MRI: magnetic field distributions by Biot Savart’s law

These Matlab routines calculate the magnetic field generated by the combination of linear filaments using Biot-Savart’s law. The directions and intensities of linear filaments can be assigned to simulate current flow. Applications of these routines include simulating the B1 field distribution using quasi-static approximation and the spatial encoding magnetic field of an MRI system.

The geometry of a 32-channel head coil array is shown here.

Using these scripts, we can calculate both the magnitude and the phase of the magnetic field generated by each individual coil. Here are plots of the magnitude and phase images for one coil across different slices.

The relative position between the imaging slice and a 32-channel head coil array can be determined freely by coding as shown here.

Here are plots of the magnitude and phase images for each RF coil in a 32-channel head coil array at a particular slice.

Usage:

This script calculates the quasi-static magnetic field given the spatial distribution of linear current filaments and FOV using Biot-Savart’s law. Additional codes are drawing the coil geometry, reading head geometry, and scaling values.

This script simulates and displays the B1 field for an 32-channel head array coil.

Data:

• A scalp surface 3D model

• The geometry of a 32-channel head coil array