# MRI quantities B1+, B1-, ratio and iSNR

Background and definitions of B_{1}^{+} and B_{1}^{-}

B_{1}^{+} is a component of the magnetic RF field. This component rotates in a plane perpendicular to the static magnetic field in an MRI machine. If the Z axis is defined as the direction of the static magnetic field, as is customary, then B_{1}^{+} is defined as:

B_{1}^{+} = (B_{x} + jB_{y})/2 |
(1) |

where:

j = sqrt (-1)

The rotating RF field is essential in producing an MRI image. MRI coil designers need to be able to plot this quantity. In addition, they need to be able to compare it with the anti-rotating component B_{1}^{-}, defined as:

B_{1}^{-} = (B*_{x} + jB*_{y})/2 |
(2) |

In an efficient coil, B1+ significantly exceeds B1-. This can be visualized in the third quantity of interest, which is defined as the ratio:

ratio = | B_{1}^{+}|/| B_{1}^{-}| |
(3) |

### Example model *(FEKO model downloadable below)*

The model is a generic 7 Tesla birdcage head coil with generic phantom with average head tissue parameters, shown below. The bottom rung has two ports, driven with equal magnitudes and 90° phase difference. Both rungs have 16 equal-value capacitors, which tune the resonance of the system. The coil’s diameter is 30 cm. The axis of the cylindrical shapes is the Z axis.

Generic "birdcage" MRI coil |
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### Using the script

The script is a POSTFEKO macro, which means that for simplicity it can be added to the Application macro library (FEKO Suite 6.3 and newer) and used to evaluate any simulation near-field request results. When the script is run the user can choose which model and configuration should be used for the evaluation as well as setting values for the iSNR calculation. A new dataset is then created and a 3D view is plotted, which contains all the MRI quantities that were calculated. 2D plot can also be plotted directly from the dataset.

The following figures show |B_{1}^{+}| at 300 MHz and the ratio of the |B_{1}^{+}|/|B_{1}^{-}| highlighting the polarization efficiency in the region of interest (ROI).

Magnitude of the complex quantity B_{1}^{+} | Ratio of the magnitudes of B_{1}^{+} and B_{1}^{-} |
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