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Resting-state Connectivity Dynamics in theHuman Brain using High-speed f MRIKishore Vakamudi
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i
KISHORE VAKAMUDI Candidate PHYSICS AND ASTRONOMY Department This thesis is approved, and it is acceptable in quality and form for publication: Approved by the Thesis Committee: STEFAN POSSE, PhD, Chair ARVIND CAPRIHAN, PhD, Committee member TUDOR I. OPREA, PhD, Committee member
ii
RESTING-STATE CONNECTIVITY DYNAMICS IN THE HUMAN BRAIN
USING HIGH-SPEED FMRI
by
Kishore Vakamudi
THESIS
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
Physics
The University of New Mexico
Albuquerque, New Mexico
July 2016
iii
freedom, reason, and truth
iv
ACKNOWLEDGEMENTS
Stefan Posse, PhD I would like to express my profound appreciation and gratitude to
my supervisor and committee chair Dr. Stefan Posse, who has the
attitude and substance of a genius. Without his persistent help,
excellent mentorship, and great support, this work would not have
been possible.
Arvind Caprihan, PhD My sincere gratitude to Dr. Caprihan for his acceptance to be on my
thesis committee and for his guidance.
Tudor I. Oprea, PhD My sincere gratitude to Dr. Oprea for his acceptance to be on my
thesis committee.
Elena S. Ackley, MS I am indebted to Elena S. Ackley for her motherly guidance and
invaluable support when I started this project and for her enormous
patience with me.
Dinesh Loomba, PhD I would like to thank Dr. Loomba for his great guidance and
encouragement as my academic advisor.
Vince D. Calhoun, PhD I would like to express my sincere gratitude to Dr. Calhoun for his
guidance and encouragement.
Sudhakar Prasad, PhD My sincere gratitude to Dr. Prasad for his support.
Nitant V. Kenkre, PhD My sincere gratitude to Dr. Kenkre for his stimulating philosophical
conversations and insights on physics.
Mickey Odom I would like express my sincere appreciation to Mickey for his support and friendship during my TA sessions.
Departments of Physics
and Astronomy and
Neurology
Sincere thanks to the departments of Physics and Astronomy, and Neurology, University of New Mexico, Albuquerque, for the financial support.
v
Colleagues A special thanks to Cameron Trapp for his help in reviewing the
thesis. Alec Landow, Kevin Fotso, Eswar Damaraju and other
colleagues from MRN, Albuquerque, and University of
Copenhagen, Denmark for their camaraderie.
At UNM Sincere thanks to Ruslan Hummatov, Dipendra Adhikari, Qufei Gu,
Esad Shobjee, Prabhakar Palni along with all my professors for their
invaluable help and guidance.
Teachers I grateful to all my teachers past and present.
Friends I am deeply indebted to all my friends for being my strength.
For everything they are.
and to my parents
Suseela and Late Sobhanachalam Vakamudi
vi
RESTING-STATE CONNECTIVITY DYNAMICS IN THE HUMAN BRAIN
USING HIGH-SPEED FMRI
by
Kishore Vakamudi
University of New Mexico, MS, 2016
ABSTRACT
Resting-state fMRI using seed-based connectivity analysis (SCA) typically involves regression of
the confounding signals resulting from movement and physiological noise sources. This not only
adds additional complexity to the analysis but may also introduce possible regression bias. We
recently introduced a computationally efficient real-time SCA approach without confound
regression, which employs sliding-window correlation analysis with running mean and standard
deviation (meta-statistics). The present study characterizes the confound tolerance of this
windowed seed-based connectivity analysis (wSCA), which combines efficient decorrelation of
confounding signal events with high-pass filter characteristics that reduce sensitivity to drifts. The
confound suppression and the strength of resting-state network (RSN) connectivity were
characterized for a range of confounding signal profiles as a function of sliding-window width and
scan duration, using simulation and in vivo data. The connectivity strength in six resting-state
networks (RSNs) and artifactual connectivity in white matter were compared between wSCA and
conventional regression-based SCA (cSCA). The wSCA approach demonstrated scalable
confound suppression that increased with decreasing sliding-window width and increasing scan
duration in both simulations and in vivo. The confound suppression for sliding-window widths ≤
15 s was comparable to that of cSCA. Twenty-eight RSNs that were previously reported in a group-
ICA study were detected in real-time at scan durations as short as 30 s and with sliding-window
widths as short as 4 s. The inter- and intra- network connectivity dynamics of the 28 resting-state
networks were studied in real-time and self-repeating connectivity patterns were identified.
vii
The wSCA is further investigated offline to study the strength and temporal fluctuations in
connectivity using 28 single-region seeds and 28 multi-region seed clusters to measure inter-
regional connectivity (IRC) in 140 functional brain regions and inter-network connectivity (INC)
among the hubs of 28 RSNs. Multi-region seed IRC maps displayed smaller temporal fluctuations
and stronger resting-state connectivity compared with single-region seed IRC maps. Dual
thresholding of the meta-statistics maps demonstrated higher spatio-temporal IRC stability in
auditory, sensorimotor, and visual cortices compared to other brain regions. The group averaged
INC matrices for single-region seeds were consistent with the functional network connectivity
matrices (FNCMs) presented in the aforementioned group-ICA study. Furthermore, we extended
the mapping of functional connectivity to the whole-brain connectivity fingerprints.
In combination with novel brain parcellation methods and advanced machine learning algorithms,
wSCA can aid in studying the spatial and temporal connectivity dynamics of the resting-state
connectivity. The robust confound tolerance, high temporal resolution, and compatibility with real-
time high-speed fMRI, make this approach suitable for monitoring data quality, neurofeedback,
and clinical research studies involving disease related changes in functional connectomics.
viii
Glossary
BOLD Blood-Oxygenation Level Dependence
CSF Cerebrospinal Fluid
EEG Electroencephalography
EPI Echo-Planar Imaging
fMRI Functional Magnetic Resonance Imaging
FNCM Functional Network Connectivity Matrix
fNIRS Functional Near-Infrared Spectroscopy
GRAPPA Generalized Autocalibrating Partially Parallel Acquisition
HRF Hemodynamic Response Function
ICA Independent Component Analysis
INCM Inter-Network Connectivity Matrix
IRCM Inter-Regional Connectivity Matrix
MEG Magnetoencephalography
MEVI Multi-slab Echo-Volumar Imaging
MNI Montreal Neurological Institute
PCA Principle Component Analysis
PCC Posterior Cingulate Cortex
PET Positron Emission Tomography
ROI Region Of Interest
rsfMRI Resting-State Functional Magnetic Resonance Imaging
RSN Resting-State Network
SCA Seed-based Connectivity Analysis
cSCA Conventional Seed-based Connectivity Analysis
wSCA Windowed Seed-based Connectivity Analysis
SNR Signal-to-Noise Ratio
TurboFIRE Turbo Functional Imaging in REal-time
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CONTENTS
Acknowledgements ................................................................................................................... iii
Abstract ....................................................................................................................................... v
Glossary ................................................................................................................................... vii
Chapter 1 Introduction
1.1. Background .................................................................................................................... 1
1.2. Thesis Organization ....................................................................................................... 3
References ............................................................................................................................. 4
Chapter 2 Nuclear Magnetic Resonance
2.1. Introduction .................................................................................................................... 5
2.2. Angular Momentum and Energy ................................................................................... 5
2.3. From Quantum To Classical .......................................................................................... 7
2.4. Classical Equations of NMR ........................................................................................ 8
2.4.1. Precession ............................................................................................................. 8
2.4.2. Excitation .............................................................................................................. 8
2.4.3. Bloch Equation...................................................................................................... 9
2.4.4. Relaxation ........................................................................................................... 10
2.5. Magnetic Resonance Imaging (MRI)........................................................................... 13
2.5.1. Zeugmatography and Slice Selection.................................................................. 14
2.5.2. Two-Dimensional Spatial Encoding and K-Space ............................................. 15
2.6. MR Contrast Mechanisms............................................................................................ 16
2.6.1. T1 contrast ........................................................................................................... 17
2.6.2. T2 contrast ........................................................................................................... 17
2.6.3. T2* contrast .......................................................................................................... 18
x
2.7. Conventional MRI ....................................................................................................... 18
2.8. Advanced fMRI ........................................................................................................... 20
2.8.1. Echo-Planar Imaging (EPI) ................................................................................. 20
2.8.2. Echo-Volumar Imaging (EVI) ........................................................................... 21
2.8.3. Multi-slab Echo-Volumar Imaging (MEVI) Reconstruction ............................. 22
2.8.4. MEVI - Advantages and Limitations .................................................................. 24
References ........................................................................................................................... 25
Chapter 3 Functional Magnetic Resonance Imaging
3.1. Introduction .................................................................................................................. 27
3.2. Blood-Oxygenation Level Dependent (BOLD) signal ................................................ 28
3.3. Hemodynamic Response Function (HRF) ................................................................... 28
3.4. Resting-state fMRI ....................................................................................................... 29
3.5. Confounding Signals in Resting-state fMRI ................................................................ 30
3.6. Preprocessing in fMRI ................................................................................................. 31
3.7. Resting-state Networks (RSNs) ................................................................................... 32
References ........................................................................................................................... 34
Chapter 4 Windowed Seed-based Connectivity Analysis
4.1. Introduction .................................................................................................................. 36
4.2. Subjects and Data Acquisition ..................................................................................... 37
4.3. Seed-based Connectivity Analysis (SCA) ................................................................... 39
4.3.1. Seed Selection ..................................................................................................... 39
4.3.2. Conventional Seed-based Connectivity Analysis (cSCA) .................................. 40
4.3.3. Windowed Seed-based Connectivity Analysis (wSCA) ..................................... 41
4.4. Simulation of Confound Suppression using Windowed SCA ..................................... 41
xi
4.5. Performance Comparison of Windowed and Conventional SCA................................ 46
4.5.1. Computational Efficiency ................................................................................. 47
4.5.2. Intra- and Inter-RSN Connectivity.................................................................... 50
4.5.3. Artifactual White Matter Connectivity ............................................................. 51
4.6. Whole-brain Connectivity Profiles .............................................................................. 52
4.7. Physiological Noise Suppression ................................................................................. 54
4.8. Mapping of Resting-state Networks ............................................................................ 55
4.9. Windowed Seed-based Connectivity Analysis ............................................................ 57
4.9.1. Confound Suppression ...................................................................................... 57
4.9.2. Frequency Selectivity of Windowed SCA ........................................................ 58
4.9.3. Conventional and Windowed SCA ................................................................... 59
4.9.4. Real-time Implementation of Windowed SCA ................................................. 59
4.9.5. Limitations ........................................................................................................ 60
References ........................................................................................................................... 61
Chapter 5 Functional Connectomics
5.1. Introduction .................................................................................................................. 67
5.2. Statistical Hierarchy ..................................................................................................... 67
5.3. Seed Selection .............................................................................................................. 68
5.4. Resting-state Networks with Multi-region Seeds ........................................................ 69
5.5. Inter-Regional Connectivity......................................................................................... 70
5.5.1. Single-subject Connectomics .............................................................................. 71
5.5.2. Group Connectomics .......................................................................................... 73
5.5.3. Spatio-temporal Stability of Inter-Regional Connectivity .................................. 78
5.6. Inter-Network Connectivity ......................................................................................... 81
5.7. Atlas-based Functional Connectomics ......................................................................... 83
References ........................................................................................................................... 85
xii
Chapter 6 High Dimensional Connectomics
6.1. Introduction .................................................................................................................. 87
6.2. Materials and Methods ................................................................................................. 87
6.3. Whole-brain Connectivity Fingerprints ....................................................................... 91
References ........................................................................................................................... 92
Chapter 7 Real-time Neurofeedback
7.1. Introduction .................................................................................................................. 93
7.2. Real-time Windowed SCA .......................................................................................... 95
7.3. Connectivity Dynamics of Resting-state Networks ..................................................... 95
7.4. Pattern Classification and Brain States ........................................................................ 96
7.5. Real-time Neurofeedback ............................................................................................ 96
References ........................................................................................................................... 98
Chapter 8 Conclusions and Future Directions
8.1. Conclusions .................................................................................................................. 99
8.2. Future Directions ......................................................................................................... 99
References ......................................................................................................................... 101
1
Chapter 1 Introduction
1.1. Background
The human brain is one of the most highly complex systems known in Nature. The discovery of
nuclear magnetic resonance (NMR) has enabled much better understanding of the brain through
magnetic resonance imaging (MRI) in conjunction with non-MR based brain imaging techniques,
such as positron emission tomography (PET), electroencephalography (EEG), and
magnetoencephalography (MEG). Brain imaging techniques have evolved significantly during the
past few decades, making MRI in particular, a powerful tool to study the structure (structural MRI)
and function of the brain (functional MRI).
The principal advantage of MRI compared to other neuroimaging techniques is the high spatial
resolution for imaging various tissue types. MRI is non-invasive and does not involve any ionizing
radiation as in X-ray or Tomography imaging. It also offers flexibility to image any plane of the
object without the physical rotation, which is extremely helpful for imaging the structure and
function of the brain [1-3]. One of the fundamental questions in neuroscience is to establish the
correspondence between the structural and functional properties of the brain. Functional MRI
(fMRI) has become a principal tool in establishing such a correspondence, based on a biophysical
mechanism known as blood-oxygenation level dependence (BOLD) [1-3]. With constantly
improving spatial and temporal resolutions, fMRI is at the forefront of non-invasive neuroimaging
techniques to map underlying structure with associated function to a higher degree of accuracy.
