Flip (or Tip) Angle
What is meant by flip angle?
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Flip angle, also called tip angle, is the amount of rotation the net magnetization (M) experiences during application of a radiofrequency (RF) pulse. It is often designated by the Greek letter alpha (α) and can be measured in degrees (°) or radians (R). For conversion 360° = 2π radians.
For a strong and rectangular RF-pulse of constant amplitude (B1) and duration (tp), the resultant flip angle (α) is approximately
For a strong and rectangular RF-pulse of constant amplitude (B1) and duration (tp), the resultant flip angle (α) is approximately
α = γ • B1 • tp
If γ is expressed in MHz/T, then multiplying the above result by 360°/cycle will give α in degrees.
Effect of a rectangular RF-pulse with amplitude B1 and duration tp to create a flip angle of α.
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Here is a solved problem that may help show how these equations may be used:
Question: Suppose we are performing conventional ¹H MRI in a scanner where the B1 field has magnitude of 2μT. How long should this RF field be applied to flip M by 180°? |
In reality actual flip angle across an image is not uniform or quite so simple to calculate. It is affected significantly by the radiofrequency pulse shape used (e.g., Gaussian, sinc, truncated-sinc), as well as slice-selection gradients, off-resonance excitations, and Bo field inhomogeneities. These effects become particularly problematic as field strengths are increased to 3.0T and above.
References
Wang J, Mao W, Qiu M et al. Factors influencing flip angle mapping in MRI: RF-pulse shape, slice-select gradients, off-resonance excitation, and Bo inhomogeneities. Magn Reson Med 2006; 56(2):463-468.
Wang J, Mao W, Qiu M et al. Factors influencing flip angle mapping in MRI: RF-pulse shape, slice-select gradients, off-resonance excitation, and Bo inhomogeneities. Magn Reson Med 2006; 56(2):463-468.