Reconstruction with Multi-Shell Multi-Tissue CSD

This example shows how to use Multi-Shell Multi-Tissue Constrained Spherical Deconvolution (MSMT-CSD) introduced by Jeurissen et al.[1]. This tutorial goes through the steps involved in implementing the method.

This method provides improved White Matter(WM), Grey Matter (GM), and Cerebrospinal fluid (CSF) volume fraction maps, which is otherwise overestimated in the standard CSD (SSST-CSD). This is done by using b-value dependencies of the different tissue types to estimate ODFs. This method thus extends the SSST-CSD introduced in [2].

The reconstruction of the fiber orientation distribution function (fODF) in MSMT-CSD involves the following steps:

1. Generate a mask using Median Otsu (optional step)

2. Denoise the data using MP-PCA (optional step)

3. Generate Anisotropic Powermap (if T1 unavailable)

4. Fit DTI model to the data

5. Tissue Classification (needs to be at least two classes of tissues)

6. Estimation of the fiber response function

7. Use the response function to reconstruct the fODF

First, we import all the modules we need from dipy as follows:

import matplotlib.pyplot as plt
import numpy as np

from dipy.core.gradients import gradient_table, unique_bvals_tolerance
from dipy.data import get_fnames, get_sphere
from dipy.denoise.localpca import mppca
import dipy.direction.peaks as dp
from dipy.io.gradients import read_bvals_bvecs
from dipy.io.image import load_nifti
from dipy.reconst.mcsd import (
    MultiShellDeconvModel,
    auto_response_msmt,
    mask_for_response_msmt,
    multi_shell_fiber_response,
    response_from_mask_msmt,
)
import dipy.reconst.shm as shm
from dipy.segment.mask import median_otsu
from dipy.segment.tissue import TissueClassifierHMRF
from dipy.viz import actor, window

sphere = get_sphere(name="symmetric724")

For this example, we use fetch to download a multi-shell dataset which was kindly provided by Hansen and Jespersen (more details about the data are provided in their paper [3]). The total size of the downloaded data is 192 MBytes, however you only need to fetch it once.

fraw, fbval, fbvec, t1_fname = get_fnames(name="cfin_multib")

data, affine = load_nifti(fraw)
bvals, bvecs = read_bvals_bvecs(fbval, fbvec)
gtab = gradient_table(bvals, bvecs=bvecs)

For the sake of simplicity, we only select two non-zero b-values for this example.

bvals = gtab.bvals
bvecs = gtab.bvecs

sel_b = np.logical_or(np.logical_or(bvals == 0, bvals == 1000), bvals == 2000)
data = data[..., sel_b]

The gradient table is also selected to have the selected b-values (0, 1000 and 2000)

gtab = gradient_table(bvals[sel_b], bvecs=bvecs[sel_b])

We make use of the median_otsu method to generate the mask for the data as follows:

b0_mask, mask = median_otsu(data, median_radius=2, numpass=1, vol_idx=[0, 1])

print(data.shape)

(96, 96, 19, 67)

As one can see from its shape, the selected data contains a total of 67 volumes of images corresponding to all the diffusion gradient directions of the selected b-values and call the mppca as follows:

denoised_arr = mppca(data, mask=mask, patch_radius=2)

/opt/homebrew/Caskroom/miniforge/base/envs/py312-test/lib/python3.12/site-packages/dipy/denoise/localpca.py:377: RuntimeWarning: invalid value encountered in divide
  denoised_arr = thetax / theta

Now we will use the denoised array (denoised_arr) obtained from mppca in the rest of the steps in the tutorial.