The methods developed to analyze the resting-state (subject laying at rest with minimal extraneous
thoughts) and task-based (while performing a specific task e.g., finger tapping, response to
auditory, visual stimuli) fMRI data can be broadly classified into model-dependent and model-free
methods [4]. These methods aim to obtain statistically meaningful results in single subjects and
groups of subjects through various analysis approaches. Seed-based connectivity analysis (SCA)
is an example of a model-dependent analysis method in which the time-dependent signal from a
particular region of interest (ROI/seed) is correlated against signals from all other regions in the
brain, resulting in a functional connectivity map [5,6]. These maps facilitate a straightforward
interpretation of the extent to which the seed region is functionally connected to the rest of the
2
brain. Model-free methods, such as principal component analysis (PCA) [7], independent
component analysis (ICA) [8,9], hierarchical [10], and normalized clustering [11] offer a
generalized data-driven approach to investigate the functional connectivity, but pose a challenge
in the interpretation of the results. Although SCA is widely used approach for fMRI analysis, it is
highly sensitive to confounds such as head motion, physiological noise (respiration and cardiac
related pulsations), and requires regression. On the other hand, regression may not only bias the
connectivity analysis, but also impairs the real-time implementation of SCA. Recent advances in
high-speed fMRI acquisition techniques such as multi-band EPI [12], echo-shifted imaging
[13], MR-encephalography [14], as well as single-shot and multi-slab echo-volumar imaging
(MEVI) [15,16] are shown to enhance sensitivity by unaliasing the physiological noise
components for detection of fluctuations in the fMRI data.
The objective of this thesis is to develop a generalized framework for mapping the functional
connectivity by combining the advanced high-speed MEVI technique with a novel seed-based
connectivity analysis, which employs a sliding-window correlation analysis with running mean
and standard deviation (meta-statistics). This novel windowed SCA (wSCA) approach [17] is
computationally efficient for real-time (online) fMRI analysis and does not require the regression
of confounding signal sources. The real-time implementation of wSCA enables detection of
dynamic changes in functional connectivity at very short time scales. The offline extension of this
methodology enables for characterizing confound tolerance in comparison with conventional
regression-based approaches and mapping functional connectivity in the entire brain through high
dimensional connectomics. The combination of wSCA with multi-slab echo-volumar high-speed
fMRI data (temporal resolution of 136 ms) is shown to provide high sensitivity for mapping
resting-state connectivity dynamics among 28 networks previously detected in a spatial group-ICA
study [18]. The robust confound tolerance achieved using wSCA and its compatibility with real-
time high-speed fMRI, make this approach suitable for monitoring data quality, neurofeedback,
and clinical research studies that involve disease related changes in functional connectomics.
3
1.2. Thesis Organization
Chapter 2 outlines the principles of nuclear magnetic resonance in obtaining MR signal and basics
of magnetic resonance imaging.
Chapter 3 briefly explains functional MRI, generation of blood-oxygenation level dependent
(BOLD) signal, and the hemodynamic response function (HRF). A brief introduction to resting-
state networks is presented.
Chapter 4 describes the methodology of the windowed seed-based connectivity analysis (wSCA).
This chapter characterizes the confound suppression of wSCA using simulations and in vivo data
and its implementation in real-time.
Chapter 5 presents the application of the wSCA approach offline to map the resting-state
connectivity in single subjects and group using 28 single- and multi- region seeds and a dual
threshold mechanism to identify the regions with stable and unstable functional connectivity.
Chapter 6 extends the mapping of functional connectivity from 28 seed regions to the high
dimensional whole-brain connectome fingerprints, generated using an automated atlas-based
implementation of the wSCA.
Chapter 7 discusses the real-time resting-state connectivity dynamics with a proof-of-concept
neurofeedback experiment and the identification of the recursive connectivity patterns.
Chapter 8 speculates on the future directions that this work might take.
4
References
1. Haacke, E. M., Brown, R. W., Thompson, M. R., and Venkatesan, R. 1999. Magnetic resonance imaging: Physical principles and sequence design. John Wiley & Sons, NY.
2. Clare, S. 1997. Functional MRI: Methods and applications. University of Oxford. 3. Hornak, J. P. 1996-2014. The basics of MRI. Center for imaging science, Rochester
institute of technology. NY. 4. Van den Heuvel, M. P., Hulshoff Pol, H. E., 2010. Exploring the brain network: A review
on resting-state fMRI functional connectivity. European Neuropsychopharmacology 20, 519–534. doi:10.1016/j.euroneuro.2010.03.008.
5. Biswal, B.B., Van Kylen, J., Hyde, J.S., 1997. Simultaneous assessment of flow and BOLD signals in resting-state functional connectivity maps. NMR Biomed. 10 (4–5), 165–170.
6. Cordes, D., Haughton, V.M., Arfanakis, K., Wendt, G.J., Turski, P.A., Moritz, C.H., Quigley, M.A., Meyerand, M.E., 2000. Mapping functionally related regions of brain with functional connectivity MR imaging. AJNR Am. J. Neuroradiol. 21 (9), 1636–1644.
7. Friston, K.J., Frith, C.D., Liddle, P.F., Frackowiak, R.S., 1993. Functional connectivity: the principal component analysis of large (PET) data sets. J. Cereb. Blood Flow Metab. 13 (1), 5–14.
8. Comon, P., 1992. ICA, a new concept? Signal Processing 36, 287-314. 9. Calhoun, V.D., Adali, T., Pearlson, G.D., Pekar, J.J., 2001. A method for making group
inferences from functional MRI data using indepen-dent component analysis. Hum. Brain Mapp. 14 (3), 140–151.
10. Cordes, D., Haughton, V., Carew, J.D., Arfanakis, K., Maravilla, K., 2002. Hierarchical clustering to measure connectivity in fMRI resting-state data. MRI, 20 (4), 305–317.
11. Van den Heuvel, M.P., Mandl, R.C., Hulshoff Pol, H.E., 2008a. Normalized group clustering of resting-state fMRI data. PLoS ONE 3 (4), e2001.
12. Feinberg, D. A., Moeller, S., Smith, S. M., Auerbach, E., Ramanna, S., et al, 2010. Multi-plexed echo-planar imaging for sub-second whole-brain fMRI and fast diffusion imaging. PLoS ONE 5(12): e 15710. doi: 10.1371/journal.pone.0015710.
13. Gibson, A., Peters, A. M., Bowtell, R., 2006. Echo-shifted multislice EPI for high-speed fMRI. Magnetic Resonance Imaging 24 (2006) 433-442. doi: 10.1016/j.mri.2005.12.030.
14. Zahneisen, B., Hugger, T., Lee, K, J., LeVan, P., Reisert, M., et al, 2012. Single-shot concentric shells trajectories for ultra-fast fMRI. MRM. doi: 10.1002/mrm.23256.
15. Mansfield, P., Harvey, P. R., Stehling, M. K., 1994. Echo-volumar imaging. Mag. Res materials in physics, Biology and Medicine 1994 Volume 2, Issue 3, 291-294.
16. Posse, S., Ackley, E., Mutihac, R., Rick, J., Shane, M., Murray-Krezan, C., et al, 2012. Enhancement of temporal resolution and BOLD sensitivity in real-time fMRI using multi-slab echo-volumar imaging. NeuroImage 61. doi: 10.1016/j.neuroimage.2012.02.059.
17. Vakamudi, K., Ackley, E. S., Trapp, C. W., Damaraju, E., Calhoun, V. D., Posse, S, 2016. Confound-Tolerant Seed-Based Sliding-Window Connectivity Analysis for Real-Time High-Speed Resting-State fMRI, Neuroimage, submitted March 2016.
18. Allen, E. A., Erhardt, E. B., Damaraju, E., Gruner. Calhoun, V. D., et al, 2011. A baseline for the multivariate comparison of resting-state networks. Front. Syst. Neurosci. 5:2.
5
Chapter 2 Nuclear Magnetic Resonance
2.1. Introduction
The discovery of nuclear magnetic resonance (NMR) had its foundation in the quantum
mechanical description of the atomic nuclei. The spin angular momentum of protons and their
interactions with a magnetic field were extensively studied by Stern, Gerlach, Rabi, and others
[1,2]. Felix Bloch [3] and Edward Purcell [4] independently measured the effect of the spin
precession in a magnetic field, which lead to the discovery of NMR in 1946.
Atomic nuclei with an odd number of protons/neutrons contribute to nuclear magnetic resonance.
For a nucleus to possess the NMR property, it must have both a non-zero magnetic moment and
angular momentum. In the case of a proton of charge ‘+e’ and mass ‘m’, the magnetic moment and
spin angular momentum arise from rotational motion due to thermal energy around its axis. Many
nuclei of biological interest, such as 1H, 3He, 13C, 15N, 17O, and 19F, have odd number of protons
and therefore possess NMR properties. Since 1H is the most abundant nucleus in biological systems
(e.g. in H2O and many organic compounds), MRI is primarily implemented for protons [5-11].
2.2. Angular Momentum and Energy
The basis for MRI can be understood from the interaction of a proton spin with the magnetic field
in the quantum mechanical framework. The magnitude of the spin angular momentum is given by
│S │ = ħ√s(s + 1) (2.1)
In a magnetic field that is applied along the Z-direction, the angular momenta have the following
values
Sz = ħms (2.2)
where the (2S+1) values of ms are given by ms = s, (s-1), (s-2), … -s.
A proton of spin ½, has two possible spin states
Sz = ±1/2 ħ (2.3)
6
The energy of a spin system placed in a magnetic field �� is given by
E = -µ·�� (2.4)
where µ is the magnetic moment. It is proportional to the spin angular momentum,
µ=γ𝑆 (2.5)
where γ is gyromagnetic ratio and is constant for a given nucleus. By combining the Eqs. 2.4 and
2.5, we can derive a Hamiltonian for the system with magnetic field applied in the Z-direction,
H= -γħ (�� ·𝑆 )
Hz= -γħBzSz (2.6)
Solving the Schrödinger equation of this Hamiltonian for the energy eigenstate, we get
H│�� s˃ = E│�� s˃
E = -γħBzms (2.7)
The change in energy of a proton as a result of transition between two spin states (±1/2),
ΔE = E−21 − E+2
1 = 𝛾ħBz (2.8)
This transition is accompanied by emission or absorption of a photon with frequency ν0
ΔE = γħBz = hν0 (2.9)
where ν0 = γ
2πBZ. For a constant field Bz
= B0z,
ω0 = 𝛾B0 (2.10)
The Eq. 2.10 is a fundamental relation in NMR, called the Larmor equation. Since the
gyromagnetic ratio ‘γ’ is constant for a given nucleus, the Larmor frequency is determined solely
by the applied magnetic field.
7
2.3. From Quantum To Classical
Although quantum mechanical theory can quantify the spin properties of an individual nucleus,
real systems contain large numbers of nuclei, and therefore, the theory must be extended to
encompass an ensemble of spins. The thermal energy associated with normal human body
temperature prevents proton spins from completely aligning in the direction of the external
magnetic field, generating more parallel spin states (low-energy) relative to anti-parallel spin states
(high-energy). The net magnetization resulting from this distribution of spin states depends on the
relative energy difference ΔE, temperature (T), and a proportionality constant (κB), called the
Boltzmann’s constant. If the probability for parallel spin states is P+1/2, and the probability for anti-
parallel spin states is P-1/2, the relative distribution of these probabilities is given by
P+2
1
P−2
1= e
∆E
κBT (2.11)
where 𝜅𝐵 = 1.3806x10-23 J/K and T is the absolute temperature. Since 𝜅𝐵 is very small ( ∆𝐸
𝜅𝐵𝑇≪ 1),
Eq. 2.11 can be approximated as
P+2
1
P−2
1≈ 1 +
∆E
κBT (2.12)
Using 𝑃+21 + 𝑃−2
1 = 1, we calculate the excess number of spins (𝑃+21 − 𝑃−2
1) that are parallel to
the magnetic field as
P+21 − P−2
1 ≈ ∆E
2κBT (2.13)
A small sample of any biological tissue contains N ∆𝐸
2𝜅𝐵𝑇 excess proton spins, where N is Avogadro
number (6.022x1023). In a magnetic field of 3 Tesla, for every million proton spins there are
approximately eighteen excess parallel proton spins. For example, in a volume element (voxel) of
size 4x4x4 mm3 (volume of 0.064 ml), the total number of excess spins will be ~8x1016. The
magnetic moment generated from such a large number of spins leads to macroscopic NMR effects
for imaging the bulk properties of the tissue, justifying the classical Boltzmann distribution
employed in studying MRI.
8
2.4. Classical Equations for NMR
2.4.1. Precession
The equation of motion of a magnetic moment vector (M ), placed in a magnetic field (B ) is
dM
dt= γM x B (2.14)
For a static magnetic field, B = B0k, the solution of this equation can be written as
M (t) = Mx0(x cosωt − y sinωt) + My0(x sinωt + y cosωt) + Mz0t (2.15)
The Eq. 2.15 describes the precession of the magnetization vector about Z-axis as shown in Fig.
