Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI
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Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI. / Dela Haije, Tom; Feragen, Aasa.
Anisotropy Across Fields and Scales. red. / Evren Özarslan; Thomas Schultz; Eugene Zhang; Andrea Fuster. Springer, 2021. s. 193-202 (Mathematics and Visualization).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI
AU - Dela Haije, Tom
AU - Feragen, Aasa
N1 - Publisher Copyright: © 2021, The Author(s).
PY - 2021
Y1 - 2021
N2 - Diffusion-weighted magnetic resonance imaging (MRI) is sensitive to ensemble-averaged molecular displacements, which provide valuable information on e.g. structural anisotropy in brain tissue. However, a concrete interpretation of diffusion-weighted MRI data in terms of physiological or structural parameters turns out to be extremely challenging. One of the main reasons for this is the multi-scale nature of the diffusion-weighted signal, as it is sensitive to the microscopic motion of particles averaged over macroscopic volumes. In order to analyze the geometrical patterns that occur in (diffusion-weighted measurements of) biological tissue and many other structures, we may invoke tools from the field of stochastic geometry. Stochastic geometry describes statistical methods and models that apply to random geometrical patterns of which we may only know the distribution. Despite its many uses in geology, astronomy, telecommunications, etc., its application in diffusion-weighted MRI has so far remained limited. In this work we review some fundamental results in the field of diffusion-weighted MRI from a stochastic geometrical perspective, and discuss briefly for which other questions stochastic geometry may prove useful. The observations presented in this paper are partly inspired by the Workshop on Diffusion MRI and Stochastic Geometry held at Sandbjerg Estate (Denmark) in 2019, which aimed to foster communication and collaboration between the two fields of research.
AB - Diffusion-weighted magnetic resonance imaging (MRI) is sensitive to ensemble-averaged molecular displacements, which provide valuable information on e.g. structural anisotropy in brain tissue. However, a concrete interpretation of diffusion-weighted MRI data in terms of physiological or structural parameters turns out to be extremely challenging. One of the main reasons for this is the multi-scale nature of the diffusion-weighted signal, as it is sensitive to the microscopic motion of particles averaged over macroscopic volumes. In order to analyze the geometrical patterns that occur in (diffusion-weighted measurements of) biological tissue and many other structures, we may invoke tools from the field of stochastic geometry. Stochastic geometry describes statistical methods and models that apply to random geometrical patterns of which we may only know the distribution. Despite its many uses in geology, astronomy, telecommunications, etc., its application in diffusion-weighted MRI has so far remained limited. In this work we review some fundamental results in the field of diffusion-weighted MRI from a stochastic geometrical perspective, and discuss briefly for which other questions stochastic geometry may prove useful. The observations presented in this paper are partly inspired by the Workshop on Diffusion MRI and Stochastic Geometry held at Sandbjerg Estate (Denmark) in 2019, which aimed to foster communication and collaboration between the two fields of research.
UR - http://www.scopus.com/inward/record.url?scp=85102565854&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-56215-1_9
DO - 10.1007/978-3-030-56215-1_9
M3 - Article in proceedings
AN - SCOPUS:85102565854
SN - 9783030562144
T3 - Mathematics and Visualization
SP - 193
EP - 202
BT - Anisotropy Across Fields and Scales
A2 - Özarslan, Evren
A2 - Schultz, Thomas
A2 - Zhang, Eugene
A2 - Fuster, Andrea
PB - Springer
T2 - Workshop on Visualization and Processing of Anisotropy in Imaging, Geometry, and Astronomy, 2018
Y2 - 28 October 2018 through 2 November 2018
ER -
ID: 285251252