Altered Functional Complexity Associated with Structural Features
in Schizophrenic Brain: A Resting-state fMRI Study
Yi-Ju Lee
1,2 a
, Su-Yun Huang
3b
, Shih-Jen Tsai
2,4,5 c
and Albert C. Yang
1,2,5,6
1
Taiwan International Graduate Program in Interdisciplinary Neuroscience,
National Yang-Ming University and Academia Sinica, Taipei, Taiwan
2
Laboratory of Precision Psychiatry, National Yang-Ming University, Taipei, Taiwan
3
Institute of Statistical Science, Academia Sinica, Taipei, Taiwan
4
Department of Psychiatry, Taipei Veterans General Hospital, Taipei, Taiwan
5
Institute of Brain Science, National Yang-Ming University, Taipei, Taiwan
6
Division of Interdisciplinary Medicine and Biotechnology, Beth Israel Deaconess Medical Center, Boston, MA, U.S.A.
Keywords: Power Law Scaling, 1/f Signal, Resting-state fMRI, Schizophrenia, Neuroscience.
Abstract: Power law scaling is a well-defined physical concept in complexity science that has been used to quantified
the dynamic signals across temporal scales. In this research, we aim to investigate the power law scaling of
resting-state fMRI signal in schizophrenic and healthy brain and to examine the potential structural properties
that may correlate to the altered functional complexity. Brain imaging data of 200 schizophrenia patients and
200 age and sex-matched healthy Han Chinese was retrieved from Taiwan Aging and Mental Illness cohort.
Power law scaling was extracted by Pwelch function. In schizophrenia, six brain regions with abnormal
complexity were correlated to the regional structural network of grey matter volume (hub at right superior
frontal gyrus) and white matter volume at right superior cerebellar peduncle and splenium of the corpus
callosum. Moreover, the identified power law scaling was correlated with clinical symptom severity. Our
findings suggest that a loss of scale-free brain signal dynamics affecting by brain morphometries proposed
the reduced complex brain activity as one of the neurobiological mechanisms in schizophrenia. This research
supports “the loss of brain complexity hypothesis” and “the dysconnectivity hypothesis of schizophrenia.”,
laying potential impact in psychiatry.
1 INTRODUCTION
The increasing amount of neuroimaging data has been
established in recent years to understand the complex
brain functions in mental disorders. To quantify the
complex brain signal data, an approach that integrates
mathematics, physics, and computational
neuroscience is required. Studies have applied
methods adopted from complexity science to more
fully understand complex brain activity, as measured
by resting-state functional Magnetic Resonance
Imaging (fMRI). Nonlinear dynamical approaches to
quantify the complexity of brain signal data may have
the potential to develop brain-based imaging markers
a
https://orcid.org/0000-0003-1008-8344
b
https://orcid.org/0000-0002-1602-2832
c
https://orcid.org/0000-0002-9987-022X
to extract fundamental features from spatial-temporal
neuroimaging data at multiple levels.
Schizophrenia is a chronic and severe mental
disorder that affects how a person thinks, feels, and
behaves. The prevalence is nearly 1% worldwide and
there have been more than 23 million people
worldwide diagnosed with schizophrenia up to 2019.
Base on the Diagnostic and Statistical Manual of
Mental Disorders, schizophrenia patients would
exhibit positive symptoms and negative symptoms
such as hallucinations and delusions, disorganized
speech and catatonic behavior, and negative
symptoms such as the decrease in emotional range,
alogia or apathy.
120
Lee, Y., Huang, S., Tsai, S. and Yang, A.
Altered Functional Complexity Associated with Structural Features in Schizophrenic Brain: A Resting-state fMRI Study.
DOI: 10.5220/0009572301200128
In Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2020), pages 120-128
ISBN: 978-989-758-427-5
Copyright
c
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
The cause of such complex illness may be
associated with genetic or environmental factors,
however, the underlying mechanism remains unclear.
Previous studies have developed models and
modalities to tackle the challenge. Dr. Yang and Tsai
(2013) raised the “loss of brain complexity hypothesis”
based on empirical evidence (Hager et al., 2017) and
clinical observation. The brain activity in healthy
state performs multiscale variability, whereas the
pathological brain could be associated with the
breakdown of brain signal dynamics into regular or
random patterns. These two types of complexity
change were associated differently with
psychopathology. The study using multiscale entropy
analysis on the blood-oxygen-level-dependent
(BOLD) signal from resting-state fMRI images of
schizophrenia, Yang et al. (2015) have shown the
evidence that the regular type of BOLD complexity
change was associated with positive symptoms of
schizophrenia, whereas the randomness type of
BOLD complexity was associated with negative
symptoms of the illness. the pathologic change of
resting-state dynamics in schizophrenia contributes to
the differences of symptoms in clinics.
