This example shows how to use Multi-Shell Multi-Tissue Constrained Spherical Deconvolution (MSMT-CSD) introduced by Tournier et al. [Jeurissen2014]. 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 [Tournier2007].

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

Generate a mask using Median Otsu (optional step)

Denoise the data using MP-PCA (optional step)

Generate Anisotropic Powermap (if T1 unavailable)

Fit DTI model to the data

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

Estimation of the fiber response function

Use the response function to reconstruct the fODF

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

```
import numpy as np
import dipy.reconst.shm as shm
import dipy.direction.peaks as dp
import matplotlib.pyplot as plt
from dipy.denoise.localpca import mppca
from dipy.core.gradients import gradient_table, unique_bvals_tolerance
from dipy.io.gradients import read_bvals_bvecs
from dipy.io.image import load_nifti
from dipy.segment.mask import median_otsu
from dipy.reconst.mcsd import (auto_response_msmt,
mask_for_response_msmt,
response_from_mask_msmt)
from dipy.segment.tissue import TissueClassifierHMRF
from dipy.reconst.mcsd import MultiShellDeconvModel, multi_shell_fiber_response
from dipy.viz import window, actor
from dipy.data import get_sphere, get_fnames
sphere = get_sphere('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 [Hansen2016]). 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('cfin_multib')
data, affine = load_nifti(fraw)
bvals, bvecs = read_bvals_bvecs(fbval, fbvec)
gtab = gradient_table(bvals, 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[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)
```

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)
```

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 [DellAcqua2014]. 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=.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()
```

```
print(ap.shape)
```

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)
```

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)
```

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)
```

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)
```

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)
```

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=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=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])
```

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 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, out_path='msdodf.png', size=(600, 600))
if interactive:
window.show(scene)
```

[Jeurissen2014]

B. Jeurissen, et al., “Multi-tissue constrained spherical deconvolution for improved analysis of multi-shell diffusion MRI data.” NeuroImage 103 (2014): 411-426.

[Tournier2007]

J-D. Tournier, F. Calamante and A. Connelly, “Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution”, Neuroimage, vol. 35, no. 4, pp. 1459-1472, (2007).

[Hansen2016]

B. Hansen and SN. Jespersen, “ Data for evaluation of fast kurtosis strategies, b-value optimization and exploration of diffusion MRI contrast”, Scientific Data 3: 160072 doi:10.1038/sdata.2016.72, (2016)

[DellAcqua2014]

F. Dell’Acqua, et. al., “Anisotropic Power Maps: A diffusion contrast to reveal low anisotropy tissues from HARDI data”, Proceedings of International Society for Magnetic Resonance in Medicine. Milan, Italy, (2014).

Example source code

You can download `the full source code of this example`

. This same script is also included in the dipy source distribution under the `doc/examples/`

directory.