As for the next step, we generate the anisotropic powermap introduced by Dell’Acqua et al.[4]. To do so, we make use of the Q-ball Model as follows:

qball_model = shm.QballModel(gtab, 8)

We generate the peaks from the qball_model as follows:

peaks = dp.peaks_from_model(
    model=qball_model,
    data=denoised_arr,
    relative_peak_threshold=0.5,
    min_separation_angle=25,
    sphere=sphere,
    mask=mask,
)

ap = shm.anisotropic_power(peaks.shm_coeff)

plt.matshow(np.rot90(ap[:, :, 10]), cmap=plt.cm.bone)
plt.savefig("anisotropic_power_map.png")
plt.close()

Anisotropic Power Map (Axial Slice)

print(ap.shape)

(96, 96, 19)

The above figure is a visualization of the axial slice of the Anisotropic Power Map. It can be treated as a pseudo-T1 for classification purposes using the Hidden Markov Random Fields (HMRF) classifier, if the T1 image is not available.

As we can see from the shape of the Anisotropic Power Map, it is 3D and can be used for tissue classification using HMRF. The HMRF needs the specification of the number of classes. For the case of MSMT-CSD the nclass parameter needs to be >=2. In our case, we set it to 3: namely corticospinal fluid (csf), white matter (wm) and gray matter (gm).

nclass = 3

Then, the smoothness factor of the segmentation. Good performance is achieved with values between 0 and 0.5.

beta = 0.1

We then call the TissueClassifierHMRF with the parameters specified as above:

hmrf = TissueClassifierHMRF()
initial_segmentation, final_segmentation, PVE = hmrf.classify(ap, nclass, beta)

>> Iteration: 0
>> Iteration: 1
>> Iteration: 2
>> Iteration: 3
>> Iteration: 4
>> Iteration: 5
>> Iteration: 6
>> Iteration: 7
>> Iteration: 8
>> Iteration: 9
>> Iteration: 10
>> Iteration: 11
>> Iteration: 12
>> Iteration: 13
>> Iteration: 14
>> Iteration: 15
>> Iteration: 16
>> Iteration: 17
>> Iteration: 18
>> Iteration: 19
>> Iteration: 20
>> Iteration: 21
>> Iteration: 22
>> Iteration: 23

Then, we get the tissues segmentation from the final_segmentation.

csf = np.where(final_segmentation == 1, 1, 0)
gm = np.where(final_segmentation == 2, 1, 0)
wm = np.where(final_segmentation == 3, 1, 0)

Now, we want the response function for each of the three tissues and for each bvalues. This can be achieved in two different ways. If the case that tissue segmentation is available or that one wants to see the tissue masks used to compute the response functions, a combination of the functions mask_for_response_msmt and response_from_mask is needed.

The mask_for_response_msmt function will return a mask of voxels within a cuboid ROI and that meet some threshold constraints, for each tissue and bvalue. More precisely, the WM mask must have a FA value above a given threshold. The GM mask and CSF mask must have a FA below given thresholds and a MD below other thresholds.

Note that for mask_for_response_msmt, the gtab and data should be for bvalues under 1200, for optimal tensor fit.

mask_wm, mask_gm, mask_csf = mask_for_response_msmt(
    gtab,
    data,
    roi_radii=10,
    wm_fa_thr=0.7,
    gm_fa_thr=0.3,
    csf_fa_thr=0.15,
    gm_md_thr=0.001,
    csf_md_thr=0.0032,
)

/opt/homebrew/Caskroom/miniforge/base/envs/py312-test/lib/python3.12/site-packages/dipy/testing/decorators.py:192: UserWarning: Some b-values are higher than 1200.
        The DTI fit might be affected.
  return func(*args, **kwargs)

If one wants to use the previously computed tissue segmentation in addition to the threshold method, it is possible by simply multiplying both masks together.

mask_wm *= wm
mask_gm *= gm
mask_csf *= csf

The masks can also be used to calculate the number of voxels for each tissue.

nvoxels_wm = np.sum(mask_wm)
nvoxels_gm = np.sum(mask_gm)
nvoxels_csf = np.sum(mask_csf)

print(nvoxels_wm)

1407

Then, the response_from_mask function will return the msmt response functions using precalculated tissue masks.

response_wm, response_gm, response_csf = response_from_mask_msmt(
    gtab, data, mask_wm, mask_gm, mask_csf
)

