Diffuse and Localized Functional Dysconnectivity in Schizophrenia

# Diffuse and Localized Functional Dysconnectivity in Schizophrenia: a
Bootstrapped Top-Down Approach

Davide Coluzzi
Dipartimento di Elettronica  Informazione e Bioingegneria
Politecnico di Milano
<EMAIL_ADDRESS>Giuseppe Baselli
Dipartimento di Elettronica  Informazione e Bioingegneria
Politecnico di Milano
<EMAIL_ADDRESS>Dipartimento di Elettronica, Informazione e
Bioingegneria, Politecnico di Milano

###### Abstract

Schizophrenia is a brain disorder leading to detached mind’s normally
integrated processes. Hence, the exploration of the symptoms in relation to
functional connectivity (FC) had great relevance in the field. Connectivity
can be investigated on different levels, going from global features to single
edges between pairs of regions, revealing diffuse and localized dysconnection
patterns. In this context, schizophrenia is characterized by a different
global integration with reduced connectivity in specific areas of the brain,
part of the Default Mode Network (DMN). However, the assessment of FC presents
various sources of uncertainty. This study proposes a multi-level approach for
more robust group-comparison.
FC data between 74 AAL brain areas of 15 healthy controls (HC) and 12 subjects
with chronic schizophrenia (SZ) were used. Multi-level analyses were carried
out by the previously published SPIDER-NET tool. Graph topological indexes
were evaluated to assess global abnormalities. Robustness was augmented by
bootstrapped (BOOT) data and the stability was evaluated by removing one
(RST1) or two subjects (RST2). The DMN subgraph was extracted and specifically
evaluated. Changes relevant to the overall local indexes were also analyzed.
Finally, the connection weights were explored to enhance common strongest
activations/deactivations.
At a global level, expected trends of the indexes were found and the
significance of modularity ($p=0.043$) was not confirmed by BOOT ($p=0.133$).
The robustness assessment tests (both RST1 and RST2) highlighted more stable
results for BOOT compared to the direct data testing. Conversely, significant
results were found in the analysis at lower levels. The DMN highlighted
reduced connectivity and strength as well as increased deactivation in the SZ
group. At local level, 13 areas were found to be significantly different
($p<0.05$) in the groups, highlighting a greater divergence in the frontal
lobe. These results were confirmed analyzing the single negative edges,
suggesting inverted connectivity between prefronto-temporal areas.
In conclusion, multi-level analysis supported by BOOT is highly recommended
when analyzing FC, especially when diffuse and localized dysconnections must
be investigated in limited samples.

