Modeling White-matter Fiber-orientation Uncertainty for Improved

Probabilistic Tractography

Adelino R. Ferreira da Silva

Dep.

de Eng.

Electrot´ecnica, Faculdade de Ciˆencias e Tecnologia, FCT,

Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

Keywords:

Probabilistic Tractography, Particle Filtering, Diffusion MRI.

Abstract:

Tractography uses ﬁber-orientation estimates to trace the likely paths of white-matter tracts through the brain,

in order to map brain connectivity non-invasively. In this paper, we propose a novel probabilistic framework

for modeling ﬁber-orientation uncertainty and improve probabilistic tractography. The main innovation in the

present formulation consists in coupling a particle ﬁltering process with a clustered-mixture model approach to

model directional data. Mixtures of von Mises-Fisher (vMF) distributions are used to support the probabilistic

estimation of intravoxel ﬁber directions. The ﬁtted parameters of the clustered vMF mixture at each voxel are

then used to estimate white-matter pathways using particle ﬁltering techniques. The technique is validated on

simulated as well as on real human brain data experiments.

1 INTRODUCTION

White matter ﬁber tracking or “tractography” uses

ﬁber-orientation estimates to trace the likely paths of

white-matter tracts through the brain. Tractography

techniques are powerful tools to capture white mat-

ter (WM) connectivity non-invasively. Before apply-

ing tractography techniques, diffusion Magnetic Res-

onance Imaging (MRI) measurements are applied to

probe the dispersion of water molecules within tis-

sue over a time. A probability distribution on the

displacement of water molecules describes the scat-

ter pattern of molecules during the diffusion time.

Since white matter axons are tiny compared to typ-

ical MRI voxels, voxels contain hundreds of thou-

sands of axon ﬁbers, which can adopt a wide range

of complex conﬁgurations. The simpler and most

commonly used method, Diffusion Tensor Imaging

(DTI) uses a Gaussian distribution to model the dis-

persion. DTI assumes that the diffusion scatter pat-

tern exhibits a single directional pattern, and is there-

fore unable to model multiple-directional ﬁber path-

ways within a voxel. Other model-based approaches,

such as the multi-tensor model (Tuch et al., 2002), or

multi-compartment models (Behrens et al., 2007; As-

saf and Basser, 2005) have been devised to account

for distinct groups of “populations” of ﬁbers. How-

ever, model-based techniques recover but a few num-

ber of dominant ﬁber-orientations, and have difﬁculty

in discriminating common anatomical ﬁber conﬁgu-

rations (Seunarine and Alexander, 2009). To resolve

complex orientations, model-free methods and High

Angular Resolution Diffusion Imaging (HARDI) pro-

tocols have been developed. For instance, Q-ball

imaging (QBI) (Tuch, 2004) is one popular HARDI-

based method used to resolve ﬁber crossings. It re-

constructs the angular proﬁle of the diffusion prop-

agator, commonly known as the (diffusion) orienta-

tion distribution function (ODF). The ODF exhibits

multiple local maxima in crossing regions, which are

used as ﬁber orientation estimates. Two more recent

model-free models are the Diffusion Spectrum Imag-

ing (DSI) (Wedeen et al., 2005), and the Generalized

q-Sampling Imaging (GQI) (Yeh et al., 2010) meth-

ods. These methods perform non-parametric recon-

structions that resolve multiple peaks in each voxel,

without requiring prior knowledge of the number of

ﬁber populations. Similarly to other methods for ODF

reconstruction, DSI and GQI use shell or grid sam-

pling schemes to extract information about the extent

of diffusion anisotropy, and map vector ﬁelds that rep-

resent the ﬁber orientations at each voxel. In contrast

to QBI, DSI and GQI are not limited to a single spher-

ical shell and a single diffusion gradient coefﬁcient

(b-value) to characterize diffusion anisotropy.

As pointed out by (Seunarine et al., 2007; Seu-

narine and Alexander, 2009), most tractography al-

gorithms still use the basic DTI single-ﬁber recon-

R. Ferreira da Silva A..

Modeling White-matter Fiber-orientation Uncertainty for Improved Probabilistic Tractography.