2.1. The precessional frequency is equal to the Larmor frequency, in accordance with Eq. 2.10.
2.4.2. Excitation
In the NMR experiment, MR signal is detected by electromagnetic coils (radiofrequency coils)
that transmit and receive electromagnetic fields at resonant frequencies of the nuclei within a static
magnetic field. When a sample is placed in the magnetic field, the magnetic moments of the nuclei
align with the static field. The radiofrequency coils then transmit electromagnetic waves
(excitation pulses) at the Larmor frequency to rotate the equilibrium spin magnetization away from
Fig. 2.1. Precession of a magnetization vector M , in a magnetic field B 0 directed along Z-
axis with an angular frequency ω.
9
the Z-axis. This process is called excitation. After the duration of the excitation pulse, the spins
undergo relaxation. The magnetization component due to the spins along the Z-axis is governed
by exponential growth, and along the transverse plane (XY), it is governed by exponential decay
which are detected by the radiofrequency receiver coils as an MR signal. The detected signal is
called the ‘Free-Induction Decay’ (FID). The energy absorbed by the nuclei during excitation is
released through longitudinal relaxation (see 2.4.4).
2.4.3. Bloch Equation
When a time-varying magnetic field B1 (t) = B1(x cosωt − y sinωt) is applied along with the
static magnetic field B = B0z, the precession of the spins follow two different types of relaxation
mechanisms to reach the original spin state. This combined effect can be studied using a
generalized equation of motion called the Bloch equation:
dM
dt= γM x B +
1
T1(M0 − Mz
) − 1
T2(Mx + My
) (2.16)
The Bloch equation describes the behavior of a net magnetization vector of a spin system in the
presence of a time-varying magnetic field, which precesses around the stationary magnetic field
component at the Larmor frequency with longitudinal changes governed by T1 and transverse plane
changes governed by T2. The solutions of Eq. 2.16 govern the dynamics of the magnetization
vector during steady-state, excitation, and relaxation.
Mathematically, solving Bloch equation is more convenient by rotating the XY plane by an angular
frequency Ω = –γB0, as shown in Fig. 2.2. The new frame of reference is called the rotating frame
of reference, in which the magnetization vector appears to smoothly tip down, while Mxy appears
stationary. The equation of motion with a time-varying magnetic field in the rotating frame of
reference (X’, Y’, Z’) is given by dM
dt= γM x B eff (2.17)
where B eff = B + Ω
γ.
10
By converting Eq. 2.16 to the rotating frame of reference, we obtain the solutions for the Bloch
equation through the following relaxation mechanisms.
2.4.4. Relaxation
Longitudinal relaxation
After the duration of the excitation pulse, the spin system gradually loses the energy that was
absorbed during excitation and retains the original energy state along the direction of the external
magnetic field (Z). This process is called longitudinal relaxation or spin-lattice relaxation [5-11].
At equilibrium, the net magnetization vector M is along the direction of the applied magnetic field
�� . This is called the equilibrium magnetization M0 , which contains only the Z component, known
as longitudinal magnetization Mz . After a 90o excitation RF pulse, which flips the longitudinal
magnetization into the transverse plane, the longitudinal magnetization reorients along the Z-axis
with time constant T1 (Fig.2.3). The dynamics of the longitudinal magnetization are described by
the Bloch equations (Eq. 2.16). The longitudinal magnetization is governed by,
dMz
dt= −
(Mz−M0)
T1 (2.18)
Fig. 2.2. Laboratory and rotatory frames of reference. The XY plane of a laboratory frame is
rotated by an angular frequency Ω = –γ𝐵0.
11
Solving for 𝑀𝑧,
Mz = M0(1 − e−T1t
) (2.19a)
T1 is the time to recover 63.2% of the equilibrium magnetization. The most commonly used
experiment to measure T1 is the ‘inversion recovery’, in which the net magnetization is inverted
along the -Z-axis using a 180o inversion RF pulse which will return to its equilibrium position
along the +Z-axis at a rate governed by T1. The magnetization is measured after a time delay
(inversion time) using a 90o pulse. A series of experiments with different inversion times allows
to measure T1 by fitting the Eq. 2.19 as a function of inversion time t,
Mz = M0(1 − 2e−T1t
) (2.19b)
Fig. 2.3. Longitudinal relaxation. a) Spins oriented along the direction of the magnetic field (Z),
b) spins flipped on to the XY-plane by a 90o pulse, c) spins reorienting along the Z-axis, and d)
spins along the Z-axis after relaxation. Graph shows the magnetization along the Z-axis over time,
with T1 being the longitudinal relaxation time.
12
Transverse relaxation
The magnetization in the transverse plane is subject to microscopic fluctuations in the local
magnetic fields resulting from the spin-spin interactions. These randomly fluctuating precessional
frequencies lead to randomly changing spin phases that decrease the net magnetization. In
transverse plane this can be described as ‘fanning out’ of the spin orientation in time (Fig. 2.4),
which corresponds to dephasing of the magnetization. The decrease of the transverse
magnetization is given by the Bloch equations (Eq. 2.16) [5-11]:
dMx
dt= My. γB −
Mx
T2 and dMy
dt= −Mx. γB −
My
T2 (2.20)
Combining the interactions of X and Y components in complex form, the net transverse
magnetization is denoted by Mxy = Mx + iMy. The solution of this combined magnetization in
both the directions is,
Mxy = Mxy0e−T2
t
. e−iωt (2.21)
where Mxy0 is the initial magnitude of the transverse magnetization after excitation.
Fig. 2.4. Transverse relaxation. a) Spins oriented along the XY-plane, b) spins start spreading
along the XY-plane causing incoherence due to phase differences, c) transverse spin relaxation
in the XY-plane. Graph shows the transverse magnetization in the XY plane, with T2 being the
transverse relaxation time.
13
2.5. Magnetic Resonance Imaging (MRI)
Magnetic field gradients are used to spatially encode the spin magnetization after excitation. These
gradient fields are vector fields represented by Gx, Gy, and Gz whose magnitude vary linearly along
the X, Y, and Z axes and oriented along the main magnetic field B0 . These gradient fields, when
combined with the static magnetic field B0 (directed along the scanner axis), generate an effective
field B that varies at every spatial location (X, Y, Z). The magnitude of the effective field thus can
be written as a linear combination of the main magnetic field and the gradient fields, at a given
location (X, Y, Z) and time t.
�� (t) = 𝐵0 + Gx(t) �� + Gy(t) ��+ Gz(t) �� (2.22)
For the purpose of imaging, these magnetic field gradients are switched dynamically after signal
excitation, to encode the spin location in the spin frequency and phase, thus modulating the
received signal. Using ω = 𝛾B in Eq. 2.21, the transverse magnetization at a given location and
time is given by,
Mxy(x, y, z, t) = Mxy0(x, y, z)e−T2
t
. e−iγBot e−iγ∫ (Gx(t)x+Gy(t)y+Gz(t)z)dtt0 (2.23)
The MR signal measured by the antenna is equal to the sum of the magnetizations over each voxel
(unit three-dimensional volume), at time 𝜏 and is given by,
S(τ) = ∭ Mxy(x, y, z)dx dy dz
x,y,z (2.24)
Substituting Mxy from Eq. 2.23 into 2.24, we get,
S(τ) = ∭ Mxy0(x, y, z)e−T2
t
. e−iγBot e−iγ∫ (Gx(t)x+Gy(t)y+Gz(t)z)dtt0 dx dy dz
x,y,z (2.25)
Eq. 2.25 is called the MR signal equation [5-11]. It states that the MR signal at any given position
and time is governed by T2 relaxation time, main magnetic field 𝐵𝑜, phase accumulated by the
effective field, and the sum of the net magnetizations across the voxels. This generalized equation
represents the relationship between the acquired signal S(τ) to the properties of the
object Mxy0(x, y, z) that is being imaged.
14
2.5.1. Zeugmatography and Slice Selection
The principle of encoding space using magnetic field gradients is called Zeugmatography [12],
introduced by Nobel Laureate Lauterbur in 1972 [13]. The term e−T2t
in Eq. 2.25 only influences
the magnitude of the signal through T2 relaxation, not the spatial location of the signal (unless T2
is short relative to the duration of spatial encoding). In addition, the demodulation of the Larmor
frequency (similar to demodulation of the carrier frequency in an FM radio) omits the term e−iγBot.
Therefore, we can eliminate these two terms from Eq. 2.25 for spatial encoding.
S(τ) = ∭ Mxy0(x, y, z)e−iγ∫ (Gx(t)x+Gy(t)y+Gz(t)z)dt
t0 dx dy dz
x,y,z (2.26)
Most of the functional and structural scans are acquired as a set of two-dimensional images and
reconstructed to form three-dimensional images. Although Eq. 2.26 is a reduced form of Eq. 2.25,
it still represents three-dimensional imaging, which is a slower process and not ideal for studying
the functional properties of the brain. This equation can be reduced to two-dimensions by first
selecting a slice of certain thickness along the Z-dimension and then acquiring the MR signal from
a single two-dimensional slice at a time.
The rectangular slices can be selected through the application of sinc modulated pulses along the
Z-axis. The frequency of precession becomes linear in the presence of a slice select gradient, given
Fig. 2.5. The frequency (ω) as in the laboratory frame as a function of position along the slice
selection axis when a gradient is applied along the Z-axis.
15
by, ω(z) = ω0 + γGzZ, where ω0 is the Larmor frequency at Z=0. The relationship is depicted in
Fig. 2.5. The slice selection depends on three factors: the central frequency of the excitation pulse
(ω), the band width (∆ω) of the radio frequency excitation field, and the strength of the gradient
field (Gz) whose thickness (TH) is given by,
𝑇𝐻 =∆𝜔𝑟𝑓
𝛾Gz (2.27)
The magnetization within the slice depends only on X and Y, and Eq. 2.26 is reduced to
S(τ) = ∬ M(x, y)e−iγ∫ (Gx(t)x+Gy(t)y)dtt0 dx dy
x,y (2.28)
2.5.2. Two-Dimensional Spatial Encoding and K-Space [14]
The two gradients Gx and Gy in Eq. 2.28 correspond to the frequency encoding gradient and phase
encoding gradient respectively [6-9]. The frequency encoding gradient changes the Larmor
frequency linearly along the gradient direction, thus enabling the localization of the MR signal
along that direction through Fourier transformation. This results in a projection image. The phase
encoding gradient is applied before the acquisition due to which, spins accumulate linearly
changing phase offsets along the gradient direction. Spatial information (i.e. spin phase encoding)
is acquired stepwise in a series of individual experiments with different phase encoding gradient
moments. The equations for these gradients in k-space formalism are given by equations 2.29a
(frequency encoding) and 2.29b (phase encoding).
kx(t) = γ
2π∫ Gx(τ)dτ
t
0 (2.29a)
ky(t) = γ
2π∫ Gy(τ)dτ
t
0 (2.29b)
These equations are also known as k-space trajectories. Using these equations, the magnetization
within the slice can be expressed in k-space notation. The relationship between the image space
and the frequency space is given by a mathematical formalism, known as Fourier transformations
[15]. This notation scheme using spatial frequencies offers computational and conceptual
16
advantages in describing the image formation from the MR signal. Using the k-space trajectories
(Eqs. 2.29) in Eq. 2.28, the MR signal equation in k-space is given by
S(τ) = ∬ M(x, y)e−i2πkx(t)xe−i2πky(t)ydx dy
x,y (2.30)
This equation describes a linear relationship between the image space and k-space. The signal can
be represented by a two-dimensional coordinate system in units of spatial frequency with kx and
ky as the axes. This coordinate system is defined as k-space. The Eq. 2.30, when operated by
inverse Fourier transform, will be converted to image space, a process known as image
reconstruction. The sampling parameter in the image space is distance and k-space is distance-1,
respectively. This infers that a larger k-space will correspond to finer details (spatial resolution) in
image space, but correspondingly will take longer time to encode, reducing the temporal
resolution. Thus, there is always a trade-off between spatial and temporal resolutions in MRI.
2.6. MR Contrast Mechanisms
The relative advantage of MRI to the other neuroimaging methods is the high degree of tissue
contrast based on differences in relaxation properties and water concentration. The contrast
between two tissue types A and B, is the relative difference between the corresponding MR signals.
Fig. 2.6. The relationship between image space and k-space through the two-dimensional
Fourier transform of a brain image.
17
For a spin echo experiment, there are two important parameters that govern the MR signal
acquisition and contrast mechanisms. These parameters are the repetition time (TR), defined as the
time interval between successive excitation pulses, and the echo time (TE), defined as the time
interval between excitation and data acquisition [9]. The TR and TE, along with the relaxation
times T1 and T2 discussed in the previous sections, determine the contrast between tissues. We
calculate this contrast by subtracting the MR signals from tissues A and B, using the following
equation.
