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Open AccessJournal ArticleDOI

Mean apparent propagator (MAP) MRI: a novel diffusion imaging method for mapping tissue microstructure

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TLDR
MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space MR signal and transform it into diffusion propagators, and provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure.
About
This article is published in NeuroImage.The article was published on 2013-09-01 and is currently open access. It has received 316 citations till now. The article focuses on the topics: Diffusion Anisotropy & Diffusion MRI.

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Dissertation

Advanced dMRI signal modeling for tissue microstructure characterization

Rutger Fick
TL;DR: An approach allows for the estimation of time-dependent q-space indices, which quantify the time-dependence of the diffusion signal, which is called qt-dMRI.

Finsler geometry and diffusion MRI

TL;DR: The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.
Journal ArticleDOI

Interpretable deep learning as a means for decrypting disease signature in multiple sclerosis.

TL;DR: The results demonstrated that dMRI features extracted in Grey Matter tissues can help in disambiguating PPMS from RRMS patients and, moreover, that LRP heatmaps highlight areas of high relevance which relate well with what is known from literature for MS disease.
Journal ArticleDOI

A theoretical signal processing framework for linear diffusion MRI: Implications for parameter estimation and experiment design.

TL;DR: A novel theoretical signal processing framework is introduced based on the EAP, and makes very limited modeling assumptions that can be used to characterize arbitrary linear diffusion estimation methods with arbitrary q‐space sampling, and can beused to theoretically evaluate and compare the accuracy, resolution, and noise‐resilience of different data acquisition and parameter estimation techniques.
Journal ArticleDOI

Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in Diffusion MRI.

TL;DR: A novel mathematical framework, called Director Field Analysis (DFA), is introduced to study local geometric structural information of white matter based on the reconstructed tensor field or spherical function field and three indices to describe three types of orientational distortion in a local spatial neighborhood are proposed.
References
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Book

Table of Integrals, Series, and Products

TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Book

Compressed sensing

TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.

A table of integrals

TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Journal ArticleDOI

Spin diffusion measurements : spin echoes in the presence of a time-dependent field gradient

TL;DR: In this article, a derivation of the effect of a time-dependent magnetic field gradient on the spin-echo experiment, particularly in the presence of spin diffusion, is given.
Book

Solving least squares problems

TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
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