Altered Functional Complexity Associated with Structural Features

in Schizophrenic Brain: A Resting-state fMRI Study

Yi-Ju Lee

1,2 a

, Su-Yun Huang

, Shih-Jen Tsai

2,4,5 c

and Albert C. Yang

1,2,5,6

Taiwan International Graduate Program in Interdisciplinary Neuroscience,

National Yang-Ming University and Academia Sinica, Taipei, Taiwan

Laboratory of Precision Psychiatry, National Yang-Ming University, Taipei, Taiwan

Institute of Statistical Science, Academia Sinica, Taipei, Taiwan

Department of Psychiatry, Taipei Veterans General Hospital, Taipei, Taiwan

Institute of Brain Science, National Yang-Ming University, Taipei, Taiwan

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

https://orcid.org/0000-0003-1008-8344

https://orcid.org/0000-0002-1602-2832

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

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 (Marković & 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.

COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk

122

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

, 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

, voxel

size = 1.0 × 1.0 × 1.0 mm

, 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

COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk

124

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

(S.D. = 79.60) in

healthy adult and 616.75 cm

(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).

COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk

126

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

127

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).

REFERENCES

Amaral, L. A., Scala, A., Barthelemy, M., & Stanley, H. E.

(2000). Classes of small-world networks. Proc Natl

Acad Sci U S A, 97(21), 11149-11152.

doi:10.1073/pnas.200327197

Amaral, S. L., Zorn, T. M., & Michelini, L. C. (2000).

Exercise training normalizes wall-to-lumen ratio of the

gracilis muscle arterioles and reduces pressure in

spontaneously hypertensive rats. J Hypertens, 18(11),

1563-1572. doi:10.1097/00004872-200018110-00006

Bassett, D. S., & Bullmore, E. T. (2017). Small-World

Brain Networks Revisited. Neuroscientist, 23(5), 499-

516. doi:10.1177/1073858416667720

Bullmore, E., & Sporns, O. (2012). The economy of brain

network organization. Nat Rev Neurosci, 13(5), 336-

349. doi:10.1038/nrn3214

Buzsaki, G., & Mizuseki, K. (2014). The log-dynamic

brain: how skewed distributions affect network

operations. Nat Rev Neurosci, 15(4), 264-278.

doi:10.1038/nrn3687

Bystritsky, A., Nierenberg, A. A., Feusner, J. D., &

Rabinovich, M. (2012). Computational non-linear

dynamical psychiatry: a new methodological paradigm

for diagnosis and course of illness. J Psychiatr Res,

46(4), 428-435. doi:10.1016/j.jpsychires.2011.10.013

Danivas, V., & Venkatasubramanian, G. (2013). Current

perspectives on chlorpromazine equivalents:

Comparing apples and oranges! Indian J Psychiatry,

55(2), 207-208. doi:10.4103/0019-5545.111475

Eguiluz, V. M., Chialvo, D. R., Cecchi, G. A., Baliki, M.,

& Apkarian, A. V. (2005). Scale-free brain functional

networks. Phys Rev Lett, 94(1), 018102.

doi:10.1103/PhysRevLett.94.018102

Friston, K. J., & Frith, C. D. (1995). Schizophrenia: a

disconnection syndrome? Clin Neurosci, 3(2), 89-97.

Gardner, D. M., Murphy, A. L., O'Donnell, H., Centorrino,

F., & Baldessarini, R. J. (2010). International consensus

study of antipsychotic dosing. Am J Psychiatry, 167(6),

686-693. doi:10.1176/appi.ajp.2009.09060802

Hager, B., Yang, A. C., Brady, R., Meda, S., Clementz, B.,

Pearlson, G. D., . . . Keshavan, M. (2017). Neural

complexity as a potential translational biomarker for

psychosis. J Affect Disord, 216, 89-99. doi:10.1016/

j.jad.2016.10.016

Marković, D., & Gros, C. (2014). Power laws and self-

organized criticality in theory and nature. Physics

Reports, 536(2), 41-74.

Mizuseki, K., & Buzsaki, G. (2014). Theta oscillations

decrease spike synchrony in the hippocampus and

entorhinal cortex. Philos Trans R Soc Lond B Biol Sci,

369(1635), 20120530. doi:10.1098/rstb.2012.0530

Piekniewski, F., & Schreiber, T. (2007, April). Emergence

of scale-free spike flow graphs in recurrent neural

networks. In 2007 IEEE Symposium on Foundations of

Computational Intelligence (pp. 357-362). IEEE.

Podvalny, E., Noy, N., Harel, M., Bickel, S., Chechik, G.,

Schroeder, C. E., . . . Malach, R. (2015). A unifying

principle underlying the extracellular field potential

spectral responses in the human cortex. J Neurophysiol,

114(1), 505-519. doi:10.1152/jn.00943.2014

Tort, A. B., Komorowski, R. W., Manns, J. R., Kopell, N.

J., & Eichenbaum, H. (2009). Theta-gamma coupling

increases during the learning of item-context

associations.

Proc Natl Acad Sci U S A, 106(49), 20942-

20947. doi:10.1073/pnas.0911331106

Voytek, B., & Knight, R. T. (2015). Dynamic network

communication as a unifying neural basis for cognition,

development, aging, and disease. Biol Psychiatry,

77(12), 1089-1097.

doi:10.1016/j.biopsych.2015.04.016

Yan, C. G., Wang, X. D., Zuo, X. N., & Zang, Y. F. (2016).

DPABI: Data Processing & Analysis for (Resting-

State) Brain Imaging. Neuroinformatics, 14(3), 339-

351. doi:10.1007/s12021-016-9299-4

Yang, A. C., Hong, C. J., Liou, Y. J., Huang, K. L., Huang,

C. C., Liu, M. E., . . . Tsai, S. J. (2015). Decreased

resting-state brain activity complexity in schizophrenia

characterized by both increased regularity and

randomness. Hum Brain Mapp, 36(6), 2174-2186.

doi:10.1002/hbm.22763

Yang, A. C., & Tsai, S. J. (2013). Complexity of mental

illness: a new research dimension. Prog

Neuropsychopharmacol Biol Psychiatry, 45, 251-252.

doi:10.1016/j.pnpbp.2013.01.018

COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk

128