DOI: 10.5220/0005069300710078

In Proceedings of the 2nd International Congress on Neurotechnology, Electronics and Informatics (NEUROTECHNIX-2014), pages 71-78

ISBN: 978-989-758-056-7

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

struction and it is not clear how to generalize them

to exploit the extra information that multiple ﬁber re-

constructions provide. Even when probabilistic trac-

tography is used to estimate the uncertainty of ﬁber-

orientations, the information used to track through

ﬁber conﬁgurations is limited to the principal diffu-

sion directions. For instance, in (Parker and Alexan-

der, 2003) ﬁber-orientations are detected by a Monte

Carlo streamline approach, and the sharpness of the

peaks are used as indicators of uncertainty. In (Seu-

narine et al., 2007), the authors have shown that the

peaks of multiple-ﬁber reconstructions provide useful

information that can be used to improve tractography

results. They used the Bingham distribution to model

the peak uncertainty in ﬁber-orientation estimates ob-

tained from the ODF. Hence, better peak shape un-

certainty estimates provided improved tractography

results. The main drawback of the above technique

is that it requires a costly and complicated calibra-

tion. The calibration procedure constructs a mapping

from two Hessian (or second derivative) eigenvalues

to Bingham parameters, using simulations on two-

tensor mixture models with known peak directions

(Seunarine et al., 2007).

The above considerations motivated us to de-

vise a probabilistic framework for modeling ﬁber-

orientation uncertainty and improve probabilistic

tractography. Two key ideas govern the present de-

velopment and implementation. First, we model

ﬁber-orientation uncertainty by using directional data

clustering to estimate white matter ﬁber orientations.

A clustered-mixture-model approach to model direc-

tional ODF data based on von Mises-Fisher (vMF)

distributions is used, in order to support the proba-

bilistic estimation of intravoxel ﬁber directions. The

generalized fractional anisotropy (GFA) (Tuch, 2004)

is applied to the reconstructed ODF in order to thresh-

old the population of acquisition directions before

clustering.

In this “clustered-vMFs” approach, each esti-

mated voxel ﬁber direction is associated with a com-

ponent of the ﬁtted mixture of vMF distributions.

Hence, each voxel ﬁber principal direction may be

speciﬁed by the summary statistics of the estimated

vMF component in the mixture. It is worth noting

that, in opposition to (Seunarine et al., 2007), no cali-

bration is required. Fitting the mixture of von Mises-

Fisher (vMF) distributions to the clustered data, auto-

matically deﬁnes the parameters deﬁning the statisti-

cal properties of the main peak directions. Moreover,

the number of ﬁtted clusters automatically deﬁne the

pattern of ﬁbers in a voxel.

The second key idea consists in using the ﬁtted

parameters of the clustered-vMFs approach at each

voxel to guide probabilistic ﬁber tracking using par-

ticle ﬁltering. Several probabilistic techniques have

been proposed in the literature to cope with direc-

tional uncertainty, partial volume effects, and errors

in ﬁber orientation estimates (Parker and Alexander,

2003; Zhang et al., 2009). Probabilistic methods gen-

erate multiple trajectories based on a distribution of

ﬁber bundles at a given seed point, in order to map the

connectionbetween the seed voxeland other voxelsof

the brain. In these techniques, Markov Chain Monte

Carlo (MCMC) methods are used to sample from

ﬁber orientation distributions. In order to make the

sampling stage more effective, several authors (Zhang

et al., 2009; Pontabry et al., 2013; Rowe et al., 2013)

have proposed to apply particle ﬁltering to recursively

estimate the posterior distribution of ﬁbers at each

propagation step. In a similar vein, in this work we

have used the Sequential Monte Carlo (SMC) frame-

work (Doucet et al., 2000) to model ﬁber trajectories.

The SMC algorithm propagates for each seed a cloud

of particles representing the density probability of the

ﬁber path passing through the seed voxel. The main

innovation in the present formulation consists in cou-

pling the particle ﬁltering process with the clustered-

vMFs estimate outlined above.

