qMRI mOOC · Chapter 4

B1 Mapping

Double angle · Actual flip angle imaging · Bloch–Siegert

Slides from the qMRLab mOOC chapter by Mathieu Boudreau and Juan Velázquez-Reyes
NeuroPoly Lab, Polytechnique Montréal

📖 B1 Mapping

What is a B1 map?

  • The amplitude of the transmit RF field (B1+) in each voxel: the flip angle you get is B1 × the flip angle set at the scanner
  • Units vary: normalized (1 = as set), flip angle (°), µT, or transmitter volts
  • Not a tissue property: the coil’s field, shaped by the body loaded in it (Sled & Pike 1998); up to ±30% across the head at 3 T

Three families of B1 mapping in the mOOC, one example each:

Recovery-based

Double angle method (DAM)

Steady-state

Actual flip angle imaging (AFI)

Phase-based

Bloch–Siegert (BS)
B1
Drag the ends · double-click to reset

A B1 map of a brain at 3 T (axial slice).

📖 Introduction · B1 Mapping

Recovery-based

Double angle method (DAM)

Double angle sequence: excitation alpha or 2 alpha, a 180 degree refocusing pulse, readout, long TR

Two images, at α and 2α; their ratio gives the actual flip angle:

$$B_1 = \frac{1}{\alpha}\arccos\left(\frac{S_{2\alpha}}{2\,S_{\alpha}}\right)$$

Example values

α / 2α60° / 120°

Assumptions

  • TR ≫ T1 (≈ 5 T1): full Mz recovery before each excitation
  • Same TE, receive coil and M0 in both images (they cancel in the ratio)
  • Uniform flip angle through the slice (ideal slice profile)
  • Actual α < 90° (magnitude images can’t tell cos α’s sign)

Benefits

  • Simple: a ratio of two magnitude images from a standard sequence
  • Spin echo: insensitive to B0 and T2*

Pitfalls

  • Slow: the long TR means minutes per slice, so usually only a few slices
  • A shorter TR, or 2D slice profiles, bias B1
  • Low precision where the actual α is small (cos α is flat near 0°)
📖 Double Angle techniques · B1 Mapping

Steady-state

Actual flip angle imaging (AFI)

AFI sequence: two alpha pulses with interleaved repetition times TR1 and TR2, each followed by spoiling

Spoiled gradient echo with two interleaved TRs; r = S2/S1, n = TR2/TR1:

$$B_1 = \frac{1}{\alpha}\arccos\left(\frac{r\,n-1}{n-r}\right)$$

Example values

α60°
TR1 / TR220 / 100 ms (n = 5)

Assumptions

  • The pulsed steady state is reached
  • Perfect spoiling: no transverse magnetization before each pulse
  • TR1, TR2 ≪ T1 (the first-order approximation behind the equation)
  • Same α and TE for both signals (M0 and T2* cancel in r)

Benefits

  • Fast 3D: a whole-brain B1 map in a few minutes
  • Short TRs, yet nearly insensitive to T1

Pitfalls

  • Incomplete spoiling biases B1: needs large spoilers plus tuned RF spoiling
  • Large spoilers lengthen TR2 and push gradient limits
  • Often needs a custom sequence on the scanner
📖 Actual Flip Angle Imaging · B1 Mapping

Phase-based

Bloch–Siegert (BS)

Bloch-Siegert sequence: excitation, then an off-resonance pulse at plus or minus omega RF, readout and spoiling

An off-resonance pulse shifts the phase by KBSB12; scans at ±ωRF cancel everything else:

$$B_1 = \sqrt{\frac{\phi_{+}-\phi_{-}}{2\,K_{BS}}}, \qquad K_{BS}=\int_{0}^{T}\frac{\left(\gamma B_{1,\mathrm{norm}}(t)\right)^{2}}{2\,\omega_{RF}}\,dt$$

Example values

BS pulseFermi, 8 ms, ±4 kHz
KBS74 rad/G² (= 0.0074 rad/µT²)

Assumptions

  • Pulse far off resonance: no excitation, and the phase shift scales as B12
  • KBS known: set by the pulse shape B1,norm(t) and offset ωRF
  • All other phase (B0, coil, chemical shift) identical at ±ωRF
  • φ+ − φ− doesn’t wrap; no motion between the two scans

Benefits

  • Phase-based: insensitive to T1, TR and the excitation flip angle
  • Fast: seconds per slice

Pitfalls

  • High SAR from the long off-resonance pulse, which limits TR and pulse power
  • Low precision at low B1: the phase grows as B12
  • The pulse lengthens TE (more T2* signal loss)
📖 Bloch–Siegert · B1 Mapping