Kernel reconstruction for delayed neural field equations

Alswaihli, J., Potthast, R. ORCID: https://orcid.org/0000-0001-6794-2500, Bojak, I. ORCID: https://orcid.org/0000-0003-1765-3502, Saddy, D. and Hutt, A. (2018) Kernel reconstruction for delayed neural field equations. The Journal of Mathematical Neuroscience, 8. 3. ISSN 2190-8567 doi: 10.1186/s13408-018-0058-8

Abstract/Summary

Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters and in particular the reconstruction of the underlying effective connectivity in biological tissues. In this work, we provide an integral equation approach to the reconstruction of the neural connectivity in the case where the neural activity is governed by a delay neural field equation. As preparation, we study the solution of the direct problem based on the Banach fixed point theorem. Then we reformulate the inverse problem into a family of integral equations of the first kind. This equation will be vector valued when several neural activity trajectories are taken as input for the inverse problem. We employ spectral regularization techniques for its stable solution. A sensitivity analysis of the regularized kernel reconstruction with respect to the input signal u is carried out, investigating the Frechet differentiability of the kernel with respect to the signal. Finally, we use numerical examples to show the feasibility of the approach for kernel reconstruction, including numerical sensitivity tests, which show that the integral equation approach is a very stable and promising approach for practical computational neuroscience.

Item Type	Article
URI	https://reading-pure-test.eprints-hosting.org/id/eprint/75097
Identification Number/DOI	10.1186/s13408-018-0058-8
Refereed	Yes
Divisions	Central Services Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics Life Sciences > School of Psychology and Clinical Language Sciences > Department of Psychology Life Sciences > School of Psychology and Clinical Language Sciences > Department of Clinical Language Sciences
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