quantitative_field_mapping

Quantitative field mapping for bSSFP.

Collect quantitative MR maps (T1, T2, flip angle), then, assuming that these won’t change during the duration of the scan, we can use these to take a single bSSFP scan each time point and solve for the off-resonance. Thus we get a field map at time point.

mr_utils.sim.ssfp.quantitative_field_mapping.get_df_responses(T1, T2, PD, TR, alpha, phase_cyc, dfs)[source]

Simulate bSSFP response across all possible off-resonances.

Parameters:
  • T1 (float) – scalar T1 longitudinal recovery value in seconds.
  • T2 (float) – scalar T2 transverse decay value in seconds.
  • PD (float) – scalar proton density value scaled the same as acquisiton.
  • TR (float) – Repetition time in seconds.
  • alpha (float) – Flip angle in radians.
  • phase_cyc (float) – RF phase cycling in radians.
  • dfs (float) – Off-resonance values to simulate over.
Returns:

resp – Frequency response of SSFP signal across entire spectrum.
Return type:

array_like
mr_utils.sim.ssfp.quantitative_field_mapping.quantitative_fm(Mxys, dfs, T1s, T2s, PDs, TR, alpha, phase_cyc, mask=None)[source]

Find field map given quantitative maps.

Parameters:
  • Mxys (array_like) – Complex transverse signal we measure.
  • dfs (array_like) – Off-resonance values to simulate over.
  • T1s (array_like) – scalar T1 longitudinal recovery value in seconds.
  • T2s (array_like) – scalar T2 transverse decay value in seconds.
  • PDs (array_like) – scalar proton density value scaled the same as acquisiton.
  • TR (float) – Repetition time in seconds.
  • alpha (float) – Flip angle in radians.
  • phase_cyc (float) – RF phase cycling in radians.
  • mask (array_like) – Boolean mask to tell which pixels we should compute df for.
Returns:

fm – Field map.
Return type:

array_like
mr_utils.sim.ssfp.quantitative_field_mapping.quantitative_fm_scalar(Mxy, dfs, T1, T2, PD, TR, alpha, phase_cyc)[source]

For scalar T1, T2, PD.

Parameters:
  • Mxy (float) – Complex transverse signal we measure.
  • dfs (array_like) – Off-resonance values to simulate over.
  • T1 (float) – scalar T1 longitudinal recovery value in seconds.
  • T2 (float) – scalar T2 transverse decay value in seconds.
  • PD (float) – scalar proton density value scaled the same as acquisiton.
  • TR (float) – Repetition time in seconds.
  • alpha (float) – Flip angle in radians.
  • phase_cyc (float) – RF phase cycling in radians.
Returns:

Off-resonace value that most closely matches Mxy prior.
Return type:

float