CAB = M0A (1 − e−
TR
T1A ) e−
TR
T2A – M0B (1 − e−
TR
T1B ) e−
TR
T2B (2.31)
2.6.1. T1 contrast
The most common static contrast mechanism used to obtain structural brain information is based
on the T1 relaxation of atomic nuclei, also known as T1-weighed imaging. The tissues show a
maximum difference in T1 values for an optimal value of TR. For an exclusive T1 contrast, T2
contrast should be minimized using short TE. For TE << T2 (e−
TR
T2 1), Eq. 2.31 becomes
CAB = M0A (1 − e−
TR
T1A ) − M0B (1 − e−
TR
T1B ) (2.32)
Therefore, in order to acquire the T1 sensitive images, short echo times and intermediate repetition
times are employed.
2.6.2. T2 contrast
The signal loss in the case of T2 weighted imaging also depends on the TR and TE values. For
optimal T2 contrast, TR should be long so that T1 contrast is minimal. For TR >> T1 (𝑒−𝑇𝑅
𝑇1 0),
Eq. 2.32 becomes,
CAB = M0Ae−
TR
T2A – M0Be−
TR
T2B (2.33)
18
T2-weighted images are generated using spin echo pulse sequences (see 2.6.3) that have longer
repetition times and intermediate echo times. T2 images play an important role in clinical
applications as they show maximal contrast between fluid regions and the brain tissue, clearly
distinguishing various types of tumors, arteriovenous malformations, and other fluid associated
pathologies. High-resolution T2 images are also used as anatomical references in fMRI along with
T1-weighted images.
2.6.3. T2* contrast
Transverse relaxation is caused not only by spin-spin relaxation, but also by regional differences
in the spin precessional frequencies due to the local inhomogeneities in the magnetic field. The
combined effect of these two factors in the decay of transverse relaxation is defined as T2*
relaxation, given by,
1
T2∗ =
1
T2+
1
T2′ (2.34)
where T2 > T2* and T2
′ represents the dephasing factor due to the field inhomogeneities. T2* imaging
can sensitively differentiate oxygenated and deoxygenated hemoglobin present in the blood and
changes in overall blood volume, forming the basis for BOLD contrast fMRI (see Chapter 3).
Similar to the T2 contrast, T2* contrast is also achieved using pulse sequences with long repetition
times and intermediate echo times that matches the T2* value in the tissue. The effect of T2
′ due to
the field inhomogeneities can be compensated using a spin echo experiment, which consists of a
90o RF pulse and a 180o refocusing RF pulse with symmetric time delay TE/2 around the 180o
refocusing RF pulse and using long TR. The amplitude of the resulting signal, which is measured
at the echo time TE depends on T2, irrespective of local magnetic field inhomogeneities
as, S ~ e−
TR
T2 .
2.7. Conventional MRI
Conventional MRI experiments use a spin echo acquisition with readout encoding and phase
encoding as described above. This type of acquisition is time consuming, since each phase
19
encoding step is acquired in a separate signal excitation. The contrast mechanisms mentioned in
the previous section enable the anatomical imaging, albeit, at very long TR values. Anatomical
images maximize contrast at the expense of speed. The schematic of a gradient echo MRI pulse
sequence with a 90o radiofrequency (RF) excitation pulse, slice selection gradient (Gx), frequency
encoding gradient (Gy), phase encoding gradient (Gz), and readout (RO) are shown in Fig. 2.7. The
gradient echo MRI experiment employs a gradient echo that is sensitive to T2* signal dephasing,
for the purpose of fast imaging. It also allows to use short repetition times and low flip angles (flip
angle, θ = γB1τ, with τ being the duration of excitation pulse) to reduce the acquisition time to
several seconds for a single slice. However, in order to investigate the function of the brain using
MRI (fMRI), even faster imaging sequences are necessary, with temporal resolution of the order
of seconds or less, for whole-brain imaging, to map the physiological and task related signal
changes of interest (e.g., BOLD).
Fig. 2.7. Schematic of a gradient echo MRI pulse sequence with a 90o radiofrequency (RF)
excitation pulse, the slice selection (Gx), frequency encoding (Gy), phase encoding (Gz)
gradients, and the readout (RO).
20
2.8. Advanced MRI
2.8.1. Echo-Planar Imaging (EPI)
Conventional methods focus on encoding k-space line-by-line, which require a large number of
excitations for a single image, depending on the image matrix size. Nobel Laureate Mansfield, in
1977, proposed a method in which the entire k-space is encoded by rapid switching of gradients
with a single excitation, called echo-planar imaging (EPI) [6-9]. EPI requires the data acquisition
to be fast in the presence of T2*/T2 relaxation signal decay. The schematic of the EPI sequence with
the corresponding k-space encoding is shown in Fig. 2.8. The negative Gx and Gy gradients will
direct the k-space encoding to start from the bottom left corner. The k-space data is acquired
through scanning alternating k-space lines in opposite directions demanding a highly powerful
gradient system for such a rapid switchback. The artifacts introduced due to inconsistencies
between the different readout gradient polarities have to be corrected before the reconstruction,
using a navigator signal acquisition that measures these inconsistencies. The prevalent artifacts in
EPI are due to the inhomogeneities in static and gradient magnetic fields. Geometrical distortions
also occur in EPI due to the long k-space acquisition times following the excitation that lead to a
Fig. 2.8. a) Schematic of EPI pulse sequence. b) The k-space encoding, based on the gradients
of the corresponding colors in the pulse sequence (a) showing the rapid zig-zag movement
through k-space due to rapidly changing gradients.
21
convolution of the “slow” phase encoding process with local frequency offsets due to magnetic
field inhomogeneities (Eq. 2.35). EPI is a widely used imaging technique for high-speed imaging
that is available on all clinical scanners. However, it still poses limitations for imaging brain
function, in particular, it is sensitive to rapid movement of the head (intra-scan movement) and
heart beat related signal pulsations. In addition, EPI being a two-dimensional technique, it is highly
sensitive to motion in and out of the image plane that cannot be corrected for. These limitations
can be addressed by a more advanced, ultra-fast three-dimensional imaging technique built upon
EPI, known as Echo-Volumar Imaging (EVI), also proposed by Mansfield [16,17].
2.8.2. Echo-Volumar Imaging (EVI) [18]
The principle of the EVI is similar to EPI, except for the absence of a slice selection step. Instead,
either the whole volume of the object is excited (using nonselective RF pulse) or slab within the
object is excited (using a slab-selective RF pulse with a Z-gradient similar to slice selection) for
spatial encoding. The EVI technique allows to acquire an entire volume in a single excitation using
repeated EPI modules with phase encoding Z-gradient between the EPI modules, to resolve the
slices within the imaging volume. The EVI sequence thus employs an echo-planar frequency
encoding gradient and two interleaved phase encoding gradients.
The data acquisition technique used in the current study is a particular extension of the
conventional EVI, called the multi-slab echo-volumar imaging (MEVI) [18], a 3D sequence
developed based on a multi-echo EPI sequence [19-21] with fly-back along the kz (Fig. 2.9). The
acquisition of slabs shortens the duration of the readout module thereby improving image quality
compared with conventional EVI. Adjacent slabs are excited sequentially to cover a larger region
across the object and encoded during a TR using repeated EPI modules with interleaved phase
encoding gradients. The EPI modules consisted of trapezoidal oscillating gradients (GRO) along
the readout direction and a series of blipped primary phase encoding gradients (GPE1) that were
rewound at the end of every partition. A blipped secondary phase encoding gradient (GPE2) that
encodes the third spatial dimension was applied after each EPI module. Kz-space was encoded
symmetrically using a dephasing gradient before the first EPI module (kmax/2). The kx – ky space
22
trajectories for each kz step were traversed in the same direction using 4-fold acceleration for
GRAPPA [22] reconstruction. Geometrical distortion was computed using Eq. 2.35 from Jezzard
and Balaban, 1995 [23]:
dpixel = γ∆B0(x, y, z)Ta (2.35)
where γ is the gyromagnetic ratio and Ta is the sampling time. Blurring of the point spread function
due to the signal relaxation in the slice direction is computed using,
FWHMTTz∗ =
√3
π
Ta
Tz∗ ∆x (2.36)
The elongated readout of MEVI increases the effective echo time and as a consequence the BOLD
contrast for small structures, compared to EPI. The effect of the long MEVI readout on BOLD
contrast can be computed as a function of kz using,
∆S(t) = S0t
Tz∗ e
−(t
Tz)∆Tz
∗
Tz∗ (2.37)
EVI reconstruction performance is further improved due to the high SNR afforded by the slab
selection compared to EPI. Numerically optimized slab selection RF pulses and spatial
oversampling of one slice on either side of each slab were used to minimize inter-slab crosstalk,
to avoid spatial aliasing and to minimize signal losses at the slab edges. The bandwidth of the RF
excitation pulse was increased almost 2-fold (time-bandwidth product:10) and the duration of the
RF pulse was decreased 4-fold from 2560 μs of the product sequence down to 640 μs to improve
the slice profile and to minimize chemical shift and susceptibility related slab displacement.
2.8.3. Multi-slab Echo-Volumar Imaging (MEVI) Reconstruction [18]
The reconstruction pipeline employs distributed computing across the scanner using the image
computation environment (ICE) integrated with the custom fMRI research tool TurboFIRE. In-
plane (kx, ky) reconstruction of complex (magnitude and phase) images for each encoded kz step
and slab was performed online on the scanner. Image reconstruction in the kz dimension included
Hamming filtering, Fourier transformation, slice ordering and concatenation of stacks of slices
23
from different slabs to form contiguous 3D image volumes. Slice ordering consisted of the
following steps: (i) the offset D of the stack of slabs from the magnet center was computed based
Fig. 2.9. a) Schematic of the MEVI sequence. The pulse sequence for each slab consists of a
trapezoidal oscillating readout gradient (GRO) along the readout direction, a blipped primary
phase encoding gradient (GPE1) that is rewound at the end of every partition and a blipped
secondary phase encoding gradient (GPE2) that encodes the third spatial dimension. (b) K-
space trajectory for each slab with 4-fold acceleration in the ky-direction.
24
on the slab prescription on the scanner console, which includes the offset of the center of the
slabstack P with respect to the magnet center along the principal axes: right-left (RL), anterior–
posterior (AP), head-foot (HF), the slab rotation angles α around the RL axis, and β around the AP
axis, as well as the slice thickness. This involves computing the normal unit vector of the slabstack
(n ) using Euler rotation matrices, projecting the position vector P onto n, and adjusting a half-slice
offset to account for the digitization of the slices:
D = RL cosα sinβ− AP sinα+ HF cosα cosβ− 0.5SLT (2.38)
(ii) D determines the aliasing of reconstructed slices along the slice direction within the encoded
FOV (FOVz), which was accounted for by a circular shift of the stack of slices for each slab. (iii)
Slices at the edge of the slab were included, if their overlap with the slab exceeded a user-selected
fraction of the slice thickness (30%).
2.8.4. MEVI – Advantages and Limitations
Using whole-brain MEVI, 4-slab data is acquired with a TR of 286 ms (4 mm isotropic voxel size)
and a 2-slab partial brain data is acquired with a TR of 136 ms for partial (4×4×6 mm3 voxel size)
on a conventional clinical 3 T scanner equipped with 12-channel head coil. Functional MRI
benefits from such high temporal resolution as it facilitates higher sensitivity gains for mapping
the resting-state fluctuations at low frequencies (0.01 – 0.1 Hz). Apart from the increased temporal
resolution and enhanced BOLD sensitivity [18], the increased SNR per unit time of 3D versus 2D
encoding [24,25] makes EVI advantageous. EVI acquisitions, however, are associated with
considerable challenges, such as the need for advanced hardware, persistent image quality
constraints due to geometrical image distortion, blurring and signal drop outs that are exacerbated
by head movement, signal drifts due to gradient instability, and steady-state effects. These
challenges are particularly pronounced at high magnetic field strengths. Additionally, practical
applications of EVI are hampered by time consuming image reconstruction of the large amounts
of data generated. The primary objective of this study is to demonstrate the applicability of the
MEVI technique in real-time resting-state fMRI by taking advantage of the high sensitivity gains.
25
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27
Chapter 3 Functional Magnetic Resonance Imaging
3.1. Introduction
Functional neuroimaging techniques are primarily divided into two categories: direct measurement
of neuronal activity or indirect measurement of neuronal activity. Electromagnetic approaches,
such as electroencephalography (EEG) and magnetoencephalography (MEG), are characterized
by the direct measurement of neuronal surface currents. The metabolic approaches, on the other
hand, are based on the indirect measurement of the neural activity and the associated neurological
and physiological changes. Functional MRI (fMRI) [1-3] belongs to the latter category, where the
neuronal activity is measured indirectly by the MR signal due to the differences in the magnetic
properties of the hemoglobin in two different oxygenation states. This is called the blood-
oxygenation level dependent (BOLD) signal. The BOLD signal generation depends on the cerebral
blood flow (CBF), cerebral blood volume (CBV), and cerebral metabolic rate of oxygen (CMRO2)
[4-9]. The complete understanding of such an indirect process requires a thorough analysis of the
brain’s metabolism, anatomical and functional neurovascular coupling, relationship between the
neuronal activity and the supply-demand chain of energy in the brain along with some additional
factors, which is beyond the scope of this thesis. Instead, this chapter focuses on the basic
properties of the BOLD signal.
