inverse solutions for localization of single cell currents based on extracellular measurements...
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![Page 1: Inverse solutions for localization of single cell currents based on extracellular measurements Zoltán Somogyvári 1, István Ulbert 2, Péter Érdi 1,3 1 KFKI](https://reader035.vdocuments.net/reader035/viewer/2022070414/5697c00f1a28abf838cca8ba/html5/thumbnails/1.jpg)
Inverse solutions for localization of single cell currents based on extracellular measurements
Zoltán Somogyvári1, István Ulbert2, Péter Érdi1,3
1 KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, Dept. Biophysics
2 Institute for Psychology of the Hungarian Academy of Sciences3 Center for Complex System Studies, Kalamazoo, Michigan, USA
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The aim: To determine the membrane currents
on a single cell, based on extracellular data!
The experimental setup: A 16 channel, extracellular (EC) electrode system is chronically implanted into cats primary auditory cortex: A1.
The high-pass filtered raw data
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The data we will work on: Mean spatio-temporal patterns of EC potential is obtained
for each putative single neuron.
StSpike clustering with Spike-o-matic.
Cluster averages of 13 putative single cells.
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The EC potential is obtained from the transmembrane current source density via Poisson-equation, but the solution of the Poisson-inverse problem is generally non-unique. Infinitely many source distribution can generate the same measured EC potential distribution.
The EC potential Ф=TJ, where J is
the CSD and T is the lead-field matrix.The affine subspace of the possible
solutions: J(x)=T+Ф+ker(T)x
The problem
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The solution in theoryFrom the multitude J(x) the proper solution can be chosen by applying a priory assumptions. In case of a single spike the proper assumptions are:
1, Each cell is a linesource, parallel to the electrode.
2, The spatial CSD distribution has a sharp negative peak (sink) at the soma, superposed onto a smooth positive (source) background. This assumption is shown to be valid during the first negative deflections of the EC spike. (Somogyvári et al. 2005)
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Requirement 1 can be incorporated into T. To comply the second requirement, the source with the sharpest peak should be chosen by founding the maximal projection of the theoretically sharpest distributions E
i and the
hyperplane T+Ф⨯ker(T):
maxi (S)=
max
i(E
i*
(T+Ф⨯ker(T)))
The solution in theory II.
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The solution in work:The new spike-CSD method
A mathematical “autofocus” algorithm results in not only the sharpest CSD picture, but an estimation for the distance of the cell.
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Tests on simulated data I.
The sCSD outperforms the traditional CSD for these sources.
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Tests on simulated data II.
The sCSD method reconstructs the original source with significantly smaller error than the traditional CSD, while provides an estimation about the cell-electrode distance also.
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Results I.
Spatio-temporal dynamics of action potentials
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Results II.
The sCSD method is able to uncover fine details and cell-type specific differences in initiation and spreading of action potentials, and even possible signs of Ranvier-nodes.
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Results III.
Initiation of the action potential and the Ranvier-spikelets.
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Results IV.
The speed of apical and basal backpropagation
differs and signs of forward propagation also observed
Two dimensional localization of
neurons, results in realistic distances
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Results V.
Henze et al. J. Neurphysiology 84 390-400 2000
Reconstruction of membrane potential, based on EC data with current-based compartmental model.
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The hope
Identification of cortical synaptic input during paired-pulse experiments, could make possible to distinguish between changes in the network/connections and in single cell response for the same input.
Somewhere here,should be the input current,which cause the cell fire
Thank You!