Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in “q-space,” and the corresponding “mean apparent propagator (MAP)” describing molecular displacements in “r-space.” We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit “displacement” sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions—the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.

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Diffusion tensor imaging is used to measure the diffusion of water in tissue. The diffusion properties carry information about the relative organization and structure of the underlying tissue. In the case of a single voxel containing both tissue and a fast diffusing component such as free water, a single diffusion tensor is no longer appropriate. A two-tensor free water elimination model has previously been proposed to correct for the case of volume mixing. Here, this model was implemented in a straightforward but novel manner without the use of spatial constraints. The optimal acquisition parameters were investigated through Monte Carlo simulations and human brain imaging studies. At a signal-to-noise ratio of 40 with 64 diffusion-weighted encoding images, the most accurate estimates of fast diffusion signal were obtained with two diffusion-weighted shells (b-value in s/mm^2 x number of directions) of 500×32 and 1500×32. The potential bias in fractional anisotropy induced by this two-compartment model was more than an order of magnitude less than the error of using the single diffusion tensor model in the presence of partial volume effects with free water. This strategy may be useful for characterizing the diffusion of tissues adjacent to cerebral spinal fluid (CSF), tissues affected by edema, and removing artifacts from blurring and ghosting of the CSF signal.

A long-standing problem in Magnetic Resonance Imaging (MRI) is the noise-induced bias in the magnitude signals. This problem is particularly pressing in diffusion MRI at high diffusionweighting. In this paper, we present a three-stage scheme to solve this problem by transforming noisy nonCentral Chi signals to noisy Gaussian signals. A special case of nonCentral Chi distribution is the Rician distribution. In general, the Gaussian-distributed signals are of interest rather than the Gaussian-derived (e.g., Rayleigh, Rician, and nonCentral Chi) signals because the Gaussiandistributed signals are generally more amenable to statistical treatment through the principle of least squares. Monte Carlo simulations were used to validate the statistical properties of the proposed framework. This scheme opens up the possibility of investigating the low signal regime (or high diffusion-weighting regime in the case of diffusion MRI) that contains potentially important information about biophysical processes and structures of the brain.

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PurposeThis study was a systematic evaluation across different and prominent diffusion MRI models to better understand the ways in which scalar metrics are influenced by experimental factors, including experimental design (diffusion‐weighted imaging [DWI] sampling) and noise.MethodsFour diffusion MRI models—diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), mean apparent propagator MRI (MAP‐MRI), and neurite orientation dispersion and density imaging (NODDI)—were evaluated by comparing maps and histogram values of the scalar metrics generated using DWI datasets obtained in fixed mouse brain with different noise levels and DWI sampling complexity. Additionally, models were fit with different input parameters or constraints to examine the consequences of model fitting procedures.ResultsExperimental factors affected all models and metrics to varying degrees. Model complexity influenced sensitivity to DWI sampling and noise, especially for metrics reporting non‐Gaussian information. DKI metrics were highly susceptible to noise and experimental design. The influence of fixed parameter selection for the NODDI model was found to be considerable, as was the impact of initial tensor fitting in the MAP‐MRI model.ConclusionAcross DTI, DKI, MAP‐MRI, and NODDI, a wide range of dependence on experimental factors was observed that elucidate principles and practical implications for advanced diffusion MRI. Magn Reson Med 78:1767–1780, 2017. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo images (SPGR) acquired with different flip angles and/or repetition times. The function relating signal intensity to flip angle and TR is non-linear; however, a linear form proposed 30 years ago is currently widely used. Here, we show that this linear method provides T1 estimates that have similar precision but lower accuracy than those obtained with a nonlinear method. We also show that T1 estimated by the linear method is biased due to improper accounting for noise in the fitting. This bias can be significant for clinical SPGR images, for example, T1 estimated in brain tissue (800ms