The spin dephasing interactions, or transverse relaxation (T2 relaxation), as discussed in chapter 2
are of particular significance in fMRI. The transverse relaxation in an ideal homogenous magnetic
field should follow a free-induction decay (FID) signal profile with a time constant T2, but in
reality, this process is more rapid in the biological tissue due to local field inhomogeneities,
resulting in a reduced time constant T2*. These field variations alter the precessional frequency of
protons, perturbing the phase and accelerating the transverse relaxation. The local magnetic field
inhomogeneities depend on the local blood supply and physiological states. These in turn depend
on the neural activity, making the inhomogeneity measurement (T2*) an indirect estimate of the
neuronal activity. Functional MRI has significantly enhanced the ability to study functional brain
connectivity though the BOLD signal. It offers excellent spatial resolution relative to EEG or MEG
and higher temporal resolution compared to positron emission tomography (PET).
28
3.2. Blood-Oxygenation Level Dependent (BOLD) Signal
Seiji Ogawa [10,11] discovered that the blood vessels can be identified on T2* images by changing
the quantity of oxygenated blood flowing through the vessels. Under normal activity conditions,
the oxygenated hemoglobin (Hb) is converted to deoxyhemoglobin (dHb) at a constant rate in the
capillaries. During the neuronal activation either by external stimuli or by internal biophysical
mechanisms, the demand for oxygen increases in the activated brain regions. This causes changes
in the cerebral blood flow (CBF) and cerebral blood volume (CBV), which in turn changes the
oxygenated hemoglobin (diamagnetic) and deoxyhemoglobin (paramagnetic) levels. Additionally,
during activation, the vascular system supplies more oxygenated hemoglobin than is being
consumed. The overcompensated oxygenated hemoglobin flushes the deoxygenated hemoglobin
from the capillaries resulting in an increase in the MR signal. This disparity between the oxygen
consumption and utilization results in a reduced signal loss due to T2* effects, which forms the
basis for generation of the BOLD signal [1-8] and results in a brighter MR image.
3.3. Hemodynamic Response Function (HRF)
The change in the MR signal caused by neuronal activity is called hemodynamic response (HDR)
which depends on the rate of change of deoxygenated hemoglobin in a given voxel (measured by
the BOLD signal). The theoretical models of BOLD signal generation can be verified through
comparison with the amplitude and time course of the measured BOLD signal due to brief stimuli,
known as the temporal impulse response function or hemodynamic response function (HRF) [12-
14]. There are various modeling schemes for illustrating HDR, the most popular one being the
canonical HRF [12-16]. It is mathematically represented by a double gamma function shown in
Eq. 3.1.
ℋ(t, θ) = c1tα1−1
Γ(α1)eβ1t + c2
tα2−1
Γ(α2)eβ2t (3.1)
where Γ(𝛼𝑖) is the Gamma function, c1 ≥ c2 and θ = [c1, α1, β1, c2, α2, β2] ϵ ℝ6. The schematic
representation of HDR is shown in Fig. 3.1.
29
The measured signal change is the convolution of the HRF with the neuronal activation pattern.
The HDR can be broadly divided into three distinct segments, called initial dip (region ‘a’),
overcompensation (region ‘b’), and undershoot (region ‘c’). The merit of the double gamma HRF
is that it can establish a closer correspondence between the physiological time scales in the brain
and the HDR. For the first 1-2 s of the HDR cycle, the T2* signal decreases below the baseline,
due to the transient increase in deoxyhemoglobin from neuronal activity. The next 2-5 seconds are
governed by the oversupply of oxygenated hemoglobin, resulting in an effective decrease in
deoxyhemoglobin and an increase of the HDR to the maximum. The third segment of the HDR is
characterized by undershoot below the baseline amplitude, due to the increased blood volume and
reduced blood flow, after the neuronal activity [3].
3.4. Resting-state fMRI
Resting-state fMRI is the study of functional interactions among brain regions when the subject is
not performing any explicit task and with minimal extraneous thoughts. Discovered 20 years ago
Fig. 3.1. The hemodynamic response (HDR) represented as a double Gamma function which
consists of a) initial dip (1-2 s), b) primary response (2-5 s), and c) undershoot (1-3 s).
30
with the seminal work of Biswal et al., 1995 [17], it is now widely used to characterize the inter-
regional functional connectivity patterns/modes based on spontaneous, low frequency (< 0.1 Hz)
BOLD signal changes. The neuronal basis of these spontaneous low frequency fluctuations is not
yet completely understood. The conventional fMRI protocols have a temporal resolution of 0.5 Hz
(TR of 2-3 s), which causes the aliasing of high frequency components into the lower frequencies
(0.01–0.1 Hz). These high frequency components stem from the cardiac and respiratory pulsations,
introducing artificial correlations between anatomically distant brain regions. It has previously
been suggested that these spontaneous low frequency fluctuations are the result of cardiac and
respiratory induced high frequency fluctuations, rather than the representation of any neuronal
activity. However, it has been well established that the resting-state signals correlate between brain
regions that are anatomically distant but functionally related, e.g., motor, auditory and visual
cortices, supporting the neuronal basis. In addition, most of the power in the resting-state
fluctuation spectrum is solely from contributions of very low frequencies, which counters the
argument of aliasing high frequencies. In summary, more observations favor the neurological basis
of the resting-state signals. It has also been widely known that cardiac and respiratory pulsations
do confound the resting-state connectivity apart from motion and hardware induced noise.
3.5. Confounding Signals in Resting-state fMRI
Resting-state fMRI has been increasingly used as an adjunct to the task-fMRI for mapping
functional connectomics in groups of healthy controls and patients [18-20]. The weak BOLD
signal changes are confounded by body and head movements [21,22], physiological noise [23],
variations in neurovascular coupling, instabilities in the scanner baseline signal, sensitivity losses
due to susceptibility variations at tissue borders, ghosting due to even-odd echo interference in the
case of EPI, among other sources [24]. Regression of the confounding signals is a widely
implemented procedure in the analysis of fMRI data. The regression of the global mean, however,
has been a topic of intense debate [25-28], since it is known to introduce negative correlations and
bias positive correlations. This has led to the implementation of alternative approaches (e.g.
scrubbing, despiking) to remove movement related artifacts that confound functional connectivity
[29].
31
3.6. Preprocessing in fMRI
Seed-based connectivity analysis (see Chapter 1), is one of the most widely used fMRI data
analysis methods, which computes the correlations between each individual voxel time course and
the time course from an ROI. For such an implementation to be statistically meaningful, the data
should be free from a variety of confounding signals mentioned earlier. Preprocessing refers to a
series of computational techniques to compensate for unwanted variability in the data and to obtain
accurate statistical results by minimizing the ambiguity caused by such confounding signals of
non-neurological origin. Preprocessing is expected to enhance the functional resolution of an fMRI
experiment. The major preprocessing steps implemented in a typical fMRI analysis are as follows:
Motion Correction
Head and body movements pose substantial problems for fMRI studies. Motion correction has
been an area of intense investigation from the early days of fMRI experiments [30]. Since fMRI
acquisition is highly sensitive to motion, the slightest head movement can introduce spurious
connectivity across the brain, leading to misinterpretation of the connectivity results. Along with
preventing head motion to the greatest extent possible, various techniques were developed to
correct for head motion during and after the scan. Motion correction is implemented using six rigid
body transformations (three translational and three rotational). The effect of the movement is
estimated using these six parameters, their (higher) derivatives and mitigated using regression
analysis.
Slice time correction
During a multi-slice fMRI acquisition, the slices may be collected using a number of RF pulses at
various time points within a TR (e.g., ascending/descending slice acquisition or interleaved
acquisition). Due to the imperfections in RF profiles, the immediate neighborhood of the selected
slice is also excited. This region should be avoided in the following slice acquisition, as the spins
are not recovered to the equilibrium. It is a common practice to excite by leaving a gap between
the slices or to excite either even or odd numbered slices to mitigate these signal changes due to
cross-slice excitation. These time differences are corrected prior to the analysis using temporal
interpolation.
32
Spatial and temporal filtering
Spatial filtering, also known as spatial smoothing, is typically implemented using a Gaussian filter
in order to distribute the intensity of each voxel to the nearby voxels. This results in a high SNR
thereby improved statistical validity of functional connectivity metrics [31]. Temporal filtering
improves functional SNR by minimizing the signal changes at unwanted frequency bands, e.g.
physiological noise components in the frequency ranges 1.0 -1.5 Hz (heart rate) and 0.2 – 0.3
(respiration). The presence of temporal autocorrelations, which can bias the connectivity results,
should be accounted for, by applying filters to remove autocorrelations in time series data, before
the analysis. This process is known as pre-whitening [32].
Coregistration
The low spatial resolution of fMRI images cannot provide finer details of the anatomy in a subject.
In most of the studies, it is necessary to map the functional activations onto high-resolution and
high contrast anatomical images in order to accurately delineate the regions associated with a
specific function. The computational technique that maps the functional images onto anatomical
images, is called coregistration.
Spatial Normalization
Human brains show extensive morphological variability. When investigating a specific function in
the brain, integration of the data over a large number of subjects is often necessary. Spatial
normalization is a mathematical technique and an extension of coregistration, through which each
brain is stretched, squeezed and warped so that the anatomy is similar to a reference brain.
Normalization is typically performed using standard atlas spaces like Talairach or MNI [33].
3.7. Resting-state Networks
The brain is an intricate network with regions that are structurally distributed but functionally
connected. Functional connectivity is defined as the temporal dependency of neuronal activation
patterns of anatomically separated brain regions. Recent advances in the fMRI acquisition and
analysis methods have been instrumental in probing the functional networks in the primate as well
33
as human brain. A vast number of group studies have established a significant number of highly
correlated functional brain regions during the resting-state condition, known as resting-state
networks [19,20]. Prototypes of some of the major classes of such networks are shown in Fig. 3.2.
Despite the fact that these studies have used different subject populations, fMRI acquisition
protocols, and analysis methods (chapter 1), they show a great deal of common features with
respect to the functional connectivity patterns.
In the case of seed-based correlation analysis, if the region of interest selected is an ipsilateral
motor, auditory, or visual cortex, a strongly correlated contralateral side is observed, supporting
the functional connectivity hypothesis. In the case of ICA, these bilateral networks are identified
based on the fluctuation frequency of a given network. These findings suggest that neurons show
spontaneous activity even in the absence of external stimuli, potentially allowing for the
continuous transmission of information to the other neurons.
Fig. 3.2. The six major classes of resting-state networks (RSNs) with blue regions representing
the principal activation regions in: a) attention network, b) auditory network, c) default-mode
network, d) frontal network, e) sensorimotor network, and f) visual network.
34
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Chapter 4 Windowed Seed-based Connectivity Analysis [1]
4.1. Introduction
Resting-state connectivity is currently studied in a wide range of neuroscience and clinical
applications [2-8]. Functional connectomics group studies across large number of subjects have
identified over a hundred RSNs, which exhibit considerable spatio-temporal non-stationarity [9-
12]. Among the methods developed to measure resting-state network (RSN) connectivity [13-17],
seed-based connectivity analysis (SCA) is well established, particularly for clinical research
studies, since it provides high sensitivity and straightforward interpretation of connectivity in
single subjects. However, the small amplitude of blood-oxygenation level dependent (BOLD)
signal changes renders resting-state fMRI sensitive to a wide range of confounds as discussed in
chapter 2 [18-26]. Studies have demonstrated that the regression of measured head movement
parameters and regionally averaged time courses from white matter and the ventricles is essential
for artifact removal. Further, the regression of the global mean has been a topic of intense debate,
since it may not only introduce anti-correlations, but also bias the positive correlations [27-39].
The realization that deconvolution of movement artifacts in post-processing using conventional
motion correction approaches and confound regression remains incomplete has led to increased
use of alternate approaches (e.g., data scrubbing, despiking) to remove residual movement related
artifacts that confound functional connectivity metrics [40-44]. Confound correction continues to
be a topic of intense research in fMRI [18,34,45-48]. Further technical development is necessary
to establish confound-tolerant resting-state mapping approaches that complement the existing
model-based and data-driven analysis methods.
We recently introduced a windowed seed-based connectivity analysis (wSCA) approach
[1,49] targeted at single-subject analysis, which provides confound suppression without the need
for regression of confounding signal changes. This wSCA approach employs sliding-window
correlation analysis with running mean and standard deviation across dynamically updated
correlation maps (meta-statistics) [1,49,50]. Furthermore, it combines high-pass filter
characteristics with decorrelation of confounding signal events by constraining the effect of the
confounds to the windows that contain the confounding signals. The computational efficiency
makes this approach suitable for real-time fMRI [51,52]. The wSCA approach is particularly well
suited for high-speed fMRI methods [53,54] that enable unaliased measurement of cardiovascular
37
and respiration related signal fluctuations. High-speed fMRI considerably enhances the sensitivity
of mapping RSNs compared with the conventional EPI. Simultaneous multi-slice (SMS) or multi-
band EPI [55,56], magnetic resonance encephalography (MREG) [57], and multi-slab echo-
volumar imaging (MEVI) [54,58] have emerged as the principal high-speed fMRI data acquisition
techniques. Using wSCA in combination with high-speed MEVI [54], we demonstrated in a
preliminary study the feasibility of mapping RSNs in eloquent cortex in patients with brain tumors,
epilepsy, and arteriovenous malformations [49].
