.. AUTO-GENERATED FILE -- DO NOT EDIT!

.. _example_streamline_tools:



=========================================================
Connectivity Matrices, ROI Intersections and Density Maps
=========================================================

This example is meant to be an introduction to some of the streamline tools
available in dipy. Some of the functions covered in this example are
``target``, ``connectivity_matrix`` and ``density_map``. ``target`` allows one
to filter streamlines that either pass through or do not pass through some
region of the brain, ``connectivity_matrix`` groups and counts streamlines
based on where in the brain they begin and end, and finally, density map counts
the number of streamlines that pass though every voxel of some image.

To get started we'll need to have a set of streamlines to work with. We'll use
EuDX along with the CsaOdfModel to make some streamlines. Let's import the
modules and download the data we'll be using.

::
  
  from dipy.tracking.eudx import EuDX
  from dipy.reconst import peaks, shm
  from dipy.tracking import utils
  
  from dipy.data import read_stanford_labels, fetch_stanford_t1, read_stanford_t1
  
  hardi_img, gtab, labels_img = read_stanford_labels()
  data = hardi_img.get_data()
  labels = labels_img.get_data()
  
  fetch_stanford_t1()
  t1 = read_stanford_t1()
  t1_data = t1.get_data()
  

We've loaded an image called ``labels_img`` which is a map of tissue types such
that every integer value in the array ``labels`` represents an anatomical
structure or tissue type [#]_. For this example, the image was created so that
white matter voxels have values of either 1 or 2. We'll use
``peaks_from_model`` to apply the ``CsaOdfModel`` to each white matter voxel
and estimate fiber orientations which we can use for tracking.

::
  
  white_matter = (labels == 1) | (labels == 2)
  csamodel = shm.CsaOdfModel(gtab, 6)
  csapeaks = peaks.peaks_from_model(model=csamodel,
                                    data=data,
                                    sphere=peaks.default_sphere,
                                    relative_peak_threshold=.8,
                                    min_separation_angle=45,
                                    mask=white_matter)
  

Now we can use EuDX to track all of the white matter. To keep things reasonably
fast we use ``density=2`` which will result in 8 seeds per voxel. We'll set
``a_low`` (the parameter which determines the threshold of FA/QA under which
tracking stops) to be very low because we've already applied a white matter
mask.

::
  
  seeds = utils.seeds_from_mask(white_matter, density=2)
  streamline_generator = EuDX(csapeaks.peak_values, csapeaks.peak_indices,
                              odf_vertices=peaks.default_sphere.vertices,
                              a_low=.05, step_sz=.5, seeds=seeds)
  affine = streamline_generator.affine
  streamlines = list(streamline_generator)
  

The first of the tracking utilities we'll cover here is ``target``. This
function takes a set of streamlines and a region of interest (ROI) and returns
only those streamlines that pass though the ROI. The ROI should be an array
such that the voxels that belong to the ROI are ``True`` and all other voxels
are ``False`` (this type of binary array is sometimes called a mask). This
function can also exclude all the streamlines that pass though an ROI by
setting the ``include`` flag to ``False``. In this example we'll target the
streamlines of the corpus callosum. Our ``labels`` array has a sagittal slice
of the corpus callosum identified by the label value 2. We'll create an ROI
mask from that label and create two sets of streamlines, those that intersect
with the ROI and those that don't.

::
  
  cc_slice = labels == 2
  cc_streamlines = utils.target(streamlines, cc_slice, affine=affine)
  cc_streamlines = list(cc_streamlines)
  
  other_streamlines = utils.target(streamlines, cc_slice, affine=affine,
                                   include=False)
  other_streamlines = list(other_streamlines)
  assert len(other_streamlines) + len(cc_streamlines) == len(streamlines)
  

We can use some of dipy's visualization tools to display the ROI we targeted
above and all the streamlines that pass though that ROI. The ROI is the yellow
region near the center of the axial image.

::
  
  from dipy.viz import fvtk
  from dipy.viz.colormap import line_colors
  
  # Make display objects
  color = line_colors(cc_streamlines)
  cc_streamlines_actor = fvtk.line(cc_streamlines, line_colors(cc_streamlines))
  cc_ROI_actor = fvtk.contour(cc_slice, levels=[1], colors=[(1., 1., 0.)],
                              opacities=[1.])
  
  vol_actor = fvtk.slicer(t1_data)
  
  vol_actor.display(40, None, None)
  vol_actor2 = vol_actor.copy()
  vol_actor2.display(None, None, 35)
  
  # Add display objects to canvas
  r = fvtk.ren()
  fvtk.add(r, vol_actor)
  fvtk.add(r, vol_actor2)
  fvtk.add(r, cc_streamlines_actor)
  fvtk.add(r, cc_ROI_actor)
  
  # Save figures
  fvtk.record(r, n_frames=1, out_path='corpuscallosum_axial.png',
              size=(800, 800))
  fvtk.camera(r, [-1, 0, 0], [0, 0, 0], viewup=[0, 0, 1])
  fvtk.record(r, n_frames=1, out_path='corpuscallosum_sagittal.png',
              size=(800, 800))
  

.. figure:: corpuscallosum_axial.png
   :align: center

   **Corpus Callosum Axial**

.. include:: ../links_names.inc

.. figure:: corpuscallosum_sagittal.png
   :align: center

   **Corpus Callosum Sagittal**

Once we've targeted on the corpus callosum ROI, we might want to find out which
regions of the brain are connected by these streamlines. To do this we can use
the ``connectivity_matrix`` function. This function takes a set of streamlines
and an array of labels as arguments. It returns the number of streamlines that
start and end at each pair of labels and it can return the streamlines grouped
by their endpoints. Notice that this function only considers the endpoints of
each streamline.

