Dynamic Bayesian Network Modeling of Hippocampal Subﬁelds

Connectivity with 7T fMRI: A Case Study

Fernando P. Santos

1

, Stephen F. Smagula

2

, Helmet Karim

3

, Tales S. Santini

3

, Howard J. Aizenstein

2

,

Tamer S. Ibrahim

3,4

and Carlos D. Maciel

1

1

Department of Electrical Engineering, S

˜

ao Carlos School of Engineering, University of S

˜

ao Paulo,

Av. Trabalhador Saocarlense, 400, 13561010, S

˜

ao Carlos, S

˜

ao Paulo, Brazil

2

Department of Psychiatry, Western Psychiatric Institute and Clinic, University of Pittsburgh School of Medicine,

3811 O’Hara Street, 15213, Pittsburgh, Pennsylvania, U.S.A.

3

Department of Bioengineering, University of Pittsburgh, 3700 O’Hara Street, 15213, Pittsburgh, Pennsylvania, U.S.A.

4

Department of Radiology, University of Pittsburgh, 200 Lothrop Street, 15213, Pittsburgh, Pennsylvania, U.S.A

Keywords:

Dynamic Bayesian Networks, fMRI, Network Modelling, Hippocampus.

Abstract:

The development of high resolution structural and functional magnetic resonance imaging, along with the new

automatic segmentation procedures for identifying brain regions with high precision and level of detail, has

made possible new studies on functional connectivity in the medial temporal lobe and hippocampal subﬁelds,

with important applications in the understanding of human memory and psychiatric disorders. Many previous

analyses using high resolution data have focused on undirected measures between these subﬁelds. Our work

expands this by presenting Dynamic Bayesian Network (DBN) models as an useful tool for mapping directed

functional connectivity in the hippocampal subﬁelds. Besides revealing directional connections, DBNs use

a model-free approach which also exclude indirect connections between nodes of a graph by means of con-

ditional probability distribution. They also relax the constraint of acyclicity imposed by traditional Bayesian

networks (BNs) by considering nodes at different time points through a Markovianity assumption. We apply

the GlobalMIT DBN learning algorithm to one subject with fMRI time-series obtained from three regions: the

cornu ammonis (CA), dentate gyrus (DG) and entorhinal cortex (ERC), and ﬁnd an initial network structure,

which can be further expanded with the inclusion of new regions and analyzed with a group analysis method.

1 INTRODUCTION

Establishing functional connectivity networks in the

brain has become a major focus with the ad-

vance of neuroimaging techniques such as elec-

troencephalography (EEG), magnetoencephalogra-

phy (MEG), and functional magnetic resonance imag-

ing (fMRI) (Wang et al., 2015; Smith et al., 2011).

Speciﬁcally, fMRI presents advantages as it has high

spatial resolution, allowing connectivity studies to

focus on very speciﬁc parts of the brain including

deeper brain structures not accessible by MEG or

EEG. Therefore, one of the areas receiving attention

in recent years is the hippocampal sub-ﬁelds and more

speciﬁcally their connectivity. The hippocampus is a

structure located in the medial temporal lobe (MTL)

and has been associated with learning and memory

(Jeneson and Squire, 2012). Alterations in its struc-

ture and connectivity are shown to be associated with

several neurological and psychiatric disorders such

as Alzheimer’s disease, epilepsy, schizophrenia, and

others (Bartsch, 2012). Studies have been stressing

the importance of considering the hippocampal sub-

structures for a better understanding of its function

and pathologies, instead of considering it as a whole

(Maruszak and Thuret, 2015). However due to the

low resolution of the fMRI data, this type of analy-

sis was not possible on the hippocampus sub-ﬁelds,

and only recently, with the newest advances on ultra-

high ﬁeld MRI with 7T scanners, higher-resolution

images are being obtained and analyzed(Duyn, 2012).

Moreover, advances in automatic segmentation proce-

dures also facilitate the extraction of regions of inter-

est (ROIs) and the usage of more data, since manual

segmentation may be very time consuming and prone

to errors (Wisse et al., 2016; Yushkevich et al., 2015).

Recently, studies have demonstrated functional subdi-

visions of the medial temporal lobe along the longitu-

178

P. Santos F., F. Smagula S., Karim H., S. Santini T., J. Aizenstein H., S. Ibrahim T. and D. Maciel C.

Dynamic Bayesian Network Modeling of Hippocampal Subﬁelds Connectivity with 7T fMRI: A Case Study.