The paper is organized as follows. Section 2

presents the underlying methodology supporting the

proposed approach, namely the particle ﬁltering strat-

egy and the clustered-vMFs model. In Section 3 we

report on experiments applied to simulated as well as

to real brain data. The results of the proposed method-

ology are compared to those from standard streamline

approaches. Section 4 draws some conclusions and

points to future working directions.

2 METHODS

2.1 Fiber Tracking Model

In a particle ﬁltering context, ﬁber tracking is formu-

lated as a non-Gaussian state space model (Doucet

and Johansen, 2011). In this model, given the prior

probability distribution that characterize the uncer-

tainty of local ﬁber orientations, a posterior distri-

bution of the target ﬁber is estimated. Given that

both the prior and the posterior distribution are non-

Gaussian, particle ﬁltering techniques are well suited

to estimate the complex geometry of the ﬁber paths,

and account for directional uncertainties. In contrast,

linear ﬁltering methods such as Kalman ﬁltering are

often inappropriate to track complex conﬁgurations.

In a volume Ω ⊂ R

, a ﬁber trajectory can be mod-

eled as a sequence of n displacement vectors u

with

NEUROTECHNIX2014-InternationalCongressonNeurotechnology,ElectronicsandInformatics

k = 1,...,n. From a given starting point u

, at each

time step k, each streamline is propagated one step

from its previous location u

(i)

k−1

with a direction vec-

tor v

(i)

sampled from the importance density by a step

size λ, such that u

(i)

= u

(i)

k−1

+λv

(i)

. The state of a par-

ticle at time step k, x

(i)

, is deﬁned by its location u

(i)

and direction vector v

(i)

As detailed in (Doucet and Johansen, 2011), parti-

cle ﬁltering algorithms can be interpreted as instances

of a single generic SMC algorithm. Earlier particle

ﬁltering algorithms, such as the popular Sequential

Importance Sampling (SIS), suffered from a degen-

eracy problem as simulation time increased: variance

of the estimates increased with time k. Degeneracy is

a key factor conditioning the application of SIS algo-

rithms. However, by introducing a re-sampling step

degeneracy can be greatly mitigated. Modern SMC

methods are a combination of SIS and resampling.

SMC methods sample sequentially from a sequence

of target probability densities π

As outlined in Algorithm 1, by a sequence of pre-

diction, weighting and selection steps, the particle

ﬁlter provides a discrete approximation of a poste-

rior distribution p(x

0:k

) on a time-varying param-

eter x

at time step k, given the observations y

0:k

for

time steps 0,1, 2,...,k, and the initial state distribu-

tion p(x

). At each time step k, N particles are prop-

agated by sampling from an importance distribution

π(x

(i)

| x

(i)

0:k−1

0:k

). In the weighting stage, impor-

tance weights w

∗(i)

are assigned in accordance to the

likelihood p(y

(i)

). The discrete approximation to

the posterior distribution p(x

| y

0:k

), denoted by ˜w

(i)

is computed by normalizing the importance weights

∗(i)

. Finally, a resampling step is used to remove par-

ticles with low weights and proliferate those with high

weights. Resampling may be applied at each time

step, or alternatively, it may be applied only when

the variance of the normalized weights is superior to

a pre-speciﬁed threshold. The threshold, designated

ESS

in Algorithm 1, is often speciﬁed in terms of

the EffectiveSample Size (ESS) criterion (Liu, 2001),

which assesses the variability of the weights by,

ESS =

∑

i=1

( ˜w

(i)

)

(−1)

. (1)

In Algorithm 1, the importance distribution

π(x

| x

(i)

0:k−1

0:k

) is a vMF distribution. The ini-

tial state distribution p(x

), is the vMF distribu-

tion parameterized by one of the components of the

clustered-vMFs estimate for the current voxel, as de-

tailed in Section 2.2. The likelihood p(y

(i)

