In biomedical imaging, edge sharpness is an important yet often overlooked image quality metric. In this work, a semi-automatic method to quantify edge sharpness is presented with application to magnetic resonance imaging (MRI). The method is based on parametric modeling of image edges. First, an edge map is automatically generated and one or more edges-of-interest (EOI) are manually selected using graphical user interface. Multiple exclusion criteria are then enforced to eliminate edge pixels that are potentially not suitable for sharpness assessment. Second, at each pixel of the EOI, an image intensity profile is read along a small line segment that runs locally normal to the EOI. Third, the profiles corresponding to all EOI pixels are individually fitted with a sigmoid function characterized by four parameters, including one that represents edge sharpness. Last, the distribution of the sharpness parameter is used to quantify edge sharpness. For validation, the method is applied to simulated data as well as MRI data from both phantom imaging and cine imaging experiments. This method allows for fast, quantitative evaluation of edge sharpness even in images with poor signal-to-noise ratio. Although the utility of this method is demonstrated for MRI, it can be adapted for other medical imaging applications. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A, 2015.

]]>The diffusion of spin-bearing particles around simple geometrical objects like cylinders and spheres abides by the form of the diffusion propagator that specifies the probability of a particle to diffuse from one position to another within a specific time span. While diffusion propagators for diffusion inside a cylinder or sphere are well-analyzed, diffusion propagators for hindered diffusion around these open geometries are rarely discussed in MR literature. Knowledge of such diffusion propagators for hindered diffusion allows quantifying the influence of diffusion processes on the MR signal around single vessels or blood residues and ultra-small iron-oxide particles, respectively, when there is no outer boundary present. In this work, analytical expressions for the diffusion propagator for hindered diffusion in one, two and three dimensions as well as the resulting correlation functions for diffusion in a dipole field around cylinders and spheres are derived. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A, 2015.

]]>When using pulsed-field gradient nuclear magnetic resonance (NMR) for measurements of translational self-diffusion, the Stejskal-Tanner equation is used to relate the signal attenuation to the experimental parameters and to estimate the diffusion coefficient. However, the conventional form of the equation is valid only if the gradient pulse shapes are perfectly rectangular, which is never the case in practice. In light of three asymmetric gradient pulse shapes having reached the NMR mainstream and been implemented into proprietary software, we present explicit expressions for the corresponding Stejskal-Tanner equations and computer code for easy implementation. We also study the bias introduced by using the common rectangular gradient pulse approximation. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A, 2015.

]]>The acceleration in Parallel MRI is achieved by reducing the number of phase encode steps during data acquisition. SENSE is a Parallel MRI algorithm which reconstructs the fully sampled MR images. Standard SENSE is limited by the noise amplification especially for higher acceleration factors. The *g*-Factor represents the noise amplification during the process of image reconstruction and it varies from pixel-to-pixel. Regularization based SENSE reconstruction uses prior knowledge to improve the quality of the reconstructed image. A method based on the use of *g*-Factor as a regularization parameter in the Tikhonov regularized SENSE reconstruction is proposed. The results show significant improvement in the reconstructed images and computation time. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 67–73, 2015.

Relaxation theory often forms the basis of various studies, like MRI contrast agents and ionic liquids, which require the understanding of the molecular dynamics or determination of molecular parameters (such as correlation times) or both. Such studies compare the explicit expressions of the relaxation times *T*_{1} and *T*_{2}, derived many years ago by quantum physicists, with their experimental findings to understand various aspects of the molecular motion. However, because of the complicated terminology and widely scattered information, the task of understanding or re-deriving the relaxation theory for even the simplest cases becomes challenging for many students and researchers new to this field. In this article, the dipolar relaxation theory for the basic, yet practical case of a two spin system is presented with a detailed description of the concepts behind it. Aiming at a beginner level and making only modest assumptions on prior knowledge, we have discussed the basics of the quantum mechanics, spherical harmonics, stochastic processes and perturbation theories. It is hoped that this article will enable the reader to understand the general framework of the relaxation theory and will be beneficial in comprehending the relaxation in more complex systems as well, which is not discussed here. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 74–113, 2015.

A simple method to execute spin algebra computations is presented. It uses the high-level numerical program Scilab and its large and convenient set of linear algebra routines. The techniques thus developed are applied to various nuclear magnetic resonance (NMR)-related simulations. Static spectra of AB and ABC spin systems are computed. Free precession of single or multispin systems are simulated using the density matrix formalism. Magnetization transfer under simple pulse sequences is examined. Matrices representing product operators are displayed and coherence orders are explained. COSY correlation maps for two and three spins are obtained without approximation. The simulation of a DQF-COSY spectrum, with its eight-step phase program, is explained. Two simple pulsed field gradient experiments are described. Computation times are under 100 s on a 1.66-GHz laptop computer. The approach is elementary, requiring only a basic knowledge of spin quantum mechanics. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 114–132, 2015.

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