Nonlinear prediction of human resting state functional connectivity based on network communication measures

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
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Volume: 04 Issue: 12 | Dec-2015, Available @ http://www.ijret.org 64
NONLINEAR PREDICTION OF HUMAN RESTING-STATE
FUNCTIONAL CONNECTIVITY BASED ON NETWORK
COMMUNICATION MEASURES
Fuliang Wang1
, Xue Chen2
, Yanjiang Wang3
1,2,3
College of Information and Control Engineering, China University of Petroleum (East China), Qingdao, P. R.
China
Abstract
Mounting evidence demonstrated that neuronal activity derived from functional magnetic resonance imaging (fMRI) relates to the
underlying anatomical circuitry measured by diffusion tensor/spectrum imaging (DTI/DSI). However, exploring the relationship
between functional connectivity (FC) and structural connectivity (SC) remains challengeable and thus has motivated a number of
computational models to investigate the extent to which the dynamics depend on the topology. Nevertheless, most of the models
are complex and difficult to treat analytically. In this paper, for simplicity, we utilize four network communication measures
extracted from SC as well as polynomial curves fitting method to predict FC. Our results indicate that all of these measures
predict FC via the nonlinear fitting method. Besides, compared with the linear method, the fitting value between predicted FC and
empirical FC attains higher after applying nonlinear process on communication measures which may help to shed light on the
function-structure relationship.
Key Words: brain connectivity; fMRI; DTI/DSI; network communication measure; nonlinear fitting
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1. INTRODUCTION
In order to fully characterize the human connectome and
functionally connected networks, there emerges advances in
DSI/DTI, fMRI, and related technologies. Usually, there are
two kinds of connectivity related to human brain. The
structural connectivity (SC) is derived from DTI/DSI and
the functional connectivity (FC) is obtained by measuring
the correlation of spontaneous Blood Oxygenation Level-
Dependent (BOLD) fluctuations [1-6]. It has been
demonstrated that human brain dynamics relates to the
underlying topology. To this end, a growing number of
studies have focused on exploring the relationship between
FC and SC by network modeling or neural mass modeling
[7-12]. However, how FC relates to SC still remains an open
question. There exists a problem that most of the
computational models are too complex and difficult to treat
analytically.
In our present study, for simplicity, we make use of four
communication measures extracted from SC — search
information, path transitivity, shortest path length, and the
number of shortest path steps — as well as polynomial
curves fitting method to predict FC. Notably, it has been
demonstrated that all of these four communication measures
can predict the strength of functional connectivity among
both connected and unconnected node pairs by linear
regression [13]. On the basis of this, we carry out an
extensive comparison of linear regression method and the
nonlinear polynomial fitting method while predicting FC
from SC. We conclude that the nonlinear curves fitting
method performs better when the order of polynomial is
appropriate.
2. MATERIALS AND METHODS
2.1 Database
Two databases, one low-resolution including 66 regions of
interest (ROIs), the other one includes 90 ROIs.
The SC matrix of the 66-ROI dataset is based upon the work
of [3]. Each element in the SC matrix represents the density
with which two different brain regions are connected. The
FC matrix was examined by measuring the corresponding
fMRI BOLD signals obtained for each brain area during
20min. Each value in the FC matrix denotes the functional
connection between two node pairs [10].
The 90-ROI dataset is a dataset as described in [14]. The
structural and diffusion MR volumes were parcellated into
90 cerebral cortical areas after diffusion tractography
processing [15]. Resting-state fMRI (rs-fMRI) was acquired
with 180 samples. 10 samples at the beginning were
discarded. Before rs-fMRI, the subjects were instructed to
think of nothing in particular. Finally, the fiber strengths
produced by the streamline tractography algorithm were
resampled into a Gaussian distribution. Both FC and SC are
averaged across the 8 individual participants.
Note that all self-connections (diagonal elements in the FC
matrix) are excluded. The resulting SC matrices and FC
matrices in the above two databases are shown in Figure.1.
Figure.1A shows SC matrix (left panel) and FC matrix (right
panel) from 66-ROI database. Figure.1B shows SC matrix
(left panel) and FC matrix (right panel) from 90-ROI
database.

