# Inverse Current-Source Density Method in 3D: Reconstruction Fidelity, Boundary Effects, and Influence of Distant Sources

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## Abstract

Estimation of the continuous current-source density in bulk tissue from a finite set of electrode measurements is a daunting task. Here we present a methodology which allows such a reconstruction by generalizing the one-dimensional inverse CSD method. The idea is to assume a particular plausible form of CSD within a class described by a number of parameters which can be estimated from available data, for example a set of cubic splines in 3D spanned on a fixed grid of the same size as the set of measurements. To avoid specificity of particular choice of reconstruction grid we add random jitter to the points positions and show that it leads to a correct reconstruction. We propose different ways of improving the quality of reconstruction which take into account the sources located outside the recording region through appropriate boundary treatment. The efficiency of the traditional CSD and variants of inverse CSD methods is compared using several fidelity measures on different test data to investigate when one of the methods is superior to the others. The methods are illustrated with reconstructions of CSD from potentials evoked by stimulation of a bunch of whiskers recorded in a slab of the rat forebrain on a grid of 4×5×7 positions.

## Keywords

Current source density Local field potentials Evoked potentials Inverse problems Rat Thalamus Somatosensory system## Anatomical Abbreviations

- APT
anterior pretectal nucleus

- cp
cerebral peduncle

- Hipp
hippocampus

- ic
internal capsule

- MG
medial geniculate nucleus

- ml
medial lemniscus

- PO
posterior thalamic nuclear group

- Rt
reticular thalamic nucleus

- SN
substantia nigra

- VPm
ventral posteromedial thalamic nucleus

- ZI
zona incerta

## Notes

### Acknowledgements

We are grateful to Wit Jakuczun for his suggestion to investigate spatial jittering as one way to improve the CSD reconstruction. This work was partly financed from the Polish Ministry of Science and Higher Education research grants N401 146 31/3239 and 2P04C 046 27.

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