Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Veera Katharina Menz
Deutsches Primaten Zentrum Göttingen
Modelling of Synaptic STDP and Analysis in a Two-Neuron Model
Synapses as the connecting elements between two brain cells are crucial in transmitting electrical signals
from one neuron to another. Donald Hebb postulated in 1949 that the transmission of signals between
two cells can be improved due to synaptic modification when both cells are active at the same time or
shortly after each other. Additionally, Bi and Poo detected in 1998 that the strength of transmitting signals
can also decrease, depending on the relative spike-timing of the connected cells (spike-timing-dependent
plasticity, short STDP).
We will discuss a mathematical model which describes the behaviour of spiking neurons and synaptic
weight change of connecting synapses in terms of spike-timing-dependent plasticity. By combining an
integrate-and-fire equation with a system of differential equations as a modification of a model of STDP by
Gorchetchnikov, Versace, and Hasselmo (2005) an STDP-curve is produced similar to the one found experimentally
by Bi and Poo (1998). This mathematical model is applied to two coupled neurons stimulated
by a constant external current and examined for long time periods both for permanent external stimulation
as well as short initial stimulation. The results are compared to data of in vivo and in vitro neurons.
Literatur
Bi, G., & Poo, M.-M. (1998). Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on
Spike Timing, Synaptic Strength, and Postsynaptic Cell Type. Journal of Neuroscience, 18(24), 10464 -
10472.
Gorchetchnikov, A., Versace, M., & Hasselmo, M. E. (2005). A mode of STDP based on spatially and
temporally local information: Derivation and combination with gated decay. Neural Networks, 18, 458 -
466.
Hebb, D. O. (1949). The Organization of Behaviour: A Neuropsychological Theory. New York: Wiley.
Ralf Müller
Department of Psychiatry and Psychotherapy, University of Cologne
Modelling coupled network oscillations to study structures in real electroencephalogram
(EEG) data as part of a multifaceted approach for the detection of psychiatric diseases
In medical science, the electroencephalogram (EEG) gives an impression of the dynamics of cortical
brain functions in humans and is used to investigate neurological and psychiatric diseases. Diverse
mathematical methods, e.g. time-frequency methods, are very helpful in disentangling the complexity of
the EEG data and thereby contribute to a better understanding of neurobiological differences between
diseases. Since microscopic and macroscopic neuronal circuits play a key role in understanding complex
psychiatric diseases, e.g. schizophrenia, different approaches in the field of mathematical modelling are
applied. We describe, how analyses and simulations of our neurophysiologically based coupled phase
oscillator model allow new insights into temporal dynamics of sensory processing, which can be detected
in real EEG data in humans.
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