::
  
  M, grouping = utils.connectivity_matrix(cc_streamlines, labels, affine=affine,
                                          return_mapping=True,
                                          mapping_as_streamlines=True)
  M[:3, :] = 0
  M[:, :3] = 0
  

We've set ``return_mapping`` and ``mapping_as_streamlines`` to ``True`` so that
``connectivity_matrix`` returns all the streamlines in ``cc_streamlines``
grouped by their endpoint.

Because we're typically only interested in connections between gray matter
regions, and because the label 0 represents background and the labels 1 and 2
represent white matter, we discard the first three rows and columns of the
connectivity matrix.

We can now display this matrix using matplotlib, we display it using a log
scale to make small values in the matrix easier to see.

::
  
  import numpy as np
  import matplotlib.pyplot as plt
  plt.imshow(np.log1p(M), interpolation='nearest')
  plt.savefig("connectivity.png")
  

.. figure:: connectivity.png
   :align: center

   **Connectivity of Corpus Callosum**

.. include:: ../links_names.inc


In our example track there are more streamlines connecting regions 11 and
54 than any other pair of regions. These labels represent the left and right
superior frontal gyrus respectively. These two regions are large, close
together, have lots of corpus callosum fibers and are easy to track so this
result should not be a surprise to anyone.

However, the interpretation of streamline counts can be tricky. The
relationship between the underlying biology and the streamline counts will
depend on several factors, including how the tracking was done, and the correct
way to interpret these kinds of connectivity matrices is still an open question
in the diffusion imaging literature.

The next function we'll demonstrate is ``density_map``. This function allows
one to represent the spatial distribution of a track by counting the density of
streamlines in each voxel. For example, let's take the track connecting the
left and right superior frontal gyrus.

::
  
  lr_superiorfrontal_track = grouping[11, 54]
  shape = labels.shape
  dm = utils.density_map(lr_superiorfrontal_track, shape, affine=affine)
  

Let's save this density map and the streamlines so that they can be
visualized together. In order to save the streamlines in a ".trk" file we'll
need to move them to "trackvis space", or the representation of streamlines
specified by the trackvis Track File format.

To do that, we will use tools available in [nibabel](http://nipy.org/nibabel)

::
  
  import nibabel as nib
  
  # Save density map
  dm_img = nib.Nifti1Image(dm.astype("int16"), hardi_img.get_affine())
  dm_img.to_filename("lr-superiorfrontal-dm.nii.gz")
  
  # Make a trackvis header so we can save streamlines
  voxel_size = labels_img.get_header().get_zooms()
  trackvis_header = nib.trackvis.empty_header()
  trackvis_header['voxel_size'] = voxel_size
  trackvis_header['dim'] = shape
  trackvis_header['voxel_order'] = "RAS"
  
  # Move streamlines to "trackvis space"
  trackvis_point_space = utils.affine_for_trackvis(voxel_size)
  lr_sf_trk = utils.move_streamlines(lr_superiorfrontal_track,
                                     trackvis_point_space, input_space=affine)
  lr_sf_trk = list(lr_sf_trk)
  
  # Save streamlines
  for_save = [(sl, None, None) for sl in lr_sf_trk]
  nib.trackvis.write("lr-superiorfrontal.trk", for_save, trackvis_header)
  

Let's take a moment here to consider the representation of streamlines used in
dipy. Streamlines are a path though the 3d space of an image represented by a
set of points. For these points to have a meaningful interpretation, these
points must be given in a known coordinate system. The ``affine`` attribute of
the ``streamline_generator`` object specifies the coordinate system of the
points with respect to the voxel indices of the input data.
``trackvis_point_space`` specifies the trackvis coordinate system with respect
to the same indices. The ``move_streamlines`` function returns a new set of
streamlines from an existing set of streamlines in the target space. The
target space and the input space must be specified as affine transformations
with respect to the same reference [#]_. If no input space is given, the input
space will be the same as the current representation of the streamlines, in
other words the input space is assumed to be ``np.eye(4)``, the 4-by-4 identity
matrix.

All of the functions above that allow streamlines to interact with volumes take
an affine argument. This argument allows these functions to work with
streamlines regardless of their coordinate system. For example even though we
moved our streamlines to "trackvis space", we can still compute the density map
as long as we specify the right coordinate system.

::
  
  dm_trackvis = utils.density_map(lr_sf_trk, shape, affine=trackvis_point_space)
  assert np.all(dm == dm_trackvis)
  

This means that streamlines can interact with any image volume, for example a
high resolution structural image, as long as one can register that image to
the diffusion images and calculate the coordinate system with respect to that
image.

.. rubric:: Footnotes

.. [#] The image `aparc-reduced.nii.gz`, which we load as ``labels_img``, is a
    modified version of label map `aparc+aseg.mgz` created by freesurfer.  The
    corpus callosum region is a combination of the freesurfer labels 251-255.
    The remaining freesurfer labels were re-mapped and reduced so that they lie
    between 0 and 88. To see the freesurfer region, label and name, represented
    by each value see `label_info.txt` in `~/.dipy/stanford_hardi`.
.. [#] An affine transformation is a mapping between two coordinate systems
    that can represent scaling, rotation, sheer, translation and reflection.
    Affine transformations are often represented using a 4x4 matrix where the
    last row of the matrix is ``[0, 0, 0, 1]``.

        
.. admonition:: Example source code

   You can download :download:`the full source code of this example <./streamline_tools.py>`.
   This same script is also included in the dipy source distribution under the
   :file:`doc/examples/` directory.

