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A Novel Riemannian Metric for Geodesic Tractography in DTI

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Computational Diffusion MRI and Brain Connectivity

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

One of the approaches in diffusion tensor imaging is to consider a Riemannian metric given by the inverse diffusion tensor . Such a metric is used for white matter tractography and connectivity analysis. We propose a modified metric tensor given by the adjugate rather than the inverse diffusion tensor. Tractography experiments on real brain diffusion data show improvement in the vicinity of isotropic diffusion regions compared to results for inverse (sharpened) diffusion tensors.

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Notes

  1. 1.

    Classification of geodesics as fibres requires additional connectivity measures [1, 16].

  2. 2.

    We use Einstein’s summation convention: \(a_{i}{b}^{i}\stackrel{\mbox{ def}}{=}\sum \limits _{i}a_{i}{b}^{i}\).

  3. 3.

    Here we consider the shortest geodesic between any given pair of points to be optimal.

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Acknowledgements

Tom Dela Haije gratefully acknowledges The Netherlands Organisation for Scientific Research (NWO) for financial support. Andrea Fuster would like to thank Lauren O’Donnell for feedback on brain white matter anatomy and Ana Achúcarro.

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Correspondence to Andrea Fuster .

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Fuster, A., Tristan-Vega, A., Haije, T.D., Westin, CF., Florack, L. (2014). A Novel Riemannian Metric for Geodesic Tractography in DTI. In: Schultz, T., Nedjati-Gilani, G., Venkataraman, A., O'Donnell, L., Panagiotaki, E. (eds) Computational Diffusion MRI and Brain Connectivity. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-02475-2_9

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