3D Variable Flip Angle (Linear)

This example illustrates motion correction of a 3D time series with variable flip angles (VFA). The motion correction is performed with 3D coregistration and using a linear signal model fit.

Setup

import numpy as np
import mdreg

# Example data included in mdreg
data = mdreg.fetch('VFA')

# Variables used in this examples
array = data['array']       # 4D signal data (x, y, z, FA)
FA = data['FA']             # The FA values in degrees
spacing = data['spacing']   # (x,y,z) voxel size in mm.

Perform motion correction

The signal model above is included in mdreg as the function mdreg.fit_spgr_vfa_lin, which require the flip angle (FA) values in degrees as input:

fit_params = {
    'func': mdreg.fit_spgr_vfa_lin,     # VFA signal model
    'FA': FA,                           # Flip angle in degress
}

For coregistration we will use elastix and a relatively coarse deformation field with grid spacing 50mm. We also ask to return the deformation field so we can inspect it:

coreg_params = {
    'package': 'elastix',
    'spacing': spacing,
    'FinalGridSpacingInPhysicalUnits': 50.0,
    'return_deformation': True,
}

We can now perform the motion correction:

coreg, fit, transfo, pars, defo = mdreg.fit(
    array,                          # Signal data to correct
    fit_image = fit_params,         # Signal model
    fit_coreg = coreg_params,       # Coregistration model
    maxit = 2,                      # Maximum number of iteration
    verbose = 2,
)

Initializing..
Iteration 1: fitting signal model
divide by zero encountered in divide
Fitting deformation field (iteration 1)
Building elastix parameter object..
Coregistering..
Calculation time for iteration 1: 0.6096879998842876 min
Iteration 2: fitting signal model
Fitting deformation field (iteration 2)
Building elastix parameter object..
Coregistering..
Calculation time for iteration 2: 0.45500829617182414 min
Total calculation time: 1.0646962960561117 min

Visualize the results

We visualise the original data and results of the computation using the builtin animation function. Since we want to call this 3 times, we define the settings up front:

plot_settings = {
    'vmin' : 0,                         # Minimum value of the colorbar
    'vmax' : np.percentile(array,99),   # Maximum value of the colorbar
}

Now we can plot the data, coregistered images and model fits separately:

anim = mdreg.plot.animation(array, title='Original data', **plot_settings)

Once Loop Reflect

anim = mdreg.plot.animation(coreg, title='Motion corrected', **plot_settings)

Once Loop Reflect

anim = mdreg.plot.animation(fit, title='Model fit', **plot_settings)

Once Loop Reflect

It’s also instructive to show the deformation field and check whether deformations are consistent with the effect of breathing motion. Since the deformation field is a vector we show here its norm:

# Get the norm of the deformation field and adjust the plot settings
defo = mdreg.defo_norm(defo)
plot_settings['vmax'] = np.percentile(defo, 90)

# Display the norm of the deformation field
anim = mdreg.plot.animation(defo, title='Deformation field', **plot_settings)

Once Loop Reflect