DOI: 10.5220/0006151601780184

In Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2017), pages 178-184

ISBN: 978-989-758-212-7

Copyright

c

2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

dinal axis of the hippocampus (Libby et al., 2012), be-

tween hippocampal and para-hippocampal structures

(Libby et al., 2012; Das et al., 2013), and across sub-

ﬁelds (Lacy and Stark, 2012; de Flores et al., 2015).

Among the methods for brain connectiv-

ity,(Friston, 2011) has divided types of connectivity

into functional and effective connectivity, with the

ﬁrst describing ”statistical dependencies among

remote neurophysiological events”, while the second

describes ”the inﬂuence that one neural system exerts

over another, either at a synaptic or population level”.

A spectrum of methods exist that fall between these

two approaches, with effective connectivity having

more complex and biologically informed models,

used for a conﬁrmatory approach, while functional

connectivity presents simpler and more generic

methods, used for a exploratory approach (i.e.,

network discovery) (Valdes-Sosa et al., 2011). The

direction of the connections between nodes is also an

important factor — and in fact, recent work by (Li

et al., 2013) reveals alterations of directional connec-

tivity in patients with Alzheimer disease, pointing to

the importance of this kind of knowledge in clinical

analysis. (Smith et al., 2011) also notes this, and

separates methods capable of describing directional

connectivity in three categories: lag-based methods

(Rodrigues and Andrade, 2014, See review in), such

as Granger causality (Granger, 1969) ; conditional

independence methods, such as Bayesian networks

(BN)(Mumford and Ramsey, 2014) and Dynamic

Causal Modeling (DCM)(Friston et al., 2003), and

higher-order statistics, such as Patel’s pairwise

conditional probability approach (Patel et al., 2006).

Dynamic Bayesian Networks (DBNs) can be re-

garded as a directed functional connectivity approach

(and thus, are used for exploratory analyses, instead

of conﬁrmatory, such as DCM) that overcomes the

limitations of acyclicity imposed by the traditional

Bayesian network framework. They are Bayesian net-

works with nodes representing the processes at dif-

ferent time points, given a Markovianity assumption;

thus, cycles may be present as a result of temporal dy-

namics. Besides, the Bayesian network framework is

able to differentiate direct from indirect connections

(or, marginal dependences) between nodes by means

of conditional probabilities (Valdes-Sosa et al., 2011).

DBNs were applied to fMRI data in many studies (Ide

et al., 2014; Bielza and Larra

˜

naga, 2014) and were

modeled either with discrete data (with the condi-

tional probability distributions (CPD) are represented

by a probability table) (Rajapakse and Zhou, 2007;

Burge et al., 2009) or with continuous data through

a gaussianity assumption (Zhang et al., 2005; Chen

et al., 2012; Wu et al., 2014). The advantage of the

ﬁrst case is that nonlinear processes are better mod-

eled, at the cost of reducing the original signal to dis-

crete values and requiring more samples, while in the

second case, processes are considered linear, but don’t

have to be discretized.

From the fact that the current state of knowledge

in hippocampal sub-ﬁelds connectivity and availabil-

ity of data demands a exploratory approach, this study

used DBNs as a tool for ﬁnding directed functional

connectivity between the hippocampal sub-ﬁelds of

the a resting state brain. This helps advance cur-

rent knowledge on the function of the medial tem-

poral lobe by introducing information on the direc-

tion of the connections, instead of only undirected and

pairwise correlations between regions. The model is

learned by an algorithm based on the search and score

paradigm, and uses the mutual information criterion

(MIT) (de Campos, 2006; Vinh et al., 2011a) to eval-

uate the goodness-of-ﬁt of a DBN structure to the data

employed. Time-series data is obtained by extracting

average ROI time-series from the BOLD fMRI data

with coregistered hippocampal sub-ﬁeld labels ob-

tained through an automatic segmentation algorithm

applied to structural T1 and T2-weighted structural

images. The highest scoring DBN structure found

for one subject shows the use of DBNs as a promis-

ing way to map the directed functional connectivity of

medial temporal lobe sub-structures using ultra-high

resolution neuroimaging.

