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B1 Mapping · Exercise 4-1

Building intuition: can you guesstimate B1 from the raw data?

Exercise 4-1 · (a)

High or low B1+? Only the two images to go on

α = 60°

2α = 120°

Click a pixel to read its value in both images.

A brain, imaged at 60° and 120° (long TR) through a receive array with arbitrary coil positions, both on one grey scale.

Press Start: a point appears for 5 seconds. Is the transmit B1+ there above or below 1?
Be quick: a right answer scores up to 1000 points, fewer the longer you take.

Hint: you can expect B1 to range between 0.5 and 1.5.

Point–
S(60°)–
S(120°)–

Exercise 4-1 · (b)

How to get every point of the quiz right

The magnetization starts along z and is tipped towards the right by the actual flip angle, 60° × B1 or 120° × B1. The signal is its transverse part (the bar below each vector). Dashed: B1 = 1. Move B1: which bar grows, which one shrinks?

B1
60° pulse–
120° pulse–
brighter–

Exercise 4-1 · (b) · another pair of angles

Does it work for another pair of angles?

At 60° and 120°: brighter at 60° → B1 > 1, brighter at 120° → B1 < 1. Does that work for other angles? Pick two angles, then move B1 from 0.5 to 1.5: which image is brighter?

angle 1 45°
angle 2 135°
B1
45° pulse–
135° pulse–
brighter–
ratio S135/S45–

Exercise 4-1 · Summary

Guesstimating B1 from the raw data

  1. Learn to guess B1 from the raw images: it can help you at the scanner, before you can process the data.
  2. 60° and 120° are a special case: the only pair that does both
    1. gives the same signal at B1 = 1, so the brighter image tells you if B1 is above or below 1;
    2. fits the double-angle equation, B1 = arccos(S2α/2Sα)/α.
  3. This holds for any receive coil: the receive field multiplies both images by the same factor in each voxel, whatever the signal, so it can’t change which one is brighter, and it cancels in the ratio.