MRI Sequence Documentation: 3D imaging Rare Double Image

RareDoubleImage is a 3D RARE (Rapid Acquisition with Relaxation Enhancement) MRI sequence that reconstructs two independent but identical k-spaces by separating odd and even echoes of the echo train.

The main goal of this approach is to improve robustness against eddy current–related artifacts and echo-dependent phase inconsistencies.

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Concept

During the echo train:

• Odd echoes are used to fill one k-space.
• Even echoes are used to fill a second, independent k-space.

Both k-spaces share the same sampling trajectory and spatial encoding, allowing them to be reconstructed into two images with identical geometry. Any discrepancies between the two images can be attributed mainly to system imperfections (e.g., eddy currents, gradient delays, phase errors).

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Advantages

• Increased robustness to eddy currents and gradient imperfections
• Redundant k-space acquisition without increasing scan time
• Enables:
  • Odd/even image comparison
  • Artifact detection

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Reconstruction Features

The sequence supports:

• Independent reconstruction of odd and even echo images
• Optional Tyger-based denoising
• Optional B₀ distortion correction
• Zero-padding (ZP) or POCS partial Fourier filling
• Flexible readout direction and axis orientation handling

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Input Parameters

RF Parameters

• Larmor frequency offset (freqOffset, kHz): Frequency offset applied to the RF carrier relative to the system Larmor frequency.

  • example: 0.0

• Excitation flip angle (rfExFA, º): Flip angle of the excitation RF pulse.

  • example: 90

• Refocusing flip angle (rfReFA, º): Flip angle of the refocusing RF pulses.

  • example: 180

• Excitation RF duration (rfExTime, µs): Duration of the excitation RF pulse.

  • example: 50.0

• Refocusing RF duration (rfReTime, µs): Duration of the refocusing RF pulses.

  • example: 100.0

Sequence Timing

• Echo spacing (echoSpacing, ms): Time between consecutive echoes in the echo train.

  • example: 10.0

• Pre-excitation time (preExTime, ms): Delay before the excitation pulse.

  • example: 0.0

• Inversion time (inversionTime, ms): Delay between inversion pulse and excitation pulse (0 disables inversion).

  • example: 0.0

• Repetition time (repetitionTime, ms): Time between consecutive sequence repetitions (TR).

  • example: 50.0

• Echo train length (etl): Number of echoes acquired per excitation.

  • example: 4

• Acquisition time (acqTime, ms): Duration of the readout window per echo.

  • example: 4.0

Imaging Parameters

• Number of scans (nScans): Number of repetitions used for signal averaging.

  • example: 1

• Field of view (fov, cm): Imaging field of view along readout, phase, and slice directions.

  • example: [12.0, 12.0, 12.0]

• Displacement field of view (dfov, mm): Offset of the imaging volume relative to the gradient isocenter.

  • example: [0.0, 0.0, 0.0]

• Number of points (nPoints): Number of samples in readout, phase, and slice directions.

  • example: [40, 40, 1]

• Axes orientation (axesOrientation): Mapping of readout, phase, and slice axes.

  • example: [2, 1, 0]
  • note: 0 = x, 1 = y, 2 = z

Gradient and Readout

• Sweep mode (sweepMode): Ordering of k-space traversal in phase encoding.

  • example: 1
  • options:
    • 0: −kmax → +kmax
    • 1: 0 → +kmax
    • 2: +kmax → 0

• Readout gradient duration (rdGradTime, ms): Duration of the readout gradient.

  • example: 5.0

• Readout dephasing time (rdDephTime, ms): Duration of the readout dephasing gradient.

  • example: 1.0

• Phase gradient duration (phGradTime, ms): Duration of the phase encoding gradient.

  • example: 1.0

• Readout preemphasis (rdPreemphasis): Scaling factor applied to the readout gradient.

  • example: 1.0

• Readout direction (rd_direction): Direction of the readout gradient polarity.

