=Paper=
{{Paper
|id=Vol-2523/paper39
|storemode=property
|title=
Comparison of Male and Female Nonlinear Brain Functional Connectivity (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2523/paper39.pdf
|volume=Vol-2523
|authors=Egor Tirikov
|dblpUrl=https://dblp.org/rec/conf/rcdl/Tirikov19
}}
==
Comparison of Male and Female Nonlinear Brain Functional Connectivity (short paper)
==
https://ceur-ws.org/Vol-2523/paper39.pdf
Comparison of Male and Female Nonlinear Brain
Functional Connectivity
Egor Tirikov 1
1 Moscow State University, Moscow, Russia
em.tirikov@gmail.com
Abstract. In this paper, linear models, genetic programming and multilayer per-
ceptron were considered for studying the nonlinear functional connectivity of the
brain. The study of functional connectivity is important, since the results obtained
can later be used to study such diseases as Parkinsonβs or Alzheimer's disease.
The advantages and disadvantages of the considered methods were described, as
well as further research plans, where gender differences in fMRI data will be
explored. Also, preliminary results was provided, which demonstrate nonlinear
relationship between brain regions.
Keywords: resting-state fMRI, nonlinear functional connectivity, data intensive
analysis
1 Introduction
Today, in many fields of science it is necessary to process large amounts of semi-struc-
tured data. Neuroinformatics, which lies in the intersection of neurophysiology and in-
formatics, is a cross-disciplinary domain of science that studies methods and tools for
analyzing human brain activity and interaction. It is a well-known data-intensive do-
main of science. The amount of collected data in neuroinformatics is estimated at order
of petabytes [1]. Therefore, complexity of using conventional approach to analysis,
methods and processing tools is high and different specialized solutions have to be spe-
cifically designed for processing such large datasets. Furthermore, not only volume, but
also different types, forms and formats of datasets pose a problem. As an example,
electroencephalography (EEG), magnetic electroencephalography (MEG) and func-
tional magnetic resonance imaging (fMRI) are all different brain signal techniques used
to analyze brain activities [2].
There are three types of brain region interaction: functional connectivity, structural
connectivity and effective connectivity [3, 4]. The study of functional connectivity is
of great importance, as the obtained results are used to study Parkinson's disease [5],
attention-deficit/hyperactivity disorder [6], Alzheimerβs disease [7], etc. For example,
in [5] it is stated that advanced Parkinsonβs disease reduces functional connectivity be-
tween the brain regions. Knowing exactly what changes occur in the brain during Park-
inson's disease helps to better diagnose on early stages and apply appropriate treatment.
fMRI measures brain activity by detecting changes in blood flow. There are two types
Copyright Β© 2019 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
404
of fMRI: task-fMRI and resting-state fMRI [8]. Primarily, resting-state fMRI data is
used to analyze functional connectivity [9]. Resting-state fMRI is collected for patients
at rest; usually patient is asked to close his/her eyes and not to focus on anything spe-
cific.
There are two types of functional connectivity: linear and nonlinear. In most cases
researches study linear functional connectivity. Linear functional connectivity implies,
that target brain region depends from others linearly, i.e.
π¦π¦ = π€π€1 π₯π₯1 + β― + π€π€ππ π₯π₯ππ ,
where π¦π¦ is a value of target brain region, π₯π₯1 , β¦ , π₯π₯ππ are values of other brain regions.
Otherwise, it is non-linear. Though simple and useful in some studies [10, 11], linear
model does not always correspond correctly to measurements. In [12, 13] it is shown
that functional connectivity has nonlinear dependence between brain regions, showing
that the problem of studying nonlinear functional connectivity is of relevance.
It is known [14β16] that functional connectivity differs for men and women. These
articles are focused on linear functional connectivity, though important, it does not pro-
vide any details if more complex dependencies in the brain also differ for men and
women. It becomes possible to make a more subtle diagnosis for both of these two
groups, to diagnose diseases at earlier stages and to develop a more suitable treatment
if it is known that such difference exists and is meaningful.
This article is devoted to developing an approach of constructing nonlinear func-
tional connectivity in terms of analytical equations to study brain activity difference for
men and women. The article is structured as follows: section 2 introduces formalization
of the application domain. Section 3 overviews methods, which are used to compute
nonlinear functional connectivity and presents recommendations. Section 4 describes
workflow, libraries and touches some implementation issues. Section 5 concludes the
article.
