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Comparison of 3 Diusion Models to Track the Hand

Motor Fibers within the Corticospinal Tract Using

Functional, Anatomical and Diusion MRI

Nicolas Wiest-Daesslé, Olivier Commowick, Aymeric Stamm, Patrick Pérez,

Christian Barillot, Romuald Seizeur, Sylvain Prima

To cite this version:

Nicolas Wiest-Daesslé, Olivier Commowick, Aymeric Stamm, Patrick Pérez, Christian Barillot, et

al.. Comparison of 3 Diusion Models to Track the Hand Motor Fibers within the Corticospinal

Tract Using Functional, Anatomical and Diusion MRI. MICCAI 2011 Workshop on Computational

Diusion MRI (CDMRI’11), Sep 2011, Toronto, Canada. pp.150-157, 2011. <inserm-00628264>

Comparison of 3 diﬀusion models to track the

hand motor ﬁbers within the corticospinal tract

using functional, anatomical and diﬀusion MRI

Nicolas Wiest-Daessl´e1,2, Olivier Commowick1, Aymeric Stamm1, Patrick

P´erez3, Christian Barillot1, Romuald Seizeur1,4, and Sylvain Prima1

1VISAGES: INSERM U746 - CNRS UMR6074 - INRIA - Univ. of Rennes I, France

2Department of Neurology, CHU Rennes, France

3Technicolor, Rennes, France

4Department of Neurosurgery, CHU Brest, France

Abstract. In this paper, we propose to compare three diﬀusion mod-

els to track the portion of the corticospinal tract dedicated to the hand

motor function (called hand motor ﬁbers hereafter), using diﬀusion, func-

tional and anatomical MRI. The clinical diﬀusion data have few gradient

directions and low b-values. In this context, we show that a newly intro-

duced model, called diﬀusion directions imaging (DDI) outperforms both

the DTI and the ODF models. This new model allows to capture several

diﬀusion directions within a voxel, with only a low number of parame-

ters. Two important results are that i) the DDI model is the only one

allowing consistent tracking from the mesencephalon to the most lateral

part of the cortical motor hand area, and that ii) the DDI model is the

only model able to show that the number of hand motor ﬁbers in the

left hemisphere is larger than in the contralateral hemisphere for right-

handed subjects; the DDI model, as the other two models, fails to ﬁnd

such a diﬀerence for left-handed subjects. To the best of our knowledge,

this is the ﬁrst time such results are reported, at least on clinical data.

1 Introduction

Diﬀusion MRI (dMRI) [11] allows in vivo and non-invasive imaging of tissue

structure. It is based on the facts that i) the diﬀusion of water molecules is

constrained by the micro-structure of the tissues (such as, typically, the white

matter ﬁbers in the brain), and that ii) MRI can be made sensitive to this diﬀu-

sion, using speciﬁc MR pulse sequences. Diﬀusion models can then be devised,

and their parameters can be estimated for further study and analysis of tissue

architecture. The simplest model is that of a Gaussian diﬀusion function, which

amounts to characterise the diﬀusion with a tensor (i.e. a 3×3 symmetric deﬁnite

positive matrix), giving its name to diﬀusion-tensor imaging (DTI) [2].

Fiber tracking, or tractography, has been developed to “reconstruct” or “dis-

sect” the ﬁber tracts in vivo, and then infer brain anatomy [18]. Many of the

association (e.g. uncinate fasciculus, cingulum) and commissural (e.g. transverse

ﬁbers of the corpus callosum) ﬁber tracts have been successfully reconstructed

2 Wiest-Daessl´e et al.

using i) clinical dMRI sequences (with few gradient directions and low b-values),

ii) the simple Gaussian diﬀusion model and iii) simple deterministic streamline

ﬁber tracking methods [17]. On the contrary, it has proved much more diﬃcult to

reconstruct projection ﬁbers, and especially the motor ﬁbers of the corticospinal

tract (CST) using such standard protocols. On one side, the anatomy of these

ﬁbers between the spinal cord and the internal capsule has been well-studied us-

ing DTI [10, 8]. On the other side, the study of these ﬁbers between the internal

capsule and the cortex, and in particular of those dedicated to a speciﬁc mo-

tor function, is much more challenging using DTI, mostly due to the numerous

crossings/kissing/merging/diverging ﬁbers in the corona radiata. A particularly

diﬃcult ﬁber bundle to track within the CST is the portion corresponding to

the motor hand area, because it is located laterally on the motor cortex [30] (as

shown by the homunculus of Penﬁeld & Rasmussen), compared to the leg or the

trunk areas for instance. In the following, we call this ﬁber bundle the HMFs,

as “hand motor ﬁbers”.

