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Spatiotemporal multi-resolution approximation of the Amari type neural field model
P Aram1, D R Freestone2, M Dewar3
1Theoretical Neuroscience Group, UMR 1106, Institut de Neurosciences des Systemes, 13385 Marseille, France; Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK.
Neuroimage
|November 3, 2012
Summary
This study introduces a new multi-resolution approximation framework for neural field models, enabling simultaneous analysis of macroscopic and microscopic brain activity. The method uses wavelets and the expectation maximization algorithm for accurate state and parameter estimation.
Area of Science:
- Computational Neuroscience
- Applied Mathematics
- Signal Processing
Background:
- Neural fields model spatiotemporal dynamics of cortical activity across scales.
- Integro-differential equations (IDEs) are effective for describing these neural field dynamics.
- Existing models may struggle to represent simultaneous macroscopic and microscopic behaviors.
Purpose of the Study:
- To develop a flexible multi-resolution approximation (MRA) framework for neural field models.
- To enable simultaneous representation of both macroscopic and microscopic system behaviors.
- To apply the expectation maximization (EM) algorithm for state and parameter estimation within this framework.
Main Methods:
- Implementation of a multi-resolution approximation (MRA) framework.
- Utilizing semi-orthogonal cardinal B-spline wavelets for the integro-difference equation (IDE) neural field model.
- Employing the expectation maximization (EM) algorithm for state and parameter estimation.
Main Results:
- A flexible framework capable of representing neural field dynamics at multiple resolutions simultaneously.
- Successful demonstration of the framework's utility using a synthetic example.
- Accurate state and parameter estimation achieved via the EM algorithm within the MRA framework.
Conclusions:
- The developed MRA framework provides a powerful tool for analyzing neural field models.
- This approach facilitates a unified understanding of brain activity across different scales.
- The framework offers a robust method for estimating neural field states and parameters.