Final answer:
The number of phase-encoding steps for a fast spin echo sequence with specific parameters can be calculated using the formula (Matrix size / NEX) x (FOV / Pixel size). In this case, the phase-encoding steps would need to be filled 2048 times in order to produce a quality image.
Step-by-step explanation:
A fast spin echo sequence is a magnetic resonance imaging (MRI) technique used to produce high-quality images. The parameter given, 256 x 224, represents the matrix size of the image. The two numbers indicate the number of pixels in the phase-encoding and frequency-encoding directions, respectively.
In this case, the parameter is set to 256 pixels in the phase-encoding direction. To properly fill the phase-encoding steps, we need to consider the number of phase-encoding steps (NEX) and the field of view (FOV). The formula to calculate the number of phase-encoding steps is: Number of phase-encoding steps = (Matrix size / NEX) x (FOV / Pixel size)
Assuming a pixel size of 1, the number of phase-encoding steps would be: (256 / 3) x (24 / 1) = 2048
Therefore, the phase-encoding steps would need to be filled 2048 times in order to correctly produce a quality fast spin echo image.