) =

·V (u

)), is deﬁned by a vMF distribution parame-

terized by the parameters of the most likely vMF clus-

ter component, for direction v

, at each point location

Input :

V Voxels’ cluster statistics

N Number of particles

ESS

Resampling threshold

for particle i = 1 to N do

∼ p(x

)

∗(i)

end

for times k = 1 to K do

for particle i = 1 to N do

(i)

∼ π(x

| x

(i)

0:k−1

0:k

)

∗(i)

= w

∗(i)

k−1

p(y

| x

(i)

)

˜w

(i)

∗(i)

∑

j=1

∗(i)

end

ESS =



∑

i=1

( ˜w

(i)

)



(−1)

if ESS < ε

ESS

then

Resample { ˜w

(i)

} according to

importance weights

end

Algorithm 1: Sequential Monte Carlo.

In the resampling stage, the usual practice is to

attribute equal importance weights to the newly in-

troduced particles (Doucet and Johansen, 2011). The

use of equal weights helps maintaining the diversity

of the population of particles at intermediate tracking

stages, which favors the exploration of new trajecto-

ries emerging from the current state. However, this

particle ﬁltering setting may be too rich for the res-

olution of the diffusion directions estimated at each

voxel. White matter axon radii are in the range

[0.1,10] µm, whereas MRI voxels typically have sides

in the range [1, 5] mm. Voxels therefore contain hun-

dreds of thousands of axon ﬁbers (Seunarine and

Alexander, 2009), but the estimated principal diffu-

sion directions are typically reduced to 2 or 3 per

voxel, originating the so-called “partial volume ef-

fects” (Alexander et al., 2001). These effects in-

troduce uncertainties in anisotropy measurements at

each voxel, which inﬂuence ODF reconstruction ac-

curacy and the anatomic validity of ﬁber track esti-

mates. An alternative procedure, is to attribute new

importance weights according to the weights already

evolved for the population of particles. This proce-

dure helps maintainingthe selection pressure overlow

ModelingWhite-matterFiber-orientationUncertaintyforImprovedProbabilisticTractography

weighted particles and reduces trajectory irregulari-

ties, driving the sequence of distributions to a max-

imum a-posterior path, at the cost of particle diver-

sity. The result is a more conservative set of esti-

mated directions, and a reduced capability of the al-

gorithm for exploring very long pathways. Nonethe-

less, it may still confer realistic ﬁber track estimates

for brain tractography.

2.2 Clustered-vMFs Model

The ﬁber tracking model outlined in Section 2.1 uses

vMF distributions as sampling distributions of inter-

est. A d-dimensional unit random vector x ∈ S

d−1

said to have d-variate vMF distribution if its probabil-

ity density function is given by

f(x|µ,κ) = c

(κ)e

κµ

, (2)

where kµk = 1, κ ≥ 0 and d ≥ 2. The normalizing

constant c

(κ) is given by

(κ) =

d/2−1

(2π)

d/2

d/2−1

(κ)

, (3)

where I

(.) represents the modiﬁed Bessel function of

the ﬁrst kind and order r. The density f(x|µ,κ) is

parameterized by the mean direction µ, and the con-

centration parameter κ. The κ parameter character-

izes how strongly the unit vectors drawn according to

f(x|µ,κ) are concentrated about the mean direction

µ. Larger values of κ imply stronger concentration

about the mean direction ((Mardia and Jupp, 2000)).

The vMF distribution is unimodal for κ > 0, and is

uniform on the sphere for κ = 0.

For directional clustering estimation, we consider

a mixture of k vMF distributions (Banerjee et al.,

2005) that serves as a model for directional ODF pro-

ﬁle data, corresponding to multiple ﬁber orientations.

A mixture of k vMF distributions has a density given

f(x|Θ) =

∑

h=1

(x|θ

), (4)

where f

(x|θ

) denotes a vMF distribution with

parameter θ

= (µ

,κ

) for 1 ≤ h ≤ k, Θ =

{α

,... , α

,θ

,...,θ

}, and the α

are non-negative

and sum to 1. The Expectation Maximization (EM)

framework is used for estimating the mean and con-

centration parameters of the mixture. The clustering

algorithms proposed by (Banerjee et al., 2005) and

implemented in (Hornik and Gr¨un, 2012) were used to

ﬁt the vMF mixture. The principal ODF proﬁle statis-

tics are extracted directly from the estimated clusters.