##  1 Introduction

The brain is the most tangled network known in nature. Indeed, it comprises
billions of neurons which form trillions of synapses between each other.
Conversely, at a macroscale extent, brain regions can be thought as connected
through fiber bundles, mirroring the anatomical structure, or functional
activations of the areas, in resting-state or during a task. All this
collective activity makes behaviour, thought, memory and consciousness
possible. In this context, clinical disorders are characterized by alterations
of the connections’ paths. For this reason, it is paramount to explore these
abnormalities to enforce our understanding of the brain in health and disease.
Considering the methods used to investigate brain networks, Magnetic Resonance
Imaging (MRI) is the dominant technique for macroscale analysis mainly because
of its safety, spatial resolution and availability. On one hand, Diffusion
Tensor Imaging (DTI) or other methods allow to visualize and examine the
organization of structural connectivity by white matter (WM) tracts. On the
other hand, functional MRI (fMRI) inspects the dynamics of activity in each
gray matter (GM) area. The functional activations of the GM areas are based on
the Blood Oxygen Level Dependent (BOLD) response.
Through these methodologies it is possible to obtain connectivity matrices,
which can be investigated in their organization and function. Thus, a matrix
(graph) can be defined as a collection of nodes (brain regions) and edges
(anatomical or functional connections) between pairs of nodes [1]. The nodes
are obtained by mapping the parcels of the network according to well-known
brain atlases defined from the structural or functional point of view [2, 3].
Accordingly, the edges represent the links detected between the regions
describing the weights of the connections. Indeed, the strength of each
connection is weighted according to the addressed connectivity measure such as
the number of fibers in the structural case, or the Pearson’s correlation in
the functional case.
The comprehension of these networks is a complex field of research named
connectomics, which can potentially address the brain at all its scales,
levels and features [4]. Focusing on the macro-scale of brain GM areas, it is
first possible to analyze and compare different networks through the
investigation of their graph-based global (top level) topological features
such as node degree, node strength, clustering coefficient, efficiency, path
length or modularity [1, 5].
Second, the brain is also known to be divided into interacting specialized
sub-networks, devoted to specific domains of behavior and cognition [6].
Extracting sub-networks is an increasingly common practice in explorative
studies to easily interpret the brain connectivity data in physiological and
pathological conditions. [6, 7, 8, 9, 10]. In this regard, we presented in a
previous study a novel software tool allowing the interactive and flexible
analysis of anatomical/functional networks and sub-networks called SPIDER-NET
[11].
Third, the above-mentioned graph indexes can also be computed at local level
providing information regarding the configuration of the single nodes.
Valuable information is extracted about hubs of the networks and regions
associated to specific disruptions, such as lesions [11, 12].
These three levels of analysis (network, sub-network and node-level) together
with the analysis of the single edges resulted helpful in the study of many
pathological conditions. Indeed, global changes of relevant properties,
different sub-network configurations, disrupted node connectivity and missing
relevant connections were already found in stroke, Alzheimer’s disease and
other pathologies [13, 14]. However, the integration and the interpretation of
the results extracted at all three levels is still difficult. The parallel
multi-level analysis can be particularly helpful in case of pathologies, such
as the schizophrenia which the localized/diffuse origin is unknown yet [15].
Schizophrenia may be characterized as a disorder of brain connectivity since
it leads to detached mind’s processes. The main symptoms of the pathology such
as reduced cognitive and emotional deficits acknowledge this breakdown [15].
More specifically, the clinical manifestations of the disorder can be
hallucinations, disorganized thinking and agitation, social isolation,
emotional flattening, anhedonia and apathy. Often, these manifestations may be
preceded by a series of prodromal symptoms, such as inability to perform one’s
job or neglect of personal hygiene.
Many studies [16, 17] explored the connections between these symptoms and
functional associations. Specifically, connectivity deficits were found on all
abovementioned levels [15]. First, a global connectivity reduction was
discovered in different studies [17, 18, 19]. Second, at interconnected sub-
network level, fronto-temporal and occipito-temporal dysconnections were found
through the use of the network-based statistics [7]. Third, amongst all brain
regions, the prefrontal cortex resulted to be one of the most affected nodes
[16, 18, 19]. More generally, Liu and colleagues found a significant
alteration of the pattern of small-world topological properties in many brain
regions of the prefrontal, parietal and temporal lobes. Four, Skudlarski and
colleagues analyzed single connectivity edges, finding differences in the
connectivity pattern originating from posterior cingulate cortex within the
Default Mode Network (DMN) suggesting to have the most affected connections by
the functional reorganization of the schizophrenia [20].
DMN is reasonably important in the context of schizophrenia since it is deeply
involved in social behavior, control of the emotional state of the individual
[21, 22], which characterize altered integrated processes by the pathology.
From different studies it resulted that connections within this circuit were
different than healthy controls, being related to emotion control and memory
[21, 23]. However, the observations for the DMN remained controversial, since
the average connectivity of the patients showed higher or lower values than
healthy controls according to the dynamic mental state and the individual
connections were subject to reorganization [20].
Indeed, although the analysis of changes in functional connectivity is a
powerful tool to analyze brain organization, due to the limitations of the
fMRI techniques, the statistical investigation of brain connectivity datasets
is often subject to uncertainty. Indeed, stationarity is often assumed in the
interpretation of the results coming from this technique. However, considering
the known dynamic and condition-dependent nature of brain activity, it is
obvious that the functional connectivity metrics such as the Pearson
correlation coefficient will change over time [24, 25, 26]. This variability
allows to define the paradigm of dynamic functional connectivity analysis,
which cannot be ignored, since it also varies within the same subject and even
between time windows within the same session. In this context, the evaluation
of functional static connectivity is subjected to uncertainty. In addition,
functional connectivity acquisitions are characterized by low signal-to-noise
ratio (SNR) and non-neural noise related to cardiac and respiratory processes
and hardware instability. Finally, other definition issues such as the window
length and other confounds remain controversial [27, 28, 29, 30].
Among all statistical methodologies, bootstrapping was already used in some
imaging problems, such as in the work conducted by Lazar and Alexander [31],
since it allows to robustly estimate the statistical features of a population
from a limited number of measurement samples, without any assumptions about
the distribution assumed by the initial data. This approach also represents an
alternative to traditional hypothesis testing, since it does not require to
have a test statistic satisfying certain assumptions largely dependent on the
experimental design and to know the properties of the data. As a result, the
main advantage of the method is that the uncertainty variability of the
estimator can be quantified, characterizing the dispersion and other errors in
the null hypothesis [32, 33]. Considering the number of bootstrap samples
used, the resulting statistics represent a random sample with replacements
from the initial distribution characterize by a smaller size. It is worth
remarking that obtaining thousands of bootstrap observations from the initial
data is not the same as collecting new data. Indeed, the approach is based on
an ensemble of simulated data (surrogates) and the usefulness of bootstrapping
is related to the quantification of statistical quantities such as the
standard error, a possible bias and a confidence interval of particular sample
of data.
In the context of investigating graph-structured data, the quantification of
the uncertainty intrinsic to the data is essential for their scientific
usefulness. In the recent probabilistic study conducted by Green and Shalizi
[34] the bootstrap was applied on simulated random graphs. It was seen that
the resampling of the synthetic data was able to approximate the distributions
of motif densities, such as, the number of times fixed subgraph appear in the
random network. In this work, the bootstrap was also applied to quantify the
uncertainty of the network metrics. Another example is given by the study
conducted by Gel and colleagues, where bootstrap was applied for the
quantification of uncertainty in graph degree distributions of collaboration
networks, where for example articles are represented as nodes and cross-
references as edges [33]. Indeed, when applying the bootstrap over a
distribution of data, the expected result is a better definition of the
variability centered with respect to the initial mean of the same distribution
at the increasing of the number of resampled data [35]. However, a limitation
of this approach is related to computational costs since the bootstrapping
methods are based on multiple resampling of the original dataset that can be
computationally expensive, especially for large datasets.
However, the bootstrapping approach was only partially applied in brain
connectivity studies. For example, in the study conducted by Wei and
colleagues this approach was used to perform connectivity matrix feature
selection in a regression task cognitive traits prediction [36]. Spearman
correlation analysis was indeed performed between connectivity and cognitive
measures in each resample subset to extract a feature vector. In a previous
study [37], the results from mean functional connectivity of Parkinson’s
disease patients were qualitatively analyzed through bootstrap.
To the best of our knowledge, there is significant potential for effectively
and more quantitatively applying bootstrap techniques on connectivity data,
although fundamental issues still need to be addressed. Indeed, connectivity
measurements are well-known to be affected by different sources of noise,
which can have a strong impact especially with limited population size. Also,
the static evaluation of functional connectivity is limited with respect to
dynamic functional connectivity [24, 28]. In this sense, it is crucial to
evaluate the robustness and the stability of potential biomarkers of brain
connectivity to improve their usability and understanding. Moreover, there is
the need to evaluate abnormalities on multiple levels, especially in
conditions characterized by both localized and diffuse degeneration, such as
schizophrenia.
Hence, the main aim of this study was the robust assessment of connectivity
indexes on different levels through the bootstrap procedure to ensure a
reliable detection of abnormalities in schizophrenia. To investigate both
diffuse and localized alterations, a top-down analysis of: i) global
connectivity deficits, ii) sub-network disruptions, extracting the DMN, iii)
dysconnectivity in individual regions and its inter-subject variability, and
iv) abnormalities in positive/negative connections resulting in
activation/deactivation circuits or communities is proposed. The methodology
was developed in the context of the SPIDER-NET tool [11] to allow automatic
multi-level investigations in group studies. Afterwards, the stability of
results is assessed by comparing bootstrapping to direct testing via a leave-
n-subject-out approach to evaluate the impact of sources of uncertainty in
functional connectivity. The whole pipeline of multi-level analysis was
validated on a dataset acquired from healthy and schizophrenic subjects
highlighting several abnormalities at the examined levels.

