Geodesic Tubes for Uncertainty Quantification in Diffusion MRI

Sengers, Rick; Florack, Luc; Fuster, Andrea

doi:10.1007/978-3-030-78191-0_22

Cited by 4 publications

(4 citation statements)

References 14 publications

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“…The effect of boundary variations of type Eq. 40a have recently been considered elsewhere (Sengers et al (2021)). These two types of perturbations are invariably present in any tractography algorithm due to DTI domain and codomain uncertainties.…”

Section: Resultsmentioning

confidence: 99%

“…30, restricted to the Riemannian case of interest. This allows us to predict the behaviour of neighbouring geodesics without explicitly solving their nonlinear geodesic equations, as long as these are sufficiently close to the fiducial geodesic x x (t), as described in Sengers et al (2021), in which families of neighbouring geodesics are defined via continuous perturbations of the side conditions, Eq. 39.…”

Section: Riemann-dti Paradigm: Geodesic Deviationmentioning

confidence: 99%

“…This case is mathematically considerably less mind-boggling since it allows us to stay within the realm of well-established Riemannian geometry. Another practical issue is the effect of noise and errors in (automatic or manual) seeding, which can be naturally accounted for by considering the concept of geodesic deviation, furnishing geodesic tracks with volumetric counterparts in the form of tubular uncertainty neighbourhoods ("geodesic tubes") (Sengers et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

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Geodesic Uncertainty in Diffusion MRI

Sengers

Florack

Fuster

2021

Front. Comput. Sci.

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We study theoretical and operational issues of geodesic tractography, a geometric methodology for retrieving biologically plausible neural fibers in the brain from diffusion weighted magnetic resonance imaging. The premise is that true positives are geodesics in a suitably constructed metric space, but unlike traditional first order methods these are not a priori constrained to connect nongeneric points on subdimensional manifolds, such as the characteristics in traditional streamline methods. By virtue of the Hopf-Rinow theorem geodesic tractography furnishes a huge amount of redundancy, ensuring the a priori existence of at least one tentative fiber between any two points and permitting additional tractometric and data-extrinsic constraints for (fuzzy or crisp) classification of true and false positives. In our feasibility study we consider a hybrid paradigm that unifies existing ideas on tractography, combining deterministic and probabilistic elements in a way naturally supported by metric geometry. Particular attention is paid to an analytical prediction of geodesic deviation on numerically computed geodesics, a ‘tidal’ effect induced by small perturbations resulting from data noise. Taking these effects into account clarifies the inherent uncertainty of geodesics, while simultaneosuly offering a dimensionality reduction of the tractography problem.

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Section: Resultsmentioning

confidence: 99%

Section: Riemann-dti Paradigm: Geodesic Deviationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Geodesic Uncertainty in Diffusion MRI

Sengers

Florack

Fuster

2021

Front. Comput. Sci.

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“…This problem has been addressed by several strategies to improve the adherence of geodesics to the white matter geometry, including "sharpening" the inverse diffusion tensor , using the adjugate of the diffusion tensor (Fuster et al, 2016), and using a conformal metric (Hao et al, 2014). One advantage to the geodesic tractography formulation is that we can do uncertainty and confidence interval analysis of the tractographies following (Sengers et al, 2021).…”

Section: Introductionmentioning

confidence: 99%

Integrated Construction of Multimodal Atlases with Structural Connectomes in the Space of Riemannian Metrics

Campbell

Dai

et al. 2022

Melba

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The structural network of the brain, or structural connectome, can be represented by fiber bundles generated by a variety of tractography methods. While such methods give qualitative insights into brain structure, there is controversy over whether they can provide quantitative information, especially at the population level. In order to enable population-level statistical analysis of the structural connectome, we propose representing a connectome as a Riemannian metric, which is a point on an infinite-dimensional manifold. We equip this manifold with the Ebin metric, a natural metric structure for this space, to get a Riemannian manifold along with its associated geometric properties. We then use this Riemannian framework to apply object-oriented statistical analysis to define an atlas as the Fréchet mean of a population of Riemannian metrics. This formulation ties into the existing framework for diffeomorphic construction of image atlases, allowing us to construct a multimodal atlas by simultaneously integrating complementary white matter structure details from DWMRI and cortical details from T1-weighted MRI. We illustrate our framework with 2D data examples of connectome registration and atlas formation. Finally, we build an example 3D multimodal atlas using T1 images and connectomes derived from diffusion tensors estimated from a subset of subjects from the Human Connectome Project.

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