The number of ﬁbers in each voxel is automatically

estimated from the reconstructed ODF proﬁle by the

vMF approach using the Bayesian Information Crite-

rion (BIC) criterion (Schwartz, 1979). In other words,

“BIC” is used to decide on the number of components

to select. All relevant statistical information about the

ODF orientation and multiple ﬁber components may

then be extracted from this ﬁtting process.

The preceding description speciﬁes a clustered

mixture-model approach to model directional ODF

data based on von Mises-Fisher (vMF) distributions.

In this “clustered-vMFs” approach, each estimated

voxel ﬁber direction is associated with a component

of the ﬁtted mixture of vMF distributions. Hence,

each voxel ﬁber principal direction may be speciﬁed

by the summary statistics of the estimated vMF com-

ponent in the mixture. Based on voxel ODF recon-

structions, our method estimates intravoxel ﬁber di-

rections by clustering mixtures of von Mises-Fischer

distributions ﬁtted to probabilistic distributions.

As opposed to other approaches where mixture of

vMF distributions are used to representdiffusion, e.g.,

(Rathi et al., 2009), our method works directly with

the sampled ODF distributions. Moreover, the pro-

posed clustered-vMFs statistical procedure does not

care for ODF reconstruction. The process of ODF

reconstruction is kept independent from the process

of statistical cluster estimation. The objective of the

clustered-vMFs model is to gather statistical infor-

mation in order to support robust probabilistic tracto-

graphic algorithms (Ferreira da Silva, 2012). There-

fore, multiple ODF reconstruction approaches can be

easily integrated in the proposed framework by a sim-

ple “plug-in” technique.

Before applying the clustered-vMFs approach we

need to obtain the ODF proﬁles at each voxel. As

pointed out in the Introduction, model-free methods

and HARDI protocols are more adequate than current

model-based methods for resolving complex orienta-

tions. Any of the model-free methods mentioned in

the Introduction, (e.g., QBI, GQI, DSI), could be used

for reconstructing ODF proﬁles. Starting with the raw

HARDI signal acquired on a grid of q-space, the ODF

proﬁle is estimated at each voxel, considering a sam-

pling density of unit vectors on a unit S

grid or shell.

To summarize anisotropic properties of the ODF and

infer the underlying crossing patterns of the ﬁbers we

use the GFA metric (Tuch, 2004),

GFA =

∑

i=1

(ψ(u

) − hψi)

(n− 1)

∑

i=1

ψ(u

)

, (5)

where hψi = (1/n)

∑

i=1

ψ(u

) = (1/n) is the mean

of the ODF, hui is the mean diffusion direction, and

h.i denotes the average over ψ. The GFA metric pro-

posed in (Tuch, 2004), is an extension for HARDI

protocols of the fractional anisotropy (FA) metric

NEUROTECHNIX2014-InternationalCongressonNeurotechnology,ElectronicsandInformatics

commonly used in diffusion tensor imaging (DTI).

When a threshold is applied to the estimated GFAs at

each voxel, the non-thresholded unit vectors provide

directional statistics information about the estimated

ODF proﬁle.

This directional clustering procedure has several

advantages compared to traditional approaches for

orientation mapping. In fact, current best practices

perform multiple maxima extraction based on proce-

dures which are very sensitive to the local modes that

appear in the reconstructed ODFs. Signal noise and

low sampling resolution yield deformed ODF recon-

struction proﬁles, thus affecting accuracy and preci-

sion in multiple orientation evaluations. In contrast,

estimating orientationsfrom clustered directionaldata

is much less sensitive to local modes in the recon-

structed ODF proﬁle. Moreover, the procedure is

more robust to noise since it estimates orientations

statistically from sampled data.