_______________________________________________________________________________________
Figure.1. Two database.
2.2 Communication Measures
In this paper, we focus on four communication measures:
shortest path length, the number of shortest path steps,
search information and path transitivity [13].
The SC of a parcellation of the human cortex into N regions
can be expressed as undirected weighted
graph
 ,G V W
formed by a set of
nodes
 1 2, , , nV v v v 
and a matrix of fiber density
values ijW w    with values in the range of [0,1],and
with
0ijw 
for regions ,i j that are not directly connected.
Converting W into a matrix of edge lengths or
distances ijL l    (here calculated using the matrix
transforms 1/L W ) allows identification of shortest paths,
comprising lists of unique weighted edges, that span the
minimum distance between each node pair. A shortest path
length ( SPL ) can be described
by
 , , ,s t si ij ktw w w   
from a source node s to a target
node t and the corresponding nodes can be expressed
by
 , , , , ,s t s i j k t  
. K denotes the number of
shortest path steps with s t K  
, and thus
1s t K  
.
Search information ( S ) quantifies the accessibility or
―hiddenness‖ of a path linking a source node s to a target
node t within the network by measuring the amount of
knowledge or information to access the path. Assuming
search information travels along the shortest path and given
the lack of directionality in the SC matrix, the search
information of bidirectional shortest–path s t  is defined
as follows [13]:
 1
2
( ) ,
( ) log ( ( )),
( ) ( )
( )
2
s t
i t
s t i
i
s t s t
s t t s
s t
P
w
S P
S S
S


 
 




 
 
 


 



(1)
Where
(1)
i t  is the first element (weighted edge) of the path
s t  and
*
s t represents the sequence of nodes
excluding the target, i.e.,
 *
, , , ,s t s i j k  
. ( )s tP   is
the probability of taking the shortest path from s to t .
Path transitivity ( PT ) describes the density of local detours
that are available along the shortest path, i.e.,
,
( ) ( ) ( )
,
2
( 1)
ik jk ik jk
k i j
ij
ik jk
k j k i
ij
i j
s t
w w w w
m
w w
m
M

 
 

  



  

 

(2)
Where ( ) 1ikw  if 0ikw  and 0 otherwise. The measure
is independent of the directionality of the path and hence
ensures ( ) ( )s t t sM M   .
3. RESULTS
3.1 Prediction of FC Based on Four Single-
predictor Models
In agreement with the previous study [13], all of these four
communication measures predict FC. The capacity of every
single-predictor was robust based on the shortest paths
computed from SC after applying an inverse transform to
convert weight to distance (see Table 1 and Table 2).
Figure.2A and Figure.3A show the scatter plot of empirical
FC versus the path transitivity and empirical FC versus the
search information based on 66-ROI database and 90-ROI
database, respectively, with red dots representing
structurally connected pairs, and black dots representing
structurally unconnected pairs. The result implies that FC
among node pairs including structurally connected pairs and
unconnected pairs are higher if the path transitivity is
stronger or the search information is weaker.
Ranking the capacity of these four single-predictor models
with linear regression method, comprising the shortest path
length (SPL), the number of shortest path steps (K), the
search information (S) and the path transitivity (PT), the
correlation between predicted FC and empirical FC is
significant across two databases (see Table 1 and Table 2).
The nonlinear polynomial fitting predictions with the path
transitivity and the search information are shown in

