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deepmr.spiral_stack

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deepmr.spiral_stack#

deepmr.spiral_stack(shape, accel=None, nintl=1, **kwargs)[source]#

Design a constant- or multi-density stack of spirals.

As in the 2D spiral case, interleaves are rotated by a pseudo golden angle with period 377 interelaves. Rotations are performed both along view and contrast dimensions. Acquisition is assumed to traverse the contrast dimension first and then the view, i.e., all the contrasts are acquired before moving to the second view. If multiple echoes are specified, final contrast dimensions will have length ncontrasts * nechoes. Echoes are assumed to be acquired sequentially with the same spiral interleaf.

Finally, slice dimension is assumed to be the outermost loop.

Parameters:

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

  • accel (Iterable[int], optional) – Acceleration factors (in-plane, slices=1). Range from 1 (fully sampled) to nintl / nslices. The default is (1, 1).

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

Keyword Arguments:

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

  • acs_shape (Iterable[int]) – Matrix size for intermediate inner (coil sensitivity estimation) spiral. The default is (None, 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 stack-of-spirals for a (128, 128, 120) voxels matrix by:

>>> head = deepmr.spiral_stack((128, 120))

A multi-shot trajectory can be generated by specifying the nintl argument:

>>> head = deepmr.spiral_stack((128, 120), 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, 16) k-space region sampled with a 4 interleaves spiral, this can be obtained as:

>>> head = deepmr.spiral_stack((128, 120), nintl=48, acs_shape=(32, 16), 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_stack((128, 120), nintl=48, acs_shape=(32, 16), 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, 16) k-space region fully covered by 4 spiral shots and an outer (128, 128, 120) region fully covered by 48 interleaves.

In-plane and slice accelerations can be specified using the accel argument. For example, the following

>>> head = deepmr.spiral_stack((128, 120), nintl=48, accel=(4, 2))

will generate the following trajectory:

>>> head.traj.shape
torch.Size([1, 720, 538, 3])

i.e., a 48-interleaves trajectory with an in-plane acceleration factor of 4 (i.e., 12 interleaves) and slice acceleration of 2 (i.e., 60 encodings).

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_stack((128, 120, 420), nintl=48)
>>> head.traj.shape
torch.Size([420, 120, 538, 3])

corresponding to 420 different contrasts, each sampled with a single spiral interleaf of 538 points, repeated for 120 slice encodings. Similarly, multiple echoes (with fixed sampling) can be specified as:

>>> head = deepmr.spiral_stack((128, 120, 1, 8), nintl=48)
>>> head.traj.shape
torch.Size([8, 5760, 538, 3])

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.

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