The HMFs are a crucial ﬁber bundle to investigate, in the context of normal

anatomy, within the more general study of handedness, cerebral dominance, and

brain asymmetry [27]. More generally, the development of diﬀusion models and

tractography methods for the CST in general, and the HMFs in particular, which

could be used in clinical routine, is key for a better understanding of pathologies

of the CST such as, typically, amyotrophic lateral sclerosis [9], Wallerian degen-

eration of the CST after ischemic stroke [31], motor dysfunctions in infants [14]

or in patients with relapsing-remitting multiple sclerosis [13].

New types of image acquisition schemes (e.g. HARDI sequences), diﬀusion

models (e.g. multiple tensors, ODF, etc.) [12] and tractography methods [18–

20] have been introduced to account for intricate ﬁber conﬁgurations, but these

techniques i) have been reported to often miss entirely the lateral portions of

the CST, and thus the HMFs [3] and ii) are not applicable at hand in a clinical

setting, mostly due to long acquisition times.

In this paper, we propose to investigate the usefulness of a new diﬀusion

model, termed Diﬀusion Directions Imaging (DDI), to track the HMFs on clinical

data, using a deterministic streamline tractography algorithm. This model allows

to capture several diﬀusion directions within a voxel, with a low number of

parameters [26, 4].

The two goals of this paper are: 1) to evaluate the ability of this new diﬀusion

model and of two other standard models (DTI/ODF) to track the left and right

HMFs, using a common tractography algorithm, in a clinical setting, i.e. with

few diﬀusion gradients (typically, less than 15) and low b-values (typically,

less that 1000s/mm2), and 2) to study whether the number of tracked HMFs

in one hemisphere is diﬀerent from that in the contralateral hemisphere, for

right-handed and left-handed subjects. Note that we do not test multi-tensor

models, as these have been shown to be unable to provide a unique solution in

the context of single-shell (one unique b-value) acquisitions [24], as is the case

here and in most standard clinical protocols.

Comparison of 3 diﬀusion models to track the hand motor ﬁbers 3

In Section 2.1, we present the three tested models, and we outline our im-

plementation thereof. In Section 2.2, we describe the common multiple ﬁbers

deterministic streamline tractography algorithm we use for these three models.

The same algorithm is used to make sure that the subsequently reported results

can be interpreted as diﬀerences in models, rather than diﬀerences in dMRI

sequences or tractography algorithms. The data are described in Section 2.3,

and we perform statistical tests and numerical evaluation in Section 3, before

discussing these results, concluding and giving some perspectives in Section 4.

2 Material & Methods

2.1 Diﬀusion models

⊲DTI model: The Gaussian model assumes that the diﬀusion process can

be captured by a tensor (6 parameters), which is proportional to the covariance

matrix of the unknown Gaussian pdf. The tensor Tis parametrised as T=

exp(M), where Mis an unknown 3 ×3 symmetric matrix, and its estimation

is done using a least-squares (LS) ﬁtting on the raw DWI intensities [7]. The LS

criterion is optimised numerically using the NEWUOA algorithm [23]. Within

a given voxel, the single putative ﬁber direction is considered to be aligned with

the direction of the eigenvectors associated to the largest eigenvalue of the tensor.

The tractography algorithm uses a log-Euclidean interpolation scheme [1].

