gre

GRE simulations.

mr_utils.sim.gre.gre.ernst(TR, T1)[source]

Computes the Ernst angle.

Parameters:
  • TR (float) – repetition time.
  • T1 (array_like) – longitudinal exponential decay time constant.
Returns:

alpha – Ernst angle in rad.
Return type:

array_like

Notes

Implements equation [14.9] from [1].

References

[1]Notes from Bernstein, M. A., King, K. F., & Zhou, X. J. (2004). Handbook of MRI pulse sequences. Elsevier.
mr_utils.sim.gre.gre.fzss(T1, TR, alpha=None)[source]

Dimensionless measure of steady-state longitudinal magnetization.

Parameters:
  • T1 (array_like) – longitudinal exponential decay time constant.
  • TR (float) – repetition time.
  • alpha (array_like, optional) – flip angle (in rad).
Returns:

Dimensionless measure of steady-state longitudinal magnetization.
Return type:

array_like

Notes

alpha=None will use the Ernst angle.

Implements equation [14.7] from [2].

References

[2]Notes from Bernstein, M. A., King, K. F., & Zhou, X. J. (2004). Handbook of MRI pulse sequences. Elsevier.
mr_utils.sim.gre.gre.gre_sim(T1, T2, TR=0.012, TE=0.006, alpha=1.0471975511965976, field_map=None, phi=0, dphi=0, M0=1, tol=1e-05, maxiter=None, spoil=True)[source]

Simulate GRE pulse sequence.

Parameters:
  • T1 (array_like) – longitudinal exponential decay time constant.
  • T2 (array_like) – Transverse exponential decay time constant.
  • TR (float, optional) – repetition time.
  • TE (float, optional) – echo time.
  • alpha (float, optional) – flip angle.
  • field_map (array_like, optional) – offresonance field map (in hertz).
  • phi (float, optional) – Reference starting phase.
  • dphi (float, optional) – phase cycling of RF pulses.
  • M0 (array_like, optional) – proton density.
  • tol (float, optional) – Maximum difference between voxel intensity iter to iter until stop.
  • maxiter (int, optional) – number of excitations till steady state.
Returns:

Complex transverse magnetization (Mx + 1j*My)
Return type:

array_like

Notes

maxiter=None will run until difference between all voxel intensities iteration to iteration is within given tolerance, tol (default=1e-5).

mr_utils.sim.gre.gre.gre_sim_loop(T1, T2, TR=0.012, TE=0.006, alpha=1.0471975511965976, field_map=None, dphi=0, M0=1, maxiter=200)[source]

Simulate GRE pulse sequence.

Parameters:
  • T1 (array_like) – longitudinal exponential decay time constant.
  • T2 (array_like) – Transverse exponential decay time constant.
  • TR (float, optional) – repetition time.
  • TE (float, optional) – echo time.
  • alpha (float, optional) – flip angle.
  • field_map (array_like, optional) – offresonance field map (in hertz).
  • dphi (float, optional) – phase-cycling of RF pulses.
  • M0 (array_like, optional) – proton density.
  • maxiter (int, optional) – number of excitations till steady state.
Returns:

Mxy – Complex transverse magnetization.
Return type:

array_like
mr_utils.sim.gre.gre.spoiled_gre(T1, T2star, TR, TE, alpha=None, M0=1)[source]

Spoiled, steady state GRE contrast simulation.

Parameters:
  • T1 (array_like) – longitudinal exponential decay time constant.
  • T2star (array_like) – Effective transverse exponential decay time constant.
  • TR (float) – repetition time.
  • TE (float) – echo time.
  • alpha (array_like, optional) – flip angle.
  • M0 (array_like, optional) – proton density.
Returns:

S – Simulated magnitude spoiled GRE image.
Return type:

array_like

Notes

alpha=None will use the Ernst angle.

Assuming a longitudinal steady-state and perfect spoiling. Note that dependence is on T2* rather than T2 because SE/STE formation is suppressed by spoiling and the signal is generated by gradient refocusing of an FID.

Implements equation [14.8] from [4].

References

[4]Notes from Bernstein, M. A., King, K. F., & Zhou, X. J. (2004). Handbook of MRI pulse sequences. Elsevier.
mr_utils.sim.gre.gre.spoiled_gre_k(T1, T2star, TR, TE, alpha=None, M0=1, k=1)[source]

Spoiled GRE contrast simulation for k excitation pulses.

See spoiled_gre().

Parameters:
  • T1 (array_like) – longitudinal exponential decay time constant.
  • T2star (array_like) – Effective transverse exponential decay time constant.
  • TR (float) – repetition time.
  • TE (float) – echo time.
  • alpha (array_like, optional) – flip angle.
  • M0 (array_like, optional) – proton density.
  • k (int, optional) – Number of excitation pulses the magnetization experiences.
Returns:

Sk – Simulated magnitude GRE image.
Return type:

array_like
Raises:

AssertionError – If k is less than 1.

Notes

alpha=None will use the Ernst angle.

Implements equations [14.10-11] from [3].

References

[3]Notes from Bernstein, M. A., King, K. F., & Zhou, X. J. (2004). Handbook of MRI pulse sequences. Elsevier.