SSFP simulation

## SSFP

Simple steady-state free precession simulation. The goal is to provide a simple to use, pip-installable solution for simulating and working with this wonderful pulse sequence.

In this package:

• bSSFP: bssfp()
• GS solution: gs_recon()
• PLANET: planet()
• 3D Region Growing Phase Correction: rgphcorr3d()
• Robust Coil Combination: robustcc()

## Installation

Should be as easy as:

```pip install ssfp
```

## Usage

See ssfp.examples for typical usage. You can run examples like:

```python -m ssfp.examples.basic_bssfp
```

Balanced steady-state free precession can be called through bssfp(). This is an implementation of equations [1–2] in [1]. These equations are based on the Ernst-Anderson derivation [2] where off-resonance is assumed to be subtracted as opposed to added (as in the Freeman-Hill derivation [3]). Hoff actually gets Mx and My flipped in the paper, so we fix that here. We also assume that the field map will be provided given the Freeman-Hill convention.

```from ssfp import bssfp

# Here's the simplest usage, see docstring for all the possible
# function arguments
sig = bssfp(T1, T2, TR, alpha)
```

We can also easily get the Geometric Solution to the elliptical signal model as described in [1] as follows:

```from ssfp import gs_recon
recon = gs_recon(phased_cycled_images, pc_axis=-1)

# Notice that we can specify the axis where the phase-cycles live
```

PLANET [4] is a method for simultaneous T1, T2 fitting for bSSFP phase-cycled data. Call like this:

```from ssfp import planet

# For a single pixel:
Meff, T1, T2, df = planet(
phased_cycled_pixels, alpha, TR, T1_guess,
```

3D Region Growing Phase Correction [5] is an algorithm for determining water and fat images from a single bSSFP acquisition. It can be called like this:

```from ssfp import rgphcorr3d
phase_corrected = rgphcorr3d(
dataset3d, cellsize=(4, 4, 4), slice_axis=-1)

# see ssfp.examples.basic_rgphcorr for full usage example
```

Robust Coil Combination for bSSFP Elliptical Signal Model [6] is a coil combination method that preserves the elliptical relationships between phase-cycled pixels. It has two variants: simple and full. By default, the simple method is called. The full method is very slow and only used for validation of the simple method. Robust coil combination can be called like this:

```from ssfp import robustcc

sx, sy, sz, num_pc, num_coils = data.shape[:]
coil_combined = robustcc(data, pc_axis=-2, coil_axis=-1)

# see ssfp.examples.basic_robustcc for more usage examples
```

# Changelog

• 1.0.0: bssfp() function overhaul to allow arbitrarily dimensioned input arrays or scalars and removes the target_pc_axis argument.

## References

 [1] (1, 2) Xiang, Qing‐San, and Michael N. Hoff. “Banding artifact removal for bSSFP imaging with an elliptical signal model.” Magnetic resonance in medicine 71.3 (2014): 927-933.
 [2] Ernst, Richard R., and Weston A. Anderson. “Application of Fourier transform spectroscopy to magnetic resonance.” Review of Scientific Instruments 37.1 (1966): 93-102.
 [3] Freeman R, Hill H. Phase and intensity anomalies in fourier transform NMR. J Magn Reson 1971;4:366–383.
 [4] Shcherbakova, Yulia, et al. “PLANET: an ellipse fitting approach for simultaneous T1 and T2 mapping using phase‐cycled balanced steady‐state free precession.” Magnetic resonance in medicine 79.2 (2018): 711-722.
 [5] Hargreaves, Brian A., et al. “Fat‐suppressed steady‐state free precession imaging using phase detection.” Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 50.1 (2003): 210-213.
 [6] N. McKibben, G. Tarbox, E. DiBella, and N. K. Bangerter, “Robust Coil Combination for bSSFP Elliptical Signal Model,” Proceedings of the 28th Annual Meeting of the ISMRM; Sydney, NSW, Australia, 2020.

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