The purpose of this research is to investigate a
well-validated nonlinear phenomenon power law
distribution – in brain activity in schizophrenic brain.
Power law is a ubiquitous principle in physics that
describe the complex nature of a given system at
multiple time scales, thus is implicated in modelling
neuronal activity that is known to have complex
behaviors. We hypothesized that the spontaneous
brain activity in schizophrenia may exhibit loss of
power-law characteristics compared to those
observed in healthy volunteers. Based on structural
MRI images, grey matter and white matter volume
would be quantified to screen the possible
relationships between structural properties and power
law scaling for schizophrenic and healthy
participants. The brain regional structural features
may be associated with the abnormal functional
complexity in schizophrenia.
2 POWER LAW SCALING OF
THE BRAIN ACTIVITY
Power law is a distribution that indicates the
relationship between two variables, where one varies
as a power of the other (Figure 1). The scaling
represents the frequency domain of nonlinear
characteristic in a dynamic system. It is a universal
phenomenon that can be observed in both social and
natural contexts. For example, it is also known as 1/f
signal (pink noise) in signal processing, Pareto
Principle (80:20 rule) in economics (Pareto, 1897)
and Zipf’s Law in linguistics (Newman, 2005). In
topology, signals from the system that exhibits power
law behavior would organize a scale-free or small-
world network (L. A. Amaral, Scala, Barthelemy, &
Stanley, 2000; Bassett & Bullmore, 2017).
Figure 1: The typical power law distribution.
Power-law distribution as a ubiquitous principle in
physics that describes the complex nature of a given
system across time scales. Using power law to extract
the fundamental features from spatial-temporal
neuroimaging data may holds great potential to
evaluate the dynamic human nervous system.
2.1 Functional Complexity in Nervous
System
Power-law scaling has been observed in Nervous
systems across species. In 2000, an investigation on
structural neural networks of all 302 neurons on
Caenorhabditis elegans (C. elegans) worm identified
a power-law distribution of aging speeds in a whole
nervous system (S. L. Amaral, Zorn, & Michelini,
2000). The neural networks have elucidated the
nonlinear dynamical complexity in neuronal signal
over a range of scales. Bystritsky, Nierenberg,
Feusner, and Rabinovich (2012) presented the result
in logarithm with the number of links at x-axis and
cumulative distribution at y-axis. The slope (the
power law distribution) in of fast aging neurons is the
furthest to negative one in compare with the younger
neurons, which shows the slope approximate to
negative one.
Despite of the nature of C. elegans is relatively
small to human nervous system, power law remains
relevant to Homo sapiens. In human brain, the power-
law phenomenon was also observed across different
levels of the human brain, such as neuronal firing rate
(Buzsaki & Mizuseki, 2014), efficacy of synaptic
transmission (Mizuseki & Buzsaki, 2014), channel
density (Bullmore & Sporns, 2012), or neural circuit-
level networks (Markov & Gros, 2014). Eguiluz,
Altered Functional Complexity Associated with Structural Features in Schizophrenic Brain: A Resting-state fMRI Study
121
Chialvo, Cecchi, Baliki, and Apkarian (2005) studied
the brain connectivity of fMRI data across different
mental tasks. The result of average scaling taken from
22 networks in log-log plot shows a negative slope.
Piekniewski (2007) adopted a similar methodology,
studying the dynamic of neuronal spikes by different
neuronal size groups. The result also shows similar
distribution: the pattern resembles a negative slope in
log-log figure with a base of 10.
The findings of power law behavior across
various physiological log scale parameters provides
an evidence on the existence of core phenomenon of
Homo sapiens sharing properties. Transforming the
information into logarithm scaling allows multi-level
data to be operated by compressing large input range
into a smaller manageable output.