  • example: 1
  • options: 1 (positive), -1 (negative)

Calibration and Noise

• Dummy pulses (dummyPulses): Number of dummy excitations applied before acquisition.

  • example: 1

• Noise acquisitions (nNoise): Number of noise-only acquisitions.

  • example: 1

• Shimming (shimming): Static shimming values applied to the system (*×1e4).

  • example: [0.0, 0.0, 0.0]

Reconstruction and Processing

• Partial Fourier fraction (parFourierFraction): Fraction of k-space acquired along the slice direction.

  • example: 0.7

• Unlock image orientation (unlock_orientation): Disable automatic image reorientation.

  • example: 0
  • options: 0 (standard orientation), 1 (raw orientation)

• Full plot (full_plot): Plot odd and even echoes separately.

  • example: True

• K-space filling method (k_fill): Method used to complete missing k-space data.

  • example: ZP
  • options: ZP, POCS

• Tyger input echoes (tyger_denoising_echoes): Echoes sent to the Tyger denoising algorithm.

  • example: all
  • options: odd, even, all

• Tyger denoising (tyger_denoising): Enable SNRAware denoising using Tyger.

  • example: 0

• Tyger distortion correction (tyger_recon): Enable distortion correction using a B₀ map (SPDS required).

  • example: 0

• Reconstruction type (recon_type): Reconstruction algorithm used.

  • example: cp
  • options: cp, artpk

• B₀ fit file (boFit_file): File used for B₀ inhomogeneity correction.

  • example: boFit_default.txt

Sampling Control

• Oversampling factor (oversampling_factor): Oversampling applied during readout.

  • example: 6

• Decimation factor (decimation_factor): Decimation factor applied after acquisition.

  • example: 3

• Additional readout points (add_rd_points): Extra points added to the readout to avoid filter artifacts.

  • example: 10

Important Notes:

• nPoints must always be even numbers for consistency in the Fourier transform process.
• The echo train length (ETL) should be chosen such that the number of phases divided by ETL is an even number.
• An exception occurs when the ETL equals the number of phases.
• The ETL must be and even number to accommodate both k-spaces.
• A schematic of the sweep modes along the phase direction can be seen in the image above.

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Outputs

The analysis generates the following outputs:

Top row: Odd echoes

1. Magnitude
2. Phase
3. k-Space

Bottom row: Even echoes

1. Magnitude
2. Phase
3. k-Space

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Raw Data

• seqName: Sequence name
• dfov: Position of the gradient isocenter (mm), dFOV[x,y,z]
• fov: Field of View [x,y,z] (cm)
• nScans: Number of scans
• freqOffset: Larmor frequency offset (kHz)
• rfExFA: Excitation flip angle (º)
• rfReFA: Refocusing flip angle (º)
• rfExTime: RF excitation time (us)
• rfReTime: RF refocusing time (us)
• echoSpacing: Echo spacing (ms)
• preExTime: Preexitation time (ms)
• inversionTime: Inversion time (ms)
• repetitionTime: Repetition time (ms)
• nPoints: Number of points, nPoints[rd, ph, sl]
• etl: Echo train length
• acqTime: Acquisition time (ms)
• axesOrientation: Axes[rd,ph,sl]
• sweepMode: Sweep mode, 0: sweep from -kmax to kmax. 1: sweep from 0 to kmax. 2: sweep from kmax to 0, val=1
• rdGradTime: Rd gradient time (ms)
• rdDephTime: Rd dephasing time (ms)
• phGradTime: Ph gradient time (ms)
• rdPreemphasis: Rd preemphasis factor
• dummyPulses: Number of dummy pulses.
• nNoise: Number of noise readouts acquired in the first batch.
• shimming: Shimming values used along the sequence to homogenize magnetic field, val=[0.0, 0.0, 0.0]
• parFourierFraction: Partial fourier fraction. Fraction of k planes aquired in slice direction
• unlock_orientation: 0 or 1 that indicates how to display image. 0: Native xyz display; 1: radiological convention.
• full_plot: Show the image withing the fov determined by the decimation and oversamplnig factors.
• k_fill: Parameter indicating how the missing k-space is filled.
• tyger_denoising_echoes: all, odd, or even, indicating the echoes used for denoising.
• tyger_recon: Boolean parameter indicating if reconstruction is done through Tyger.
• tyger_denoising: Boolean parameter indicating if denoising is done through Tyger TEP.
• recon_type: Indicates the type of reconstruction run in Tyger
• boFit_file: Path indicating where the b0 map is located.
• rd_direction: Polarity of the gradient readout.
• oversampling_factor: Oversampling factor used during readout.
• decimation_factor: Decimation factor used during decimation.
• add_rd_points: Additional readout points in each acquisition windows.
• input_keys: keys indicating the input fileds.
• input_strings: list of input strings.
• axes_enable: Axes enable. Use 0 for directions with matrix size 1, use 1 otherwise
• rf_ex_amp: Amplitude of the excitation rf pulse in a.u. of red pitaya.
• rf_re_amp: Amplitude of the rf refocusing pulse in a.u. of red pitaya.
• resolution: Nominal pixel size along readout, phase and slice direction
• grad_rise_time: Gradient Rise Time (s)
• larmorFreq: Larmor frequency (MHz)
• partialAcquisition: While doing partial acquisition, this is the number of extra slices acquired next to half nSlices / 2
• rd_grad_amplitude: Amplitude of the readout gradient in T/m
• ph_grad_amplitude: Máximum applied gradient along phase direction in T/m
• sl_grad_amplitude: Máximum applied gradient along slice direction in T/m
• rd_deph_amplitude: Amplitude of the dephasing gradient applied along readout direction in T/m
• sweepOrder: Array with the index representing the order of acquired phase lines.
• ph_gradients: List of applied phase gradient along the sequence in T/m
• sl_gradients: List of applied slice gradient along the sequence in T/m
• bw_MHz: Acquisition bandwidth (MHz)
• sampling_period_us: sampling period (us).
• sampling_time_s: sampling time (s) pero acquisition window.
• n_readouts: Number of acquired points for each batch.
• n_batches: Number of executed batches for the sequence.
• data_over: oversampled data as acquired from the red pitaya according to the decimation factor.
• data_decimated: decimated data according to the decimation factor.
• data_noise: noise acquisitions.
• data_dummy: Datas acquired along one echo train after first dummy pulse.
• data_signal: data acquired withing the pulse sequence. without noise or dummy acquisitions with dimension
• data_full_even_echoes: Data corresponding to even echoes.
• data_full_odd_echoes: Data corresponding to odd echoes.
• kSpace3D_even_echoes: numpy array with the acquired k-space from even echoes.
• kSpace3D_odd_echoes: numpy array with the acquired k-space from odd echoes.
• image3D_even_echoes: Image acquired from even echoes.
• image3D_odd_echoes: Image acquired from odd echoes.
• kSpace3D: numpy array with the synthetic k-space with dimensions [nSlices, nPhases, nReadouts]
• image3D: numpy array with the resulting image with dimensions [nSlices, nPhases, nReadouts]
• kMax_1/m: numpy array with the maximum k value for readout, phase and slice.
• sampled_odd numpy array with four columns for [k_readout, k_phase, k_slices, data] (1/m, 1/m, 1/m, mV), corresponding to odd echoes.
• sampled_eve numpy array with four columns for [k_readout, k_phase, k_slices, data] (1/m, 1/m, 1/m, mV), corresponding to even echoes.
• sampled numpy array with four columns for [k_readout, k_phase, k_slices, data] (1/m, 1/m, 1/m, mV), corresponding to the average image.
• sampledCartesian: numpy array with four columns resampled to cartesian grid.
• fileName: File name (.mat).