##  2 Methods

###  2.1 Data Acquisition and Study Population

Data used in this study were collected in the context of the work conducted by
Zalesky and colleagues [7]. Regarding the written informed consent and ethical
approval, reference is made to the original work. The anonymized connectivity
dataset is publicly available at https://nitrc.org/projects/nbs/. The dataset
is composed by 15 healthy controls - HC (mean age 33.3 years, $\sigma$ = 9.2
years, 14 males) and 12 subjects with chronic schizophrenia - SZ (mean age
32.8 years, $\sigma$ = 9.2 years, 10 males). The patients were diagnosed
according to standard operational criteria in the Diagnostic and Statistical
Manual of Mental Disorders IV (American Psychiatric Association, 2000). The
matching of the two populations was done according to age, pre-onset IQ and
years of education. SZ subjects did not receive medication on the day of
acquisition to reduce acute drug effects on the data. T2*-weighted echo-planar
images depicting blood oxygenation level dependent contrast were acquired
through a 1.5 Tesla scanner (GE Signa, General Electric, Milwaukee, WI). As
regards the matrix construction: the nodes were defined according to a subset
of areas of the AAL atlas, whereas the edges were obtained computing the
correlation between times series which were previously preprocessed. More
specifically, scale 3 of the wavelet transform ($0.03<f<0.06$ Hz) was
considered and the filtered time series were corrected for fluctuations of
signals through linear regression against reference time courses extracted
from seed regions. Some AAL nodes were excluded since it was not possible to
correctly estimate the node-averaged time series, due to poor coverage in some
subjects. The resulting connectivity matrices for each subject have dimensions
74 × 74. More details on ethical approval, imaging parameters and processing
are reported in the cited work [7].
Generally, after composing the matrix, a threshold is defined to emphasize its
topological features by removing spurious associations. Among all methods,
absolute and density thresholding are the most common in connectivity studies
[5, 38]. In this case, we decided to not threshold the matrices since it
introduces a confound on properties of the graphs in the context of a group
study. On one hand, different levels of sparsity can be obtained by applying
the same threshold to all matrices. In this case, it is thus not possible to
rule out systematic density variations as the main reason of group
abnormalities of graph-based metrics. On the other hand, matrices can be
matched according to sparsity using density thresholding, hence selecting a
distinct threshold value. In this case, whether the weight distribution in SZ
is reduced, the application of density thresholding can strongly affect
weighted indexes results [19, 39]. Furthermore, no thresholding allowed to
work on all raw connectivity measures, avoiding the loss of information of the
original data and assessing the results of the bootstrap methodology in
relation to all sources of uncertainty. On one hand, all weakest and thus
possible spurious connections were maintained to account them in the robust
evaluation of the indexes through bootstrapping. On the other hand, the
density differences are only given by the deletion of the negative
connections, also allowing the investigation of binary topological indexes.
Hence, two versions of same matrix were obtained to analyze separately
positive/negative edges and, thus, activations and deactivations.

###  2.2 Top-Down Bootstrapping Approach for Group Comparison

Figure 1: Pipeline of the top-down approach proposed. The functional
connectivity matrices of the two populations were analyzed from the global
level, extracting the DMN as sub-network of interest and investigating the
distributions of the local indexes to the edge level, assessing correlations
and anticorrelations.

The top-down bootstrapping approach to enable the HC vs SZ group comparison
consists of different steps of analysis, done on different levels. The
analysis pipeline was built starting from the top level, related to the global
characteristics of the matrices coming from the two populations, until the
bottom level, related to the single connections. The procedure is summarized
in Figure 1.
First, the global topological indexes were obtained to evaluate the
abnormalities in the network topology and global deficits. In order to enable
a robust investigation, the values of these properties were bootstrapped, as
reported in Section 2.2.1. Second, bootstrapping was also applied on the
extracted sub-network of interest (DMN) and local indexes to visualize
significant changes between groups and different subjects of the same groups
(see Section 2.2.2). Finally, the negative connections of the group mean
matrixes were analyzed in Section 2.2.3. In this section, the analysis of the
communities was performed to enhance common deactivations. Afterwards, a
qualitative investigation of strongest and most frequent negative connections
reflecting anticorrelations was performed.
The group comparison functions required by the present study were implemented
as upgrade of our previously developed SPIDER-NET tool, freely available to
researchers [11] The current upgrades will be included in a new release.

####  2.2.1 Global Connectivity

The global topological indexes from the graph theory which were considered are
reported in the Figure 2.

Figure 2: Table of all graph properties considered, divided according to the
level of analysis. The segregation and integration properties can be globally
assessed through the average of all local values. The mathematical expressions
reported indicate global case formulation.

The indexes are divided according to integration/segregation indexes (e.g.
path length, clustering coefficient), mesoscale analysis (e.g. modularity,
rich-club coefficient) and related to whole network structure organization
(e.g. small-worldness).
The degree/strength represent the sum of edges/weights connected to the node.
The clustering coefficient quantifies local edge density by counting the
triangles average. A triangle occurs if a neighbor of the node is also a
neighbor of another neighbor of the node. In the weighted case, the number of
triangles is replaced with the geometric mean of its weights. The
characteristic path length is a measure of integration which expresses the
average shortest path between node pairs. The global efficiency is the average
inverse of the characteristic path length, and it represents how efficiently
the information travels through the network. All the segregation and
integration metrics can be local and global, simply by averaging the values
across all nodes. Mesoscale analysis reveals how much the network present a
particular structure. Specifically, the modularity computed through Newman’s
approach [40] quantifies to what extent the intra-/inter-community link
densities are anomalous in comparison to chance. Large values typically reveal
significant community structures. Maximized coreness statistic is a measure of
how much the network follows the core/periphery paradigm, which is a partition
of the network into two groups, where the number and weight of the edges is
maximized in the core and minimized within the periphery.
The density is a measure of sparsity of the network. It is the ratio between
the number of actual connections and the maximum number of possible
connections. A small-world network is a structure in which most nodes are not
neighbors of one another. Conversely, the neighbors of any given node are
likely to be neighbors of each other, resulting in an easy access by most
nodes to every other node with a small number of steps. Small-world networks
associate short path length and high clustering coefficient.

