Ctrl+K

deepmr.spiral_proj

Contents

deepmr.spiral_proj#

deepmr.spiral_proj(shape, accel=None, nintl=1, order='ga', **kwargs)[source]#

Design a constant- or multi-density spiral projection.

The trajectory consists of a 2D spiral, whose plane is rotated to cover the 3D k-space. In-plane rotations are sequential. Plane rotation types are specified via the order argument.

Parameters:

  • shape (Iterable[int]) – Matrix shape (in-plane, contrasts=1, echoes=1).

  • accel (Iterable[int], optional) – Acceleration factors (in-plane, radial). Range from 1 (fully sampled) to nintl / $\pi$ * shape[0]. The default is (1, 1) if ncontrast == 1 and (1, ``$\pi$ * shape[0]) if ncontrast > 1.

  • nintl (int, optional) – Number of interleaves to fully sample a plane. The default is 1.

  • order (str, optional) –

    Spiral plane rotation type. These can be:

    • ga: Pseudo golden angle variation of periodicity 377.

    • ga::multiaxis: Pseudo golden angle, i.e., same as ga but views are repeated 3 times on orthogonal axes.

    • ga-sh: Shuffled pseudo golden angle.

    • ga-sh::multiaxis: Multiaxis shuffled pseudo golden angle, i.e., same as ga-sh but views are repeated 3 times on orthogonal axes.

    The default is ga.

Keyword Arguments:

  • moco_shape (int) – Matrix size for inner-most (motion navigation) spiral. The default is None.

  • acs_shape (int) – Matrix size for intermediate inner (coil sensitivity estimation) spiral. The default is None.

  • acs_nintl (int) – Number of interleaves to fully sample intermediate inner spiral. The default is 1.

  • variant (str) –

    Type of spiral. Allowed values are:

    • center-out: starts at the center of k-space and ends at the edge (default).

    • reverse: starts at the edge of k-space and ends at the center.

    • in-out: starts at the edge of k-space and ends on the opposite side (two 180° rotated arms back-to-back).

Returns:

head – Acquisition header corresponding to the generated spiral.

Return type:

Header

Example

>>> import deepmr

We can create a single-shot spiral projection for a matrix of (128, 128, 128) voxels by:

>>> head = deepmr.spiral_proj(128)

An in-plane multi-shot trajectory can be generated by specifying the nintl argument:

>>> head = deepmr.spiral_proj(128, nintl=48)

Both spirals have constant density. If we want a dual density we can use acs_shape and acs_nintl arguments. For example, if we want an inner (32, 32) k-space region sampled with a 4 interleaves spiral, this can be obtained as:

>>> head = deepmr.spiral_proj(128, nintl=48, acs_shape=32, acs_nintl=4)

This inner region can be used e.g., for Parallel Imaging calibration. Similarly, a triple density spiral can be obtained by using the moco_shape argument:

>>> head = deepmr.spiral_proj(128, nintl=48, acs_shape=32, acs_nintl=4, moco_shape=8)

The generated spiral will have an innermost (8, 8) single-shot k-space region (e.g., for PROPELLER-like motion correction), an intermediate (32, 32) k-space region fully covered by 4 spiral shots and an outer (128, 128) region fully covered by 48 interleaves.

In-plane acceleration can be specified using the accel argument. For example, the following

>>> head = deepmr.spiral_proj(128, nintl=48, accel=4)

will generate the following trajectory:

>>> head.traj.shape
torch.Size([1, 4824, 538, 2])

i.e., a 48-interleaves trajectory with an in-plane acceleration factor of 4 (i.e., 12 interleaves), repeated for 402 planes covering the 3D k-space sphere.

Multiple contrasts with different sampling (e.g., for MR Fingerprinting) can be achieved by providing a tuple of ints as the shape argument:

>>> head = deepmr.spiral_proj((128, 420), nintl=48)
>>> head.traj.shape
torch.Size([420, 48, 538, 2])

corresponding to 420 different contrasts, each sampled with a different fully sampled plane. Similarly, multiple echoes (with fixed sampling) can be specified as:

>>> head = deepmr.spiral_proj((128, 1, 8), nintl=48)
>>> head.traj.shape
torch.Size([8, 19296, 538, 2])

corresponding to a 8-echoes fully sampled k-spaces, e.g., for QSM and T2* mapping.

Notes

The returned head (deepmr.Header()) is a structure with the following fields:

  • shape (torch.Tensor):

    This is the expected image size of shape (nz, ny, nx).

  • t (torch.Tensor):

    This is the readout sampling time (0, t_read) in ms. with shape (nsamples,).

  • traj (torch.Tensor):

    This is the k-space trajectory normalized as (-0.5 * shape, 0.5 * shape) with shape (ncontrasts, nviews, nsamples, 3).

  • dcf (torch.Tensor):

    This is the k-space sampling density compensation factor with shape (ncontrasts, nviews, nsamples).

  • TE (torch.Tensor):

    This is the Echo Times array. Assumes a k-space raster time of 1 us and minimal echo spacing.

Contents