Note that we can also get directly the response functions by calling the auto_response_msmt function, which internally calls mask_for_response_msmt followed by response_from_mask. By doing so, we don’t have access to the masks and we might have problems with high bvalues tensor fit.

auto_response_wm, auto_response_gm, auto_response_csf = auto_response_msmt(
    gtab, data, roi_radii=10
)

/opt/homebrew/Caskroom/miniforge/base/envs/py312-test/lib/python3.12/site-packages/dipy/testing/decorators.py:192: UserWarning: Some b-values are higher than 1200.
        The DTI fit might be affected. It is advised to use
        mask_for_response_msmt with bvalues lower than 1200, followed by
        response_from_mask_msmt with all bvalues to overcome this.
  return func(*args, **kwargs)

As we can see below, adding the tissue segmentation can change the results of the response functions.

print("Responses")
print(response_wm)
print(response_gm)
print(response_csf)
print("Auto responses")
print(auto_response_wm)
print(auto_response_gm)
print(auto_response_csf)

Responses
[[1.56692320e-03 4.46085143e-04 4.46085143e-04 1.62131485e+02]
 [1.34276461e-03 3.52534556e-04 3.52534556e-04 1.62131485e+02]]
[[9.72067588e-04 8.03258278e-04 8.03258278e-04 1.83944994e+02]
 [8.84867552e-04 7.24112459e-04 7.24112459e-04 1.83944994e+02]]
[[1.48269864e-03 1.33687318e-03 1.33687318e-03 2.54087379e+02]
 [1.19307328e-03 1.03487796e-03 1.03487796e-03 2.54087379e+02]]
Auto responses
[[1.70814058e-03 5.99497542e-04 5.99497542e-04 1.66589967e+02]
 [1.37647490e-03 4.22844899e-04 4.22844899e-04 1.66589967e+02]]
[[1.02876747e-03 8.64284096e-04 8.64284096e-04 1.90155949e+02]
 [9.05450074e-04 7.52760292e-04 7.52760292e-04 1.90155949e+02]]
[[1.33298612e-03 1.19461602e-03 1.19461602e-03 2.31346774e+02]
 [1.09567957e-03 9.48548376e-04 9.48548376e-04 2.31346774e+02]]

At this point, there are two options on how to use those response functions. We want to create a MultiShellDeconvModel, which takes a response function as input. This response function can either be directly in the current format, or it can be a MultiShellResponse format, as produced by the multi_shell_fiber_response method. This function assumes a 3 compartments model (wm, gm, csf) and takes one response function per tissue per bvalue. It is important to note that the bvalues must be unique for this function.

ubvals = unique_bvals_tolerance(gtab.bvals)
response_mcsd = multi_shell_fiber_response(
    sh_order_max=8,
    bvals=ubvals,
    wm_rf=response_wm,
    gm_rf=response_gm,
    csf_rf=response_csf,
)

As mentioned, we can also build the model directly and it will call multi_shell_fiber_response internally. Important note here, the function unique_bvals_tolerance is used to keep only unique bvalues from the gtab given to the model, as input for multi_shell_fiber_response. This may introduce differences between the calculated response of each method, depending on the bvalues given to multi_shell_fiber_response externally.

response = np.array([response_wm, response_gm, response_csf])
mcsd_model_simple_response = MultiShellDeconvModel(gtab, response, sh_order_max=8)

Note that this technique only works for a 3 compartments model (wm, gm, csf). If one wants more compartments, a custom MultiShellResponse object must be used. It can be inspired by the multi_shell_fiber_response method.

