Numerical calculations of the static magnetic field in three-dimensional multi-tissue models of the human head

Collins, Christopher M.; Yang, Bin; Yang, Qing; Smith, Michael B.

doi:10.1016/s0730-725x(02)00507-6

Cited by 92 publications

(73 citation statements)

References 10 publications

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“…Each of the studies described here involved calculation of the field over a 256 3 matrix, which was accomplished in 1 minute on a Sun Workstation (E280R with a 900 MHz UltraSPARC-IIIϩ processor). This time compares favorably with that needed for real-space calculations using iterative methods carried out on similar matrix sizes (10,11). The most time-consuming part of the computation is the calculation of the forward and inverse 3DFFTs; consequently, the computational time is expected to scale approximately as N 3 log 2 (N) for matrix size N 3 (20).…”

Section: Discussionmentioning

confidence: 92%

Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility

Marques

Bowtell

2005

Concepts Magn. Reson.

392

536

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ABSTRACT:Inhomogeneous B 0 -magnetic fields generate distortion in magnetic resonance images, particularly those produced using echo planar imaging, and are responsible for signal reduction due to intravoxel dephasing in gradient echo experiments. Such effects increase in magnitude in proportionality with the static field strength, and with the growing use of high-field (3 T and above) systems in medical imaging, it is increasingly important to be able to quantify field inhomogeneities. Here, we describe the implementation and use of a method for rapidly calculating frequency shifts due to spatially varying magnetic susceptibility that is based on an approach previously used to calculate long-range dipolar field effects. The method relies on a simple expression that relates the three-dimensional Fourier transforms of the magnetization distribution and the field, and can naturally include the effect of the sphere of Lorentz. It has been used to evaluate field inhomogeneity in the head due to the variation of magnetic susceptibility with tissue type and to calculate the change in field inhomogeneity that occurs due to small rotations of the head. In addition, this approach has been used to simulate the effect of lung volume changes in generating respiration induced resonant offsets in the brain.

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Section: Discussionmentioning

confidence: 92%

Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility

Marques

Bowtell

2005

Concepts Magn. Reson.

392

536

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“…B ជ nuc is proportional to the macroscopic magnetic field (B ជ mac ), but also depends on the screening effect produced by the electronic shell around the nucleus () and on the bulk magnetic susceptibility (). The nucleus is assumed to be within a small sphere of Lorentz (8,9):…”

Section: Theorymentioning

confidence: 99%

“…Previous approaches reported in literature were based on finite difference calculations (7)(8)(9), Green function method (10), or integral methods (11). These methods provide accurate solutions but are time consuming and thus less suitable for real-time 3D data processing.…”

Section: Introductionmentioning

confidence: 99%

A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility

Salomir

Senneville

Moonen

2003

Concepts Magn Reson

359

405

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A fast calculation method for the magnetic field distribution due to (dynamic) changes in susceptibility may allow real-time interventional applications. Here it is shown that a direct relationship can be obtained between the magnetic field perturbation and the susceptibility distribution inside the MR magnet using a first order perturbation approach to Maxwell's magneto-static equations, combined with the Fourier transformation technique to solve partial derivative equations. The mathematical formalism does not involve any limitation with respect to shape or homogeneity of the susceptibility field. A first order approximation is sufficient if the susceptibility range does not exceed 10 Ϫ4 (or 100 ppm). The formalism allows fast numerical calculations using 3D matrices. A few seconds computation time on a PC is sufficient for a 128 ϫ 128 ϫ 128 matrix size. Predicted phase maps fitted both analytical and experimental data within 1% precision.

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“…More recently, a number of models have more recently been produced based on image data and/or high resolution photographic data of the interior of the human body from cadavers (21,26), followed by manually-intensive segmentation of spatial information into a finite number of tissue types. While some models of portions living humans have been created through the years (27)(28)(29)(30), and even a section of a mother including a fetus (31), recently impressive efforts including high-resolution whole-body imaging of human subjects in vivo followed by labor-intensive manual segmentation have yielded an increasing number of high-resolution models of the entire human body (32,33). Due to the image-based nature of the data acquired and segmented to produce models of the human body, these models are most often represented as a distribution of a finite number of tissues at locations on a regular threedimensional grid.…”

Section: Methods Of Rf Field Calculation Used In Mri With Consideratimentioning

confidence: 99%

Calculation of radiofrequency electromagnetic fields and their effects in MRI of human subjects

Collins

Wang

2011

Magn. Reson. Med.

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Radiofrequency magnetic fields are critical to nuclear excitation and signal reception in Magnetic Resonance Imaging (MRI). The interactions between these fields and human tissues in anatomical geometries results in a variety of effects regarding image integrity and safety of the human subject. In recent decades numerical methods of calculation have been used increasingly to understand the effects of these interactions and aid in engineering better, faster, and safer equipment and methods. As MRI techniques and technology have evolved through the years, so too have the requirements for meaningful interpretation of calculation results. Here we review the basic physics of RF electromagnetics in MRI and discuss a variety of ways RF field calculations are used in MRI in engineering and safety assurance from simple systems and sequences through advanced methods of development for the future.

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Numerical calculations of the static magnetic field in three-dimensional multi-tissue models of the human head

Cited by 92 publications

References 10 publications

Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility

Application of a Fourier-based method for rapid calculation of field inhomogeneity due to spatial variation of magnetic susceptibility

A fast calculation method for magnetic field inhomogeneity due to an arbitrary distribution of bulk susceptibility

Calculation of radiofrequency electromagnetic fields and their effects in MRI of human subjects

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