Parameter optimization in models of the olfactory neural system

Abstract We model a mammalian neural olfactory system that is characterized anatomically by modifiable synaptic connections, and physiologically by the spatio-temporal interactions among neural ensembles under external inputs. The behavior of each ensemble is represented by a second order ordinary differential equation (ODE) relating the aggregate activation of cells to system parameters and stimuli from anloutside environment. Parameter optimization rules that lead to minimizing the distance between the computed output patterns of the model and the evoked unit and EEG potentials from experimental data are derived by the methods of error propagation and the calculus of variations. In addition, the existence and uniqueness of the equation set are proved to assure the propriety of the parameter adaptation by these methods. Several subsets (KO, KI, KII) of the olfactory neural (KIII) model are simulated in software. Numerical results support the mathematical analyses, and the system parameters are thus optimized. Our experience with realistic models of neural systems has shown that hundreds of equations and thousands of parameters are required, and the performance of the models may be sensitive to minor software changes, such as adapting them to new machines. We propose that a set of reliable parameter optimization algorithms, including specification of performance criteria, should be an integral component of a realistic neural model.

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