Power law’s negative slope of brain-network
activity can be explained by two possible
mechanisms. First is the underlying population
spiking statistics (Voytek & Knight, 2015). Brain
signals in logarithm with two ends of continuous
distribution extending several orders of magnitude
indicates that a large number of neurons spike
simultaneously with a small groups of aberrant
neurons spiking at different time points. In this way,
the aggregate local field potential (LFP) would make
the slope negative. In contrast, the units within the
population spike relatively asynchronously would
lead to a flatter slope (Podvalny et al., 2015; Voytek
& Knight, 2015). The second underlying mechanism
is the decoupling of population spiking activity from
the ongoing low-frequency oscillatory neural field,
which results in neural noise increasing (Tort,
Komorowski, Manns, Kopell, & Eichenbaum, 2009;
Voytek & Knight, 2015). Features of cortical circuits,
such as redundancy and degeneracy, recurrent
excitatory loops coupled with feedback and
feedforward inhibition, create substrates for wide-
dynamic range, log-linear computation.
Quantifying the power law scaling of neuronal
signals allows the researchers to explain and evaluate
the nonlinear dynamic system in the frequency
domain, for which its change in complexity can be
quantified rigorously via spectral analysis of resting-
state fMRI signal in this research.
2.2 Bold fMRI Signal
Base on the physiological mechanism, neurovascular
coupling, the fMRI technique is established base on
the mechanism that the activated neuron consumes
more oxygen to satisfied the energy need. The
haemoglobin which carries the oxygen is
paramagnetic due to the presence of oxygen ion. MR
signal creating the BOLD contrast effect based on
such paramagnetic state, with the contrast of
oxyhemoglobin and de-oxyhemoglobin to generate
the MR signal. The resting-state fMRI image is
conducted base on the BOLD response in the absence
of specific task. This research use complexity
analysis with the resting-state BOLD signal acquired
by MRI.
2.3 Quantifying Power Law Scaling
To extract the power law scaling of BOLD signals in
each voxel, we first applied the Fourier Transform to
the resting-state fMRI signal for each voxel to convert
the time domain data into the frequency domain of the
power spectrum (bin = 0.002 Hz), in order to quantify
power-law scaling of the resting-state fMRI signal.
Second, the data was visualized in a logarithm plot
with the base equal to 10 on both axes to quantify the
power spectrum across scales. Third, linear
regression was deployed to derive a slope estimate,
which was the scaling property of the given resting-
state fMRI signal.
Figure 2 shows an example of a 30 years old
healthy male’s resting-state fMRI image. The 4D
BOLD time series data of a voxel at (24, 14, 36 of
MNI coordinate) left precuneus is acquired (A). A 3D
power spectrum density was acquired after applying
fast Fourier transform on the result of A (B). After
transforming the signal distribution to logarithm, we
use linear regression to acquire the slope of power
spectrum density distribution, which is power law
scaling.
The slope of the frequency scaling approaching
minus one would provide evidence for the power law
behavior of the given resting-state fMRI signal.
Therefore, such scaling analysis will be helpful for
quantifying the complex dynamics of spontaneous
brain activity in order to determine the state of brain
activity at the complex state of 1/f power law scaling
behavior (Figure 3; left panel), reduced complexity as
the slope of scaling becomes less steep (middle
panel), and the brain signal to be an uncorrelated
noise as the slope of scaling becomes flat (right
panel).
In this research, the power law scaling is
calculated voxel-wise for both schizophrenic patients
and healthy participants.
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Figure 2: Quantifying power law scaling of brain BOLD
signal in a voxel from real data.
3 METHODS
3.1 Study Cohort
Functional brain imaging data of 200 age and sex
matched schizophrenic patients (age mean = 43.56 ±
12.64; male = 49.5%) and 200 healthy subjects (age
mean = 43.56±13.41; male = 49.5%), who were right-
handed
Han Chinese, were retrieved from Taiwan
Figure 3: Power law scaling in different states.
Aging and Mental Illness (TAMI) cohort. Diagnosis
of schizophrenia was screened and confirmed by two
psychiatrists based on criteria given in the Diagnostic
and Statistical Manual of Mental Disorders (DSM–
IV-TR). The schizophrenia patients have the average
onset of 28 years old and average duration of onset
being 15 years, and their score of Mini-Mental State
Examination (MMSE) and the Positive and Negative
Syndrome Scale (PANSS) is acquired.