The present chapter characterizes the confound suppression and intra- and inter-RSN
connectivity strength of the wSCA as a function of sliding-window width, resting-state frequency,
and scan duration, both in computer simulations and in vivo in single subjects. The confound
tolerance and sensitivity for mapping six RSNs is compared with regression-based conventional
SCA (cSCA) in single subjects. We also investigated the feasibility of mapping 28 RSNs in single
subjects that were previously detected in a group-ICA study [59] with optimized processing
parameters for real-time connectivity mapping.
4.2. Subjects and Data Acquisition
Resting-state scans were acquired in 5 right-handed healthy controls (3 female and 2 male) aged
between 21-50 years using a scan duration of 5 minutes. These 5 subjects are a subset of data
studied previously [49,54]. Subjects were instructed to keep their eyes open, clear their mind, relax
and fixate on a cross-hair presented on a computer screen. Institutionally reviewed, informed
written consent was obtained.
Data were collected using a 3T Siemens TIM Trio clinical scanner equipped with 12-channel (4
Subjects) and 32-channel (1 Subject) head array coils [49,54]. A high-speed MEVI pulse sequence
was used for data acquisition with fly-back along the kz – direction, as described in [54]. Multiple
adjacent slabs were excited sequentially in a single TR and encoded using repeated EPI modules
with interleaved phase encoding gradients, fourfold acceleration using generalized autocalibrating
partially parallel acquisition (GRAPPA), 6/8 partial Fourier encoding, and oversampling along the
slab-direction. The MEVI scan parameters: 2 slabs, TR: 136 ms, TEeff : 28 ms, α: 10º, two slabs in
38
Table 4.1. Seed locations adopted from a spatial group-ICA study [59]. This table lists the 28 seeds that belongs to seven classes of RSNs and the corresponding independent components (ICs), MNI coordinates, and the functional brain regions. For optimization of the preprocessing parameters, six seeds are chosen from six classes of networks indicated by an asterisk [*] (RSN* seeds: ATN*, AUN*, DMN*, FRN*, SMN*, and VSN*).
R e s t in g -s ta te N e tw o r k
I n d e p e n d e n t C o m p o n e n t
C o o r d in a te s in M N I te m p la te
F u n c t io n a l B r a in R e g io n
B r o d m a n n A r e a
A T N IC 3 4 * ( -4 7 , -5 7 , 3 9 )* L e ft in fe r io r p a r ie ta l lo b u le B A 4 0
IC 6 0 (4 2 , -5 6 , 4 2 ) R ig h t in fe r io r p a r ie ta l lo b u le B A 4 0
IC 5 2 ( -3 3 , -6 4 , 3 1 ) L e ft a n g u la r g y ru s B A 3 9
IC 7 2 (0 , -5 3 , 6 1 ) B ila te ra l p re c u n e u s B A 0 7
IC 7 1 (5 7 , -4 4 , 1 1 ) R ig h t s u p e r io r te m p o ra l g y ru s B A 4 0
IC 5 5 (0 , 2 2 , 4 5 ) B ila te ra l c in g u la te g y ru s B A 4 0
A U N IC 1 7 * ( -5 1 , -1 8 , 7 )* L e ft s u p e r io r te m p o ra l g y ru s B A 2 2
B G N IC 2 1 (2 5 , -1 , 0 ) R ig h t p u ta m e n
D M N IC 5 0 * (1 , -6 4 , 4 3 )* B ila te ra l p re c u n e u s B A 0 7
IC 5 3 (0 , -5 2 , 2 2 ) B ila te ra l p o s te r io r c in g u la te c o r te x B A 2 3
IC 2 5 (0 , 4 1 , 4 ) B ila te ra l a n te r io r c in g u la te c o r te x B A 3 2
IC 6 8 ( -2 6 , 2 6 , 4 2 ) L e ft m id d le f ro n ta l g y ru s B A 0 8
F R N IC 4 2 * (5 0 , -2 3 , 2 )* R ig h t in fe r io r f ro n ta l g y ru s B A 4 5
IC 2 0 ( -5 5 , 2 2 , 7 ) L e ft in fe r io r f ro n ta l g y ru s B A 2 3
IC 4 7 ( -4 8 , 1 7 , 2 9 ) L e ft m id d le f ro n ta l g y ru s B A 0 9
IC 4 9 (3 1 , 5 5 , 7 ) R ig h t m id d le f ro n ta l g y ru s B A 1 0
S M N IC 0 7 * ( -5 2 , -9 , 3 1 )* L e ft p re c e n tra l g y ru s B A 0 6
IC 2 3 ( -3 5 , -2 7 , 5 4 ) L e ft p re c e n tra l g y ru s B A 0 4
IC 2 4 (3 7 , -2 5 , 5 3 ) R ig h t p re c e n tra l g y ru s B A 0 4
IC 2 9 (1 , -2 8 , 6 1 ) B ila te ra l p a ra -c e n tra l lo b u le B A 0 6
IC 3 8 ( -5 5 , -3 4 , 3 7 ) L e ft s u p ra m a rg in a l g y ru s B A 0 2
IC 5 6 (1 , -3 , 6 1 ) B ila te ra l s u p p le m e n ta ry m o to r a re a B A 0 6
V S N IC 4 6 * (1 , -8 7 , -2 )* B ila te ra l l in g u a l g y ru s B A 1 7 , 1 8
IC 6 4 (1 , -7 1 , 1 3 ) B ila te ra l c a lc a r in e g y ru s B A 1 7 , 1 8
IC 6 7 ( -1 5 , -5 6 , -8 ) L e ft l in g u a l g y ru s B A 1 8
IC 4 8 (2 9 , -7 6 , -8 ) R ig h t l in g u a l g y ru s B A 1 8 , 1 9
IC 3 9 (4 8 , -6 3 , -8 ) R ig h t in fe r io r te m p o ra l g y ru s B A 3 7
IC 5 9 (2 , -8 4 , 2 8 ) B ila te ra l c u n e u s B A 1 9
39
AC/PC orientation, slab thickness: 42 mm, inter-slab gap: 10%, matrix per slab: 64×64×8, Field
of View (FOV) per slab: 256×256×48 mm3, reconstructed voxel dimensions: 4×4×6 mm3, 13
slices, 2200 scan repetitions, scan time: 5 min and 16 s. The in-plane image reconstruction was
performed on the scanner and the through-plane reconstruction was performed in real-time using
our custom TurboFIRE (Turbo Functional Imaging in Real-time) fMRI analysis tool [49,60].
4.3. Seed-based Connectivity Analysis (SCA)
The reconstructed data were processed using TurboFIRE (version v5.12.4.0.2) on an Intel Xeon
E5530, 6 core, 2.4 GHz workstation. The processing steps included: six-parameter rigid body
motion correction [61], spatial normalization into MNI space using a look-up table approach [62]
with a 4×4×4 mm3 target voxel size, spatial smoothing of raw images using an 8×8×8 mm3
Gaussian spatial filter, and a 2 s moving average time domain low-pass filter [63,64] to suppress
signal fluctuations due to cardiac and respiratory pulsations. A 10% threshold was applied to the
intensity of the raw images to avoid any spurious correlations outside of the brain. A maximum of
six regions of interest (ROI) were simultaneously processed in TurboFIRE to create dynamic
reference vectors for online correlation analysis [65]. In addition to the display of sliding-window
meta-statistics maps, the cross-correlation values between the six ROI time courses were
continuously displayed in the form of 6×6 color-coded correlation matrices in a separate window.
Non-thresholded meta-statistics tables and the corresponding maps were obtained for all the voxels
at the end of the scan for six seed regions. This processing pipeline was used to monitor
connectivity in six RSNs during the ongoing scan using spatial normalization by mapping the MNI
atlas into subject space. To obtain meta-statistics for all 28 ROIs across subjects (see Table 4.1),
this pipeline was repeated offline for sets of six ROIs using spatial normalization into MNI space.
The analysis of the time series was limited to 1400 scan repetitions due to computer memory
limitations.
4.3.1. Seed Selection
The 28 single-voxel seeds were selected from the peak activations of the 28 RSNs that belong to
seven major classes of RSNs: attention (ATN), auditory (AUN), basal ganglia (BGN), default-
mode (DMN), frontal (FRN), sensorimotor (SMN), and visual (VSN) identified in [59] based on
40
the maximum t-score value and the spatial extent of the cluster (Table 1). The effective full width
half maximum (FWHM) of a single pixel seed region after spatial filtering was approximately
12×12×14 mm3. The coordinates of the seed locations were selected after spatial normalization
into MNI space and automatically assigned using the Talairach Daemon (TD) database [66,67].
The 140 brain regions from the TD database are shown in Table 4.2. The transformation from MNI
to Talairach coordinates was performed using Matthew Brett’s formula (http://www.mrc-
cbu.cam.ac.uk/Imaging/mnispace.html).
4.3.2. Conventional Seed-based Connectivity Analysis (cSCA)
Regression-based conventional SCA was performed in five subjects to compare with the
windowed SCA. Prior to performing connectivity analysis, voxel time courses were denoised using
a univariate general linear model (GLM) framework implemented in SPM
Table 4.2. Brain segmentation and region assignment based on the Talairach Daemon database.
These 70 regions are mapped to both left and right hemispheres, covering 140 functional brain
regions (BA: Brodmann Area).
1 B A 0 1 1 5 B A 1 9 2 9 B A 3 4 4 3 A m y g d a la 5 7 M a m m illa ry B o d y
2 B A 0 2 1 6 B A 2 0 3 0 B A 3 5 4 4 A n te r io r C o m m is s u re
5 8 M e d ia l D o rs a l N u c le u s
3 B A 0 3 1 7 B A 2 1 3 1 B A 3 6 4 5 A n te r io r N u c le u s 5 9 M e d ia l G e n ic u lu m B o d y
4 B A 0 4 1 8 B A 2 2 3 2 B A 3 7 4 6 C a u d a te B o d y 6 0 M e d ia l G lo b u s P a l l id u s 5 B A 0 5 1 9 B A 2 3 3 3 B A 3 8 4 7 C a u d a te H e a d 6 1 M id lin e N u c le u s
6 B A 0 6 2 0 B A 2 4 3 4 B A 3 9 4 8 C a u d a te T a i l 6 2 P u lv in a r
7 B A 0 7 2 1 B A 2 5 3 5 B A 4 0 4 9 C o rp u s C a llo s u m 6 3 P u ta m e n 8 B A 0 8 2 2 B A 2 7 3 6 B A 4 1 5 0 D e n ta te 6 4 R e d N u c le u s
9 B A 0 9 2 3 B A 2 8 3 7 B A 4 2 5 1 H ip p o c a m p u s 6 5 S u b s ta n ia N ig ra
1 0 B A 1 0 2 4 B A 2 9 3 8 B A 4 3 5 2 H y p o th a la m u s 6 6 S u b th a la m ic N u c le u s 1 1 B A 1 1 2 5 B A 3 0 3 9 B A 4 4 5 3 L a te ra l D o rs a l
N u c le u s
6 7 V e n tra l A n te r io r N u c le u s
1 2 B A 1 3 2 6 B A 3 1 4 0 B A 4 5 5 4 L a te ra l G e n ic u lu m B o d y
6 8 V e n tra l L a te ra l N u c le u s
1 3 B A 1 7 2 7 B A 3 2 4 1 B A 4 6 5 5 L a te ra l G lo b u s
P a l l id u s
6 9 V e n tra l P o s te r io r L a te ra l
N u c le u s 1 4 B A 1 8 2 8 B A 3 3 4 2 B A 4 7 5 6 L a te ra l P o s te r io r
N u c le u s
7 0 V e n tra l P o s te r io r M e d ia l
N u c le u s
41
(http://www.fil.ion.ucl.ac.uk/spm/software/spm12). Following the coregistration of functional
images with anatomical images (and normalization into MNI space), time courses were obtained
from the motion corrected data using automated delineation of voxels of interest from each of the
delineated sub-regions of WM and CSF. The regression was performed with AFNI software
(https://afni.nimh.nih.gov/afni/) and custom MATLAB scripts using 14 independent regressors:
the mean time courses from white matter (WM) and cerebrospinal fluid (CSF), and 12 individual
motion parameters (6 rigid body motion estimates and their derivatives). Neither scrubbing nor
despiking was used. The subsequent seed-based connectivity analysis was performed with
TurboFIRE using conventional cumulative correlation analysis (i.e. mean and SD of correlations
across the entire scan without a moving average filter).
4.3.3. Windowed Seed-based Connectivity Analysis (wSCA)
A schematic overview of the wSCA approach is shown in Fig. 4.1. The time courses of the regions
of interest (ROIs/seeds) are extracted from the preprocessed data. The signal time course within
each seed region is used as an input for generating a dynamic reference vector model [65]. The
cross-correlation coefficients between the seed time courses and the individual voxel time courses
at each TR, using sliding-window correlation analysis described in Gembris et al., 2000 [60]. The
meta-statistics approach (running mean and SD of Pearson's correlation coefficients) uses an
efficient running variance algorithm [50] to compute cumulative meta-maps of the mean and SD
of the correlations during the scan [49]. The initial 50 scans (7 s of data acquisition) were discarded
to account for non-steady-state signal changes.