2 METHODS

2.1 MRI Data

Images were collected from older adults diagnosed

with late-life depression, at the Department of Radi-

ology of University of Pittsburgh (NIH Project num-

ber 1R01MH111265-01). Scanning was done on a

7T human MRI system (Magnetom, Siemens Med-

ical Systems, Erlangen, Germany) with a 20-to-8-

channel transmit and 32-channel adjustable receive

coil (Ibrahim et al., 2013).

Structural T1 and T2-weighted images were used

for identifying the subregions with the automatic

segmentation. An axial, whole-brain T1 was ob-

tained with a Magnetization Prepared Rapid Gra-

dient Echo (MPRAGE) sequence with 3D orien-

tation, isotropic resolution 0.7mm3 and parame-

ters TR/TI/TE=3000/1200/2.47 ms, 6 ﬂip angle,

FoV=192 × 220, 280 × 320 acquisition matrix and

an acquisition time 10 min and 31 s. Axial, whole-

brain T2-weighted images used a 3D Turbo Spin Echo

(TSE) sequence with 0.37 × 0.37mm in plane reso-

Dynamic Bayesian Network Modeling of Hippocampal Subﬁelds Connectivity with 7T fMRI: A Case Study

179

lution and 1.5mm slice thickness; parameters were

TR/TE=7900/56 ms, 130 ﬂip angle, FoV=165 × 189,

32 interleaved slices and acquisition time 5 min

and 25 s. Finally, 4D axial, whole-brain (exclud-

ing the cerebellum) BOLD fMRI data were acquired

with a gradient echo planar (EPI) sequence with 155

time points and 2.3mm isotropic voxel size, 46 in-

terleaved slices, TR/TE=2500/20 ms, 70 ﬂip angle,

FoV=1546 × 1546, 96 × 96 acquistion matrix and ac-

quisition time 6 min and 27 s. Patients rested with

eyes open and lights off.

2.2 Segmentation and Preprocessing

Three ROIs are considered in the model: the den-

tate gyrus (DG), the four ﬁelds of the cornu ammo-

nis (CA14) (considered as one) and the entorhinal

cortex (ERC) from only one hemisphere of a subject

(Bartsch, 2012, See). The reason for choosing only

these is that as the number of nodes included in a

DBN model grows, the number of time points needed

for learning need to grow as well (Koller and Fried-

man, 2009) — and, with one subject, only 155 time

points are available. The ROIs are identiﬁed in the

T2-weighted images using an automatic segmentation

procedure applied to the images using the ASHS soft-

ware developed by (Yushkevich et al., 2015). ASHS

uses a multi-atlas label fusion approach for obtaining

the hippocampal subﬁelds with T1 and T2-weighted

images (For a review of methods, see Dill et al.,

2015). A 7T atlas, based on images obtained in the

PREDICT-MR study (Wisse et al., 2014), tested with

ASHS in (Wisse et al., 2016) and made available pub-

licly, was used.

Preprocessing and image registering was done

with the statistical parametric mapping software

(SPM12) (Penny et al., 2011). Functional images

were slice-time corrected (reference slice was the

temporally middle slice with sinc interpolation), mo-

tion corrected (mean scan was used as reference with

mutual information as the similarity metric and 4th

degree B-spline interpolation), and smoothed with a

Gaussian smoothing kernel (FWHM of 8mm). The

T2-weighted images and segmentation labels are reg-

istered and resliced to match the functional image.

Time-series from the voxels of the ROIs are extracted

from the functional image according the aligned seg-

mentation labels. A mean intensity normalization is

applied: the average value of the ROI in each time

point is subtracted from each time-series, and normal-

ization is applied, with values ranging from -1 to 1.

Time-series of each ROIs are then averaged, yielding

one time-series for each ROI (Ide et al., 2014).

Time-series extracted from the ROIs are usually

non-stationary and present DC level trends that hin-

der the ability to use sequential time points for train-

ing a DBN (i.e., the supposition of ergodicity). These

trends are usually considered irrelevant to the model

and thus are removed by linear detrending methods

(Ide et al., 2014) and normalization. However, one

must consider the possibility that these trends can be

non-linear and present discontinuities, so that tradi-

tional detrending methods may not achieve stationary

time-series. Therefore, the Singular Spectrum Analy-

sis (SSA) technique is an interesting option due to its

model-free characteristic and ability to remove com-

plex trends (i.e., not just linear or quadratic) and dis-

continuities with very few speciﬁcation parameters

(Golyandina and Zhigljavsky, 2013). We employ this

technique in the present work, by applying to each

time-series obtained from the ROIs. SSA’s main idea

is to ”decompose the original series into the sum of a

small number of independent and interpretable com-

ponents such as a slowly varying trend, oscillatory

components and structure-less noise” (Hassani, 2007)

and reconstruct it according to the components de-

sired — in case, the lowest oscillatory components

(which can be regarded as containing the direct cur-

rent (DC) level), represented by the largest eigen-

values obtained in the Singular Value Decomposition

(SVD) of the time-series’ embedding matrix (Golyan-

dina and Zhigljavsky, 2013).