3 EXPERIMENTAL RESULTS

3.1 Fiber Bundle Simulation

To validate the ﬁber tracking model described in Sec-

tion 2 we performed simulations with synthetic ﬁelds

of diffusion proﬁles. Firstly, we simulated diffu-

sion proﬁles at each voxel by generating diffusion-

weighted signals for single and multiple ﬁbers simula-

tions, using the method detailed in (Ferreira da Silva,

2013). Secondly, we estimated ODF proﬁles by ap-

plying the model-free GQI method to extract infor-

mation about the extent of diffusion anisotropy, and

map vector ﬁelds that represent the ﬁber orientations

at each voxel. Thirdly, the clustered-vMFs approach

was used to obtain summary statistics of the vMF

components in the mixture of von Mises-Fisher dis-

tributions. Finally, the SMC algorithm was applied to

guide probabilistic ﬁber tracking. The parameters of

the clustered-vMFs approach at each voxel were used

to propagate a cloud of particles, according to the ﬁt-

ted density probability for the ﬁber bundle trajectory

being tracked. Based on the resampling strategy out-

lined in Section 2.1 for path tracking, we derivea map

of ﬁber pathways for the simulated ﬁeld of diffusion

proﬁles.

Figure 1(a) shows an example of a simulated dif-

fusion ﬁeld of crossing bundles, the ﬁeld of recon-

structed ODF proﬁles, and the ﬁeld of estimated prin-

cipal directions. We speciﬁed two voxels as seed vox-

els (see the left panel of Figure 1(a)) and applied the

probabilistic SMC algorithm to obtain the tracks rep-

resented in Figure 1(b). The SMC algorithm was ap-

plied with 100 particles and 5 ﬁbers per seed voxel.

For comparison purposes we have also applied a stan-

dard deterministic streamline tracking procedure to

the same simulation. The streamline procedure fol-

lows the tractographic approach outlined in Mori and

van Zijl (Mori and van Zijl, 2002) to map ﬁber tracts.

As seen in Figure 1(c), the streamline algorithm is

unable to resolve regions of crossing ﬁber conﬁgura-

tions. Typically a single directional path is selected in

these regions. In contrast, the probabilistic method is

able to map multiple ﬁber pathways in crossing ﬁber

regions.

3.2 Human Brain Data Experiments

In this Section we report on experiments using a DI-

COM data set provided by the “Advanced Biomedi-

cal MRI Lab, National Taiwan University Hospital”.

Speciﬁcally, we have used the data set “DSI 203-point

2mm” publicly available from

http://dsi-studio.

labsolver.org/download-images

. This data set is

from a normal 24-year-old male volunteer, and has

been provided as a demonstration data set in con-

nection with the “DSI Studio” software for diffusion

MR images analysis (Yeh et al., 2010). The data

set was obtained with an echo planar imaging dif-

fusion sequence with twice-refocused echo, dimen-

sion 96 × 96 × 60, and slice thickness 1.9 mm. Fur-

ther details on the data set speciﬁcation are available

from the internet address mentioned above. We have

tested our model with the two b-tables that accompa-

nies the data set. One is a b-table for a S

-like grid

denoted by “dsi203

bmax4000.txt”. The other is the

b-table for the 3D-DSI sampling scheme used in the

DICOM data acquisition. This b-table has 203 points

uniformly distributed on a 3D grid limited to the vol-

ume of the unit sphere. In both tables, the b-values

range from 0 to 4000. The ODF reconstructions were

performed with 321 points uniformly distributed on

the unit S

hemisphere.

