Physical foundations, models, and methods of diffusion magnetic resonance imaging of the brain: A review

Abstract

ABSTRACT:The foundations and characteristics of models and methods used in diffusion magnetic resonance imaging, with particular reference to in vivo brain imaging, are reviewed.The first section introduces Fick's laws, propagators, and the relationship between tissue microstructure and the statistical properties of diffusion of water molecules. The second section introduces the diffusion-weighted signal in terms of diffusion of magnetization (Bloch-Torrey equation) and of spin-bearing particles (cumulant expansion). The third section is dedicated to the rank-2 tensor model, the b b-matrix, and the derivation of indexes of anisotropy and shape. The fourth section introduces diffusion in multiple compartments: Gaussian mixture models, relationship between fiber layout, displacement probability and diffusivity, and effect of the b-value. The fifth section is devoted to higher-order generalizations of the tensor model: singular value decompositions (SVD), representation of angular diffusivity patterns and derivation of generalized anisotropy (GA) and scaled entropy (SE), and modeling of non-Gaussian diffusion by means of series expansion of Fick's laws. The sixth section covers spherical harmonic decomposition (SHD) and determination of fiber orientation by means of spherical deconvolution. The seventh section presents the Fourier relationship between signal and displacement probability (Q-space imaging, QSI, or diffusion-spectrum imaging, DSI), and reconstruction of orientation-distribution functions (ODF) by means of the Funk-Radon transform (Q-ball imaging, QBI).

Autism Attenuates Sex Differences in Brain Structure: A Combined Voxel-Based Morphometry and Diffusion Tensor Imaging Study

“…Our DTI results demonstrate AS-related changes in microstructural organization, consistent with reduced axonal density or myelination, 49 in the CC, cingulum, and CR, as inconsistently reported in previous literature, [32][33][34][35][36][37] selectively in males but not in females. Studies of patients with callosal agenesis have demonstrated that reduced interhemispheric connectivity, in addition to impacting intelligence quotient intellect and information integration, may lead to specific emotional and social deficits resembling those typical of ASCs.…”

Rapid generation of biexponential and diffusional kurtosis maps using multi-layer perceptrons: a preliminary experience

“…Several models, in particular the biexponential and diffusional kurtosis models, have been proposed [1,2]. A review can be found in [3].…”

From Second to Higher Order Tensors in Diffusion-MRI

“…The orthogonal effects are, however, often overlooked, since their strength is typically small in comparison to the diffusion-weighting gradients, and using the b-factor (b = B 11 + B 22 + B 33 ) greatly simplifies calculations (reference 44 in [27]). …”

“…For the sake of simplicity let us also assume at first without loss of generality that the gradients are applied along the xaxis and that g denotes only the magnitude of the gradient vector (Fig-2.1) [27]. The dephasing resulting from the two gradient pulses is then inria-00496858, version 1 -1 Jul 2010…”

“…Equation (27) can also be used to interpret the signal as the characteristic function or the complex cumulant generating function of the EAP. This realization permits us to rewrite the logarithm of the signal in function of the cumulants of the EAP.…”