Estimation of parameters in three dimensional volume models for signal processing in neurons by optimization multigrid

• Antragsteller: Professor Dr. Gillian Queisser; Professor Dr. Gabriel Wittum
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2006 bis 2011
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 25616632

Signal processing in neurons is a highly complex phenomenon, which is still far from being understood. Modelling is indispensable for understanding, since the experimental options, though incredibly refined in the last decades, are still limited. Due to complextiy of the geometric features and the difficulty to access the realistic morphology, models have been restricted either to neural networks, neglecting the geometry of the single neuron, or to compartment modelling, where a neuron is approximated as a tree made up from cylindric compartments. We recently derived the first volume oriented model for signal processing in dendrites, resulting in partial differential equations. These equations contain several parameters which have to be determined from measurements. Thus, a classical optimization problem arises with partial differential equations as constraints. In the present project, we will apply the SQP-multigrid approach, derived by Schulz and Wittum to the problem of estimating parameters in the signal processing model. Convergence is analyzed in the framework of transforming smoothers for optimization problems. In a further step, this approach will be extended to a full model for active signal processing in neurons. Another important topic of the project is robust multigrid methods for optimization problems.

• DFG-Verfahren: Schwerpunktprogramme
• Teilprojekt zu: SPP 1253: Optimierung mit partiellen Differentialgleichungen