As for the simulation procedure outlined in Sec-

tion 3.1, we obtained estimates of the voxels’ ODF

proﬁles using GQI basis functions. To summarize

anisotropic properties of the ODF and infer the un-

derlying crossing patterns of the ﬁbers we used the

GFA metric. A GFA threshold of 0.3 was applied on

the normalized ODFs, prior to vMF clustering esti-

mation. The SMC algorithm was then applied to es-

timate ﬁber paths. The following is a summary of

tractography results applied to two Regions Of Inter-

est (ROIs). For the ﬁrst ROI, 43 seeds were placed

along the Corpus Callosum (CC) region in sagittal

view, as illustrated in Figure 2(a). We then applied the

clustered-vMFs method followed by SMC to track the

ModelingWhite-matterFiber-orientationUncertaintyforImprovedProbabilisticTractography

(a)

(b) (c)

Figure 1: (a) Simulated diffusion ﬁeld with seeds marked in light-blue rectangle (left panel), ﬁeld of reconstructed ODF

proﬁles (middle panel), and ﬁeld of estimated principal directions (right panel); (b) Fiber pathways mapped using the proposed

probabilistic approach; (c) Fiber pathways mapped using a standard streamline approach.

ﬁber paths from each seed by propagating 150 parti-

cles, for a maximum of 300 steps. Five starting ﬁbers

were randomly placed within each voxel for tracking

initiation. All selected principal diffusion directions

estimated for the seed voxel were tracked. Figure 2(b)

shows tractography results of the corpus callosum for

sagittal slice 48. For comparison purposes, the same

ROI and seeds were used to drive a standard determin-

istic streamline algorithm. Similarly, 5 starting ﬁbers

were randomly placed within each voxel for tracking

initiation. The results are shown in Figure 2(c).

The second ROI used for testing was the corti-

cospinal tract (CST), which connects the spinal cord

to the cerebral motor cortex. Tractographyof the CST

is a challenging task. On the one hand, in some re-

gions of the brain other fascicles may cross with the

CST. On the other hand, the CST itself is made of sev-

eral bifurcating sub-fascicles to ensure connections

with the whole motor cortex. Unsurprisingly, stan-

dard deterministic streamline algorithms fail to map

the CST accurately, because they are unable to cope

with the complexity of bifurcating pathways. Five

seeds used placed on each side of the CST-ROI bun-

dle for coronal slice 53 as illustrated in Figure 3(a).

This ﬁgure visualizes the location of the chosen seeds,

by overlaying the GFA image with the ﬁrst two main

ﬁber directions at each voxel for coronal slice 53. Fig-

ure 3(b) shows tractography results of the CST for

coronal slice 53 using the proposed approach. Fig-

ure 3(c) shows similar tractography results for the de-

terministic streamline algorithm.

4 CONCLUSIONS

We have presented a methodology to support im-

proved probabilistic tractography in comparison with

currently used approaches. The methodology builds

statistical inferences at each voxel based on clusters

of vMF distributions to drive sequential Monte Carlo

NEUROTECHNIX2014-InternationalCongressonNeurotechnology,ElectronicsandInformatics

(a)

(b)

(c)

Figure 2: Corpus Callosum tractography: a) GFA image

with seeds’ locations in red; b) Probabilistic tractography

using the proposed approach; c) Tractography using a stan-

dard streamline algorithm.

(a)

(b)

(c)

Figure 3: CST tractography: a) GFA image with seeds’ lo-

cations in red; b) Probabilistic tractography using the pro-

posed approach; c) Tractography using a standard stream-

line algorithm.

ModelingWhite-matterFiber-orientationUncertaintyforImprovedProbabilisticTractography

path estimates. We have shown how the improve-

ment of ﬁber directional estimates can beneﬁt the

particle ﬁltering tracking process. Moreover, by de-

coupling the two stages, statistical directional esti-

mation and probabilistic ﬁber tracking, the proposed

methodology is well-suited to support a wide range

of methods for ODF reconstruction. The methodol-

ogy provides a better account of white matter path-

ways in regions with complex ﬁber conﬁguration than

streamline-oriented approaches. However, compar-

ing results of in vivo ﬁber tracking is a difﬁcult task

in general. In the future, we intend to test the pro-

posed methodology for performing human brain con-

nectivity analysis. Connectivity networks may pro-

vide alternative validation tools for quantitative com-

parisons.

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NEUROTECHNIX2014-InternationalCongressonNeurotechnology,ElectronicsandInformatics