##### Statistical Tests and Robustness Assessment

Mann–Whitney tests (MW) were performed to assess statistically significant
differences in the global indexes between the two groups. Because of the
dimensions of the sample (#HC = 15; #SZ = 12), the intrinsic uncertainty given
by the non-stationarity of the data [24] and the possible presence of spurious
connections due to the limitations in the fMRI processing [28], which can
significantly affect the results, the reliability of significant group
differences was also tested. First, bootstrap hypothesis testing (BOOT) was
performed on all global indexes and compared to MW testing. BOOT allows for a
better estimation of the null distribution of network measures, providing
confidence intervals to evaluate the uncertainty of the statistics and more
robust abnormalities detection [41]. The procedure to test bootstrap
hypothesis was the following: The procedure to test bootstrap hypothesis was
the following:

  1. 1.

Calculation of the test statistic $\hat{\theta}=|\tilde{x}-\tilde{y}|$, given
$x_{1},\ldots,x_{N}$ a random sample from distribution $F$ with median
$\tilde{x}$ and $y_{1},\ldots,y_{N}$ another independent random sample from
distribution $G$ with median $\tilde{y}$.

  2. 2.

Bootstrapping: extraction of $B$ sets of random samples $x^{*}$ (size $N$) and
$y^{*}$ (size $M$) with replacement from $x$ and $y$, respectively.

  3. 3.

Calculation of the test statistic
$\hat{\theta}^{*}_{b}=|\tilde{x}^{*}_{b}-\tilde{y}^{*}_{b}|$ for each
resample.

  4. 4.

These $B$ resampled test statistics are then made into a null distribution by
$\hat{\theta}^{\prime}_{b}=\hat{\theta}^{*}_{b}-\hat{\theta}$.

  5. 5.

Estimate of the p-value as

$p=\frac{\sum_{b=1}^{B}\left[C\left(\hat{\theta}_{b}^{\prime}\geq\hat{\theta}\right)+1\right]}{B+1}$

where $C\\{condition\\}=1$ when the condition is true and $0$ otherwise.

F and G represent the distributions of a global index in HC and SZ, thus N and
M representing the number of HC and SZ, 15 and 12 respectively. The resampling
from these two sets is carried out 5000 ($B$ \- number of resamples) times for
all bootstrap hypothesis tests and the test statistic is the difference in
medians [42].
Second, the robustness of the measures was assessed through a leave-n-subject-
out approach, with $n$ equal to 1 and 2. The variations of the statistics
computed through both methods were analyzed changing the population samples
according to the two procedures.
The first one, hereafter referred as RST1, evaluates the variation of the
p-values obtained removing all subjects one at a time from the populations
values to perform MW tests and to create new resamples for BOOT. The second
one, hereafter referred as RST2, evaluates the variation of the p-values
obtained randomly removing pairs of subjects from the populations values to
perform both tests. In this case, 350 random extractions of pairs of subjects
were performed. The total possible pairs which can be extracted are
$27*26=702$, thus we decided to run the test for about 50% of the
possibilities. RST2 is summarized in Figure 3.
Then, mean and standard deviation across all tests were evaluated for both
procedures.

Figure 3: Schema representing the robustness statistical test randomly
removing two subjects (black squares) at each iteration (RST2). In this case,
$N$ is equal to 350.

####  2.2.2 Local Topological Properties and Sub-Network Extraction

Afterwards, local topological properties related to the specific nodes of the
network across all subjects in the two groups were analyzed. These indexes are
the local counterpart of the global ones, as reported in the Section 2.2.1 and
Figure 2. In this regard, we obtained the distributions of these values
assessing differences in the local structure and in the variability across the
two groups. Specifically, we focused on degree and strength. The former helps
to represent the influence of negative connections, being the original
matrixes complete and divided by using a threshold in 0. The latter instead
identifies node or set of nodes whose weighted values differ in the two
populations. In this case, we performed MW and BOOT, as reported in the
previous section 2.2.1, on the local index values. The resampling was
performed with 5000 samples for all BOOT tests. Furthermore, these differences
were investigated across the nodes of the different lobes and the nodes
within/outside the DMN to obtain the most deviating local values between the
two groups. The distributions per areas and the inter-subject variability,
which can be related to the different intra-group characteristics, were
highlighted.
In order to perform these analyses, we divided the nodes according to the
lobes and we extracted the DMN from all matrices of both groups. Specifically,
we defined the DMN according to previous studies highlighting the regions
characterizing the network [43, 44, 45, 46, 47]. Generally, the brain regions
found to be activated within the DMN comprise the medial frontal cortex, the
medial temporal lobe, the posterior cingulate cortex, the ventral precuneus
and the inferior parietal cortical regions. Apart from these typical core
areas, lateral temporal cortex, hippocampal formation and amygdala are also
often reported as parts of the network [44, 46] Thus, from the typical
Broadmann areas comprising the DMN (BA: 9, 10m, 10r, 10p, 23/31, 24, 29/30,
32a, 32c, 39, 49) and these additional regions, a list of 13 AAL parcels from
the left hemisphere and 12 AAL parcels from the right hemisphere was obtained.
The parcel which is present only in the left hemisphere is the amygdala since
the right counterpart was not present in the data, due to the previously
described issue of poor coverage in some subjects (see Section 2.1) [7]. The
sub-networks were then composed of these nodes and the edges existing between
pairs of DMN areas (“Extract” mode in SPIDER-NET), maintaining the intra-lobe
connections.

####  2.2.3 Connection-Level Investigation

The examination of the single connections was performed computing the mean
matrix of the groups which were compared to visualize differences in weights
and deactivation. Thus, the average networks composed by all negative
contributions were obtained. Then, community detection analysis through the
Newman’s method [40] implemented in the Brain Connectivity Toolbox [48] and
embedded into SPIDER-NET [11] was performed. The resulting negative sub-
networks were obtained and analyzed. In addition, connectograms were drawn
considering the entire network with no thresholding apart the separation of
positive and negative edges. The rationale was to analyze graphs formed by all
brain regions and edges, or all the DMN areas and edges. Thresholding was
applied only for graphical purposes in some connectogram figures where density
obscured the main connections, as highlighted in the captions.

