Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that reveals tissue magnetic susceptibility. It relies on having a high quality field map, typically acquired with a relatively long echo spacing and long final TE. Applications of QSM outside the brain require the removal of fat contributions to the total signal phase. However, current water/fat separation methods applied on typical data acquired for QSM suffer from three issues: inadequacy when using large echo spacing, over-smoothing of the field maps and high computational cost. In this paper, the general phase wrap and chemical shift problem is formulated using a single species fitting and is solved using graph cuts with conditional jump moves. This method is referred as simultaneous phase unwrapping and removal of chemical shift (SPURS). The result from SPURS is then used as the initial guess for a voxel-wise iterative decomposition of water and fat with echo asymmetric and least-squares estimation (IDEAL). The estimated 3-D field maps are used to compute QSM in body regions outside of the brain, such as the liver. Experimental results show substantial improvements in field map estimation, water/fat separation and reconstructed QSM compared to two existing water/fat separation methods on 1.5T and 3T magnetic resonance human data with long echo spacing and rapid field map variation.
The frequency-dependent critical current of a superconductor strip and Roebel cable has been studied using a 2D finite element simulation. It is shown that the critical current of the superconductor increases with frequency as f 1/n , where n is the exponent of the power law flux creep model. Transport ac loss in a superconductor strip decreases with frequency as f −2/n when the amplitude of the applied ac current is far less than its critical current. However, when the applied current is large and becomes comparable to the critical current, the transport ac loss decreases with frequency as 1/ f . The analytical results are substantiated with available experimental data and the results of a 2D finite element simulation.
The goal of deconvolution is to recover an image x from its convolution with a known blurring function. This is equivalent to inverting the linear system y = Hx.
The frequency dependence of magnetic ac loss of thin superconductor strip subjected to an ac magnetic field perpendicular to the surface of the strip is investigated by incorporating a flux creep model into the critical state model of Brandt and Indenbom. It is found that the reduced ac loss exhibits a maximum value at a frequency f m , which is a rapidly varying function of the applied ac magnetic field. At low magnetic field, f m becomes zero, and ac loss decreases with frequency as a power law (∼ f −2/n ). Whereas at high magnetic field f m becomes infinite and ac loss increases with frequency, still following the power law (∼ f 1/n ). The analytical results are substantiated with experimental data and the results of a 2D finite element simulation.
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