The signal decay with increasing b‐factor at fixed echo time from brain tissue in vivo has been measured using a line scan Stejskal–Tanner spin echo diffusion approach in eight healthy adult volunteers. The use of a 175 ms echo time and maximum gradient strengths of 10 mT/m allowed 64 b‐factors to be sampled, ranging from 5 to 6000 s/mm2, a maximum some three times larger than that typically used for diffusion imaging. The signal decay with b‐factor over this extended range showed a decidedly non‐exponential behavior well‐suited to biexponential modeling. Statistical analyses of the fitted biexponential parameters from over 125 brain voxels (15 × 15 × 1 mm3 volume) per volunteer yielded a mean volume fraction of 0.74 which decayed with a typical apparent diffusion coefficient around 1.4 µm2/ms. The remaining fraction had an apparent diffusion coefficient of approximately 0.25 µm2/ms. Simple models which might explain the non‐exponential behavior, such as intra‐ and extracellular water compartmentation with slow exchange, appear inadequate for a complete description. For typical diffusion imaging with b‐factors below 2000 s/mm2, the standard model of monoexponential signal decay with b‐factor, apparent diffusion coefficient values around 0.7 µm2/ms, and a sensitivity to diffusion gradient direction may appear appropriate. Over a more extended but readily accessible b‐factor range, however, the complexity of brain signal decay with b‐factor increases, offering a greater parametrization of the water diffusion process for tissue characterization. Copyright © 1999 John Wiley & Sons, Ltd.

The structural heterogeneity of tumor tissue can be probed by diffusion MRI (dMRI) in terms of the variance of apparent diffusivities within a voxel. However, the link between the diffusional variance and the tissue heterogeneity is not well-established. To investigate this link we test the hypothesis that diffusional variance, caused by microscopic anisotropy and isotropic heterogeneity, is associated with variable cell eccentricity and cell density in brain tumors. We performed dMRI using a novel encoding scheme for diffusional variance decomposition (DIVIDE) in 7 meningiomas and 8 gliomas prior to surgery. The diffusional variance was quantified from dMRI in terms of the total mean kurtosis (MKT), and DIVIDE was used to decompose MKT into components caused by microscopic anisotropy (MKA) and isotropic heterogeneity (MKI). Diffusion anisotropy was evaluated in terms of the fractional anisotropy (FA) and microscopic fractional anisotropy (μFA). Quantitative microscopy was performed on the excised tumor tissue, where structural anisotropy and cell density were quantified by structure tensor analysis and cell nuclei segmentation, respectively. In order to validate the DIVIDE parameters they were correlated to the corresponding parameters derived from microscopy. We found an excellent agreement between the DIVIDE parameters and corresponding microscopy parameters; MKA correlated with cell eccentricity (r = 0.95, p < 10−7) and MKI with the cell density variance (r = 0.83, p < 10−3). The diffusion anisotropy correlated with structure tensor anisotropy on the voxel-scale (FA, r = 0.80, p < 10−3) and microscopic scale (μFA, r = 0.93, p < 10−6). A multiple regression analysis showed that the conventional MKT parameter reflects both variable cell eccentricity and cell density, and therefore lacks specificity in terms of microstructure characteristics. However, specificity was obtained by decomposing the two contributions; MKA was associated only to cell eccentricity, and MKI only to cell density variance. The variance in meningiomas was caused primarily by microscopic anisotropy (mean ± s.d.) MKA = 1.11 ± 0.33 vs MKI = 0.44 ± 0.20 (p < 10−3), whereas in the gliomas, it was mostly caused by isotropic heterogeneity MKI = 0.57 ± 0.30 vs MKA = 0.26 ± 0.11 (p < 0.05). In conclusion, DIVIDE allows noninvasive mapping of parameters that reflect variable cell eccentricity and density. These results constitute convincing evidence that a link exists between specific aspects of tissue heterogeneity and parameters from dMRI. Decomposing effects of microscopic anisotropy and isotropic heterogeneity facilitates an improved interpretation of tumor heterogeneity as well as diffusion anisotropy on both the microscopic and macroscopic scale.

Abstract-A new method for noise filtering in images that follow a Rician model-with particular attention to magnetic resonance imaging-is proposed. To that end, we have derived a (novel) closed-form solution of the linear minimum mean square error (LMMSE) estimator for this distribution. Additionally, a set of methods that automatically estimate the noise power are developed. These methods use information of the sample distribution of local statistics of the image, such as the local variance, the local mean, and the local mean square value. Accordingly, the dynamic estimation of noise leads to a recursive version of the LMMSE, which shows a good performance in both noise cleaning and feature preservation. This paper also includes the derivation of the probability density function of several local sample statistics for the Rayleigh and Rician model, upon which the estimators are built.Index Terms-Linear minimum mean square error (LMMSE) estimator, MRI filtering, noise estimation, Rician noise.