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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

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Anisotropic field-of-views in radial imaging.

P Z Larson1, P T Gurney, D G Nishimura

  • 1Magnetic Resonance Systems Research Laboratory, Stanford University, Stanford, CA 94305, USA. peder@mrsrl.stanford.edu

IEEE Transactions on Medical Imaging
|February 14, 2008
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New algorithms enable anisotropic field-of-view (FOV) shapes in radial magnetic resonance imaging (MRI). This improves undersampled applications by reducing artifacts and allows for faster imaging without compromising quality.

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Area of Science:

  • Medical Imaging
  • Magnetic Resonance Imaging (MRI)
  • Image Reconstruction

Background:

  • Radial imaging techniques like projection-reconstruction (PR) are vital in MRI for dynamic imaging, angiography, and short-T(2) imaging.
  • These methods offer robustness to flow and motion, diffuse aliasing, and support for short readouts and echo times.
  • A limitation of standard PR is its inability to support anisotropic field-of-view (FOV) shapes, hindering optimization for specific imaging targets.

Purpose of the Study:

  • To introduce fast, simple algorithms for 2-D and 3-D PR and 3-D cones acquisitions that support anisotropic FOVs.
  • To demonstrate how matching sampling density to desired FOV shapes can reduce aliasing artifacts or scan times.
  • To enable new radial imaging applications previously limited by FOV constraints.

Main Methods:

  • Development of algorithms for 2-D and 3-D projection-reconstruction (PR) and 3-D cones acquisitions.
  • Matching frequency space sampling density to user-defined anisotropic FOV shapes.
  • On-the-fly computation of acquisition trajectories on a scan-by-scan basis.

Main Results:

  • Algorithms successfully enable tailored anisotropic FOVs in radial MRI.
  • Demonstrated reduction in aliasing artifacts for undersampled acquisitions.
  • Achieved scan time reduction without aliasing in fully-sampled applications.
  • Enabled novel applications like imaging elongated regions or thin slabs with isotropic resolution.
  • No loss in scan time to volume efficiency observed with anisotropic FOVs.

Conclusions:

  • The developed algorithms effectively support anisotropic FOVs in radial MRI acquisitions.
  • These advancements expand the applicability of radial imaging, offering improved artifact control and efficiency.
  • New possibilities are unlocked for specialized imaging tasks, enhancing MRI's versatility.