Written informed consent was obtained from all
participants before the scanning sessions following
the protocol for TAMI cohort approved by the review
board at Taipei Veterans General Hospital, Taipei,
Taiwan. All personal information and imaging data
are de-identified for the subsequent analyses. It is
worth mentioning that the TAMI cohort has recruited
more than 1000 subjects so far, including a large
sample of patients with healthy aging and patients
covering major mental illness. All imaging data were
acquired by the same 3.0T MRI Siemens Tim Trio
machine with constant protocol at National Yang-
Ming University.
3.2 Brain Images
3.2.1 Structure MRI and Resting-state fMRI
Acquisition
The fMRI scanning was performed at National Yang
Ming University on a 3.0 T MRI scanner (Siemens
Magnetom Tim Trio, Erlangen, Germany). Resting-
state scanning was scheduled in the morning,
conducted in the darkened scanner room, and lasted
approximately 10 minutes. The instruction requires
the subject to relax with eyed open. The reminder was
asked routinely by the technician during the scans to
avoid the subject from falling asleep, otherwise,
rescanning is acquired.
The MRI scanner is equipped with a 12-channel
head coil. Whole-brain resting-state BOLD
functional MRI images were collected using a T2*-
Altered Functional Complexity Associated with Structural Features in Schizophrenic Brain: A Resting-state fMRI Study
123
weighted gradient-echo-planar imaging (EPI)
sequence with following imaging parameters:
repetition time TR= 2500 ms, echo time = 27 ms, field
of view =220×220 mm
2
, voxel size= 3.4×3.4×3.4
mm3, flip angle =77°, matrix size =64×64. A total of
200 EPI images were acquired along the AC–PC
plane for each run. High-resolution structural MRI
images were acquired with 3-D magnetization-
prepared rapid gradient echo sequence (TE= 3.5 ms,
TI = 1100 ms, field of view= 256 ×256 mm
2
, voxel
size = 1.0 × 1.0 × 1.0 mm
3
, flip angle= 7°, matrix size
= 256×256). All structural MRI scans were visually
reviewed by an experienced neuroradiologist to
confirm that participants were free from any
morphologic abnormality.
3.2.2 Resting-state fMRI Data Preprocessing
The functional and anatomical image preprocessing
was performed by DPARSF and SPM12 under
MATLAB9.2. The first 5 of 200 data points are
routinely discarded to eliminate the time difference
between actual neural activation and cerebral blood
flow response. Functional images were realigned and
coregistered to the subjects own anatomical images.
Slice timing is adopted to correct the scanning time
between slices. Segmentation is operated and all
functional images are normalized to standard
Montreal Neurological Institute (MNI) space.
Nuisance effect is removed by constant and linear de-
trend in whole brain. BOLD signal of white matter
and CSF are taken as covariate regressors. Derivative
12 is adopted as head motion regression model. In
addition to six rigid body head motion parameters, the
first six eigenvectors of white matter signal and the
first six eigenvectors from CSF were regressed out by
linear regression for each voxel. The band pass
filtering is set 0.01 to 0.1 Hz. Moreover, fast Fourier
Transform (fFT) is operated to extract power law
spectrum from each voxel of functional resting
images with customized pwelch code in MATLAB.
Finally, Gaussian smoothing with 8 mm full width at
half maximum (FWHM) is applied to all functional
data by SPM 12. The structural properties were
quantified by T1 image. the Automated Anatomical
Labeling (AAL) and International Consortium for
Brain Mapping (ICBM) were used for the
measurement of regional GMV and white matter
volume.
3.3 Software
The resting-state fMRI images preprocessing was
operated by DPARSF_V4.3_170105 (Data
Processing Assistant for Resting-State fMRI; Yan)
(Yan, Wang, Zuo, & Zang, 2016) and SPM12
(Statistical Parametric Mapping, Department of
Imaging Neuroscience, London, UK) under
MATLAB 2017a (Version 9.2). Statistical analysis
was conducted by SPM12 and MATLAB. Brain
image results are reviewed presented by BrainNet
Viewer (Version 1.53, Beijing Normal University,
China) and MRIcron (Georgia Tech Center for
Advanced Brain Imaging, the Georgia state, USA).
3.4 Statistical Analysis
T-test is applied to compare the relationship of brain
structural parameters and signal complexity between
interested groups. The significance of voxel-wise
comparison p value is set <0.05 correction for
multiple comparison by family-wise error (FEW)
method. Pearson correlation is operated to access the
relationship between power law scaling and grey and
white matter volume. The structural network will be
conducted by Pearson correlation with Bonferroni
correction. In schizophrenia group, the correlation
between abnormal power law scaling in identified key
brain regions and the score of the PANSS was
analysed. To control possible confounding, age and
sex of all participants are covariates.