2 Related Works
Available Datasets
There are multiple datasets in neuroinformatics, among them there are 1000 Functional
connectivity project (FCP) [17], Human connectome project (HCP) [1] and Human
Brain Project (HBP) [18].
The organizers of FCP collected 1200 data sets of resting-state fMRI from 33 inde-
pendent sources. For each dataset, information about age, sex of subjects and image
processing center is provided. There is a huge difference between age groups, number
of samples, frequencies and slices for these datasets.
HCP is a project that was launched in 2009. There are three directions in HCP Pro-
ject: HCP young adult 1200, HCP lifespan Studies and Connectomes Related to Disease
Studies. First project studies brain connectivity within healthy brain of young adult.
Second project studies difference in brain connectivity between different age groups.
Last project studies difference in brain connectivity between healthy and diseased brain.
405
The goal of the HCP project is to build a network map that is supposed to explain
the anatomical and functional connections inside the brain of a healthy person.
HBP project began in 2013 and is designed for 10 years. There are six research plat-
forms: Neuroinformatics, Brain Simulation, High Performance Analytics and Compu-
ting, Medical Informatics, Neuromorphic Computing and Neurorobotics. This is cur-
rently the largest project for brain research. The goal of this project is the development
of scientific infrastructure in neurophysiology, medicine and computer technology.
This project not only research human brain, but also rodentsβ brain and other species.
It also investigates ethical issues arising from the study of the brain.
HCP dataset includes not processed and preprocessed fMRI data [19]. Preprocessed
data is data with remove head movement and resizing of images. There are two types
of fMRI available: 3T fMRI and 7T fMRI [20].
Fig. 1. Difference between different types of fMRI
It is planned to use 3T fMRI, because there are more people images than for 7T fMRI
(1032 people vs 138 people). Four experiments were done for each person. Each ex-
periment lasted 14.4 minutes, timestep was 0.72 seconds. fMRI image is a 4D image
(spatial and time coordinates), which uses NIFTI format [21].
Methods for Searching Nonlinear Functional Connectivity
General linear models. General linear model (GLM) is a well-known procedure to
compute statistical linear models. It may be written as π¦π¦ = π€π€1 π₯π₯1 + β― + π€π€ππ π₯π₯ππ .
It is one of the most popular method in neurophysiology [10, 11, 22, 23]. Its popu-
larity is explained by the fact that the method has low computational complexity. It can
be seen that assumption, that variables are linearly dependent is made. It should be
noted, that GLM can be used for constructing nonlinear relationship with some modi-
fication. For this purpose, functions ππππ are defined, where ππππ is nonlinear combination
of input variables, so the resulting function is following:
π¦π¦ = π€π€1 ππ1 (π₯π₯1 , β¦ π₯π₯ππ ) + β― + π€π€ππ ππππ (π₯π₯1 , β¦ π₯π₯ππ ).
406
The disadvantage of this approach is that these functions need to be defined in ad-
vance. Since it is impossible to sort out all combinations of functions, it is likely to
overlook meaningful functions.
Genetic Programming. Genetic programming is a method that helps to restore non-
linear functional dependence. This method is based on the idea of biological evolution.
At the beginning there is a set of functions (usually, they are set randomly). Then the
iterative process begins, in which the functions are changed in any way and those hav-
ing best approximation are selected.
For convenience, the function is represented as a tree. For example, on Fig. 2 a func-
tion ππ(π₯π₯, π¦π¦) = (sin π₯π₯ + 3π¦π¦)cos (π₯π₯π₯π₯) is depicted.
Fig. 10. Example of function in tree structure view
At each operation (selection, mutation and crossover) are iteratively repeated. In
crossover operation two trees are taken, then random node in each tree for these func-
tions is swapped. Mutation operation differs from crossover in that there is only one
function involved. This operation consists on that a random node is selected and either
it changes itself or the entire subtree that corresponds to that node.
This method does not require any assumptions about the functional dependences in
advance; however, the complexity of genetic programming algorithm grows exponen-
tially with search space increase. It poses a problem, because fMRI data is a high di-
mensional data. Some researches [24] try to bypass this problem by combining deter-
ministic approach and genetic programming. They first built a simple model with a
large number of signs, and then selected a few best ones. On these selected traits, they
already apply the method of genetic programming. This approach has its advantages
and disadvantages. The authors conducted an experiment, where they applied a genetic
algorithm on the original features and on those already selected. It is shown that that
with the same number of iterations, the algorithm with the selected features produces
smaller error. The disadvantage of this approach is that by selecting signs, dependence
information between several regions is lost, since simpler model can consider them not
important. Other approach is to decrease search space with PCA/ICA [14].