##  3 Results

First, the global topological properties were assessed. Table 1 summarizes the
results obtained from the comparison between HC and SZ of the overall indexes
using nonparametric test and bootstrap hypothesis testing. The results from
the robustness tests are also summarized in Table 1.
It is possible to notice that HC presented increased values for all
segregation indexes and efficiency. Conversely, concerning the characteristic
path length, mesoscale analysis, and small-worldness SZ resulted to have
higher values. Differences are then enhanced in the comparison between MW and
BOOT. In particular, higher p-values in BOOT are found for the weighted
characteristic path length and modularity indexes. Specifically, the latter
highlighted a statistically significant ($p<0.05$) difference between HC and
SZ modularity that was not confirmed by using BOOT. The robustness assessment
highlighted more stable results for BOOT. Indeed, it is worth noting that the
mean of the p-values, considering all indexes and removing both one and two
subjects, remains closer with BOOT than the MW test in almost all indexes
considered. In few cases (binary and weighted clustering coefficient in RST1)
the difference between the mean of the robust assessment tests and initial
tests is slightly minor in MW or comparable. Furthermore, the variability was
assessed, resulting in lower standard deviation employing BOOT with respect to
MW in almost all indexes. In few cases (e.g. weighted characteristic path
length and modularity in RST2) this reduction is not enhanced with comparable
values. Second, DMN was extracted from all subjects of the two populations. In
Figure 4 the connectograms of this sub-network obtained averaging all positive
connections across the whole populations are shown. It is worth noting that
from a visual inspection a greater number of weak connections is highlighted
in the SZ group, represented by the yellow edges in Figure 4.

Table 1: Results of the statistical tests performed on global indexes.

Graph Index | Whole Comparison | RST1 (#Sub=1) | RST2 (#Sub=2)
---|---|---|---
|  HC data (mean$\pm$std) |  SZ data (mean$\pm$std) |  PMW |  PBOOT |  PMW (mean$\pm$std) |  PBOOT (mean$\pm$std) |  PMW (mean$\pm$std) |  PBOOT (mean$\pm$std)
Degree (Density) |  71.746$\pm$2.178 |  69.207$\pm$5.149 |  0.130 |  0.086 |  0.146$\pm$0.05 |  0.089$\pm$0.044 |  0.162$\pm$0.079 |  0.103$\pm$0.063
Strength |  37.053$\pm$7.362 |  31.680$\pm$10.246 |  0.124 |  0.079 |  0.143$\pm$0.047 |  0.096$\pm$0.029 |  0.155$\pm$0.071 |  0.108$\pm$0.045
Bin CC |  0.986$\pm$0.025 |  0.960$\pm$0.057 |  0.150 |  0.124 |  0.150$\pm$0.052 |  0.130$\pm$0.038 |  0.184$\pm$0.089 |  0.138$\pm$0.057
Wei CC |  0.489$\pm$0.105 |  0.415$\pm$0.144 |  0.150 |  0.105 |  0.155$\pm$0.052 |  0.119$\pm$0.027 |  0.183$\pm$0.082 |  0.128$\pm$0.050
Bin CPL |  1.017$\pm$0.030 |  1.052$\pm$0.071 |  0.130 |  0.084 |  0.153$\pm$0.052 |  0.089$\pm$0.044 |  0.162$\pm$0.079 |  0.102$\pm$0.063
Wei CPL |  2.216$\pm$0.610 |  2.618$\pm$0.892 |  0.124 |  0.129 |  0.151$\pm$0.061 |  0.150$\pm$0.054 |  0.155$\pm$0.072 |  0.159$\pm$0.072
Bin Eff |  0.991$\pm$0.015 |  0.974$\pm$0.035 |  0.130 |  0.086 |  0.150$\pm$0.052 |  0.089$\pm$0.044 |  0.162$\pm$0.079 |  0.102$\pm$0.063
Wei Eff |  0.525$\pm$0.085 |  0.466$\pm$0.113 |  0.113 |  0.078 |  0.147$\pm$0.051 |  0.099$\pm$0.023 |  0.143$\pm$0.065 |  0.111$\pm$0.041
Modularity |  0.004$\pm$0.009 |  0.016$\pm$0.026 |  0.043 |  0.133 |  0.053$\pm$0.018 |  0.128$\pm$0.019 |  0.059$\pm$0.030 |  0.144$\pm$0.036
Coreness |  0.018$\pm$0.022 |  0.037$\pm$0.036 |  0.164 |  0.122 |  0.141$\pm$0.060 |  0.122$\pm$0.039 |  0.199$\pm$0.091 |  0.138$\pm$0.061
Small-Worldness |  1.003$\pm$0.005 |  1.015$\pm$0.019 |  0.178 |  0.085 |  0.146$\pm$0.062 |  0.090$\pm$0.013 |  0.214$\pm$0.098 |  0.096$\pm$0.030

The global version of the degree represents the mean of all edges associated
to all nodes, whereas the density is the ratio between the number of present
edges and the number of possible edges in the network. For this reason, the
result coincides, and it is reported only once. HC: Healthy Controls; SZ:
Schizophrenic Patients; RST: Robust Statistical Test; MW: Mann Whitney Test;
BOOT: Bootstrap Hypothesis Test; #Sub: number of subjects removed; CC:
Clustering Coefficient; CPL: Characteristic Path Length; Eff: Efficiency.

Figure 4: Connectograms composed by only nodes of the DMN and positive
connections between pairs of these nodes.

Second, we analyzed the local values of the indexes in the DMN and across the
lobes, showing the distributions of the values of the degree across the same
group in Figure 5. Differences between DMN regions and the other areas in SZ
and HC, because of the different influence of the negative connections, were
highlighted. Specifically, the most variable indexes resulted to be located
within the DMN for the SZ group. On the other hand, they are more distributed
across all the brain regions in HC group, even resulting more variable in the
areas not included in the DMN. More precisely, one of the most variable values
of the degree in both groups was the one assumed by the amygdala, located at
the end of the first yellow box in Figure 5, representing the left hemisphere
nodes of the DMN.
Afterwards, the strength was analyzed, and the resulting distributions are
shown in Figure 6. First, it was noticed that the distributions of the SZ have
a slightly higher variability in the majority of the nodes with respect to HC.
More specifically, the most variable local indexes among their populations
were extracted from frontal, parietal lobes and subcortical structures. On the
other hand, general slightly higher values of strength are present in the HC
group. Furthermore, the distributions of the strengths are shown in Figure 6
highlighting statistically significant differences ($p<0.05$) found through
both MW and BOOT (in red). Most of the differences were found in regions of
the frontal lobe of both hemispheres. Significance of BOOT only (in pale
brown) resulted in the left orbital part of inferior frontal gyrus,
postcentral gyrus, Heschl’s gyrus, and right Rolandic operculum nodes.
Significance of MW only (in yellow) was found in the in right calcarine
fissure and the surrounding cortex node. The complete list of the significant
different node strengths is reported in the caption of Figure 6.

