TY - GEN

T1 - Riemann-Finsler geometry for diffusion weighted magnetic resonance imaging

AU - Florack, Luc

AU - Fuster, Andrea

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84936990790&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-54301-2_8

DO - 10.1007/978-3-642-54301-2_8

M3 - Conference contribution

SN - 978-3-642-54300-5

T3 - Mathematics and Visualization

SP - 189

EP - 208

BT - Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

A2 - Westin, C.-F.

A2 - Vilanova, A.

A2 - Burgeth, B.

PB - Springer

CY - Berlin

T2 - 4th Meeting on Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

Y2 - 11 December 2011 through 16 December 2011

ER -