Multilayer Perceptron. Another method for computing analytical form of functional
connectivity is multilayer perceptron (MLP). MLP is a class of feedforward networks,
consisting of at least three layers: input, hidden and output. Fig. 3 depicts a simple
407
example of MLP. In analytical form it is π¦π¦ = 4ππ(βπ₯π₯1 + 3π₯π₯2 ) β 2ππ(2π₯π₯2 + π₯π₯3 ). Func-
tion ππ called activation functions. The activation function is commonly used:
1. RELU (rectified linear unit) function: π¦π¦ = max(0, π₯π₯);
2. Identity function: π¦π¦ = π₯π₯;
1
3. Logistic function: π¦π¦ = ;
1+ππ βπ₯π₯
ππ π₯π₯ βππ βπ₯π₯
4. Tanh function: π¦π¦ = .
ππ π₯π₯ +ππ βπ₯π₯
Fig. 3. Example of multilayer perceptron
This model allows moving away from assumptions about the form of functional de-
pendence. The disadvantage is that this model requires much more computing time than
simpler models. Another disadvantage is that if the constructed model is large enough,
the analytical form is difficult to read and analyze.
Functional Connectivity Difference for Men and Women
In [14] the approach for computing functional linear connectivity is presented, though
it does not provide more complex relations, which are of great interest. In this article
[15], the authors caused negative emotions in men and women with the help of the
olfactory system. All subjects were divided by gender. Using statistical tests, it was
found that the activation of neurons in men and women is different. In another article
[16], the authors also studied gender differences in fMRI, but at rest. Statistical tests
were also used, and differences were found in some areas of the brain. The disadvantage
of these two works is that here only a difference between some regions of the brain was
found, but the reasons for these changes were not shown. The aim of this work is to
search for nonlinear functional connections between brain regions in analytical form.
If it can be getting an analytical form of relations between regions of the brain, then in
the future it can be use various mathematical methods in order to understand exactly
how one region depends on others.
408
3 Implementation
Workflow
Workflow is depicted on Fig. 4. First, using HCP preprocessed resting fMRI dataset,
regions of interest are extracted. Most popular method for getting information about
brain regions (often brain regions name regions of interest (ROI)) is atlas (atlases define
mapping of voxels to brain regions). Recently, it also became possible to use machine
learning methods to extract ROI time series [25]. This task is performed using atlases
from NiLearn [26] and NiPy [27] Python packages.
Fig. 11. Workflow
For each region of interest following procedure is applied: 1) data is split into train
and test datasets for men and women; 2). set of equation is constructed using some
algorithm and is validated on test data. As each region of interest is processed inde-
pendently, each procedure is packaged into PySpark [28] job.
After that, equations are concatenated together. Statistical testing is invoked later to
produce gender connectivity matrix, as in [14].
Preliminary Results
This section provides a comparison of the three models described above. Computa-
tional part was executed on machine with two Intel Xeon e5-2670 v2, 96 gigabytes of
RAM and three GPUs Nvidia Titan X Pascal with 36Gb of video RAM total.
The R2 score metric was used for model quality assessment. The results are depicted
on Fig. 5.
L1 regularization is used in the construction of linear regression to reduce number
of dependent regions.
During the execution of genetic programming, an additional feature which comes
from the linear model is used. Unless it is used, the results are worse than linear regres-
sion. This could be due to the fact that there are too many free variables and not enough
iterations to find global optimum. Genetic programming gave better results than linear
regression. The multilayer perceptron gives the worst result, so additional heuristics are
needed to improve its performance.
409
Fig. 4. Model Comparison
Following formulas are obtained.
