Conference paper · Book chapter
Conceptual Parallels Between Stochastic Geometry and Diffusion-Weighted MRI
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.
Language: | English |
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Publisher: | Springer |
Year: | 2021 |
Pages: | 193-202 |
Proceedings: | 2018 Workshop on Visualization and Processing of Anisotropy in Imaging, Geometry, and Astronomy |
Series: | Mathematics and Visualization |
ISBN: | 303056214X , 303056214x , 3030562158 , 9783030562144 and 9783030562151 |
ISSN: | 16123786 and 2197666x |
Types: | Conference paper and Book chapter |
DOI: | 10.1007/978-3-030-56215-1_9 |
ORCIDs: | 0000-0003-3507-3288 and Feragen, Aasa |