# Static Magnetic Field Calculations

In order to align all of the hydrogen nuclei in the body, very strong static magnetic fields are used in MRI. Because body tissues have a different magnetic permeability than that of air, unwanted distortions in a static magnetic field can occur near air-tissue boundaries. This can cause problems with imaging methods very sensitive to distortions in static magnetic fields, such as methods used in functional MRI. For example, Figure 1 was acquired with a fast echo-planar imaging sequence on a plane just above the nasal cavity. The large black spot is due to distortions because of the boundary here.

We have performed thorough calculations of the static field distortions in a human head model and verified the results experimentally (ref). Figures 2, 3, and 4 show the results of some of these calculations. The calculations were made with the finite element method and a mesh of about 50,000 tetrahedrons using "Maxwell 3D field simulator" software produced by Ansoft, Inc., on an IBM RISC system/6000, model 550 with 256 Mbytes RAM. The model contains frontal, nasal, ethmoid, and maxillary sinuses. The permeability of all sinuses and the air surrounding the model were set to that of air. The permeability of all tissue was set to that of water.

More recently we have developed our own code to calculate the magnetic fields throughout more complete models of the human head, with many tissues having different permeabilities. Figures 5 and 6 show the results of some of these calculations with units in parts-per-million deviation from the applied field strength. The calculations were made with a finite difference method and a mesh of about a few million cells. The calculated field distributions matched experimentally-measured distributions very well.

# Related Publications

- Li S, Dardzinski BJ, Collins CM, Yang QX, Smith MB. Three-dimensional mapping of the static magnetic field inside the human head. Magn Reson Med. 1996 Nov;36(5):705-14.
- Collins CM, Yang B, Yang QX, Smith MB. Numerical calculations of the static magnetic field in three-dimensional multi-tissue models of the human head. Magn Reson Imaging. 2002 Jun;20(5):413-24.
- Maril N, Collins CM, Greenman RL, Lenkinski RE. Strategies for shimming the breast. Magn Reson Med. 2005 Nov;54:1139-1145.