_______________________________________________________________________________________
Figure.2B and Figure.3B. The fitting between FC and
empirical FC rises rapidly and then retains stable after a
critical point across a range of polynomial orders. The
curves shown on these scatter diagrams of Figure.2A and
Figure.3A indicate the nonlinear fit (blue) at an appropriate
polynomial order and linear fit (yellow). More details are
shown in Figure.2 and Figure.3.
Figure.2. Prediction of FC with path transitivity and search
information on 66-ROI database. (A) The scatter plot of
empirical FC versus the path transitivity and empirical FC
versus the search information with red dots representing
structurally unconnected pairs. The yellow line indicates the
linear fit, and the blue curve indicates the nonlinear fit at the
third polynomial order. (B) The correlation between the
empirical FC and predicted FC by the path transitivity and
the search information varying with polynomial order.
Figure.3. Prediction of FC with the path transitivity and the
search information on 90-ROI database. (A) The scatter plot
of empirical FC versus the path transitivity and empirical FC
versus the search information with red dots representing
structurally unconnected pairs. The yellow line indicates the
linear fit, and the blue curve indicates the nonlinear fit at the
fourth polynomial order. (B) The correlation between the
empirical FC and predicted FC by the path transitivity and
the search information varying with polynomial order.
Table 1 and Table 2 shows the correlation values between
the empirical FC and predicted FC using four single-
predictor models with linear method and nonlinear method
at an appropriate polynomial order computed for all pairs
(Rall), only structurally connected pairs (Rcon), and only
structurally unconnected pairs (Runcon). Assume both search
information and path transitivity travel along the shortest
path. All correlation values computed for all pairs (Rall),
only structurally connected pairs (Rcon), and only structurally
unconnected pairs (Runcon), were significant ( 0.001P  ). SPL
denotes shortest path length; K represents the number of
shortest path steps; S is search information; PT is path
transitivity.
Comparing the effectiveness of prediction with two
methods, we can find that every single-predictor model with
nonlinear polynomial fitting method shows better
performance than with linear regression method among
both-hemisphere (BH) prediction, right-hemisphere (RH)
prediction and inter-hemisphere (IH) prediction.
3.2 Prediction of FC Based on Multi-predictor
Models
A joint linear multi-predictor model comprising all four
communication measures above presents higher capacity of
predicting FC than each linear single-predictor model in line
with the previous research [13] across two databases (Table
1 and Table 2). Similarly, our results indicate that the joint
nonlinear multi-predictor model shows better prediction
than each nonlinear single-predictor model and even better
performance than the joint linear multi-predictor model.
Figrue.4 shows the patterns of predicted FC simulated by
linear multi-predictor model and nonlinear multi-predictor
model at a proper polynomial order. Figure.4A demonstrates
empirical FC from 66-ROI database (left), the predicted FC
simulated by linear multi-predictor model (middle) and the
predicted FC simulated by nonlinear multi-predictor model
at the seventh polynomial order (right). Figure.4B illustrates
empirical FC from 90-ROI database (left), the predicted FC
simulated by linear multi-predictor model (middle) and the
predicted FC simulated by nonlinear multi-predictor model
at the fourth polynomial order (right).
The corresponding correlations between simulated FC and
empirical FC of two databases are Rall = 0.4511 (linear
regression model, 66-ROI database), Rall = 0.5283
(nonlinear regression model, 66-ROI database), Rall =
0.4296 (linear regression model, 90-ROI database) and Rall =
0.4674 (nonlinear regression model, 90-ROI database).

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Figure.4. Empirical FC and predicted FC derived from linear and nonlinear regression model across two databases.
Table 1. The prediction of FC based on 66-ROI database using linear single-predictor and multi-predictor models as well as
nonlinear single-predictor and multi-predictor models.
Linear Nonlinear
FC predictors BH RH IH BH RH IH
SPL Log(SPL)
Rall 0.1476 0.3163 0.1043 0.4285 0.5048 0.4255
Rcon 0.5011 0.5081 0.5018 0.5545 0.6279 0.5160
Runcon 0.0193 -0.0056 0.0066 0.1139 0.1203 0.2057
K Log(K)
Rall 0.3094 0.3908 0.2266 0.4276 0.5408 0.3544
Rcon 0.4922 0.5008 0.5295 0.5261 0.5618 0.5303
Runcon 0.0073 -0.0454 -0.0005 0.2172 0.2679 0.2380
S Log(S)
Rall 0.2854 0.3944 0.2034 0.4669 0.5292 0.4341
Rcon 0.5357 0.5914 0.6146 0.4873 0.4952 0.6217
Runcon 0.0347 0.0324 0.0140 0.2572 0.3220 0.2640
PT PT
Rall 0.2504 0.2873 0.1917 0.4506 0.4455 0.4865
Rcon 0.3996 0.3051 0.5138 0.5151 0.4546 0.6201
Runcon -0.1498 -0.1572 -0.1687 0.1683 0.0884 0.2322
All measure
predictors
Rall 0.4511 0.5502 0.3951 0.5283 0.5890 0.5067
Rcon 0.5442 0.5930 0.6401 0.6076 0.6320 0.6285
Runcon 0.1143 0.1989 0.0911 0.2758 0.2795 0.3147
Table 2. The prediction of FC based on 90-ROI database using linear single-predictor and multi-predictor models as well as
nonlinear single-predictor and multi-predictor models.
Linear Nonlinear
FC predictors BH RH IH BH RH IH
SPL Log(SPL)
Rall 0.3941 0.4693 0.3557 0.4511 0.5183 0.4144
Rcon 0.5872 0.5904 0.5580 0.5990 0.6013 0.5679
Runcon 0.0930 -0.0640 0.1265 0.0924 -0.0694 0.1737
K Log(K)
Rall 0.3094 0.3908 0.2266 0.4003 0.5576 0.2915
Rcon 0.4922 0.5008 0.5295 0.5329 0.5886 0.5658
Runcon 0.0073 -0.0454 -0.0005 0.1419 0.2536 0.1497
S Log(S)
Rall 0.2908 0.2920 0.2955 0.4396 0.5416 0.3668
Rcon 0.5390 0.5705 0.4767 0.5708 0.6018 0.5000
Runcon -0.0002 -0.1264 0.0734 0.1026 0.0986 0.1266
PT PT
Rall 0.1686 0.2514 0.1051 0.2151 0.3593 0.0782
Rcon 0.0545 0.2805 -0.1090 0.1692 0.3498 -0.0179
Runcon 0.0008 0.0543 0.0639 0.0253 0.1121 0.0255
All measure
predictors
Rall 0.4296 0.4814 0.3953 0.4674 0.5439 0.4277
Rcon 0.5701 0.5603 0.5533 0.6121 0.6116 0.5880
Runcon 0.1599 0.0196 0.1608 0.1168 -0.0204 0.1572

