FAU Erlangen-Nuremberg


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Prof. Dr. Gabriel Wittum


Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
Uni Heidelberg
Im Neuenheimer Feld 368
69120 Heidelberg

phone: 06221 548855
fax: 06221 548860

email: wittum@iwr.uni-heidelberg.de



Estimation of Parameters in Three Dimensional Volume Models for Signal Processing in Neurons by Optimization Multigrid

We have developed mathematical models with which we can investigate functional properties of signal coding in brain cells, in particular neurons. Signal processing in neurons takes place on different levels. For one, electrical signals are propagated in the dendritic tree, towards or away from the soma. Secondly, electrical information that reaches the soma is partially re-coded as a calcium wave that propagates towards and into the cell nucleus, activating cascades which result in the expression of certain genes. To address both signal processing in the dendritic tree of the neuron and calcium signaling at the cell nucleus, we have developed three dimensional volume models of neurons and of neuron cell nuclei on which PDEs describe the underlying signaling processes. Embedded in these equations are a number of parameters, such as neuronal membrane capacitance, inner- and outer-neuronal capacitance or diffusion parameters for nuclear calcium. In some cases literature is rare concerning the actual values of these parameters. This is where our project steps in. The target of this project is to develop a method based on the multiple shooting technique for PDEs to master the full extent of parameter identification in signal processing in neurons.

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