Now we build the MSMT-CSD model with the response_mcsd as input. We then call the fit function to fit one slice of the 3D data and visualize it.

mcsd_model = MultiShellDeconvModel(gtab, response_mcsd)
mcsd_fit = mcsd_model.fit(denoised_arr[:, :, 10:11])

/opt/homebrew/Caskroom/miniforge/base/envs/py312-test/lib/python3.12/site-packages/cvxpy/problems/problem.py:1481: UserWarning: Solution may be inaccurate. Try another solver, adjusting the solver settings, or solve with verbose=True for more information.
  warnings.warn(

The volume fractions of tissues for each voxel are also accessible, as well as the sh coefficients for all tissues. One can also get each sh tissue separately using all_shm_coeff for each compartment (isotropic) and shm_coeff for white matter.

vf = mcsd_fit.volume_fractions
sh_coeff = mcsd_fit.all_shm_coeff
csf_sh_coeff = sh_coeff[..., 0]
gm_sh_coeff = sh_coeff[..., 1]
wm_sh_coeff = mcsd_fit.shm_coeff

The model allows one to predict a signal from sh coefficients. There are two ways of doing this.

mcsd_pred = mcsd_fit.predict()
mcsd_pred = mcsd_model.predict(mcsd_fit.all_shm_coeff)

From the fit obtained in the previous step, we generate the ODFs which can be visualized as follows:

mcsd_odf = mcsd_fit.odf(sphere)

print("ODF")
print(mcsd_odf.shape)
print(mcsd_odf[40, 40, 0])

fodf_spheres = actor.odf_slicer(
    mcsd_odf, sphere=sphere, scale=1, norm=False, colormap="plasma"
)

interactive = False
scene = window.Scene()
scene.add(fodf_spheres)
scene.reset_camera_tight()

print("Saving illustration as msdodf.png")
window.record(scene=scene, out_path="msdodf.png", size=(600, 600))

if interactive:
    window.show(scene)

