MR Hardware: Improving Homogeneity
How is magnetic field mapping performed?
After the magnet has been placed in its bay (and if superconducting, ramped to full field), an initial plot of its internal magnetic field is generated. This is done by by inserting a directional magnetometer (also called a gaussmeter or teslameter) into the scanner bore as shown in the photos below. A magnetometer measures the resonance frequency of a known small sample of water contained within the probe tip thus allowing the magnetic field at each point in space to be accurately determined. A special positioning apparatus ("jig") allows precise placement of the probe at various locations and angles within the gantry, and a magnetic field map of 300+ points is generated.
Magnetometer (arrow) in bore of cylindrical superconducting magnet during initial field mapping. The rigging device allows it to be systematically placed at different angles and positions.
|
Mapping of the magnetic field in an open bore scanner using a magnetometer mounted on a different type of jig apparatus designed for vertical field magnets.
|
|
This initial field map will no doubt demonstrate that the actual magnetic field (Bactual) varies significantly in magnitude and direction across the bore, and is far away from the ideal desired field (Bideal), a constant field of magnitude Bo directed along the z-axis). Complex fields such as Bactual are commonly described using a mathematical formulation known as spherical harmonics. Spherical harmonics are the 3D analog of Fourier series (used in other MRI contexts) and closely related to Taylor series (taught in elementary calculus courses). The underlying concept is that any field like Bactual can be expanded into a sum of weighted terms reflecting each spherical harmonic component: |
Any complex magnetic field can be expressed in terms of a sum of weighted spherical harmonics of different orders. Order 0 is a constant value. Order 1 contains simple linear harmonics, here principally directed and labeled in the Cartesian coordinate system as Z, Y, and X respectively. The 2nd Order has five harmonics, called Z², ZX, X²-Y², ZY, and XY. Order 3 has seven harmonics, a few of which are ilustrated. As the order increases so do both the number and complexity of the harmonics.
|
Bactual = Bideal + {3 linear harmonics} + {5 second order harmonics} + {7 third order} + • • •
Printout of calculated harmonics
A special computer program calculates the spherical harmonic components after input of the field map raw data. This software then directs the service engineer how to reduce the inhomogeneities through a process called shimming.
References
Keller P. Technologies for precision field mapping (pdf). MetroLab Instruments (www.metrolab.com), Geneva, 2006.
Wendt M. Second order shimming of high field magnets (pdf). Siemens Medical Systems. A sales brochure but contains good information on active shims and spherical harmonics.
Keller P. Technologies for precision field mapping (pdf). MetroLab Instruments (www.metrolab.com), Geneva, 2006.
Wendt M. Second order shimming of high field magnets (pdf). Siemens Medical Systems. A sales brochure but contains good information on active shims and spherical harmonics.
Related Questions
An MR salesman claims his scanner has better "homogeneity" than that of his competitor. What is he talking about?
How is passive shimming performed?
How does active shimming work?
An MR salesman claims his scanner has better "homogeneity" than that of his competitor. What is he talking about?
How is passive shimming performed?
How does active shimming work?