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deepmr.sinusoidal_fa

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deepmr.sinusoidal_fa#

deepmr.sinusoidal_fa(fa_max=(35.0, 43.0, 70.0, 45.0, 27.0), length=200, spacing=10, recovery=0, offset=5.0, head=None)[source]#

Design a multi-segment sinusoidal flip angle train.

The resulting train, similar to the one introduced by Jiang et al. [1], consists of len(fa_max) sinusoidal section (positive wave), each of length length` separed by constant flip angle sections of length ``spacing. The n-th sinusoidal section peaks at fa_max[n] [deg]. The train is followed by a constant flip angle section of length recovery. The overall schedule minimum flip angle is determined by the offset parameter (in [deg]).

Parameters:

  • fa_max (Iterable[float], optional) – Maximum flip angle in [deg] per sinusoidal segment. The default is (35., 43., 70., 45., 27.) [deg].

  • length (int, optional) – Sinusoidal segment length. The default is 200 pulses.

  • spacing (int, optional) – Zero degrees flip angle pulses in between segments. The default is 10.

  • recovery (int, optional) – Constant flip angle recovery train length. The default is 0.

  • offset (float, optional) – Minimum flip angle in [deg]. The default is 5. [deg].

  • head (Header, optional) – Pre-existing acquisition header. If provided, interpolate FA train to ncontrast = head.traj.shape[0] and include it in the head.FA field. The default is None.

Returns:

If head is not provided, returns sinusoidal flip angle train in [deg] as a torch.Tensor. If head is provided, insert flip angle train (linearly interpolated to ncontrast = head.traj.shape[0]) in head.FA field.

Return type:

torch.Tensor | deepmr.Header

Examples

>>> import deepmr

A 5 sections flip angle train with 10-pulses long separation and no recovery (e.g., for 2D MR Fingerprinting) can be generated as:

>>> fa_train = deepmr.sinusoidal_fa((35., 43., 70., 45., 27.), 200, 10)

A final 100 constant flip angle segment (e.g., for 3D MR Fingerprinting) can be added via the recovery argument:

>>> fa_train = deepmr.sinusoidal_fa((35., 43., 70., 45., 27.), 200, 10, recovery=100)

References

[1] Jiang, Y., Ma, D., Seiberlich, N., Gulani, V. and Griswold, M.A. (2015), MR fingerprinting using fast imaging with steady state precession (FISP) with spiral readout. Magn. Reson. Med., 74: 1621-1631. https://doi.org/10.1002/mrm.25559

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