ODF
(96, 96, 1, 724)
[ 2.07819397e-03  2.48056889e-03  3.86317738e-03  5.80318112e-04
  4.13450501e-03  1.90510861e-03  2.91056542e-04  2.78808950e-03
  4.18908921e-05  3.61958970e-03  3.17237838e-03  1.23186090e-03
  1.38676232e-03  8.99152866e-05  3.14832163e-04  1.06892957e-03
  1.41825726e-03  3.65070379e-03  2.38250941e-03  9.38942356e-04
 -4.67702568e-04 -2.34357229e-04  3.36801020e-03  1.26912924e-03
  3.69950448e-03 -9.43861871e-04  7.76332334e-04 -2.76965057e-04
  1.30105513e-03  1.04356019e-03  5.12702942e-03  2.57674067e-03
  4.04510936e-03  2.23442424e-03  1.49056228e-04  1.99149700e-03
  1.66042016e-04  3.10946414e-03 -4.39300078e-04  1.83495625e-03
  1.67843779e-03  1.53254789e-02  6.33471409e-04  6.11565718e-03
  8.00278023e-04  4.98227330e-03  4.41515801e-03  5.36097977e-04
  1.15859621e-03  1.28331076e-02  9.97839734e-04  2.42637736e-03
  2.32416120e-03  3.95430344e-03  3.73620758e-02  9.07359260e-04
  4.61738361e-03  1.29678673e-03  2.62750988e-03  1.58723140e-03
  5.94548779e-04  2.10784012e-03  5.20042914e-02  5.50135856e-04
  5.07379628e-03  1.28699862e-03  3.87638912e-03  4.55356793e-02
  5.39732048e-04  2.96030402e-03  2.09439424e-02  1.07074878e-04
 -5.64342252e-04  8.94125547e-04  2.86817699e-03  1.04562301e-01
  9.90321192e-04  4.46903789e-03  9.94198316e-04  1.67351437e-03
  3.07922379e-02 -5.42989381e-05  3.02894434e-03  8.06017373e-02
  3.00443786e-04  1.01026621e-03  9.62710991e-04  2.05185017e-03
  1.29846537e-01  3.48944537e-04  2.69262470e-03  1.72415715e-02
 -1.83042591e-05  1.02239573e-02  1.61051689e-04  2.71427461e-03
  1.70664466e-01  1.20885237e-03  1.81182893e-03  3.72282936e-04
  8.35450334e-04  1.03993364e-01  6.83646690e-04  2.88310692e-03
  7.98688769e-02  1.12299493e-03  1.16502966e-03  4.87089565e-04
  9.11524042e-04  2.34079283e-01 -1.65542623e-05  4.88922363e-04
  8.12219624e-03  6.70655936e-04  5.23346100e-02  3.43813347e-03
  3.15633085e-03  1.97143551e-01  2.90622199e-03  1.01889036e-03
  7.93710007e-05  1.52279438e-05  2.17271730e-01  1.25254560e-03
  5.87380649e-04  5.43598600e-02  2.60994960e-03  1.65058430e-02
  4.63470182e-03  1.22384636e-03  3.12773778e-01  8.85653822e-04
  8.14586308e-04  1.77664617e-03  1.21709957e-03  1.36277507e-01
  1.00149315e-02  2.15089758e-03  1.70157210e-01  5.43197131e-03
  7.28292374e-03  2.31501996e-03 -3.25902169e-04  3.38710836e-01
  5.73876799e-04 -3.15229642e-04  2.47936185e-02  3.56338317e-03
  5.83792975e-02  1.77440136e-02  1.96635855e-03  3.26243670e-01
  3.85722562e-03  8.64078001e-03  1.06838050e-04  1.04555163e-03
  2.53992561e-01  1.45864228e-02 -1.04756400e-05  1.09634648e-01
  6.54845037e-03  2.48961940e-02  1.38681294e-02  4.19466814e-04
  4.19583387e-01  2.42192035e-04  7.49746735e-03  6.49303974e-03
  3.41843434e-03  1.33030323e-01  3.63123941e-02  1.10201510e-03
  2.68332713e-01  6.72911840e-03  2.44350286e-02  4.39052455e-03
  6.86860441e-04  3.73857661e-01  1.33382036e-02  3.02057132e-03
  5.03885597e-02  5.29565370e-03  5.82095643e-02  4.01674891e-02
  1.40213897e-03  4.21585971e-01  1.75680535e-03  2.81140382e-02
  6.34829726e-04  2.39614203e-03  2.33580077e-01  4.94860840e-02
 -6.65061333e-05  1.70904466e-01  6.38132479e-03  4.45167177e-02
  2.18533114e-02  1.13296334e-03  4.50528233e-01  8.23909465e-03
  2.07433362e-02  1.45461738e-02  2.95002361e-03  1.10818063e-01
  7.53487264e-02  7.02700617e-04  3.42558305e-01  3.29635527e-03
  5.63540384e-02  4.46209339e-03  1.24832761e-03  3.35102386e-01
  4.88873403e-02  6.82259677e-03  8.01056189e-02  2.98621188e-03
  6.64901754e-02  5.95809057e-02  2.06006364e-03  4.48670256e-01
  3.63229030e-03  5.61980546e-02  1.67269383e-03  1.00770942e-03
  1.80023822e-01  1.02478689e-01 -2.59898050e-04  2.19738552e-01
  2.13595424e-03  8.04725397e-02  2.31177763e-02  1.03230831e-03
  4.00851960e-01  3.63056657e-02  3.32697472e-02  2.46096185e-02
  1.48486417e-04  9.25061276e-02  1.11447111e-01  1.54846471e-03
