initialize_3D_seiffert_shells

mrinufft.trajectories.trajectory3D.initialize_3D_seiffert_shells(Nc, Ns, nb_shells, curve_index=0.5, nb_revolutions=1, shell_tilt='uniform', shot_tilt='uniform')

Initialize 3D trajectories with Seiffert shells.

The implementation is based on work from [Er00] and [Br09], using Jacobi elliptic functions to define Seiffert spirals over shell/sphere surfaces.

Parameters:

• Nc (int) – Number of shots

• Ns (int) – Number of samples per shot

• nb_shells (int) – Number of concentric shells/spheres

• curve_index (float) – Index controlling curve from 0 (flat) to 1 (curvy), by default 0.5

• nb_revolutions (float) – Number of revolutions, i.e. times the curve passes through the upper-half of the z-axis, by default 1

• shell_tilt (str, float, optional) – Angle between consecutive shells along z-axis, by default “uniform”

• shot_tilt (str, float, optional) – Angle between shots over a shell surface along z-axis, by default “uniform”

Returns:

3D Seiffert shell trajectory

Return type:

array_like

References

[IN95]

Irarrazabal, Pablo, and Dwight G. Nishimura. “Fast three dimensional magnetic resonance imaging.” Magnetic Resonance in Medicine 33, no. 5 (1995): 656-662.

[Er00]

Erdös, Paul. “Spiraling the earth with C. G. J. jacobi.” American Journal of Physics 68, no. 10 (2000): 888-895.

[Br09]

Brizard, Alain J. “A primer on elliptic functions with applications in classical mechanics.” European journal of physics 30, no. 4 (2009): 729.