2.3 Learning Discrete Dynamic

Bayesian Networks

We start by deﬁning a Dynamic Bayesian Network

(DBN). Let X

(t)

= {X

(t)

1

, X

(t)

2

, . . . , X

(t)

N

}be a set of

N time-series of length T , where X

(t)

i

is a random

variable representing the process X

i

at time slice

t. A DBN models the joint probability distribution

X

(1)

∪ X

(2)

. . . ∪ X

(T )

by means of a directed acyclic

graph (DAG) G encoding the conditional indepen-

dences between the random variables of the sys-

tem (Friedman et al., 1998). Three assumptions are

made: (1) ﬁrst order Markovianity, i.e., ∀t, (X

(t+1)

⊥

X

(0:t−1)

|X

(t)

), (2) stationarity, i.e., P(X

(t)

|X

(t−1)

) is

independent of t, and (3) Markov causal condition,

i.e., (X

(t)

i

⊥ Nd(X

(t)

i

)|Pa(X

(t)

i

)), where Nd(X

(t)

i

) are

the non-descendant nodes of X

(t)

i

, and Pa(X

(t)

i

) are

the parent nodes of X

(t)

i

in the DAG G (Neapolitan

et al., 2004). Thus, this permits the decomposition of

the joint probability distribution of all the processes

of the system as:

P(X

(0:t)

) = P(X

(0)

)

T

∏

t=1

P(X

(t)

|X

(t−1)

) (1)

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

180

X

(t−1)

X

(t)

Y

(t−1)

Y

(t)

Z

(t−1)

Z

(t)

A

(t−1)

A

(t)

B

(t−1)

B

(t)

C

(t−1)

C

(t)

A

B

C

(a) (b) (c)

Figure 1: Examples of DBNs. (a) presents a DBN with only

inter time-slice edges, which can be represented as a cycli-

cal graph as shown in (b) (used in the present study). (c)

presents a DBN with both intra and inter time-slice edges.

and the further decomposition of the joint transi-

tion probability P(X

(t)

|X

(t−1)

) as:

P(X

(t)

|X

(t−1)

) =

N

∏

i=1

P(X

(t)

i

|Pa(X

(t)

i

) (2)

These decompositions thus permit both network

inference algorithms for unknown variables and the

formulation of scoring metrics and other structure

learning procedures from data (such as the one used

and presented further) (Neapolitan et al., 2004).

DBNs can include edges between nodes in a same

time slice t (intra time slice) and between time slices

t − 1 and t (inter time slice) (time slices t − 2 and

on can be included by relaxing the Markovianity as-

sumption to permit higher orders, such as in (Xuan

et al., 2012) and (Santos and Maciel, 2014)). Figure 1

(c) illustrates this type of network. However, for sim-

plicity, many authors consider DBNs including only

inter time slice edges (Xuan et al., 2012; Smith et al.,

2006). This last case permits an equivalent graph rep-

resentation without specifying time-series at different

time points and thus without the acyclicity restriction,

such as shown in Figure 1(a,b).

DBN graphs can be learned from data through

many approaches, among which are conditional in-

dependence tests, score metrics, and model averag-

ing (such as Markov Chain Monte Carlo) (Koller

and Friedman, 2009). In this paper we employ the

score metrics approach for discrete models (dDBNs),

in which, after searching through a space of possi-

ble graph structures, a scoring function determines

how good this structure is given the data. Partic-

ularly, we employ the GlobalMIT method, imple-

mented in a Matlab/C++ toolkit (Vinh et al., 2011a).