  3.66207618e-01  8.69827448e-04  9.88722223e-02  2.62563824e-03
 -2.45950496e-04  2.50953589e-01  1.06737025e-01  7.63297210e-03
  1.05470615e-01 -1.54984383e-04  9.20058485e-02  6.53633515e-02
  1.93584964e-03  4.00639040e-01  2.04792098e-02  8.22611069e-02
  3.35319468e-03  3.34433859e-04  1.25263335e-01  1.55943878e-01
  2.72215430e-05  2.38473404e-01 -5.31554116e-04  1.29384830e-01
  1.74368496e-02 -7.71571848e-04  2.98499400e-01  8.77486229e-02
  3.76454989e-02  3.38067351e-02  1.90919442e-03  9.26599617e-02
  1.27656479e-01  2.24225059e-03  3.30608450e-01  8.83647236e-03
  1.39530201e-01  6.23380689e-04  2.02865238e-03  1.60562810e-01
  1.71004378e-01  5.55224326e-03  1.17127333e-01  2.57579584e-03
  1.33600452e-01  5.51661163e-02 -1.63708142e-04  2.99784929e-01
  5.82597409e-02  9.44015531e-02  5.19105865e-03  1.07878237e-02
  9.10037403e-02  1.87524277e-01  8.63229514e-04  2.18749803e-01
  5.56688954e-03  1.79054622e-01  9.10357390e-03  2.45220433e-03
  1.85215698e-01  1.51322362e-01  3.20937098e-02  3.85036124e-02
  1.66356111e-02  1.13196136e-01  1.16839829e-01  9.33405933e-04
  2.49660975e-01  3.33779555e-02  1.62828367e-01 -2.43129847e-04
  2.14112316e-02  9.27402686e-02  2.17155893e-01  2.94753072e-03
  1.09286280e-01  1.61274058e-02  1.80868616e-01  3.55720392e-02
  1.38598149e-03  1.84370835e-01  1.10953917e-01  8.72244551e-02
  6.11560295e-03  4.28019034e-02  8.27587415e-02  1.83522763e-01
  8.39934601e-04  1.66755842e-01  2.42426690e-02  2.12527850e-01
  2.83709433e-03  2.57704045e-02  9.48342871e-02  2.04452619e-01
  2.09923080e-02  3.60720306e-02  4.72655725e-02  1.45779054e-01
  8.54721773e-02  4.73331175e-04  1.52938382e-01  7.17779632e-02
  1.58762993e-01 -1.04042480e-04  7.07066651e-02  5.70571341e-02
  2.25624177e-01  1.14091580e-03  8.35477744e-02  3.99773766e-02
  2.17731612e-01  1.65009051e-02  2.12298936e-02  8.90775556e-02
  1.60863347e-01  6.51733843e-02  5.28036399e-03  9.78310481e-02
  9.35960381e-02  1.46777795e-01  2.07819397e-03  2.48056889e-03
  3.86317738e-03  5.80318112e-04  4.13450501e-03  1.90510861e-03
  2.91056542e-04  2.78808950e-03  4.18908921e-05  3.61958970e-03
  3.17237838e-03  1.23186090e-03  1.38676232e-03  8.99152866e-05
  3.14832163e-04  1.06892957e-03  1.41825726e-03  3.65070379e-03
  2.38250941e-03  9.38942356e-04 -4.67702568e-04 -2.34357229e-04
  3.36801020e-03  1.26912924e-03  3.69950448e-03 -9.43861871e-04
  7.76332334e-04 -2.76965057e-04  1.30105513e-03  1.04356019e-03
  5.12702942e-03  2.57674067e-03  4.04510936e-03  2.23442424e-03
  1.49056228e-04  1.99149700e-03  1.66042016e-04  3.10946414e-03
 -4.39300078e-04  1.83495625e-03  1.67843779e-03  1.53254789e-02
  6.33471409e-04  6.11565718e-03  8.00278023e-04  4.98227330e-03
  4.41515801e-03  5.36097977e-04  1.15859621e-03  1.28331076e-02
  9.97839734e-04  2.42637736e-03  2.32416120e-03  3.95430344e-03
  3.73620758e-02  9.07359260e-04  4.61738361e-03  1.29678673e-03
  2.62750988e-03  1.58723140e-03  5.94548779e-04  2.10784012e-03
  5.20042914e-02  5.50135856e-04  5.07379628e-03  1.28699862e-03
  3.87638912e-03  4.55356793e-02  5.39732048e-04  2.96030402e-03
  2.09439424e-02  1.07074878e-04 -5.64342252e-04  8.94125547e-04
  2.86817699e-03  1.04562301e-01  9.90321192e-04  4.46903789e-03
  9.94198316e-04  1.67351437e-03  3.07922379e-02 -5.42989381e-05
  3.02894434e-03  8.06017373e-02  3.00443786e-04  1.01026621e-03
  9.62710991e-04  2.05185017e-03  1.29846537e-01  3.48944537e-04
  2.69262470e-03  1.72415715e-02 -1.83042591e-05  1.02239573e-02
  1.61051689e-04  2.71427461e-03  1.70664466e-01  1.20885237e-03
  1.81182893e-03  3.72282936e-04  8.35450334e-04  1.03993364e-01
  6.83646690e-04  2.88310692e-03  7.98688769e-02  1.12299493e-03
  1.16502966e-03  4.87089565e-04  9.11524042e-04  2.34079283e-01
 -1.65542623e-05  4.88922363e-04  8.12219624e-03  6.70655936e-04
  5.23346100e-02  3.43813347e-03  3.15633085e-03  1.97143551e-01
  2.90622199e-03  1.01889036e-03  7.93710007e-05  1.52279438e-05