⊲ODF model: The orientation distribution function (ODF) describes the ori-

entational structure of the diﬀusion function [28]. The raw DWI intensities are

modelled with a modiﬁed basis of spherical harmonics, whose ccoeﬃcients

are estimated using a LS ﬁtting including a Laplace-Beltrami regularisation

term. The number of unknown coeﬃcients depends on the order lof the basis:

c= (l+ 1)(l+ 2)/2. This LS problem has a closed-form solution, from which the

optimal ODF (or to be precise, an approximation thereof) can be computed

analytically using the Funk-Hecke theorem [5]. Then, ODF sharpening is per-

formed using spherical deconvolution to compute the ﬁber ODF [6]. Within a

given voxel, the putative ﬁber directions are selected as the local maxima of

the normalised, sharpened ODF for which the ODF function value is above a

user-speciﬁed threshold set here to 0.1. These local maxima are computed using

NEWUOA (with starting points homogeneously distributed on the unit sphere),

and they are sorted according to their ODF function value. The tractography

algorithm uses a trilinear interpolation scheme [12].

⊲DDI model: The diﬀusion function is modelled as a mixture of distributions

with a common parametric form [26]. The number of mixture components is that

of the number mof diﬀerent ﬁber directions within the voxel. In essence, the

pdf of each of these distributions is deﬁned as the convolution of a von Mises-

Fisher pdf (which models the direction of the ﬁber) and of a centered cylin-

drical Gaussian pdf (which models the amplitude of the diﬀusion along the

ﬁber). The covariance matrix of the Gaussian distribution is actually a function

4 Wiest-Daessl´e et al.

of the two parameters of the von Mises-Fisher distribution: the mean direction µ

(unit vector) and the concentration parameter κ. A scalar parameter λ, assumed

to be identical for all ﬁber directions, completes the model. Therefore, to allow

for mﬁbers, the DDI model requires 3m+ 1 parameters. An anisotropy value ξ,

akin to the fractional anisotropy (FA) (resp. the generalised FA (GFA) [28]) in

the DTI (resp. ODF) model, is also deﬁned. The 3m+ 1 unknown parameters

are estimated using a LS ﬁtting on the raw DWI intensities, and this optimi-

sation is performed using NEWUOA. Within a given voxel, the putative ﬁber

directions are a natural output of this model, sorted according to their diﬀusion

function values. Note that, as of now, the number of ﬁbers min this model is set

to 2, and automated estimation thereof will be a topic of future investigation.

The tractography algorithm uses a trilinear interpolation scheme.

2.2 The common multiple ﬁbers tractography algorithm

Our goal is to track the ﬁbers linking two ROIs. Our deterministic streamline

algorithm can be viewed as an extension of the original FACT method [16],

adapted to ODF and DDI models, using a breadth-ﬁrst-type search. It must be

made clear that for the DTI model, the tractography is led without considering

multiple directions; we omit this important detail below for the sake of clarity.

Starting from one of the two ROIs, we deﬁne nstarting points within each

voxel of the ROI. The DTI/ODF/DDI models at these starting points are esti-

mated using the previously described interpolation schemes. For each of these

starting points, we compute the two principal putative directions (deﬁned using

the previously described sorting out procedures), we follow the ﬁrst direction

with a step size of lmillimeters and we record the second direction for future

use, as it can be indicative of crossing/kissing/merging/diverging ﬁbers. We

then reestimate the DTI/ODF/DDI models at this new spatial position (using

the previously described interpolation schemes), and we compute all the pu-

tative directions for each model. Among these, we follow the one closest (i.e.

with minimal angular diﬀerence) to the previously estimated ﬁrst direction. A

second direction, having the highest ODF/diﬀusion function value among the

remaining putative ﬁber directions, is recorded for future use. The tracking of

the main ﬁber is achieved when i) the angle between two successively estimated

ﬁrst directions is higher than α, or when ii) FA/GFA/ξis lower than β, or when

iii) the ﬁber reaches the border of a precomputed brain mask [25]. Once this

main ﬁber has been tracked, we perform the same tracking from all the possi-

ble crossing/kissing/merging/diverging points that have been recorded along its

path. Importantly, for these trackings, the stepping rule and stopping criteria

are identical as those for the main ﬁber, but we do not record any possible mixed

ﬁber conﬁguration along these secondary paths, for which we only follow the ﬁrst

direction at each step. The same tracking is then led on the second ROI, and

only the tracts linking the two ROIS are kept for further analysis. In practice,

we choose the parameters n= 1, l= 1, α= 60 degrees and β= 0.15.

