Stream function optimization for gradient coil design

Tomasi, Dardo

doi:10.1002/1522-2594(200103)45:3<505::aid-mrm1066>3.0.co;2-h

Cited by 54 publications

(65 citation statements)

References 16 publications

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“…The stream function parameters were adjusted in order to minimize the dimensionless error function [8],…”

Section: Simulated Annealingmentioning

confidence: 99%

“…The gradient field produced by the gradient coil at a given point of the space, G, was calculated at N points in the ROI [8], by using the Biot-Savart law. …”

Section: Simulated Annealingmentioning

confidence: 99%

“…Recently I presented the fast simulated annealing (FSA) method, a novel optimization technique for the design of selfshielded gradient coils with cylindrical geometry [8][9][10]. It combines the simulated annealing (SA) [11][12][13][14] and the target field (TF) [3][4]15] techniques to optimize the standard stream functions used to design gradient coils.…”

Section: Introductionmentioning

confidence: 99%

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Optimization of biplanar gradient coils for magnetic resonance imaging

Tomasi

2006

Braz. J. Phys.

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"Open" magnetic resonance imaging (MRI) scanners are frequently based on electromagnets or permanent magnets, and require self-shielded planar gradient coils to prevent image artifacts resulting from eddy currents in metallic parts of the scanner. This work presents an optimization method for the development of self-shielded gradient coils with biplanar geometry for "Open" MRI scanners. Compared to other optimization methods, this simple approach results in coils that produce larger uniform gradient volumes, and have simple and scalable manufacture.

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“…The stream function parameters were adjusted in order to minimize the dimensionless error function [8],…”

Section: Simulated Annealingmentioning

confidence: 99%

“…The gradient field produced by the gradient coil at a given point of the space, G, was calculated at N points in the ROI [8], by using the Biot-Savart law. …”

Section: Simulated Annealingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization of biplanar gradient coils for magnetic resonance imaging

Tomasi

2006

Braz. J. Phys.

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“…Turner [8] applies a target-field method in which the desired field is specified, and the corresponding current distribution on the cylindrical surface is computed. Optimization algorithms are used in the conjugate-gradient method by Wong and Jesmanowicz [9], in the simulated-annealing method by Crozier and Doddrell [10], and in the stream-functions method by Tomasi [11] in which the current distribution is discretized by use of one-dimensional wires. Trakic et al [12] incorporate transient eddy currents in a numerical study of a coil-optimization process; they modify a gradient-coil design by combining the fields created by the coil and the eddy currents to generate a spatially homogeneous magnetic gradient field.…”

Section: Introductionmentioning

confidence: 99%

Eddy currents in MRI gradient coils configured as rings and patches

2011

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The current distribution in a set of parallel rings and patches, called islands, positioned at the surface of a cylinder, is investigated. The current is driven by an externally applied source current. The islands are rectangular pieces of copper (patches) placed in parallel between the rings. The eddy currents in the islands induce currents in the rings that vary in the tangential direction. From the quasi-static Maxwell equations, an integral equation for the current distribution in the strips is derived. The Galerkin method, using global basis functions, is applied to solve this integral equation. It shows fast convergence. The global basis functions are Legendre polynomials in the axial direction and 2π -periodic trigonometric functions in the tangential direction. The Legendre polynomials efficiently cope with the singularity of the kernel function of the integral equation. Explicit numerical results are shown for three configurations. Apart from the current distributions, the resistance and self-inductance of the three systems of rings and islands are computed. The resulting tool can be used to qualitatively understand eddy currents in z-gradient coils, and as such enable the incorporation of eddy currents in the optimization of gradient-coil design.

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“…For cylindrical gradients, a one dimensional stream function is used to specify currents on the cylinder surface (4,5). For planar gradients, however, the problem becomes two dimensional, requiring two dimensional stream functions (6)(7)(8)(9).…”

Section: Introductionmentioning

confidence: 99%

Local bi‐planar gradient array design using conformal mapping and simulated annealing

Moon

Goodrich

Hadley

et al. 2009

Concepts Magn Reson

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Many magnetic resonance imaging applications require high spatial and temporal resolution. The improved gradient performance required to achieve high spatial and temporal resolution may be achieved by using local gradient coils such as planar gradient inserts. The planar gradient set provides higher gradient performance because it is placed inside of the imaging bore of the magnet (within the body gradients) in close proximity to the imaging region. Although the wire patterns for planar gradients can be designed using two dimensional stream functions and simulated annealing, optimization of the two dimensional stream functions can be much more computationally intensive and time consuming than optimizing the one dimensional stream functions required for cylindrical gradients. To address this problem, we have developed a simple and rapid method for the design of planar gradient inserts to produce a high strength local gradient field and a reasonably uniform imaging region. By using conformal mapping, the two dimensional problem can be simplified to a faster and more easily calculated one dimensional problem. The mapping transforms the magnetic field and wire patterns in the cylindrical system into a magnetic field and wire patterns in the bi-planar geometry providing a tool for bi-planar gradient coil design using a one dimensional stream function.

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Stream function optimization for gradient coil design

Cited by 54 publications

References 16 publications

Optimization of biplanar gradient coils for magnetic resonance imaging

Optimization of biplanar gradient coils for magnetic resonance imaging

Eddy currents in MRI gradient coils configured as rings and patches

Local bi‐planar gradient array design using conformal mapping and simulated annealing

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