  2.17271730e-01  1.25254560e-03  5.87380649e-04  5.43598600e-02
  2.60994960e-03  1.65058430e-02  4.63470182e-03  1.22384636e-03
  3.12773778e-01  8.85653822e-04  8.14586308e-04  1.77664617e-03
  1.21709957e-03  1.36277507e-01  1.00149315e-02  2.15089758e-03
  1.70157210e-01  5.43197131e-03  7.28292374e-03  2.31501996e-03
 -3.25902169e-04  3.38710836e-01  5.73876799e-04 -3.15229642e-04
  2.47936185e-02  3.56338317e-03  5.83792975e-02  1.77440136e-02
  1.96635855e-03  3.26243670e-01  3.85722562e-03  8.64078001e-03
  1.06838050e-04  1.04555163e-03  2.53992561e-01  1.45864228e-02
 -1.04756400e-05  1.09634648e-01  6.54845037e-03  2.48961940e-02
  1.38681294e-02  4.19466814e-04  4.19583387e-01  2.42192035e-04
  7.49746735e-03  6.49303974e-03  3.41843434e-03  1.33030323e-01
  3.63123941e-02  1.10201510e-03  2.68332713e-01  6.72911840e-03
  2.44350286e-02  4.39052455e-03  6.86860441e-04  3.73857661e-01
  1.33382036e-02  3.02057132e-03  5.03885597e-02  5.29565370e-03
  5.82095643e-02  4.01674891e-02  1.40213897e-03  4.21585971e-01
  1.75680535e-03  2.81140382e-02  6.34829726e-04  2.39614203e-03
  2.33580077e-01  4.94860840e-02 -6.65061333e-05  1.70904466e-01
  6.38132479e-03  4.45167177e-02  2.18533114e-02  1.13296334e-03
  4.50528233e-01  8.23909465e-03  2.07433362e-02  1.45461738e-02
  2.95002361e-03  1.10818063e-01  7.53487264e-02  7.02700617e-04
  3.42558305e-01  3.29635527e-03  5.63540384e-02  4.46209339e-03
  1.24832761e-03  3.35102386e-01  4.88873403e-02  6.82259677e-03
  8.01056189e-02  2.98621188e-03  6.64901754e-02  5.95809057e-02
  2.06006364e-03  4.48670256e-01  3.63229030e-03  5.61980546e-02
  1.67269383e-03  1.00770942e-03  1.80023822e-01  1.02478689e-01
 -2.59898050e-04  2.19738552e-01  2.13595424e-03  8.04725397e-02
  2.31177763e-02  1.03230831e-03  4.00851960e-01  3.63056657e-02
  3.32697472e-02  2.46096185e-02  1.48486417e-04  9.25061276e-02
  1.11447111e-01  1.54846471e-03  3.66207618e-01  8.69827448e-04
  9.88722223e-02  2.62563824e-03 -2.45950496e-04  2.50953589e-01
  1.06737025e-01  7.63297210e-03  1.05470615e-01 -1.54984383e-04
  9.20058485e-02  6.53633515e-02  1.93584964e-03  4.00639040e-01
  2.04792098e-02  8.22611069e-02  3.35319468e-03  3.34433859e-04
  1.25263335e-01  1.55943878e-01  2.72215430e-05  2.38473404e-01
 -5.31554116e-04  1.29384830e-01  1.74368496e-02 -7.71571848e-04
  2.98499400e-01  8.77486229e-02  3.76454989e-02  3.38067351e-02
  1.90919442e-03  9.26599617e-02  1.27656479e-01  2.24225059e-03
  3.30608450e-01  8.83647236e-03  1.39530201e-01  6.23380689e-04
  2.02865238e-03  1.60562810e-01  1.71004378e-01  5.55224326e-03
  1.17127333e-01  2.57579584e-03  1.33600452e-01  5.51661163e-02
 -1.63708142e-04  2.99784929e-01  5.82597409e-02  9.44015531e-02
  5.19105865e-03  1.07878237e-02  9.10037403e-02  1.87524277e-01
  8.63229514e-04  2.18749803e-01  5.56688954e-03  1.79054622e-01
  9.10357390e-03  2.45220433e-03  1.85215698e-01  1.51322362e-01
  3.20937098e-02  3.85036124e-02  1.66356111e-02  1.13196136e-01
  1.16839829e-01  9.33405933e-04  2.49660975e-01  3.33779555e-02
  1.62828367e-01 -2.43129847e-04  2.14112316e-02  9.27402686e-02
  2.17155893e-01  2.94753072e-03  1.09286280e-01  1.61274058e-02
  1.80868616e-01  3.55720392e-02  1.38598149e-03  1.84370835e-01
  1.10953917e-01  8.72244551e-02  6.11560295e-03  4.28019034e-02
  8.27587415e-02  1.83522763e-01  8.39934601e-04  1.66755842e-01
  2.42426690e-02  2.12527850e-01  2.83709433e-03  2.57704045e-02
  9.48342871e-02  2.04452619e-01  2.09923080e-02  3.60720306e-02
  4.72655725e-02  1.45779054e-01  8.54721773e-02  4.73331175e-04
  1.52938382e-01  7.17779632e-02  1.58762993e-01 -1.04042480e-04
  7.07066651e-02  5.70571341e-02  2.25624177e-01  1.14091580e-03
  8.35477744e-02  3.99773766e-02  2.17731612e-01  1.65009051e-02
  2.12298936e-02  8.90775556e-02  1.60863347e-01  6.51733843e-02
  5.28036399e-03  9.78310481e-02  9.35960381e-02  1.46777795e-01]
Saving illustration as msdodf.png