Figure 5: Distributions of the local degree values in the two populations
divided according to nodes of DMN in left and right hemisphere (yellow) or not
(gray). Figure 6: Distributions of the local strength values in the two
populations divided according to the lobes. The order and colors of the lobes
is the same as the connectograms (Figures 4 and 7) from the left to the right
hemisphere. Strength of nodes which are statistically significant different
($p<0.05$) between the two populations are shown in different colors according
to the different methods used: pale brown for bootstrap hypothesis testing,
yellow for Mann-Whitney and red for statistically significantly different
nodes found by both. More specifically, both methods identify differences in
the left Rolandic operculum, supplementary motor area, medial orbital superior
frontal gyrus, insula, anterior cingulate and paracingulate gyri, hippocampus,
Heschl’s gyrus and right supplementary motor area, bootstrap hypothesis
testing in left orbital part of the inferior frontal gyrus, postcentral gyrus,
right Rolandic operculum and right Heschl’s gyrus and Mann-Whitney test in the
right calcarine fissure and surrounding cortex.

Third, we analyzed the negative connections from the group average matrixes.
Results from community detection analysis are shown in Figure 7. Three
communities, a) b) and c) on top of the Figure, composed of 32, 22, 20 brain
regions respectively were identified for the negative SZ group. Four
communities, a) b) c) and d) on bottom, composed of 20, 15, 20 and 19 regions
respectively were identified for the negative HC group. A difference between
the formed communities is the inclusion of most frontal, limbic and temporal
regions in the community a) of SZ group, which is not observable in any HC
community. Furthermore, the configuration of parietal regions from both
hemispheres, mostly included in the community a) in HC, is not noticeable in
SZ, where these regions are divided according to hemisphere b) and c) of SZ,
also appearing to be clustered with the contralateral occipital lobe.

Figure 7: Connectograms of the communities detected in the negative average
group networks. On top, the three communities found in the SZ group
(modularity=0.079), whereas, on bottom, the four communities of HC group
(modularity=0.165). The edges are color-coded in red, orange, and yellow to
represent the strongest, middle, and weakest negative connections within the
community, respectively. No thresholding was applied.

Then we visualize the strongest and frequent negative edges in the whole brain
and in the DMN, as shown in Figure 8. Specifically, the connectograms formed
by the average of all matrixes composed by the negative edges in the whole
brain (7a and 7b) and in the DMN (7c and 7d) are shown applying a threshold to
keep 5% strongest negative edges. First, SZ average network resulted to have
more negative connections in the whole brain with respect to HC. Another great
difference noticed both in the number of preserved negative edges and in their
weights was in the inter-hemispheric connectivity of the frontal lobe, as well
as the parietal. In addition, it is possible to notice in SZ a greater number
of negative connections in the occipital lobe with respect to HC. The
configurations given by the only strongest connections in DMN highlighted
similarities and differences. Among all, connections between amygdala and some
frontal regions were in common, whereas strong edges between the parietal
lobes of the two hemispheres were found only in HC. In SZ parietal regions are
instead connected to amygdala and superior frontal gyrus. Finally, HC average
matrix revealed an important edge between the latter, but in the right
hemisphere, and the middle frontal gyrus, that was not found in SZ.

Figure 8: Connectograms of negative average group networks. a) and b) are the
results on the whole-brain, c) and d) on only the DMN of SZ and HC groups
respectively. 5% density thresholding is applied on the shown connectograms
for graphical clarity only.