Comparison of 3 diﬀusion models to track the hand motor ﬁbers 5

2.3 Data

The data consist of dMRI, anatomical (aMRI) and functional (fMRI) MRI on 14

right-handed (8 males, 6 females) and 9 left-handed (6 males, 3 females) healthy

volunteers. The mean age was 30.3 (21 to 45). Handedness was determined using

the Oldﬁeld questionnaire [22]. The aMRI, dMRI and fMRI data were acquired

using standard sequences on a Philips Achieva 3T system:

–aMRI: T1-w 3D TFE, 184 sagittal slices of size 256×256 (1mm×1mm) and

1mm thickness.

–fMRI: gradient echo EPI using BOLD contrast, 24 contiguous axial slices

of size 128×128 (1.8mm×1.8mm) and 4mm thickness. The hand motor task

consisted in opening and closing the hand, and was implemented in a stan-

dard block design. Motion correction, slice-timing and detection of the acti-

vation areas for both right and left hands were performed within SPM5.

–dMRI: single shot EPI, 60 contiguous axial slices of size 128×128 (2mm×

2mm) and 2mm thickness. Diﬀusion gradients were applied in 15 non-col-

linear directions with b= 800s/mm2. Each diﬀusion-weighted MRI was

corrected for eddy current-induced geometric distortions [21] and denoised

using the Rician non-local means algorithm [29]. Given this low number of

directions, the (modiﬁed) spherical harmonics basis of order 4 (15 parame-

ters) was used for ODF estimation, while 6 parameters (resp. 7) were to be

estimated for the DTI (resp. DDI) model.

For each subject, the aMR and fMR images were rigidly registered to the B0

image of the dMRI sequence [15]. A ﬁrst ROI was manually delineated by an

expert neuroanatomist in an axial slice on the aMRI data through the superior

part of the mesencephalum, both on left and right sides. Tractography was then

performed between these two anatomical ROIs and the two (left and right) cor-

tical functional ROIs to reconstruct the HMFs using the three above-mentioned

diﬀusion models and the previously described tractography algorithm.

3 Results

3.1 Connections between the ROIs

Our objective here was to evaluate whether the three diﬀusion models, coupled

with the tractography algorithm, were able to connect fully, partially, or not at

all, the anatomical and functional ROIs. First of all, we split each functional ROI

into a medial and a lateral area, the latter corresponding to the extremity of the

hand representation on the motor homunculus, i.e. the thumb. Then for each

model DTI/ODF/DDI, each hemisphere, and each of the 23 subjects, we com-

puted a discrete score of 0, 1 or 2 depending on the quality/strength (subjectively

based on the number of ﬁbers) of the connection between the anatomical ROI and

the medial part of the functional ROI; in a word, we estimated 3 ×2×23 = 138

scores. Similarly, we computed another set of 138 scores for the connection with

6 Wiest-Daessl´e et al.

the lateral part of the functional ROI. At last, the overall number of ﬁbers com-

posing the reconstructed HMFs, i.e. linking the two (anatomical and functional)

ROIs, was also computed.

The Pearson χ2test is particularly adequate to handle such qualitative, dis-

crete scores. We performed pairwise Pearson χ2tests with a signiﬁcance level of

0.05, corrected for multiple comparisons (Bonferroni) to compare DTI vs ODF,

ODF vs DDI, and DDI vs DTI for the medial and lateral areas. To compare

the overall number of ﬁbers, we ﬁrst showed that the data were not Gaussian-

distributed using the Jarque-Bera test, and then we performed pairwise sign

tests (which allows to test for diﬀerences in medians) with a signiﬁcance level of

0.05, corrected for multiple comparisons (Bonferroni).