3.5 Experimental Design
In this research, we focus on validating power law
phenomenon in dynamic human brain activity. The
purpose of the first study is to fundamentally
understand how power law spectrum of the resting-
state BOLD signal varies in different brain
morphological tissues in schizophrenic and healthy
participants. The association between abnormal
power law scaling and the clinical severity measured
by PANSS in schizophrenic patients is examined. The
second study aims to understand how grey matter
change (such as local or global volume decreased)
would effect on power law of dynamic BOLD signal.
In study 2, we firstly access the brain regions where
both power law scaling and grey matter volume
(GMV) show significance between groups.
Following we use Pearson correlation with
Bonferroni multiple-comparison correction to
investigate the correlation between power law scaling
and GMV in the identified brain region. In addition,
we select the brain regions which show high GMV
correlation to the identified regions to conduct the
structural network. The third study aims to screen the
possible association between white matter volume
and power law scaling. Such study design will allow
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us to integrate structural and functional results to
identify basic principles of multi-scale neuronal
dynamic and inter-individual variability in mental
illness patients and healthy groups, uttering a
comprehensive meaning from a broader view.
4 RESULTS
4.1 Power Law Change of rs-fMRI in
Different Anatomical Regions
The t-test was used to compare the power-law scaling
between schizophrenic patients and healthy adults,
with the extent threshold k = 35 voxels. Parametric
images were assessed for cluster-wise significance
using a cluster-defining threshold of FWE p < 0.05.
The result visualization is shown in Figure 4,
presenting the distribution of voxel-wise t-value
across the brain. In Figure 4, red color indicates
positive t value whereas blue color represents more
negative t value. The swift of power-law scaling of
resting-state fMRI signal indicates the state change in
the brain system. The results reveal that
schizophrenic patients, with the average onset of 28
years old and average duration of illness being 15
years, have significantly four more positive power-
law scaling and two more negative power-law scaling
than healthy adults at anatomical clusters.
Figure 4: The t-map visualization of different power law
scaling observed in schizophrenic and healthy participants.
The four more positive clusters included left
precuneus (k = 17,555; peak coordinate (mm) = -18,
-66, 18; t = 7.72), with sub-cluster at left middle
occipital gyrus (peak coordinate (mm) = -21, -93,18 ;
t = 6.97), left medial dorsal nucleus (k = 183; peak
coordinate (mm) = -6,-15, 3; t =5.99), right inferior
frontal gyrus (k = 160; peak coordinate (mm) = 42,
21, 30; t = 4.26), and right middle temporal gyrus (k
= 48; peak coordinate (mm) = 51, -39, -3; t = 3.93).
All these four clusters have p (FWE-cor) < 0.001 at
voxel level. The equivalent k = 37 of left Insula
reached threshold of k = 35, however, at cluster level,
the uncorrected p remained marginally significant.
On the other hand, healthy adults demonstrated
significantly higher power-law scaling than
schizophrenic patients in two regions: right putamen
(k = 60; peak coordinate (mm) = 18, 6, -3; t = -3.11)
and left putamen (k = 44; peak coordinate (mm) = -
18, 9, 3; t = -3.11).
Two anatomical clusters presenting more
negative power-law scaling in schizophrenic patients
are right putamen (k = 60; peak coordinate (mm) =
18, 6, -3; t = -3.11) and left putamen (k = 44; peak
coordinate (mm) = -18, 9, 3; t = -3.11). These two
clusters have p (FRD-cor) < 0.001 at the voxel level.
4.1.1 Correlation of Power Law Scaling and
Clinical Severity in Schizophrenia
The Pearson correlation between the abnormal
power-law scaling and score of PANSS is calculated.
Interestingly, significant correlations with p-value <
0.05 were found in the key regions where the slope of
power-law scaling was more positive in
schizophrenic patients. The positive correlation was
found between the power-law scaling slope in left
precuneus and score of item G5 (mannerisms &
posturing, r = 0.15, p = 0.04) and left thalamus and
score of item N3 (passive/apathetic social
withdrawal, r = 0.17, p = 0.02). Negative correlations
were found between right middle frontal gyrus and
score of item P4 (r = -0.15, p = 0.03) and right middle
temporal gyrus and score of item P4 (excitement, r =
-0.15, p = 0.03).