##  4 Discussion

In this work, we proposed a multi-level approach for the case-control analysis
of connectivity data structured on different levels of investigation. In
particular, the assessment of the connectivity from global indexes to single
edges (brain activations/deactivations) was carried out on a population
characterized by chronic schizophrenia, thought to cause both diffused and
focalized dysconnectivity patterns. The multi-level analysis resulted to
potentially favor more robust results in contexts where the focus is not well-
known and statistical tests can be easily biased by uncertainty.
First, global-level results were analyzed. As previously mentioned, this level
was examined according to three main investigations. All experiments comprised
the evaluation of 11 graph-based indexes, either binary or weighted, which are
amongst the most widespread in connectivity studies [1, 49, 50, 51]. The first
analysis involved the comparison between HC and SZ groups, compared through
two statistical tests (MW vs BOOT). In Table 1 we showed the values of the
indexes along with the p-values obtained from both tests. The increased
segregation indexes and efficiency in HC with respect to SZ is in line to what
reported from previous studies [18, 16], as well as reduced path length,
mesoscale analysis and small-worldness. More specifically, MW highlighted one
statistically significant difference between the two population in the
modularity ($p\textsubscript{MW}=0.043$). The modularity resulted to be
significantly higher in SZ providing evidence that the deletion of negative
connections, in this case analyzed separately, tend to create families in SZ
that in HC are less visible. However, it is worth noting that similar studies
presented different results for this particular index and also uncertainty for
clustering coefficient and characteristic path length, indicating either
increased or reduced values in SZ [15, 16, 17, 52, 53, 54, 55, 56], probably
dependent on the thresholding method. For these reasons, as previously
mentioned, the reliability of these results was assessed through BOOT because
of the reduced size of the dataset, the presence of the uncertainty due to the
non-stationarity of the functional connectivity and the possible presence of
spurious connections. The results of the bootstrap hypothesis testing
highlights differences with respect to the standard nonparametric approach. On
one hand, the modularity did not present significant difference
($p\textsubscript{BOOT}=0.133$). On the other hand, a trend towards lower
p-values can be noticed for all other indexes, except the weighted path length
($p\textsubscript{MW}=0.124$; $p\textsubscript{BOOT}=0.129$) and the above-
mentioned modularity. One of the most replicated results is the significant
difference found in the efficiency between HC and SZ. According to different
studies, functional connectivity fluctuations appear to be coordinated
throughout the brain so as to realize global variations in network efficiency,
which could represent a balance between optimizing information processing and
minimizing metabolic expenditure [15, 57, 58]. Furthermore, examining studies
with a greater number of subjects [59], or of dynamic connectivity [57], the
results obtained through BOOT seem to be closer than MW. At this stage of
understanding, we may speculate that BOOT seems to provide an alternative
method to test more robustly the differences between functional connectivity
of two groups, especially when composed by low number of data and subjects.
However, we acknowledge that there is considerable debate among researchers as
to uncertainty influence and integration of dynamical functional connectivity
data. For this reason, we extended the analysis comparing MW and BOOT through
robustness assessment tests. In particular, the variability of the statistical
estimate was evaluated at the removal of one or two subjects from the whole
population, just as in leave-n-subject-out cross validation. In Table 1 the
results of these experiments are summarized, finding clear support for the
hypothesis of more stability and reliability of the BOOT results. In
particular, the index mean values obtained by BOOT across the random
extractions (27 for leave one out and 350 for leave two out) of subjects to be
removed remain much more stable with respect to the values obtained with
entire sample (e.g., degree - RST1: $p\textsubscript{MW=0.130}$;
$mean(p\textsubscript{MW})=0.146$; $p\textsubscript{BOOT}=0.086$;
$mean(p\textsubscript{BOOT})=0.089$; RST2: $mean(p\textsubscript{MW})=0.162$;
$mean(p\textsubscript{BOOT})=0.103$). Also, the standard deviation across all
iterations resulted to be much lower by using BOOT than MW (e.g., small-
worldness - RST1: $std(p\textsubscript{MW})=0.062$;
$std(p\textsubscript{BOOT})=0.013$; RST2: $std(p\textsubscript{MW})=0.098$;
$std(p\textsubscript{BOOT})=0.030)$. The observations regarding mean and
standard deviation can be generalized to all indexes considered, resulting in
less variable results or, in few cases remaining similar to MW. More
specifically, the cases of the resulting mean of binary and weighted
clustering coefficient for RST1, or the standard deviation of the weighted
characteristic path length and modularity for RST2, which anyway did not
result to be less stable with BOOT. In general, the results highlighted a
higher stability and robustness of the BOOT in RST1 and RST2, providing
support to its possible use when dealing with a small dataset which is also
affected by uncertainty of the measures.
It is worth discussing that the results revealed by the robustness tests may
answer the question of evaluating the results of the functional connectivity
in a more reliable way. Although the needs for dynamic functional acquisition
[24, 27, 60] and of more attractive methods for removing spurious connections
are well-known [15, 61, 62, 63], having a reliable method to evaluate
functional connectivity of small datasets, which can potentially approximate
to results from greater datasets and avoid the loss of information, can help
in the interpretation and understanding.
Second, focusing on the results of the second level, comprising sub-network
(DMN) and local indexes, interesting findings were noticed. It is worth noting
that a first visual difference between the mean matrix of the groups was
visible. Indeed, in Figure 4, the connectograms highlight weaker connections
in the DMN of SZ with respect to HC, in agreement to previous studies [21,
59]. However, no significant differences between the indexes of the sub-
networks were found. On the other hand, the evaluation of the local indexes
allowed to identify some notable patterns. From Figure 5, it is indeed
possible to notice that the most varying local degrees are those referred to
nodes of the DMN, especially in the SZ group. Analyzing, instead, the results
in Figure 6 on the strength index, the differences are less visible although a
slightly greater value is noticed across all nodes of the HC group, together
with a confirmed greater variability distributed across the whole brain in the
SZ group. On one hand, these findings report a greater presence of negative
connections in the DMN of SZ, which can be seen as an inverted connectivity
nature between prefronto-temporal areas, in agreement to diversity found in a
previous study [64]. This is particularly indicative considering the
involvement of the DMN in SZ [21] and that many symptoms of the pathology
mirrors a failure in the integration between the generated behaviour and
concurrent perceptive phenomena [65]. On the other hand, this variability can
also be influenced by the limitations of the data. It is indeed well-known as
one of the states identified by performing dynamical connectivity experiments
can be traced to the DMN [60].
Furthermore, we analyzed the nodes which had the greatest variability of the
degree index and that mostly differed in the strength value. Amygdala, medial
orbital part of the superior and inferior frontal gyrus and part of the
cingulate cortex resulted to be the nodes which were most affected by the
presence of negative connections in the SZ group. Interestingly, amygdala,
which is also a well-known hub of the brain [66], part of the superior frontal
gyrus and cingulate cortex are all part of the DMN, whereas the inferior
frontal gyrus not. However, the inferior frontal gyrus was widely studied
because of its divergent characteristics of anatomical/functional connectivity
in SZ and its relation to semantic processing [67]. The enhanced variability
may be indeed related to specific characteristics and deficiencies of the
patients, which may be potentially investigated through correlation studies
with demographic and severity variables, or, in this case, semantic function
tests, as already widely done in literature [59, 49, 55]. Afterwards, we also
computed MW and BOOT tests on the local values of the strength, highlighting
the nodes mostly differing in the value of this index between the two
populations. In general, it is possible to notice that the most different
local indexes are those referred to frontal, parietal lobes and subcortical
structures, in agreement to previous study [7, 46, 68]. In particular,
significance of left orbital part of inferior frontal gyrus, postcentral
gyrus, Heschl’s gyrus and right Rolandic operculum nodes were found by BOOT
and right calcarine fissure and surrounding cortex node by MW. The results on
these areas appear to be in line with previous studies, where these nodes were
found to be different, although the case of Heschl’s and postcentral gyri were
found in the specific case of SZ patients with auditory hallucinations [55,
69, 70].
