Quantifying topological invariants of neuronal morphologies

Lida Kanari; Paweł Dłotko; Martina Scolamiero; Ran Levi; Julian Shillcock; Kathryn Hess; Henry Markram

Quantifying topological invariants of neuronal morphologies

Lida Kanari, Paweł Dłotko, Martina Scolamiero, Ran Levi, Julian Shillcock, Kathryn Hess, Henry Markram

Mathematical Science

Research output: Working paper

Abstract

Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspection and quantitatively described based on morphometric parameters. Neither process provides a solid foundation for categorizing the various morphologies, a problem that is important in many fields. We propose a stable topological measure as a standardized descriptor for any tree-like morphology, which encodes its skeletal branching anatomy. More specifically it is a barcode of the branching tree as determined by a spherical filtration centered at the root or neuronal soma. This Topological Morphology Descriptor (TMD) allows for the discrimination of groups of random and neuronal trees at linear computational cost.

Original language	English
Publisher	ArXiv
Pages	1-15
Number of pages	15
Publication status	Submitted - 28 Mar 2016

Bibliographical note

Acknowledgments
LK and JCS were supported by Blue Brain Project. P.D. and R.L. were supported in part by the Blue Brain Project and by the start-up grant of KH. Partial support for P.D. has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions). MS was supported by the SNF NCCR ”Synapsy”.

Keywords

topological analysis
neuronal
structures
trees
morphologies

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https://arxiv.org/abs/1603.08432Licence: Unspecified

Cite this

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abstract = "Nervous systems are characterized by neurons displaying a diversity of morphological shapes. Traditionally, different shapes have been qualitatively described based on visual inspection and quantitatively described based on morphometric parameters. Neither process provides a solid foundation for categorizing the various morphologies, a problem that is important in many fields. We propose a stable topological measure as a standardized descriptor for any tree-like morphology, which encodes its skeletal branching anatomy. More specifically it is a barcode of the branching tree as determined by a spherical filtration centered at the root or neuronal soma. This Topological Morphology Descriptor (TMD) allows for the discrimination of groups of random and neuronal trees at linear computational cost.",

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AU - Levi, Ran

AU - Shillcock, Julian

AU - Hess, Kathryn

AU - Markram, Henry

N1 - Acknowledgments LK and JCS were supported by Blue Brain Project. P.D. and R.L. were supported in part by the Blue Brain Project and by the start-up grant of KH. Partial support for P.D. has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions). MS was supported by the SNF NCCR ”Synapsy”.

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KW - structures

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M3 - Working paper

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BT - Quantifying topological invariants of neuronal morphologies

PB - ArXiv

ER -

Quantifying topological invariants of neuronal morphologies

Abstract

Bibliographical note

Keywords

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