From Second to Higher Order Tensors in Diffusion-MRI

Ghosh, Aurobrata; Deriche, Rachid

doi:10.1007/978-1-84882-299-3_15

Cited by 5 publications

(6 citation statements)

References 36 publications

(71 reference statements)

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“…While practical, this assumption limited the ability of the DTI to describe complex, singular and intricate fiber configurations (U-shape, kissing or crossing fibers). To overcome this limitation, so-called Diffusion Spectrum Imaging (DSI) and High Angular Resolution Diffusion Imaging (HARDI) methods such as Q-ball imaging and other multi-tensors, compartment models and high order tensor models were developed to resolve the orientationnality of more complicated fiber bundle configurations (Schultz et al, 2013;Jones, 2011;Johansen-Berg and Behrens, 2009;Ghosh et al, 2013;Ghosh and Deriche, 2009).…”

Section: Advanced Dmri For Structural Connectivitymentioning

confidence: 99%

“…In particular, the exploration of high order tensors and the development of the theory of tensor invariants as a mathematical framework for computing new bio-markers for dMRI offer exciting and innovative research direction to better characterize white matter abnormalities (Ghosh and Deriche, 2009;Schultz et al, 2013). High order tensors will also allow to go beyond simple bio-markers, such as those derived from the classical second order diffusion tensor.…”

Section: Advanced Dmri For Structural Connectivitymentioning

confidence: 99%

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Computational brain connectivity mapping: A core health and scientific challenge

Deriche

2016

Medical Image Analysis

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One third of the burden of all the diseases in Europe is due to problems caused by diseases affecting brain. Although exceptional progress have been obtained for exploring the brain during the past decades, it is still terra-incognita and calls for specific efforts in research to better understand its architecture and functioning. To take up this great challenge of modern science and to solve the limited view of the brain provided just by one imaging modality, this article advocates the idea developed in my research group of a global approach involving new generation of models for brain connectivity mapping and strong interactions between structural and functional connectivities. Capitalizing on the strengths of integrated and complementary non invasive imaging modalities such as diffusion Magnetic Resonance Imaging (dMRI) and Electro & Magneto-Encephalography (EEG & MEG) will contribute to achieve new frontiers for identifying and characterizing structural and functional brain connectivities and to provide a detailed mapping of the brain connectivity, both in space and time. Thus leading to an added clinical value for high impact diseases with new perspectives in computational neuro-imaging and cognitive neuroscience.

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Section: Advanced Dmri For Structural Connectivitymentioning

confidence: 99%

Section: Advanced Dmri For Structural Connectivitymentioning

confidence: 99%

Computational brain connectivity mapping: A core health and scientific challenge

Deriche

2016

Medical Image Analysis

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“…However, the limitations of DTI are also well known. More reliable, higher order dMRI models are now available [50].…”

Section: Diffusion Mri Modelsmentioning

confidence: 99%

A survey of current trends in diffusion MRI for structural brain connectivity

Ghosh

Deriche

2015

J. Neural Eng.

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In this paper, we review the state of the art in diffusion magnetic resonance imaging (dMRI) and we present current trends in modelling the brain's tissue microstructure and the human connectome. dMRI is today the only tool that can probe the brain's axonal architecture in vivo and non-invasively, and has grown in leaps and bounds in the last two decades since its conception. A plethora of models with increasing complexity and better accuracy have been proposed to characterise the integrity of the cerebral tissue, to understand its microstructure and to infer its connectivity. Here, we discuss a wide range of the most popular, important and well-established local microstructure models and biomarkers that have been proposed from these models. Finally, we briefly present the state of the art in tractography techniques that allow us to understand the architecture of the brain's connectivity.

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“…This constraint reflects the fact that we would like to interpret ℛ as a “residual” probability density. Ghosh and Deriche [GD09] compare two methods to enforce nonnegativity in this sense for symmetric fourth‐order tensors; unfortunately, they do not easily carry over to the higher orders. Therefore, we use soft constraints [TCC07] to include the condition ℛ≽ 0 in an approximative way.…”

Section: Computing the Hifivementioning

confidence: 99%

HiFiVE: A Hilbert Space Embedding of Fiber Variability Estimates for Uncertainty Modeling and Visualization

Schultz

Schlaffke

Schoelkopf

et al. 2013

Computer Graphics Forum

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(a) Plot of probability density estimates.(b) Corresponding 95% confidence cones.(c) Proposed HiFiVE glyphs. Figure 1:Four quite different fiber probability distributions (a) lead to the same cones of uncertainty (b), a current standard visualization of variability in fiber directions. We propose a novel glyph that highlights the differences between them (c). AbstractObtaining reproducible fiber direction estimates from diffusion MRI is crucial for successful fiber tracking. Modeling and visualizing the probability distribution of the inferred fiber directions is an important step in evaluating and comparing different acquisition schemes and fiber models. However, this distribution is usually strongly dominated by its main direction, which makes it difficult to examine when plotted naively. In this work, we propose a new visualization of the fiber probability distribution. It is based on embedding the probability measure into a particular reproducing kernel Hilbert space. This permits a decomposition into an embedded delta peak, representing the main direction, and a non-negative residual. They are then combined into a new glyph representation which visually enhances the residual, in order to highlight even subtle differences. Moreover, the magnitude of the delta peak component quantifies precision of the main fiber direction. We demonstrate that our new glyph provides a more detailed impression of the uncertainty than the current standard method, cones that contain 95% of the estimated directions. We use our new method to contribute to the validation of different ways of resampling the data (bootstrapping), and to visualize the differences between alternative acquisition schemes and models for high angular resolution diffusion imaging (HARDI).

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From Second to Higher Order Tensors in Diffusion-MRI

Cited by 5 publications

References 36 publications

Computational brain connectivity mapping: A core health and scientific challenge

Computational brain connectivity mapping: A core health and scientific challenge

A survey of current trends in diffusion MRI for structural brain connectivity

HiFiVE: A Hilbert Space Embedding of Fiber Variability Estimates for Uncertainty Modeling and Visualization

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