Geodesic Tubes for Uncertainty Quantification in Diffusion MRI

Rick Sengers; Luc Florack; Andrea Fuster

doi:10.1007/978-3-030-78191-0_22

Geodesic Tubes for Uncertainty Quantification in Diffusion MRI

Rick Sengers, Luc Florack, Andrea Fuster

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

Abstract

Based on diffusion tensor imaging (DTI), one can construct a Riemannian manifold in which the dual metric is proportional to the DTI tensor. Geodesic tractography then amounts to solving a coupled system of nonlinear differential equations, either as initial value problem (given seed location and initial direction) or as boundary value problem (given seed and target location). We propose to furnish the tractography framework with an uncertainty quantification paradigm that captures the behaviour of geodesics under small perturbations in (both types of) boundary conditions. For any given geodesic this yields a coupled system of linear differential equations, for which we derive an exact solution. This solution can be used to construct a geodesic tube, a volumetric region around the fiducial geodesic that captures the behaviour of perturbed geodesics in the vicinity of the original one.

Original language	English
Title of host publication	Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings
Editors	Aasa Feragen, Stefan Sommer, Julia Schnabel, Mads Nielsen
Publisher	Springer
Pages	279-290
Number of pages	12
ISBN (Print)	9783030781903
DOIs	https://doi.org/10.1007/978-3-030-78191-0_22
Publication status	Published - 2021
Event	27th International Conference on Information Processing in Medical Imaging, IPMI 2021 - Virtual, Online Duration: 28 Jun 2021 → 30 Jun 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12729 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	27th International Conference on Information Processing in Medical Imaging, IPMI 2021
City	Virtual, Online
Period	28/06/21 → 30/06/21

Bibliographical note

Funding Information:
This work is part of the research programme ?Diffusion MRI Tractography with Uncertainty Propagation for the Neurosurgical Workflow? with project number 16338, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). The work of A. Fuster is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is financially supported by the Netherlands Organisation for Scientific Research (NWO). We would like to thank neurosurgeon Geert-Jan Rutten for sharing the two clinical datasets used in our experiments at the Elisabeth TweeSteden Hospital (ETZ) in Tilburg, The Netherlands, and for fruitful discussions.

Keywords

Diffusion tensor imaging
Geodesic deviation
Geodesic tractography
Riemannian geometry
Uncertainty quantification

Access to Document

10.1007/978-3-030-78191-0_22

Cite this

Sengers, R., Florack, L., & Fuster, A. (2021). Geodesic Tubes for Uncertainty Quantification in Diffusion MRI. In A. Feragen, S. Sommer, J. Schnabel, & M. Nielsen (Eds.), Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings (pp. 279-290). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12729 LNCS). Springer. https://doi.org/10.1007/978-3-030-78191-0_22

Sengers, Rick ; Florack, Luc ; Fuster, Andrea. / Geodesic Tubes for Uncertainty Quantification in Diffusion MRI. Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. editor / Aasa Feragen ; Stefan Sommer ; Julia Schnabel ; Mads Nielsen. Springer, 2021. pp. 279-290 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "Based on diffusion tensor imaging (DTI), one can construct a Riemannian manifold in which the dual metric is proportional to the DTI tensor. Geodesic tractography then amounts to solving a coupled system of nonlinear differential equations, either as initial value problem (given seed location and initial direction) or as boundary value problem (given seed and target location). We propose to furnish the tractography framework with an uncertainty quantification paradigm that captures the behaviour of geodesics under small perturbations in (both types of) boundary conditions. For any given geodesic this yields a coupled system of linear differential equations, for which we derive an exact solution. This solution can be used to construct a geodesic tube, a volumetric region around the fiducial geodesic that captures the behaviour of perturbed geodesics in the vicinity of the original one.",

keywords = "Diffusion tensor imaging, Geodesic deviation, Geodesic tractography, Riemannian geometry, Uncertainty quantification",

author = "Rick Sengers and Luc Florack and Andrea Fuster",

note = "Funding Information: This work is part of the research programme ?Diffusion MRI Tractography with Uncertainty Propagation for the Neurosurgical Workflow? with project number 16338, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). The work of A. Fuster is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is financially supported by the Netherlands Organisation for Scientific Research (NWO). We would like to thank neurosurgeon Geert-Jan Rutten for sharing the two clinical datasets used in our experiments at the Elisabeth TweeSteden Hospital (ETZ) in Tilburg, The Netherlands, and for fruitful discussions. ; 27th International Conference on Information Processing in Medical Imaging, IPMI 2021 ; Conference date: 28-06-2021 Through 30-06-2021",