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4. DISCUSSION
Since the mid 1990s, the dynamics of resting-state brain
triggered much interest in the study of neuroscience. Several
large-scale computational models were proposed to explore
the relationship between the anatomical structure and the
functional dynamics. Despite the difference between
models, the model parameters were adjusted when the
system operates at the critical point (i.e. the fitting between
the empirical FC and simulated FC is optimal when the
system operates at the edge of an instability) [16]. For
simplicity, here four communication measures are extracted
from SC in order to predict FC without looking for the
instable point.
We have demonstrated that each communication measure
shows better capacity of predicting FC by means of
nonlinear polynomial fitting model than linear regression
model. A joint nonlinear multi-predictor model presents
stronger prediction across two databases among structurally
connected pairs, structurally unconnected pairs and all node
pairs. Nevertheless, the capacity of predicting inter-
hemispheric links is weak relatively which may restrict the
simulation of all node pairs accordingly. Making a thorough
research on inter-hemispheric connections seems to be vital.
Besides, we find there exists few structurally isolated
vertices while show functional correlations with other
vertices. The inaccuracy of DTI/DSI might lead to the
existence of these points. Evidence has documented that
there is an inherent limitation in determining long-range
anatomical projections by diffusion MRI tractography [17].
One of the great significances of the research on the
structure-function relation is offering help for health and
disease. Resting-state alterations have been found in
Alzheimer’s disease (AD), schizophrenia, dementia and
many other mental diseases which attract a mounting
number of studies in functional and anatomical brain
networks [18-20]. Our research probably help understand
these challenges and questions in human disease.
ACKNOWLEDGEMENT
This work was supported by the China Scholarship Council
(201306455001) and the National Natural Science
Foundation of P.R. China (Grant No. 61271407). We would
like to thank Olaf Sporns and Farras Abdelnour for sharing
the 66-ROI and 90-ROI SC and FC datasets, respectively.
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BIOGRAPHIES
Fuliang Wang received the bachelor's
degree from China University of Petroleum
(East China) in 2013. He is currently a
postgraduate with College of Information
and Communication Engineering, China
University of Petroleum (East China). His
research interests include neural networks
and pattern recognition.
Chen Xue received the bachelor's degree
from China University of Petroleum (East
China) in 2013. She is currently a Ph.D.
student with College of Control theory and
Control Engineering, China University of
Petroleum (East China). Her research
interests include neural networks and
neural mass model, neuroscience.
Yanjiang Wang received the M.S. degree
from Beijing University of Aeronautics and
Astronautics, Beijing, China, in 1989 and
the Ph.D. degree from Beijing Jiaotong
University, Beijing, China, in 2001. Now
he is a professor of the College of
Information and Control Engineering,
China University of Petroleum, Qingdao,
China. He is also the head of the Institute of Signal and
Information Processing, China University of Petroleum.
Currently, his research interests include bio-inspired pattern
recognition, cognitive memory modeling, and human brain
connectivity.

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