Linear regression:
π₯π₯0 = 0.05π₯π₯2 + 0.43π₯π₯3 + 0.008π₯π₯4 β 0.003π₯π₯6 β 0.05π₯π₯7 β 0.01π₯π₯9 + 0.2π₯π₯11 β
0.05π₯π₯12 + 0.05π₯π₯20 β 0.04π₯π₯23 + 0.04π₯π₯25 + 0.09π₯π₯27 + 0.12π₯π₯29 + 0.03π₯π₯30 +
0.07π₯π₯31 + 0.04π₯π₯32 β 0.03π₯π₯34 + 0.09π₯π₯40 β 0.01π₯π₯32 β 0.005π₯π₯20
2
+ 0.02π₯π₯3 π₯π₯6 ;
Multilayer perceptron:
β1 = β0.005π₯π₯1 + 0.005π₯π₯2 + 0.29π₯π₯3 β 0.02π₯π₯4 β 0.02π₯π₯5 β 0.0008π₯π₯6 β
0.006π₯π₯7 + 0.02π₯π₯8 β 0.02 β 0.02 β 0.006π₯π₯11 β 0.02π₯π₯12 + 0.02π₯π₯13 + 0.003π₯π₯14 β
0.02π₯π₯15 + 0.007π₯π₯16 + 0.07π₯π₯17 β 0.01π₯π₯18 + 0.002π₯π₯19 β 0.02π₯π₯20 + 0.015π₯π₯21 β
0.04π₯π₯22 + 0.03π₯π₯23 β 0.02π₯π₯24 + 0.01π₯π₯25 β 0.03π₯π₯26 + 0.04π₯π₯27 β 0.007π₯π₯28 +
0.01π₯π₯29 β 0.01π₯π₯30 + 0.03π₯π₯31 β 0.007π₯π₯32 β 0.04π₯π₯33 β 0.06π₯π₯34 + 0.03π₯π₯35 +
0.007π₯π₯36 + 0.05π₯π₯37 + 0.02π₯π₯38 + 0.05π₯π₯39 β 0.006π₯π₯40 + 0.04π₯π₯41 β 0.005π₯π₯42 β
0.02π₯π₯43 + 0.002π₯π₯44 + 0.03π₯π₯45 β 0.002π₯π₯46 + 0.05π₯π₯47 ;
β2 = 0.003π₯π₯1 β 0.05π₯π₯2 + 0.03π₯π₯3 β 0.1π₯π₯4 + 0.06π₯π₯5 β 0.13π₯π₯6 β 0.03π₯π₯7 β
0.06π₯π₯8 + 0.007π₯π₯9 β 0.03π₯π₯10 β 0.06π₯π₯11 β 0.02π₯π₯12 + 0.01π₯π₯13 + 0.21π₯π₯14 β
0.004π₯π₯15 β 0.09π₯π₯16 + 0.06π₯π₯17 + 0.31π₯π₯18 + 0.02π₯π₯19 + 0.01π₯π₯20 β 0.002π₯π₯21 +
0.13π₯π₯22 β 0.04π₯π₯23 + 0.07π₯π₯24 + 0.01π₯π₯25 + 0.02π₯π₯26 β 0.01π₯π₯27 β 0.2π₯π₯28 β
0.002π₯π₯29 + 0.004π₯π₯30 + 0.009π₯π₯31 + 0.001π₯π₯32 β 0.09π₯π₯33 + 0.01π₯π₯34 β 0.01π₯π₯35 β
0.02π₯π₯36 β 0.18π₯π₯37 + 0.02π₯π₯38 β 0.05π₯π₯39 + 0.07π₯π₯40 + 0.04π₯π₯41 + 0.02π₯π₯42 +
0.008π₯π₯43 β 0.03π₯π₯44 β 0.01π₯π₯45 + 0.09π₯π₯46 β 0.06π₯π₯47 ;
1 1
π₯π₯0 = 0.1218 β 0.2706 .
1+ππ ββ1 1+ππ ββ2
2
Genetic programming: π₯π₯0 = π₯π₯13 π₯π₯14 π₯π₯25 π₯π₯9 + π¦π¦1 , where π¦π¦1 is the same function as
function for linear regression.
410
It can be seen that genetic programming algorithm produces the most readable form
of result.
4 Conclusion
The research is done as thesis for Masterβs Program βBig data: infrastructures and prob-
lem-solving techniquesβ in the department of Computational Mathematics and Cyber-
netics of Moscow State University. Several methods are studied to find the nonlinear
functional connectivity between regions of the human brain. Though genetic program-
ming does not perform well in high dimensional space and needs proper features, it
shows best results compared to linear regression and multilayer perceptron.
As future work, it is planned to 1) build analytical functions separately for men and
women; 2) improve the results for multilayer perceptron, so that it can be used for ob-
taining analytical formulas; 3) test hypotheses for functional connectivity difference for
men and women.
Acknowledgements
This work is supervised by Dmitry Kovalev, Federal Research Center βInformatics and
Controlβ of Russian Academy of Sciences.
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