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

Ghosh, Aurobrata; Deriche, Rachid

doi:10.1088/1741-2560/13/1/011001

Cited by 9 publications

(7 citation statements)

References 137 publications

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“…However, DTI yields only a fraction of the information potentially accessible by diffusion MRI, mainly due to the fact that the DTI is unable to quantify non-Gaussian diffusion [ 29 ]. In the brain, non-Gaussian diffusion is known to be substantial and arises from diffusion barriers, such as cell membranes and organelles as well as water-containing compartments (both extracellular and intracellular) with differing diffusion properties.…”

Section: Introductionmentioning

confidence: 99%

Divergent topological networks in Alzheimer’s disease: a diffusion kurtosis imaging analysis

Cheng

Zhang

Peng

et al. 2018

Transl Neurodegener

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BackgroundBrain consists of plenty of complicated cytoarchitecture. Gaussian-model based diffusion tensor imaging (DTI) is far from satisfactory interpretation of the structural complexity. Diffusion kurtosis imaging (DKI) is a tool to determine brain non-Gaussian diffusion properties. We investigated the network properties of DKI parameters in the whole brain using graph theory and further detected the alterations of the DKI networks in Alzheimer’s disease (AD).MethodsMagnetic resonance DKI scanning was performed on 21 AD patients and 19 controls. Brain networks were constructed by the correlation matrices of 90 regions and analyzed through graph theoretical approaches.ResultsWe found small world characteristics of DKI networks not only in the normal subjects but also in the AD patients; Grey matter networks of AD patients tended to be a less optimized network. Moreover, the divergent small world network features were shown in the AD white matter networks, which demonstrated increased shortest paths and decreased global efficiency with fiber tractography but decreased shortest paths and increased global efficiency with other DKI metrics. In addition, AD patients showed reduced nodal centrality predominantly in the default mode network areas. Finally, the DKI networks were more closely associated with cognitive impairment than the DTI networks.ConclusionsOur results suggest that DKI might be superior to DTI and could serve as a novel approach to understand the pathogenic mechanisms in neurodegenerative diseases.

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Section: Introductionmentioning

confidence: 99%

Divergent topological networks in Alzheimer’s disease: a diffusion kurtosis imaging analysis

Cheng

Zhang

Peng

et al. 2018

Transl Neurodegener

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“…A natural complement to the formulation of a multiscale hypothesis is the construction of a multiscale network. Take, for example, the primary organ of human curiosity: the human brain can naturally be divided into cortical and subcortical areas whose boundaries can be drawn either by using anatomical information such as cytoarchitecture (Brodmann, 1909), or by using functional information such as patterns of activity (Glasser et al, 2016). Each of these parcels is thought to perform specific computations or produce specific cognitive functions, with subdivisions into larger parcels mapping on to coarser functions and subdivisions into smaller parcels mapping on to finer functions (Betzel & Bassett, 2016).…”

Section: Simple Fundamental Concepts From Network Sciencementioning

confidence: 99%

On Curiosity: A Fundamental Aspect of Personality, a Practice of Network Growth

Zurn

Bassett

2018

Personality Neuroscience

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Human personality is reflected in patterns—or networks—of behavior, either in thought or action. Curiosity is an oft-treasured component of one’s personality, commonly associated with information-seeking proclivities with distinct neurophysiological correlates. The markers of curiosity can differ substantially across people, suggesting the possibility that personality also determines the architectural style of one’s curiosity. Yet progress in defining those styles, and marking their neurophysiological basis, has been hampered by fairly fundamental difficulties in defining curiosity itself. Here, we offer and exercise a definition of the practice of curiosity as knowledge network building, one particular pattern of thought behavior. To unpack this definition and motivate its utility, we begin with a short primer on network science and describe how the mathematical object of a network can be used to map items and relations that are characteristic of bodies of knowledge. Next, we turn to a discussion of how networks grow, how their growth can be modeled, and how the practice of curiosity can be formalized as a process of network growth. We pay particular attention to how individuals may differ in how they build their knowledge networks, and discuss how the sort, manner, and action of building can be modulated by experience. We discuss how this definition of the practice of curiosity motivates new experiments and theory development at the interdisciplinary intersection of network science, personality neuroscience, education, and curiosity studies. We close with a note on the potential of network science to inform studies of other domains of personality, and the patterns of thought– or action–behavior characteristic thereof.

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“…DTI cannot discern between complex fibre bundle configurations such as fiber crossings or kissings. With the advent of higher angular resolution diffusion imaging or Q-ball imaging, higher order models of the diffusion signal were thus investigated [GD16]. Figure 1.2 illustrates, at a sample of voxels, diffusion as the graph of a function on the sphere.…”

Section: Biomarkers In Neuroimagingmentioning

confidence: 99%

Rational Invariants of Even Ternary Forms Under the Orthogonal Group

2018

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In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group O 3 on the space R[x, y, z] 2d of ternary forms of even degree 2d. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to determining the invariants for the action on a subspace of the finite subgroup B 3 of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed B 3 -equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the B 3 -invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the O 3 -invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed B 3 -invariants to determine the O 3 -orbit locus and provide an algorithm for the inverse problem of finding an element in R[x, y, z] 2d with prescribed values for its invariants. These computational issues are relevant in brain imaging.the action of O 3 on R[x, y, z] 4 is determined as a subset of a minimal generating set of polynomial invariants of the action of O 3 on the elasticity tensor in [OKA17]. There, the problem is mapped to the joint action of SL 2 (C) on binary forms of different degrees and resolved by Gordan's algorithm [GY10, Oli17] so that the invariants are given as transvectants.A generating set of rational invariants separates general orbits [PV94, Ros56] -this remains true for any group, even for non-reductive groups. Rational invariants can thus prove to be sufficient, and sometimes more relevant, in applications [HL12, HL13, HL16] and in connection with other mathematical disciplines [HK07b,Hub12]. A practical and very general algorithm to compute a generating set of these first appeared in [HK07a]; see also [DK15]. The case of the action of O 3 on R[x, y, z] 4 , a 15-dimensional space, is nonetheless not easily tractable by this algorithm. In the case of R[x, y, z] 4 , the 12 generating invariants we construct in this article are seen as being uniquely determined by their restrictions to a slice Λ 4 , which is here a 12dimensional subspace. The knowledge of these restrictions is proved to be sufficient to evaluate the invariants at any point in the space R[x, y, z] 4 . The underlying slice method is a technique used to show rationality of invariant fields [CTS07]. We demonstrate here its power for the computational aspects of Invariant Theory.

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

Cited by 9 publications

References 137 publications

Divergent topological networks in Alzheimer’s disease: a diffusion kurtosis imaging analysis

Divergent topological networks in Alzheimer’s disease: a diffusion kurtosis imaging analysis

On Curiosity: A Fundamental Aspect of Personality, a Practice of Network Growth

Rational Invariants of Even Ternary Forms Under the Orthogonal Group

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