurcation that goes from a punctual attractor to a stochastic non-physiologic limit cycle. Far from being epilepsy -from authors' point of view- a chaos of a limit cycle corresponds to the establishment of non functional recurrent activity.

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