This site will look better in a browser that supports web standards, but it is accessible to any browser or Internet device.

### QUESTIONS» Image Creation

How is the MRI image created? This section explores slice selection, spatial encoding and the FFT.

# Fourier Transform in MRI

## Why is the Fourier transform appropriate for use in MRI?

We use phase differences to correspond to position.

We use frequency to correspond to position, according to the the Larmor equation.

INCORRECT. In MRI we do not use phase differences to correspond to position. (We can't measure phase, remember.) Phase encoding does involve the introduction of phase differences between the rows in an imaging slice, but this does not allow us to determine the source (position) of signals. Rather, different rates of change of phase are introduced for the rows in an imaging slice, over many MRI signals. Different rates of change of phase are equivalent to different frequencies, and this is used to encode position in the rows of an image.

Phase encoding can be difficult to grasp. Try again.

The FT allows us to indentify the amplitude of signals produced at different frequencies (the range of frequencies is caused by the frequency encoding gradient).

CORRECT. The frequency encoding gradient causes a temporary range of Larmor frequencies across the image slice. Using the Fourier transform, we can work out which column in a slice a particular frequency signal came from.

Additionally, using the FT in the phase encoding direction can separate the different rates-of-change of phase which have been introduced to the different levels in an imaging slice. (More on this in later questions.)

The range of frequencies is in the kilohertz range around the Larmor frequency of the main magnetic field (which may be tens of MHz).

Books: Q&A in MRI p72, MRI The Basics p90, MRI From Picture to Proton p346
Online: Basics of MRI