Particle Filtering Tractography

Particle Filtering Tractography (PFT) [1] uses tissue partial volume estimation (PVE) to reconstruct trajectories connecting the gray matter, and not incorrectly stopping in the white matter or in the corticospinal fluid. It relies on a stopping criterion that identifies the tissue where the streamline stopped. If the streamline correctly stopped in the gray matter, the trajectory is kept. If the streamline incorrectly stopped in the white matter or in the corticospinal fluid, PFT uses anatomical information to find an alternative streamline segment to extend the trajectory. When this segment is found, the tractography continues until the streamline correctly stops in the gray matter.

PFT finds an alternative streamline segment whenever the stopping criterion returns a position classified as ‘INVALIDPOINT’.

This example is an extension of An introduction to the Probabilistic Direction Getter and Using Various Stopping Criterion for Tractography examples. We begin by loading the data, fitting a Constrained Spherical Deconvolution (CSD) reconstruction model, creating the probabilistic direction getter and defining the seeds.

import numpy as np

from dipy.core.gradients import gradient_table
from dipy.data import default_sphere, get_fnames
from dipy.direction import ProbabilisticDirectionGetter
from dipy.io.gradients import read_bvals_bvecs
from dipy.io.image import load_nifti, load_nifti_data
from dipy.io.stateful_tractogram import Space, StatefulTractogram
from dipy.io.streamline import save_trk
from dipy.reconst.csdeconv import ConstrainedSphericalDeconvModel, auto_response_ssst
from dipy.tracking import utils
from dipy.tracking.local_tracking import LocalTracking, ParticleFilteringTracking
from dipy.tracking.stopping_criterion import CmcStoppingCriterion
from dipy.tracking.streamline import Streamlines
from dipy.viz import actor, colormap, has_fury, window

# Enables/disables interactive visualization
interactive = False

hardi_fname, hardi_bval_fname, hardi_bvec_fname = get_fnames(name="stanford_hardi")
label_fname = get_fnames(name="stanford_labels")
f_pve_csf, f_pve_gm, f_pve_wm = get_fnames(name="stanford_pve_maps")

data, affine, hardi_img = load_nifti(hardi_fname, return_img=True)
labels = load_nifti_data(label_fname)
bvals, bvecs = read_bvals_bvecs(hardi_bval_fname, hardi_bvec_fname)
gtab = gradient_table(bvals, bvecs=bvecs)

pve_csf_data = load_nifti_data(f_pve_csf)
pve_gm_data = load_nifti_data(f_pve_gm)
pve_wm_data, _, voxel_size = load_nifti(f_pve_wm, return_voxsize=True)

shape = labels.shape

response, ratio = auto_response_ssst(gtab, data, roi_radii=10, fa_thr=0.7)
csd_model = ConstrainedSphericalDeconvModel(gtab, response)
csd_fit = csd_model.fit(data, mask=pve_wm_data)

dg = ProbabilisticDirectionGetter.from_shcoeff(
    csd_fit.shm_coeff, max_angle=20.0, sphere=default_sphere, sh_to_pmf=True
)

seed_mask = labels == 2
seed_mask[pve_wm_data < 0.5] = 0
seeds = utils.seeds_from_mask(seed_mask, affine, density=2)

CMC/ACT Stopping Criterion

Continuous map criterion (CMC) [1] and Anatomically-constrained tractography (ACT) [2] both use PVEs information from anatomical images to determine when the tractography stops. Both stopping criterion use a trilinear interpolation at the tracking position. CMC stopping criterion uses a probability derived from the PVE maps to determine if the streamline reaches a ‘valid’ or ‘invalid’ region. ACT uses a fixed threshold on the PVE maps. Both stopping criterion can be used in conjunction with PFT. In this example, we used CMC.

voxel_size = np.average(voxel_size[1:4])
step_size = 0.2

cmc_criterion = CmcStoppingCriterion.from_pve(
    pve_wm_data,
    pve_gm_data,
    pve_csf_data,
    step_size=step_size,
    average_voxel_size=voxel_size,
)

Particle Filtering Tractography

pft_back_tracking_dist is the distance in mm to backtrack when the tractography incorrectly stops in the WM or CSF. pft_front_tracking_dist is the distance in mm to track after the stopping event using PFT.

The particle_count parameter is the number of samples used in the particle filtering algorithm.

min_wm_pve_before_stopping controls when the tracking can stop in the GM. The tractography must reaches a position where WM_pve >= min_wm_pve_before_stopping before stopping in the GM. As long as the condition is not reached and WM_pve > 0, the tractography will continue. It is particularlyusefull to set this parameter > 0.5 when seeding tractography at the WM-GM interface or in the sub-cortical GM. It allows streamlines to exit the seeding voxels until they reach the deep white matter where WM_pve > min_wm_pve_before_stopping.

pft_streamline_gen = ParticleFilteringTracking(
    dg,
    cmc_criterion,
    seeds,
    affine,
    max_cross=1,
    step_size=step_size,
    maxlen=1000,
    pft_back_tracking_dist=2,
    pft_front_tracking_dist=1,
    particle_count=15,
    return_all=False,
    min_wm_pve_before_stopping=1,
)
streamlines = Streamlines(pft_streamline_gen)
sft = StatefulTractogram(streamlines, hardi_img, Space.RASMM)
save_trk(sft, "tractogram_pft.trk")

if has_fury:
    scene = window.Scene()
    scene.add(actor.line(streamlines, colors=colormap.line_colors(streamlines)))
    window.record(scene=scene, out_path="tractogram_pft.png", size=(800, 800))
    if interactive:
        window.show(scene)

Corpus Callosum using particle filtering tractography

# Local Probabilistic Tractography
prob_streamline_generator = LocalTracking(
    dg,
    cmc_criterion,
    seeds,
    affine,
    max_cross=1,
    step_size=step_size,
    maxlen=1000,
    return_all=False,
)
streamlines = Streamlines(prob_streamline_generator)
sft = StatefulTractogram(streamlines, hardi_img, Space.RASMM)
save_trk(sft, "tractogram_probabilistic_cmc.trk")

if has_fury:
    scene = window.Scene()
    scene.add(actor.line(streamlines, colors=colormap.line_colors(streamlines)))
    window.record(
        scene=scene, out_path="tractogram_probabilistic_cmc.png", size=(800, 800)
    )
    if interactive:
        window.show(scene)

Corpus Callosum using probabilistic tractography

References

[1] (1,2)

Gabriel Girard, Kevin Whittingstall, Rachid Deriche, and Maxime Descoteaux. Towards quantitative connectivity analysis: reducing tractography biases. NeuroImage, 98:266–278, September 2014. URL: https://doi.org/10.1016/j.neuroimage.2014.04.074, doi:10.1016/j.neuroimage.2014.04.074.

[2]

Robert E. Smith, Jacques-Donald Tournier, Fernando Calamante, and Alan Connelly. Anatomically-constrained tractography: Improved diffusion MRI streamlines tractography through effective use of anatomical information. NeuroImage, 62(3):1924–1938, September 2012. URL: https://doi.org/10.1016/j.neuroimage.2012.06.005, doi:10.1016/j.neuroimage.2012.06.005.