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Sengers, R , Florack, L & Fuster, A 2021, Geodesic Tubes for Uncertainty Quantification in Diffusion MRI. in A Feragen, S Sommer, J Schnabel & M Nielsen (eds), Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12729 LNCS, Springer, pp. 279-290, 27th International Conference on Information Processing in Medical Imaging, IPMI 2021, Virtual, Online, 28/06/21. https://doi.org/10.1007/978-3-030-78191-0_22

Geodesic Tubes for Uncertainty Quantification in Diffusion MRI. / Sengers, Rick ; Florack, Luc ; Fuster, Andrea.

Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. ed. / Aasa Feragen; Stefan Sommer; Julia Schnabel; Mads Nielsen. Springer, 2021. p. 279-290 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12729 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Florack, Luc

AU - Fuster, Andrea

N1 - Funding Information: This work is part of the research programme ?Diffusion MRI Tractography with Uncertainty Propagation for the Neurosurgical Workflow? with project number 16338, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO). The work of A. Fuster is part of the research program of the Foundation for Fundamental Research on Matter (FOM), which is financially supported by the Netherlands Organisation for Scientific Research (NWO). We would like to thank neurosurgeon Geert-Jan Rutten for sharing the two clinical datasets used in our experiments at the Elisabeth TweeSteden Hospital (ETZ) in Tilburg, The Netherlands, and for fruitful discussions.

PY - 2021

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N2 - Based on diffusion tensor imaging (DTI), one can construct a Riemannian manifold in which the dual metric is proportional to the DTI tensor. Geodesic tractography then amounts to solving a coupled system of nonlinear differential equations, either as initial value problem (given seed location and initial direction) or as boundary value problem (given seed and target location). We propose to furnish the tractography framework with an uncertainty quantification paradigm that captures the behaviour of geodesics under small perturbations in (both types of) boundary conditions. For any given geodesic this yields a coupled system of linear differential equations, for which we derive an exact solution. This solution can be used to construct a geodesic tube, a volumetric region around the fiducial geodesic that captures the behaviour of perturbed geodesics in the vicinity of the original one.

AB - Based on diffusion tensor imaging (DTI), one can construct a Riemannian manifold in which the dual metric is proportional to the DTI tensor. Geodesic tractography then amounts to solving a coupled system of nonlinear differential equations, either as initial value problem (given seed location and initial direction) or as boundary value problem (given seed and target location). We propose to furnish the tractography framework with an uncertainty quantification paradigm that captures the behaviour of geodesics under small perturbations in (both types of) boundary conditions. For any given geodesic this yields a coupled system of linear differential equations, for which we derive an exact solution. This solution can be used to construct a geodesic tube, a volumetric region around the fiducial geodesic that captures the behaviour of perturbed geodesics in the vicinity of the original one.

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KW - Geodesic deviation

KW - Geodesic tractography

KW - Riemannian geometry

KW - Uncertainty quantification

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M3 - Conference contribution

SN - 9783030781903

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 279

EP - 290

BT - Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings

A2 - Feragen, Aasa

A2 - Sommer, Stefan

A2 - Schnabel, Julia

A2 - Nielsen, Mads

PB - Springer

T2 - 27th International Conference on Information Processing in Medical Imaging, IPMI 2021

Y2 - 28 June 2021 through 30 June 2021

ER -

Sengers R , Florack L , Fuster A. Geodesic Tubes for Uncertainty Quantification in Diffusion MRI. In Feragen A, Sommer S, Schnabel J, Nielsen M, editors, Information Processing in Medical Imaging - 27th International Conference, IPMI 2021, Proceedings. Springer. 2021. p. 279-290. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-78191-0_22

Geodesic Tubes for Uncertainty Quantification in Diffusion MRI

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