GlobalMIT adapts the MIT scoring metric proposed

by (de Campos, 2006), devised initially for static

Bayesian networks, to DBNs and uses an optimized

search algorithm operating under polynomial time

(Vinh et al., 2011b). The MIT scoring metric eval-

uates the goodness-of-ﬁt of a network ”as the total

mutual information shared between each node and its

parents, penalized by a term which quantiﬁes the de-

gree of statistical signiﬁcance of this shared informa-

tion” (Xuan et al., 2012), and was shown to compete

favorably with other scoring metrics such as Bayesian

Dirichlet equivalence (BDe) and Bayesian Informa-

tion Critertion (BIC) (de Campos, 2006). For a can-

didate graph G with N nodes and their corresponding

{r

1

, . . . , r

n

} discrete states, and a dataset D with N

D

observations, the MIT score is deﬁned as (de Cam-

pos, 2006):

S

MIT

(G : D) =

=

N

∑

i=1

Pa(X

i

)6=

/

0

{2N

D

·I(X

i

, Pa(X

i

)) −

s

i

∑

j=1

χ

α,l

iσ( j)

}

(3)

where I(X

i

, Pa(X

i

)) is the mutual information be-

tween X

i

and its parents, and χ

α,l

iσ( j)

is the value such

that p(χ

2

(l

i

j) ≤ χ

α,l

i j

) = α (the chi-square distribu-

tion at signiﬁcance level 1 − α, with the term l

iσ

i

( j)

deﬁned as:

l

iσ

i

( j)

=

=

(

(r

i

− 1)(r

iσ

i

( j)

− 1)

∏

j−1

k=1

r

iσ

i

(k)

, j = 2, . . . , s

i

(r

i

− 1)(r

iσ

i

( j)

− 1), j = 1

(4)

where σ

i

= {σ

i

(1), . . . , σ

i

(s

i

)} is any permuta-

tion of the index set {1, . . . , s

i

} of Pa(X

i

), with the

ﬁrst variable having the greatest number of states, the

second having the second, and so on.

The GlobalMIT algorithm then investigates, for

each node, every potential parent set of increasing car-

dinality until the globally optimal solution is found.

This guarantees a polynomial worst-case time com-

plexity, given the assumptions that the DBN includes

only inter time slices (thus eliminating the necessity

of checking acyclicity of candidate graphs) and vari-

ables have the same number of discrete states (con-

sidering also the MIT scoring criterion is used in the

algorithm) (Vinh et al., 2011a). GlobalMIT is also

deterministic, and thus have advantage over stochas-

tic global optimization methods, since it does not get

stuck in local minima (Vinh et al., 2011b). The algo-

rithm also uses the following decomposition property

of mutual information:

I(X

i

, Pa(X

i

) ∪ X

j

) = I(X

i

, Pa(X

i

)) + I(X

i

, X

j

|Pa(X

i

))

(5)

which permits an incremental calculation of mutual

information, with cached intermediary values to pre-

vent redundant computation, and thus a better efﬁ-

ciency.

Dynamic Bayesian Network Modeling of Hippocampal Subﬁelds Connectivity with 7T fMRI: A Case Study

181

Figure 2: Resulting labels from the automatic segmenta-

tion procedure implemented in ASHS (Yushkevich et al.,

2015). Labels are shown at the T2-weighted structural im-

age with 0.x0.x0. mm, but are afterwards registered to the

functional images for the ROI time-series extraction proce-

dure and network learning.

Figure 3: Highest scoring DBN structure with the Glob-

alMIT score applied to the hippocampal subﬁelds nodes.

CA stands for cornu ammonis; DG, dentate gyrus and ERC,

entorhinal cortex.

3 RESULTS AND DISCUSSION

Automatic segmentation of hippocampal sub-ﬁelds

was applied to T1 and T2-weighted images of one

subject, as shown in Figure 2. After the registra-

tions and preprocessing, three ROI time-series were

extracted and from the fMRI image: CA, DG and

ERC. Then, SSA technique was applied to remove

complex trends in the signals - time-series were de-

composed into 50 components, and 2 of the lowest

oscillatory components (related to the largest eigen-

values of the SVD decomposition) were removed. Fi-

nally, data were discretized to 5 bins (d = 5) and the

GlobalMIT algorithm was applied for obtaining the

discrete DBN structure. After structure search, the

high scoring graph was the one presented in Figure 3,

with signiﬁcance level of α = 0.95.