4.4. Simulations of Confound Suppression using Windowed SCA
The confound suppression of the wSCA approach was characterized and quantified in a series of
simulations as a function of the sliding-window width and frequency. The mathematical modeling
of the wSCA approach was implemented using custom MATLAB scripts. The simulations were
performed for a 70 s time series as a function of the sliding-window width (4 – 70 s) and RSN
frequency (0.0001-0.5 Hz). Resting-state fMRI signal fluctuations were simulated for two
42
scenarios: (a) identical resting-state signal oscillation in two brain regions (two nodes of an RSN)
with added random noise (SNR = 1), and (b) uncorrelated random signal changes in two brain
regions. The following commonly observed confounding signals were added to the two simulation
models: a linear signal drift, a signal offset, and a signal spike. These confounding signals were
introduced into one of the nodes of the RSN in (a), thus decreasing connectivity, and into both
brain regions in the case of uncorrelated noise in (b), introducing artifactual connectivity. The
addition of the above confounding signals to both the nodes of the simulated RSN, scenario (a),
was also investigated. The simulations were averaged over 100 iterations with different
instantiations of random noise and the standard deviation was computed. The confound
Fig. 4.1. Windowed seed-based connectivity analysis (wSCA). Extraction of time courses
from seed regions and computation of seed-based sliding-window correlations with running
mean and standard deviation (meta-statistics) across the correlation maps.
43
44
suppression of the wSCA was quantified in terms of Fisher Z-transformed correlation coefficients.
The simulations in Fig. 4.2A show the estimation of connectivity (Fisher Z-transformed correlation
coefficients) in the presence of a confound in one of the two nodes of the RSN as a function of
sliding-window width. The connectivity increases with decreasing window width for the three
confound types (drift, offset, and spike) until it reaches a value near the confound-free case (i).
The corresponding simulations of two brain regions without resting-state connectivity in Fig. 4.2C
show the opposite case. The introduction of confounds in both brain regions results in decreasing
connectivity with decreasing window width until it reaches a value near the confound-free case
(ix). Of note, wSCA does not change the intrinsic connectivity between two brain regions in the
absence of confounds, independent of sliding-window width (Fig. 4.2 i, ix). Fig. 4.2B shows the
frequency dependence of confound suppression for the case of Fig. 4.2A (confound in one of the
two RSN nodes) which is independent of the RSN frequency above a threshold frequency. This
threshold frequency increases with decreasing sliding-window width, below which the confound
suppression decreases with decreasing frequency. The frequency dependence of the connectivity
for the offset (iii, vii, xi) and the spike (iv, viii, xii) displays an oscillating behavior, an interference
pattern reflecting the frequency content of the confound. The magnitude of changes in repeated
instantiations of the confounds were very small as shown in the error bars in Fig.4.2, even for
shorter windows.
In addition, we simulated the case of adding single instances of the confounding signals to both
nodes of the RSN (data not shown), which in case of the maximum window width increased the
Z-scores beyond the confound-free case. With decreasing sliding-window width the Z-scores
decreased to the confound-free case with a similar profile as in Fig. 4.2A. The combinations of
multiple confounds in both nodes of the RSN further increased the Z-scores and resulted in a
steeper decrease with decreasing sliding-window width. Further, we also simulated multiple
instances of the confounds (repeated spikes of 4 s length, continuous box car, continuous saw-
tooth) in both the nodes of the RSN, showing similar confound suppression behavior as in the
previous case of a single instance, although with higher Z-scores for the maximum window width.
Nonetheless, consistent confound suppression was found for the shortest sliding-window. These
additional results further substantiate the robustness of confound suppression using wSCA in the
presence of multiple serial and overlapping confounding signal changes. In summary, the shorter
45
Fig. 4.3A. Resting-state connectivity and confound suppression in vivo in 6 major RSNs using
windowed SCA in comparison with conventional SCA. Meta-mean maps are displayed as a
function of sliding-window width (30 s, 15 s, 8 s, and 4 s) and scan duration (30 s, 60 s, 120 s,
and 180 s) in a representative subject. The confound reduction with decreasing sliding-window
width results in a decrease of spurious connectivity in white matter and in gray matter regions
that are unrelated to the 6 major RSNs. The green arrows indicate the seed locations. The maps
are in neurological orientation at zero meta-mean correlation threshold with slice locations given
by the Z-coordinates.
46
the sliding-window, the stronger the confound suppression, but the higher the cut-off frequency
that restricts the confound suppression at low frequencies. The simulations suggest that a sliding-
window of 15 s provides a compromise between the overall degrees of confound suppression and
the suppression efficiency at the low frequencies that constitute the resting-state frequency
spectrum.
4.5. Performance Comparison of Windowed and Conventional SCA
The confound suppression performance of the windowed and conventional SCA methods was
characterized as a function of sliding-window (4s, 8 s, 15 s, and 30 s) using two types of
connectivity analyses: (a) the comparison of the strength of the intra- and inter-network
connectivity in six RSNs using six single-voxel seeds, and (b) the comparison of the strength of
the artifactual connectivity using 4 supraventricular white matter single-voxel seeds [coordinates:
(-26, -38, 48), (26, 7, 31), (-26, -39, 41), (-30, 11, 27)].
The intra- and inter-network connectivity maps were computed for all voxels to assess the residual
artifactual connectivity across the entire brain. The average positive connectivity (average across
the regions with mean positive correlations) and the average negative connectivity (average across
the regions with mean negative correlations) were computed by segmenting the connectivity maps
Fig. 4.3B. Comparison of average positive connectivity and negative connectivity across 140
brain regions and the 6 RSNs shown in Fig. 4.3A as measured by the conventional SCA and
the windowed SCA as a function of sliding-window width and scan duration.
47
into 140 atlas-based brain regions and averaging across the 6 RSNs and 5 subjects. For each of the
6 RSNs, the intra-network connectivity was computed by averaging the region-wise correlation
values across a subset of regions (ATN: BA32, 33; AUN: BA41, 42; DMN: BA7, 23, 31; FRN:
BA9, 10; SMN: BA1-4, VSN: BA17-19) and the extra-network connectivity was computed by
averaging the region-wise correlation values across the remainder of the 140 brain regions. The
intra- and extra-network connectivity for each of the six RSNs as a function of sliding-window
width and scan duration for both wSCA and cSCA was presented as a color map.
The connectivity maps using WM seeds were computed at zero meta-mean threshold to quantify
the residual artifactual connectivity across the entire brain. The positive global mean artifactual
connectivity (average across the regions with mean positive correlations) and the negative global
mean artifactual connectivity (average across the regions with mean negative correlations) were
computed by segmenting the connectivity maps into 140 atlas-based brain regions.
4.5.1. Computational Efficiency
The data processing time for cSCA was on the order of 35-45 min including extraction of
regressors, GLM analysis for confound regression, and correlation analysis using 6 seeds. The
processing time for analyzing 28 seed regions was approximately 60 min for a 5 min scan. The
wSCA analysis was performed in real-time (with online motion correction and spatial
normalization of the MNI atlas into subject space) with time delay of less than a TR after image
reconstruction. The major time delay during online processing was due to the image reconstruction
on the scanner itself as described in [54]. During offline wSCA analysis, the processing time per
image volume (using spatial normalization by mapping the individual images into MNI space) was
120 ms and the total processing time for analyzing 28 seed regions was 15 min.
48
Fig. 4.3C. Intra-network and extra-network connectivity measured with conventional SCA
and windowed SCA in the 6 RSNs shown in Fig. 4.3A as a function of sliding-window width
(4 s, 8 s, 15 s, and 30 s) and scan duration (30 s, 60 s, 120 s, and 180 s). The color bar shows
the Z-scores of correlation coefficients (for cSCA) and meta-mean correlations (for wSCA)
ranging from -0.25 (blue) to +0.25 (red).
49
Fig. 4.4A. Subject-wise comparison of artifactual connectivity with conventional SCA and windowed SCA using white matter seeds. a) Artifactual connectivity in the raw data, b) conventional SCA with regression (cSCA), and (c-f) windowed SCA with sliding-window width of: c) 30 s, d) 15 s, e) 8 s, and f) 4 s. The maps are in neurological orientation at zero meta-mean correlation threshold with slice locations given by Z-coordinates. The color bar shows the Z-scores of correlation coefficients and meta-mean correlations ranging from -1 (blue) to +1 (red).
50
4.5.2. Intra- and Inter-RSN Connectivity
The resulting correlation maps (cSCA) and meta-mean maps (wSCA) were displayed at zero-
correlation threshold to show the apparent connectivity in the entire brain for the 6 classes of RSNs.
The example of a representative subject shown in Fig. 4.3A for the cSCA maps displays a decrease
in the apparent connectivity with scan duration particularly in the case of ATN, FRN, and SMN
and consistent confound suppression across the scan length in the case of AUN, DMN, and VSN.
The wSCA meta-mean maps in Fig. 4.3A (with 30 s, 15 s, 8 s, and 4 s sliding-windows) display:
improving localization of the RSNs with decreasing non-specific connectivity in cortical regions,
and increasing degrees of confound suppression in WM and CSF, as functions of increasing scan
durations and decreasing sliding-window widths. While the confound tolerance increases with
decreasing sliding-window width, the correlation coefficients decrease due to the rejection of more
Fig. 4.4B. Comparison of the average positive connectivity and the average negative connectivity
across 140 brain regions in the five subjects shown in Fig. 4.4A as measured by the conventional
SCA and the windowed SCA using the four WM seeds as a function of sliding-window width
(4 s, 8 s, 15 s, and 30 s).
51
strongly connected low frequency components, as expected. The results show that the connectivity
in most of the RSNs stabilizes within a minute. Although the connectivity dynamics are subject-
and RSN- specific, the overall connectivity patterns detected using wSCA are consistent across
subjects, showing robust confound tolerance at scan durations as short as 30 s. The wSCA
measured overall widely distributed bilateral connectivity among RSNs, in contrast to cSCA,
particularly in AUN and SMN. The spatial extent of connectivity is larger in the case of longer
sliding-windows and decreases with shorter windows as a function of scan duration, as predicted
by the simulations.
The overall positive and negative connectivity among the six RSNs is shown in Fig. 4.3B across
5 subjects using cSCA and wSCA as a function of sliding-window width and scan duration.
Conventional SCA showed a consistent decrease in both positive and negative connectivity as a
function of scan duration whereas wSCA showed a slight increase in positive connectivity in the
case of 4 s, 8 s and 15 s windows and a stronger increase in the case of 30 s window. The negative
connectivity decreased as a function of scan duration for the shorter windows (4 s, 8 s, 15 s) and
increased for the 30 s window, consistent with higher confound suppression for shorter sliding-
window widths.
Fig. 4.3C shows that the overall intra-network connectivity across 5 subjects is higher with wSCA,
particularly in AUN. VSN showed stronger connectivity using both methods whereas ATN showed
lower connectivity with cSCA relative to wSCA. The extra-network connectivity in SMN is higher
with cSCA and more negative in the AUN compared with wSCA. Conventional SCA did not show
significant differences as a function of scan duration among networks whereas wSCA showed an
increase in the connectivity as a function of scan duration.
4.5.3. Artifactual White Matter Connectivity
The degree of artifactual connectivity in the data (without using regression or sliding-window
meta-statistics) is shown in Fig. 4.4Aa as a reference for the confound suppression due to the
wSCA and cSCA. Fig. 4.4Ab demonstrates considerable suppression of background connectivity
in the cSCA correlation maps with the exception of S5. Figs. 4.4A c, d, e, and f show that the
confound suppression with wSCA increases with decreasing sliding-window width as predicted
by simulations. The spatial extent of the connectivity in the case of cSCA is constrained to the seed
52
region itself, whereas wSCA results in a slightly larger spatial extent. The same spatial smoothing
was used for both approaches. Interestingly, wSCA shows much stronger confound suppression in
the case of S5 compared to cSCA.
Fig. 4.4B shows overall lower positive and negative artifactual connectivity for cSCA across the
140 brain regions among five subjects compared to wSCA. The Z-scores of the positive
connectivity of wSCA were stronger than those of cSCA, even at the shortest sliding-window
width, and increased with increasing sliding-window width (4 s: 39%, 8 s: 53%, 15 s: 63%, 30 s:
71%). The Z-scores of the negative connectivity of the wSCA were stronger than those of cSCA,
yet only weakly dependent on sliding-window width (4 s: 39%, 8 s: 33%, 15 s: 37%, 30 s: 30%).
4.6. Whole-brain Connectivity Profiles
The connectivity strength across 140 brain regions was averaged across the 6 RSNs defined above
and quantified as a function of the sliding-window width (1 s, 2 s, 4 s, 6 s, 8 s, 15 s, 30 s, 60 s, 90
s, and 120 s). The resulting connectivity profiles were averaged across 5 subjects. The network-
wise sliding-window dependency was computed by Fisher Z-transforming the meta-mean
correlation across the 140 brain regions as a function of sliding-window width with RSN* seeds
(Table 4.1). The strength of the connectivity profiles for six single-voxel seeds (RSN* seeds)
across 70 regions in the left hemisphere (Fig. 4.5a) and 70 regions in the right hemisphere (Fig.