Pearson’s correlation is used to evaluate the
relationship between the dosage of antipsychotic
drugs and power-law scaling of resting-state fMRI
signals in the identified brain regions. The
antipsychotic dosage was transformed into
chlorpromazine (CPZ) equivalence dosage based on
empirical studies (Danivas & Venkatasubramanian,
2013; Gardner, Murphy, O'Donnell, Centorrino, &
Baldessarini, 2010). There was no significant
correlation between CPZ dosage and the power-law
scaling in six brain regions.
4.2 Grey Matter Structural Correlates
of Power Law Scaling
Healthy adult and schizophrenic patients have
significant difference in total grey volume (t = 4.76;
Altered Functional Complexity Associated with Structural Features in Schizophrenic Brain: A Resting-state fMRI Study
125
p = 0.00) and MMSE score (t = 3.53; p = 0.00). The
total grey volume is 634.96 cm
3
(S.D. = 79.60) in
healthy adult and 616.75 cm
3
(S.D. = 69.66) in
schizophrenic patients. The mean MMSE score is
28.00 (S.D. = 4.72) and 26.43 (S.D. = 4.17) in healthy
and schizophrenia participants, respectively.
4.2.1 Candidate Brain Regions
Identification
Across all AAL regions, we identified the candidate
brain regions where both groups showing
significance in GMV and power law scaling. The
results of t- test showed that schizophrenia patients
and healthy participants have significant difference of
power law scaling in 66 AAL regions and difference
in GMV in 81 AAL regions with significant level less
than .05. Sixty-one candidate brain regions were
identified where both group showing significant
difference in GMV and power law scaling based on
AAL atlas.
The relationship between GMV and power law
scaling in the candidate brain regions was examined
with Pearson correlation. With Bonferroni correction
for multiple comparison (p < 0.00056), schizophrenic
brain showed significant correlation between GMV
and power law scaling in 32 AAL regions. On the
other hand, healthy participants had significant
correlation of GMV and power law scaling in two
AAL regions, right superior frontal gyrus
(dorsolateral part) and left inferior occipital gyrus.
Moreover, the found significant correlation
coefficient were negative for schizophrenia and
positive for healthy brain. As a result, right superior
frontal gyrus (AAL4) was the key region where
power law scaling and GMV show significant
correlation in both groups, where the correlation
coefficient is -0.22 (p=0.000019) in schizophrenic
brain and 0.17 (p =0.000213) for healthy brain.
4.2.2 The Possible Structural Network
Contributing to Abnormal Complexity
With the dorsolateral part of right superior frontal
gyrus (AAL4) as the hub, we then explored the
possible structural network that may support the
functional complexity change. The grey matter
structural network is defined by the Pearson
correlation of GMV in AAL brain regions. In table 3,
the result shows the top 10 most correlated brain
regions to AAL4 for healthy and schizophrenic brain.
As the result, top 1 to top 5 identified satellite regions
were the same for both groups with the same order.
The GMV AAL4 is highly positively correlated to the
GMV of AAL 3 (left dorsolateral part of superior
frontal gyrus), AAL 6 (right orbital part of superior
frontal gyrus), AAL 5 (left orbital part of super frontal
gyrus) and AAL 20 (right supplementary motor area).
The top five ranking correlated regions are organized
a cluster at superior frontal gyrus in healthy and
schizophrenic patients. The top 6 to 10 correlation
ranking to AAL 4 regions are shared for both groups:
AAL 10 (right orbital part of middle frontal gyrus),
AAL 9 (left orbital part of middle frontal gyrus), AAL
1 (left precentral gyrus), AAL 16 (right orbital part of
inferior frontal gyrus) and AAL 19 (left
supplementary motor area), organizing another
cluster linking to the hub.
The most different structural connections to
AAL4 between schizophrenic and healthy brain is
calculated. The connection difference was quantified
by subtraction of each Pearson correlation coefficient
between groups. The result shows in Figure 5.
Schizophrenia and healthy brain shown most
correlation difference (Difference > 0.1) to right
superior-frontal gyrus at bilateral superior temporal
gyrus, bilateral lenticular nucleus (pallidum) and
bilateral thalamus.
Figure 5: The Structure Network of Right Superior Frontal
Gyrus (Blue for Healthy; Red for Schizophrenia).