MSMT-CSD Peaks and ODFs.

References

[1]

Ben Jeurissen, Jacques-Donald Tournier, Thijs Dhollander, Alan Connelly, and Jan Sijbers. Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data. NeuroImage, 103:411–426, December 2014. URL: https://doi.org/10.1016/j.neuroimage.2014.07.061, doi:10.1016/j.neuroimage.2014.07.061.

[2]

Jacques-Donald Tournier, Fernando Calamante, and Alan Connelly. Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution. NeuroImage, 35(4):1459–1472, May 2007. URL: https://doi.org/10.1016/j.neuroimage.2012.06.005, doi:10.1016/j.neuroimage.2007.02.016.

[3]

Brian Hansen and Sune Nørhøj Jespersen. Data for evaluation of fast kurtosis strategies, b-value optimization and exploration of diffusion MRI contrast. Scientific Data, 3(1):160072, August 2016. URL: https://doi.org/10.1038/sdata.2016.72, doi:10.1038/sdata.2016.72.

[4]

Flavio Dell’Acqua, Luis Lacerda, Marco Catani, and Andrew Simmons. Anisotropic Power Maps: A diffusion contrast to reveal low anisotropy tissues from HARDI data. In Joint Annual Meeting ISMRM-ESMRMB 2014 SMRT 23rd Annual Meeting, volume. Milan, Italy, 2014. International Society for Magnetic Resonance in Medicine (ISMRM).