Riemann-Finsler geometry for diffusion weighted magnetic resonance imaging

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

9 Citations (Scopus)
7 Downloads (Pure)

Abstract

We consider Riemann-Finsler geometry as a potentially powerful mathematical framework in the context of diffusion weighted magnetic resonance imaging. We explain its basic features in heuristic terms, but also provide mathematical details that are essential for practical applications, such as tractography and voxelbased classification. We stipulate a connection between the (dual) Finsler function and signal attenuation observed in the MRI scanner, which directly generalizes Stejskal-Tanner’s solution of the Bloch-Torrey equations and the diffusion tensor imaging (DTI) model inspired by this. The proposed model can therefore be regarded as an extension of DTI. Technically, reconstruction of the (dual) Finsler function from diffusion weighted measurements is a fairly straightforward generalization of the DTI case. The extension of the Riemann differential geometric paradigm for DTI analysis is, however, nontrivial.

Original languageEnglish
Title of host publicationVisualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
EditorsC.-F. Westin, A. Vilanova, B. Burgeth
Place of PublicationBerlin
PublisherSpringer
Pages189-208
Number of pages20
ISBN (Electronic)978-3-642-54301-2
ISBN (Print)978-3-642-54300-5
DOIs
Publication statusPublished - 2014
Event4th Meeting on Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data - Dagstuhl, Germany
Duration: 11 Dec 201116 Dec 2011

Publication series

NameMathematics and Visualization
ISSN (Print)1612-3786

Conference

Conference4th Meeting on Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
CountryGermany
CityDagstuhl
Period11/12/1116/12/11

Fingerprint Dive into the research topics of 'Riemann-Finsler geometry for diffusion weighted magnetic resonance imaging'. Together they form a unique fingerprint.

Cite this