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4.3 White Matter Structural Correlates
of Power Law Scaling
Thirteen ICBM regions showing significant different
white matter volume between schizophrenic and
healthy brain were identified. Pearson correlation
with multiple comparison correction was used. The
results showed no significant correlation for healthy
participants. For the schizophrenic patients, ICBM 13
(right superior cerebellar peduncle) and ICBM 15
(splenium of corpus callosum) showed the most
negative correlation (r = -0.15 to -0.32; p < 0.038) at
the brain regions where power law scaling shows
significant difference between groups and that may
correlate to GMV in schizophrenia.
5 DISCUSSION
The key findings in this study include (1) the
difference in power law scaling behavior in different
anatomical regions indicates that patients with
schizophrenia are associated with the abnormal
complexity of spontaneous brain activity in grey
matter; (2) the identified brain regions with abnormal
complexity found in schizophrenic patients are
correlated to psychotic symptoms such as mannerism
and posturing, excitement, and passive or apathetic
social withdrawal; (3) The abnormal functional
complexity in schizophrenia may be stemmed from
the structural network of GMV, with the hub at the
dorsal lateral part of right superior frontal gyrus.
The study findings indicate that spectral density
of resting-state fMRI signals in healthy volunteers
exhibit a higher power in lower frequency bands and
lower power in higher frequency bands, compared to
schizophrenic patients, and such scaling behavior is
more close to 1/f characteristics in healthy volunteers
than that observed in patients with schizophrenia.
These findings suggest that schizophrenic patients
may have a loss of 1/f power law scaling which
indicates a possible loss of scale-free brain signal
dynamics. Our findings may link to the underlying
pathophysiology of schizophrenia. For example, the
more negative power law scaling in putamen may
indicate over-activity of dopaminergic neurons,
which is associated with cognitive dysfunction in
schizophrenia.
From the perspective of complexity science,
signals observed in a dysfunctional system may show
random or regular behaviors. Change in power law
scaling toward a flat slope indicates a loss of multi-
scale complexity, which is possibly associated with a
lack of thinking or behavioral flexibility commonly
observed in psychotic patients. Additionally,
flattened power law scaling observed in
schizophrenic patients may also indicate an increased
noise of information flow in the neuronal systems,
which may be associated with abnormal structural or
functional connectivity.
The findings provide the evidences supporting the
disconnection hypothesis raised by Friston and Frith
(1995). By analysis the data from schizophrenic
patients, the functional complexity is effected by
brain structures. The altered functional complexity,
quantified by power law, representing the
discontinuity in time-series. Such dysconnectivity is
significantly correlated to grey matter and white
matter structure.
There are two limitations of this study. The use of
linear model on power spectrum may overlook certain
dynamics. Due to relatively short resting-state fMRI
time series, the frequency resolution of power
spectrum may be limited by the use of Fourier
transform. In the future, longer scanning time or
higher sampling rate at data acquiring may be
considered to increase the spatial resolution. The
results from white matter volume may be validated by
the use of Diffusion Tensor Images.
6 CONCLUSIONS
The application of complexity science in
neuroscience has overcome common concerns of
typical statistic methods, and has presented insights
complementary to traditional biological knowledge.
The power law phenomenon is emerged based on the
integration of various biological mechanisms across
temporal and spatial levels, supporting the nonlinear
behavior of neuronal activity in human central
nervous system. Based on frequency domain, power
law scaling plays a role to differentiate schizophrenia
and healthy brain by analyzing resting-state brain
imaging signal. The results of this study support “the
loss of brain complexity hypothesis,” (Yang & Tsai,
2013) and the “dysconnectivity hypothesis of
schizophrenia” (Friston & Frith, 1995), suggest the
reduced complex brain activity as one of
neurobiological mechanisms in schizophrenia. Such
abnormal functional brain complexity proposing the
power law scaling as a ubiquitous principle of
governing brain signal dynamics, which serves a
great potential clinical impact in psychiatry.
Altered Functional Complexity Associated with Structural Features in Schizophrenic Brain: A Resting-state fMRI Study
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ACKNOWLEDGEMENTS
This work was supported by the Brain Research
Center, National Yang-Ming University from The
Featured Areas Research Center Program within the
framework of the Higher Education Sprout Project by
the Ministry of Education (MOE) and the Ministry of
Science and Technology (MOST) of Taiwan (grant
MOST 108-2634-F-075-002).
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