The network structure found reveals a mutual con-

nection between CA and DG ﬁelds and a directed

connection from DG to ERC. This indicates that the

connection between CA and ERC is mediated by the

DG, and this ﬁnding may explain why the DG is more

functionally connected to the parahippocampal and

cingulate cortices than the CA (de Flores et al., 2015)

((Libby et al., 2012) shows that connections between

the hippocampal subﬁelds and the parahippocampal

cortex are mediated by the ERC). A fuller understand-

ing of these connections, however, would require an

analysis at group level, since this reﬂects results found

for one subject.

4 CONCLUSION & FUTURE

WORK

Advances with ultra-ﬁeld MRI, yielding high-

resolution fMRI data, and automatic segmentation

procedures for sub-ﬁeld identiﬁcation are opening the

way for studies on sub-ﬁeld level connectivity analy-

ses in the brain. In this study, we demonstrated the

feasibility of a directed functional connectivity analy-

sis of hippocampal sub-ﬁelds data obtained with ultra-

high resolution neuroimaging, automatic segmenta-

tion and DBN models. The resulting DBN models are

able to identify direction of connections and differen-

tiate direct from indirect connections between ROIs,

which may better explain the function of each hip-

pocampal sub-ﬁeld. Also, in the preprocessing steps,

we included a novel application of the SSA technique

for removing complex trends and discontinuities from

time-series in a ﬂexible, model-free way and with

very few speciﬁcation parameters.

Results, however, were obtained for only one sub-

ject, and thus the next step of work will be a group

level analysis, including data from multiple subjects,

for a more complete interpretation of results. DBN

group analysis techniques are described in (Li et al.,

2007) and (Li et al., 2008), in which three main

groups are distinguished: ”the virtual-typical- subject

(VTS) approach which pools or averages group data

as if they are sampled from a single, hypothetical vir-

tual typical subject; the individual-structure (IS) ap-

proach that learns a separate BN for each subject, and

then ﬁnds commonality across the individual struc-

tures, and the common-structure (CS) approach that

imposes the same network structure on the BN of ev-

ery subject, but allows the parameters to differ across

subjects” (Li et al., 2008). An investigation of inter-

subject conformities and variations can yield impor-

tant results for functional and clinical studies(Bielza

and Larra

˜

naga, 2014) on the hippocampus and medial

temporal lobe, such as identiﬁcation of early stages of

progression of Alzheimer’s disease (Das et al., 2013).

Another future step consists in including more

ROIs, for a more complete network model — until

now, usage of data of only one subject (thus, with

only 155 time points) limits the number of nodes to

be included in the network. Important regions to be

added are the remaining parts of the medial temporal

lobes — the subiculum (part of the hippocampus), the

perirhinal cortex (PRC) and the parahippocampal cor-

tex (PHC)— and also the anterior and posterior cin-

gulate cortices; all of these from both the right and left

hemispheres, as investigated in previous work such as

(Lacy and Stark, 2012) and (de Flores et al., 2015).

A study with a seed-to-voxel correlation analysis will

BIOSIGNALS 2017 - 10th International Conference on Bio-inspired Systems and Signal Processing

182

be also conducted for identifying relevant activation

areas to be included (such as described in (Ide et al.,

2014)).

Requirements of data for learning DBNs can be

naturally overcome with some types of analysis at

group level — (Burge et al., 2009), for example,

employs a cross-validation procedure, including data

from multiple subjects. The requirements can also

be overcome by means of multi-modal learning tech-

niques, which use data from multiple types of im-

ages to reduce the search space of networks or mod-

els. (Schulz et al., 2004), for example, performs

an integrated MEG and fMRI for connectivity anal-

ysis, (Rykhlevskaia et al., 2008) performs a survey of

methods integrating structural and functional images

for connectivity analysis, and (Zhu et al., 2014) sur-

veys of methods integrating diffusion tensor imaging

(DTI) with functional images. (Iyer et al., 2013), for

example, uses DTI data as a baseline matrix for an

Bayesian network structure learning procedure — an

important insight that may be further incorporated.

ACKNOWLEDGEMENTS

This work was supported by grants T32 MH019986

and P30 MH090333 from the National Institutes

of Health (USA), grant 2016/02621-0 from So

Paulo Research Foundation (FAPESP/Brazil), grant

475064/2013-5 from National Council of Techno-

logical and Scientiﬁc Development (CNPq/Brazil),

and grant BEX 13385/13-5 from Capes Foundation

(Brazil).

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