The community detection analysis of the anticorrelations highlighted
differences between the two groups. First, in SZ, most nodes from frontal,
limbic and temporal lobes are clustered together in the first community. This
deactivation organization may be relevant in the study of failed activity
inhibition of schizophrenia characterized by selective disruption of an
automatic inhibitory process, and failure to limit the current contents of
consciousness [71, 72]. In the parietal lobes configuration other differences
were noticed, especially regarding the clustering with contralateral occipital
lobe in SZ. In other studies [73, 74, 75], these lobes were investigated in
relation to SZ highlighting important functions. For example, it was
hypothesized that cognitive deficits and delusions may be related to
malfunctions in the parietal lobe [75] or that the maintenance of visuospatial
information is associated to a network of occipital cortex regions [73]. It
would be of great interest to study correlations between symptoms and activity
in these communities, as the contralateral negative cooperation may reinforce
the hypothesis of an involvement of parieto-occipital sub-network in auditory
hallucination, such as the positive correlation found in an EEG and MEG study
[74], or the relations to other disorganization symptoms.
Third, the connectogram pattern of negative edges obtained by averaging all
the negative contributions in the whole brain and DMN of the groups
highlighted interesting indications. Primarily, SZ resulted to have more and
strongest negative connections in the whole brain with respect to HC. Second,
an increased deactivation in the occipital lobe appear to confirm the results
previously obtained through network based statistics, which found
dysconnections in the same areas [7]. Then, the number and the weight of the
preserved negative correlations are generally greater in SZ in the frontal,
which includes prefrontal as well, and parietal lobes, in agreement to what
previously shown on sub-network and nodes. This finding appears to be in line
with previous studies where different organization of the connectivity was
found in prefrontal and frontal lobes [76, 23]. As said, the anticorrelations
could indicate an abnormal inhibition of some regions or lobes activity. In
the context of DMN, except the connections from amygdala to the frontal
regions expected to be common to both groups being a well-known hub of the
brain networks, as abovementioned [66], a different configuration of the edges
was noticed. First, in the HC group, the parietal lobes of the two hemispheres
are deactivated with strong interactions that are not present in the SZ group,
in agreement to community detection analysis. In this case, parietal regions
of DMN mostly communicate with amygdala and superior frontal gyrus.
Furthermore, HC group is characterized by a very strong negative connection
between middle frontal gyrus and the medial orbital part of the superior
frontal gyrus that is not even present in the SZ group. These findings may be
related to significant small-world topology abnormalities found in regions of
the prefrontal and parietal lobes in a previous study [16]. Indeed, the
difference of negative network involving the DMN regions of the parietal lobe
is the most evident, both for the number of edges and their interactions with
the DMN regions of the frontal lobe. From previous works [21, 77, 78], it is
known as intrinsic task-positive and task-negative networks exist in HC during
rest, comprising some areas of these lobes. It can be speculated that this
organization may be responsible for external environmental and self-
referential processing respectively and serves mental processes. In
individuals with SZ or paranoid tendencies, abnormal negative connectivity
within and between these two networks could cause them to be oversensitive to
both internal thoughts and external stimuli. In this sense, abnormal presence
of anticorrelations, together with a low integration between the two networks,
may reflect abnormal inhibition of the other circuit and that extrospective
and introspective thinking is switched back and forth in an overly excessive
manner [21, 79]. In this work, differences were also found in the temporal
lobe that, however, in deactivation analysis of our dataset remained
comparable. Minor differences given by the presence of some negative weak
connections in HC which are not present in SZ were found in the regions of the
DMN of the limbic lobe, confirming the affection of the functional
reorganization of the SZ originating from posterior cingulate cortex [20].
This resulted to be in line with previous findings on cingulate gyrus in SZ
and its importance in functional integration [80].
However, it is worth noting that the small size of the HC and SZ groups
available for this study is a limitation. A subsequent validation of the
bootstrap method on graph-based indexes obtained from a wider functional
connectivity dataset would be attractive. Although the greater stability to
changes of the measures and a trend towards results of larger studies is
promising, validation with more subjects is needed. A related limitation
concerns the lack of discrimination among different types and severity levels
of schizophrenia [21]. Also, the leave-k-subject-out procedure to test the
statistical analyses may be performed on dynamical connectivity data. Thus,
the assessment of the influence of the different states which are assumed
during a resting-state fMRI would reinforce the potential of the approach in
underpinning usability and give better understanding of the functional
activations and deactivations.
Second, one of the main aims of the study was the validation of the approach
through bootstrapping of the indexes accounting all connections, which include
uncertainty as well, but without any loss of information or arbitrary
thresholding of spurious edges and very low correlations. The results obtained
through BOOT were more stable in comparison to standard nonparametric tests,
being robust to noise, but at the same time it is paramount to focus and apply
new and different thresholding methods to assess their influence, as briefly
mentioned. Examples are percolation or spanning tree approaches [15, 17, 61,
62, 63] appearing to be less arbitrary than typical density or absolute
thresholding and which may potentially improve even more the estimates. The
former, for example, was widely employed in a number of studies to find a
potential optimal deletion of the spurious edges maintaining brain network
structure and connectedness [81, 82, 10, 83]. In this perspective, results
from bootstrap analysis may be investigated in relation to percolation
analysis. Another possibility could be to apply bootstrapping of the groups at
connection-level to obtain more robust templates for comparison, identify
errors and quantify the uncertainty of the measure.
Third, the top-down approach was implemented in the SPIDER-NET tool which
automatically allows the investigation of topological properties that are the
most widespread in brain connectivity studies [11]. However, some of the
indexes analyzed have intrinsic limitations, such as the weakness of Newman’s
modularity to detect small modules [84]. In addition, thresholding methods can
strongly affect the results of community analyses and topological indexes. For
this reason, further investigations and comparisons to other methods, such as
random walk-based approaches for community detection, would be of great
interest.
Finally, the robust multi-level approach helped to identify differences in the
connectivity of SZ patients. More specifically, it did not result in increased
or decreased connectivity with respect to HC but in a different configuration,
highlighted by the bootstrapping. As said, the most replicated graph-feature
is the efficiency, whereas other features appear to be more affected by the
pre-processing and there is no strict agreement. Also, the great intra-group
variability, particularly relevant for SZ, plays an important role that may be
investigated in future considering the clinical condition and severity of the
patients or other specific characteristics and deficits. From these
considerations, the results confirmed that the connectivity in SZ is not
systematically increased/decreased but generally different, as already
reported in another study [20]. Nonetheless, it is clear and replicated that
some areas are affected more in SZ [15, 54]. However, it remains unclear
whether SZ abnormalities are the result of a localized dysconnection exerting
widespread effects throughout the brain, or a whole-brain dysfunction that
affects certain regions more. New investigations would be certainly needed to
further investigate the causes and effects related to the onset of the
condition.

##  5 Conclusion

In this work, we described a multi-level robust approach for the investigation
of the brain connectivity. Starting from the measures of global connectivity,
which can be robustly and more stably explored through bootstrapping, general
abnormalities in case-control groups can be identified. In some cases where
the connectivity is not evidently increased/reduced, or particularly different
in some areas, going towards lower levels can be helpful. In this case, we
analyzed separately the functional connectivity in the DMN, beyond those
indexes related to specific nodes. Finally, the activations and the
deactivations were investigated. The whole procedure is developed in the
SPIDER-NET software tool (https://caditer.dongnocchi.it/spidernet/) to
automatically help in the different level investigations of various pathology
to better understand their nature and effects.

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