The p-values are reported in Tab. 1, left, and mainly show that i) the ODF

model was able to track more medial ﬁbers than the DTI model, but as many

lateral ﬁbers, and that ii) the DDI model did not track more medial ﬁbers than

the ODF model, but did track more lateral ﬁbers, at the 0.05 signiﬁcance level.

These two results are conﬁrmed by the sign test on the overall number of ﬁbers.

3.2 Asymmetry of the hand motor ﬁbers

Our objective here was to evaluate whether the three diﬀusion models, coupled

with the tractography algorithm, were able to show signiﬁcant diﬀerences (in

terms of number of ﬁbers) between the left and right reconstructed HMFs, in

right-handed (14) and left-handed (9) subjects. We pooled males and females

for increased statistical power. After showing that the data were not Gaussian-

distributed using the Jarque-Bera test, we performed pairwise sign tests with a

signiﬁcance level of 0.05, corrected for multiple comparisons (Bonferroni).

The p-values are reported in Tab. 1, right, and mainly show that i) none

of the models is able to show diﬀerences in left-handed subjects, but that ii)

the DDI model is the only model allowing to show that the bundle of HMFs is

larger (in terms of number of ﬁbers) in the left hemisphere than in the right for

right-handed subjects.

Medial Lateral # Fibers

DTI vs ODF 2.6×10−93.4×10−13.3×10−7

ODF vs DDI 3.7×10−27.6×10−12 3.1×10−7

DDI vs DTI 1.3×10−14 5.5×10−14 2.8×10−14

RH LH

DTI 0.0923 1

ODF 0.5811 0.1797

DDI 0.0189 0.5078

Table 1. p-values of the statistical tests. Left table: “Is there a signiﬁcant diﬀerence

(level=0.05) between the 3 models in recovering tracts reaching the medial and lateral

areas of the functional ROI, in each hemisphere, for the 23 subjects? And in the overall

number of tracked ﬁbers?”. Right table: “Are the 3 models able to show signiﬁcant

diﬀerences (level=0.05), in terms of number of ﬁbers, between the left and right tracked

HMFs, for the 14 right-handed (RH) and the 9 left-handed (LH) subjects?”.

Comparison of 3 diﬀusion models to track the hand motor ﬁbers 7

Fig. 1. Tractography of the HMFs in the left and right hemispheres. From

left to right: DTI, ODF and DDI. Note that we use the neurological convention, i.e.

the left (resp. right) hemisphere is displayed on the left (resp. right). The DDI model

is the only one able to consistently reach the lateral area within the functional ROI.

4 Discussion, Conclusion & Perspectives

In this paper, we showed that i) the DDI model outperforms both the DTI and

the ODF models to track the HMFs (see Fig. 1), and, maybe more importantly,

that ii) the DDI model is the only model able to show that the number of

HMFs in the left hemisphere is larger than in the contralateral hemisphere for

right-handed subjects, which seems to ﬁt the intuitive idea that the hand motor

ﬁbers in the hemisphere contralateral to the dominant hand should be some-

what more developed than those in the other hemisphere. Interestingly, the DDI

model, as the other two models, failed to ﬁnd such a diﬀerence for left-handed

subjects, which may suggest that left-handedness is not simply a mirrored right-

handedness. This is already known from e.g. the notoriously diﬀering patterns of

hemispheric dominance for language between left and right-handed subjects, but

to our knowledge, this is the ﬁrst time such results are reported on white matter

ﬁbers, at least on clinical data. These results must now be further investigated

in light of the huge literature on brain asymmetry and cerebral dominance [27].

In particular, recruiting more males/females and right/left-handed subjects for

increased statistical power and population-speciﬁc analysis would be necessary

to conﬁrm these ﬁrst results, of potentially important anatomical signiﬁcance.

As expected, the DTI model performs very poorly when tracking the HMFs.

Importantly, we stress here that we do not state that the DDI model outper-

forms the ODF model in general, but only in this particular experimental setting.

Low angular resolution of the order-4 ODF model can explain why it is outper-

formed here. It would be of high interest to try to replicate our experiments on

HARDI data using higher-order ODF models and improved (e.g. probabilistic)

tractography methods, to further support our ﬁrst ﬁndings.

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