The derivation of the multicomponent diffusion law is revisited. Following Furry Am. J. Phys. 16, 63 1948 , Williams Am. J. Phys. 26, 467 1958 ; Combustion Theory, 2nd ed. Benjamin/ Cummings , Menlo Park, CA,1985 heuristically rederived the classical kinetic theory results using macroscopic equations, and pointed out that the dynamics of the mixture fluid had been assumed inviscid. This paper g...

Abstract The problem of dynamic reconstruction of an unknown coordinate in a system of nonlinear equations describing the process of innovation diffusion from results of observations of phase state is considered. An algorithm for solving this problem, which is stable with respect to informational noises and computational errors, is suggested. The algorithm is based on the principle of auxiliary...

Diffusion Weighted Images (DWI) normally shows a low Signal to Noise Ratio (SNR) due to the presence of noise from the measurement process that complicates and biases the estimation of quantitative diffusion parameters. In this paper, a new denoising methodology is proposed that takes into consideration the multicomponent nature of multi-directional DWI datasets such as those employed in diffus...

In this article, the underlying theory of clinical diffusion MR imaging, including diffusion tensor imaging (DTI) and fiber tractography, is reviewed. First, a brief explanation of the basic physics of diffusion-weighted imaging (DWI) and apparent diffusion coefficient (ADC) mapping is provided. This is followed by an overview of the additional information that can be derived from the diffusion...

Quantitative diffusion imaging is a powerful technique for the characterization of complex tissue microarchitecture. However, long acquisition times and limited signal-to-noise ratio represent significant hurdles for many in vivo applications. This article presents a new approach to reduce noise while largely maintaining resolution in diffusion weighted images, using a statistical reconstructio...

PURPOSE This 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. METHODS Four diffusion MRI models-diffusion tensor imaging (DTI), diffusion kurtosis imaging (DKI), mean apparent pro...

PURPOSE MR diffusion imaging was performed to investigate changes in water diffusion in patients with cerebral infarction. METHODS Diffusion maps of the apparent diffusion coefficient (ADC) were created to show local water mobility in the brain tissue in 15 patients. These ADC maps were compared with conventional T2-weighted images. RESULTS Distinct subregions with different water diffusion...

Diffusion-weighted MRI (DWI) allows the detection of malignancies in the abdomen and pelvis. Lesion detection and characterization using DWI largely depends on the increased cellularity of solid or cystic lesions compared with the surrounding tissue. This increased cellularity leads results in restricted diffusion as indicated by reduction in the apparent diffusion coefficient (ADC). Low pretre...

A method of performing diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) of the fetal brain in utero is proposed. The major difficulty of performing diffusion imaging in utero is the presence of motion. By modifying conventional single-shot spin-echo echo-planar DWI with a short repetition time sequence, a sequence that performs DWI and DTI within a breath-hold of the mother (...