4.5b), across 5 subjects show distinct patterns of connectivity across certain regions. The strength
increases with increasing sliding-window width. However, some regions show negative
connectivity at short window widths. The increase in connectivity strength with increasing window
width is particularly pronounced in subcortical regions at the expense of temporal resolution and
degree of confound rejection. The average connectivity in the right hemisphere was stronger than
in the left hemisphere, particularly in BAs 35-41 and the subcortical regions, a finding that was
consistent across three out of the five subjects. The slope of this increase depends on the choice of
the RSN* seed. Shorter sliding-windows provide higher temporal resolution for monitoring
dynamic changes in high frequency connectivity (0.1-0.5 Hz), but decrease the Fisher Z-score,
53
which is dominated by low frequency connectivity (< 0.1 Hz). Fig. 4.5c also displays distinct
differences in global connectivity for different seed regions. The ATN*, AUN* and FRN* seeds
display stronger connectivity even at the shortest window widths, suggesting a higher global
spectral power density between 0.1 to 0.5 Hz for these seed regions.
Fig. 4.5. Connectivity profiles across 140 brain regions as a function of the sliding-window
width. The meta-mean correlation coefficients averaged across six RSNs* and five subjects are
plotted for window widths of 1 s, 2 s, 4 s, 8 s, 15 s, 30 s, 60 s, 90 s, and 120 s across (a) the 70
left; and (b) the 70 right-hemispheric regions. The numbers 1-70 correspond to the brain regions
listed in Table. 4.2. (c) Z-scores of meta-mean correlation coefficients averaged across 140
brain regions as a function of sliding-window width (1-120 s).
54
4.7. Physiological Noise Suppression
A moving average temporal low-pass filter was employed to suppress the physiological noise due
to cardiac and respiratory pulsations [63]. Previous studies [63,64] have demonstrated that a 2 s
window can reduce the effective variance in the hemodynamic baseline signal, resulting in
considerable reduction of the physiological noise, without the need for external physiological
monitoring and signal deconvolution. Suppression of physiological noise was quantified for
window widths of 0 s, 1 s, 2 s, 4 s, 6 s, and 8 s using symmetric and asymmetric Hamming filters
with filter windows of 25%, 50%, 75%, and 100% of the data vector, to attenuate the ringing and
Fig. 4.6. Temporal moving average filter. Suppression of cardiovascular and respiratory
pulsations in the frequency spectra of the time courses of the six RSNs* seeds as a function of
the moving average low-pass filter width in a single-subject: (a) no filter, (b) 2 s, (c) 4 s, and
(d) 8 s. The arrow shows the magnified section of the spectrum. Sliding-window width: 15 s,
symmetric Hamming filter: 50% data vector. Maximum amplitude: 120 (arbitrary units).
55
overshoot effects of the boxcar filter. A Fourier transform of the single-region seed time courses
was performed and the amplitude of the noise components in the spectrum was quantified as a
function of the filter window. The combination of the moving average time domain low-pass filter
of a frequency analysis of the time courses obtained from the above RSN* seeds without temporal
filter (0 s) (Fig. 4.6) shows the presence of strong cardiac and respiratory peaks in attention and
auditory networks at 0.5 Hz and 1 Hz, respectively. The spectrum with 1 s filter also contained and
the width of the sliding-window (high-pass filter) corresponds to band-pass filter. The suppression
of these pulsations is strongly enhanced by increasing the filter width to 2 s, resulting in a ~53%
and ~40% drop in the amplitude of the cardiac and respiratory peaks in the attention and auditory
networks, respectively. The longer filter widths of 4 s, 6 s, and 8 s show a smaller increase in
suppression with the cardiac respiratory peaks being close to the noise level. A 2 s temporal
averaging window is thus chosen as a compromise, to increase sensitivity and maintain temporal
resolution, while and attenuating the cardiac and respiratory pulsations.
4.8. Mapping of Resting-state Networks
Twenty-eight RSNs that were previously reported in a spatial group-ICA study [59] were mapped
in individual subjects using wSCA with 15 s sliding-window and 2 s temporal averaging filter. The
coordinates of the 28 single-voxel seed locations were identical to the maxima reported in Fig. 4A
of [59]. The resulting meta-mean maps were displayed at a threshold of 0.6. Windowed SCA
enabled mapping of 28 RSNs in single subjects using a 15 s sliding-window. In each of the 7
classes of RSNs, it was possible to map a subset of 6 RSNs in real-time with scans as short as 1
min. The majority of the RSN patterns shown in Fig. 4.7 using the most informative axial meta-
mean threshold maps in a representative single-subject (displayed at a threshold of 0.6), have
features that are very similar to the RSNs reported in [59], including ATN - IC34, IC52, IC72;
DMN - IC25, IC50, IC53, IC68; FRN - IC20, IC42, IC49; SMN - IC23, IC24, IC29; and VSN -
IC48, IC67. The other RSNs (ATN - IC55, IC60; SMN - IC38, IC56; and VSN - IC39, IC46, IC64)
show more widely distributed connectivity patterns that extend into the contralateral hemisphere,
compared with the ICA derived RSNs. Few RSNs (e.g., ATN - IC71, SMN - IC074, VSN - IC59)
show less extensive connectivity patterns compared to the ICA derived RSNs.
56
Fig. 4.7. Twenty-eight RSN patterns obtained with windowed SCA in a representative single-
subject. The meta-mean correlation maps from seven major classes of networks (ATN, AUN,
BGN, DMN, FRN, SMN, and VSN) using 28 single-voxel seeds, displayed using the most
informative axial slice locations (Z-coordinates) in neurological orientation for comparison with
Fig. 4A of the group-ICA study by [59]. The meta-mean maps are threshold at 0.6.
57
4.9. Windowed Seed-based Connectivity Analysis
Unambiguous quantification of resting-state signal changes and the characterization of spatio-
temporal fluctuations of RSNs in single subjects has serious challenges. Resting-state fMRI signal
changes in BOLD contrast fMRI are approximately an order of magnitude smaller than the
conventional task related signal changes (e.g., in sensorimotor, visual, and attention regions),
making the analysis of resting-state connectivity highly sensitive to head movement and
physiological noise sources [18,68-73]. It has also been shown that physiological noise increases
with magnetic field strength, which limits sensitivity gains in resting-state fMRI [21-24,74,75].
This requires deconvolution during post-processing [45], which has proven challenging in part due
to aliasing of cardiac pulsations in conventional fMRI acquisition methods. There has been
increasing evidence that conventional approaches to movement correction during post-processing
are incomplete due to the convolution of rigid body movement, geometrical image distortions,
regional image intensity changes, and spin history effects. This, combined with the fact that the
micro-movements can impact the connectivity in a systematic way has led to the use of data
scrubbing [41-44,76]. The current wSCA methodology addresses some of the limitations of
existing approaches.
4.9.1. Confound Suppression
This study extends the wSCA methodology [49] by quantifying the confound suppression and the
strength of the measured resting-state connectivity as a function of fluctuation frequency and
sliding-window width in comparison with regression-based cSCA, both in computer simulations
and in vivo [1]. The simulations of confound suppression using wSCA, with single and multiple
instances of the confounding signals in one or both nodes of the RSN, demonstrate a comparable
degree of confound suppression for all simulated confound waveforms. Since the confound
suppression of wSCA was shown to be similar for combinations of these waveforms, it is expected
to extend to arbitrary waveforms. As a function of the sliding-window width, wSCA provides a
selectable trade-off between the degrees of confound suppression and the frequency bandwidth for
mapping resting-state fluctuations. This frequency selectivity enabled sensitive detection of
intrinsic differences in the fluctuation frequency spectra among RSNs. The 15 s sliding-window
was selected to capture the minimum resting-state fluctuation frequency (on the order of fmin ~
58
0.06 Hz) in accordance with the rule of thumb described in [77], window width (W) ≥ 1/fmin.
However, we were also able to show the detection of functional connectivity at much shorter
window widths at correspondingly reduced sensitivities, as discussed in [78]. With respect to
cSCA, the wSCA methodology demonstrates comparable tolerance to confounds such as head
movement, physiological noise, unrelated signal changes in WM and CSF, and high sensitivity for
detecting RSNs. Windowed SCA is particularly well suited for the high temporal resolution due to
the sensitivity gains offered by high-speed fMRI acquisition methods. High-speed fMRI enables
sampling of a wider resting-state frequency spectrum beyond the 0.25 Hz that is detected in
conventional EPI studies with a TR of 2 s, thus improving the mapping of intra- and inter-network
connectivity (e.g. [79]). The high sensitivity and temporal resolution of our MEVI approach
enables mapping of 28 resting-state networks (RSNs) in single subjects that were previously
described in [59] over 600 subjects.
4.9.2. Frequency selectivity of Windowed SCA
Windowed SCA performs both high-pass filtering of the resting-state frequency spectrum and de-
correlates the effects of spurious signal changes across the time domain. The range of sliding-
window widths used in this study (2-30 s) restricts resting-state fluctuations to frequencies between
0.03-0.5 Hz, which carry the majority of temporal information for segregating RSNs. While
decreasing the sliding-window width increases the temporal resolution, which is desirable for
characterizing short-term fluctuations in resting-state connectivity, it also curtails the sensitivity
for detecting RSNs in a network dependent manner. The degree to which the sliding-window
suppresses the effect of the confounding signals depends on the frequency spectrum of the RSN
under consideration, as shown in the simulations. Networks such as ATN, AUN, SMN, and VSN
exhibit considerable high frequency connectivity (0.3-0.5 Hz), detected using sliding-windows as
short as 1 - 2 s. These networks also exhibit smaller spatio-temporal fluctuations across subjects
relative to the other networks. Although shorter sliding-windows show stronger confound
suppression at the expense of connectivity dynamics at lower frequencies, window widths in the
range between 8-15 s provide a reasonable compromise for mapping the minimum resting-state
fluctuation frequency (~0.06 Hz), as discussed above. The addition of the temporal moving
59
average filters (2 - 4 s) provides a high frequency cut-off (0.5 -0.25 Hz) to reduce the effects of
cardiac pulsatility, resulting in band-pass filter characteristics and enhancing the detection
sensitivity [63,64].
4.9.3. Conventional and Windowed SCA
Regression is highly effective in reducing spurious connectivity with white matter seed regions,
constraining the connectivity patterns to the seed voxel itself (Fig. 4.4A). It is well known that
regression analysis is performed under the assumption that the regressors and the underlying
resting-state signal fluctuation time courses are orthogonal (e.g. [80,81]. Collinearity between the
regressors and the resting-state signal fluctuations, therefore, results in a decrease of the measured
connectivity. Our data show that the signal fluctuations in auditory cortex are partly correlated
with WM seed time courses, resulting in strong suppression after regression. Regression of the
global mean, employed in conventional seed-based methods to improve the specificity of the
activations and effective artifact removal [31,32], has been a topic of intense debate
[25,28,29,33,34,37-39]. Global signal regression may not only introduce anti-correlations [27,36],
but also bias the positive correlations and has been shown to correlate with partial pressure
variation effects of carbon dioxide [30,82]. In contrast, wSCA preserves connectivity in the
auditory cortex and provides a higher level of positive connectivity in most networks. It also
appears to be more consistent in suppressing confounds in the case of strong anti-correlations
between different white matter regions (S5 in Fig. 4.4A). These intrinsic differences in confound
suppression contribute to distinct dependencies of positive connectivity (Fig. 4.3B, 4.4B) on the
scan duration, particularly in the auditory and sensorimotor cortices (Fig. 4.3C).
4.9.4. Real-time implementation of Windowed SCA
Conventional SCA with regression of the confounding signals requires cumulative computation of
the regressors, which is computationally intensive for real-time implementation and may suffer
possible bias due to the confound regression across the growing time series. A number of alternate
approaches have recently been explored for seed-based [83-87] and ICA-based real-time analyses
[88]. The wSCA methodology targeted at single-subject analysis, builds on our earlier
developments of the real-time analysis methods [60,61,65]. The computational efficiency of the
60
wSCA approach makes it suitable for mapping functional connectivity during an ongoing scan.
This is desirable not only for characterizing the elusive and fluctuating ‘brain states’ [86,87,89]
along with designing novel neurofeedback experiments, but also for assessing the data quality,
particularly in clinical applications. Additionally, this approach is suitable to measure changes in
brain states (e.g. drowsiness) and state of attention for applications in neuroscience and clinical
research studies in real-time [84-87] which cannot be monitored adequately with the existing
approaches. In clinical settings, wSCA will enable real-time RSN mapping to characterize regional
alterations in network connectivity patterns in patients with brain diseases, e.g., tumors, epilepsy
and arteriovenous malformations. Further developments of this methodology may enable
controlled self-regulation of functional connectivity in RSNs using real-time neurofeedback,
which would complement existing approaches for neurofeedback of task-based activation studies
[90-94].
4.9.5. Limitations
The degree of confound suppression achieved with wSCA is limited by the frequency selectivity,
which is determined by the sliding-window width. A high degree of confound suppression using
shorter windows thus sacrifices sensitivity for detecting very low frequency connectivity. A
correction of the correlation thresholds for the degrees of freedom as a function of sliding-window
width has not been applied in the present study and is under investigation. We expect that the
increase in threshold with decreasing sliding-window width resulting from this correction will
decrease artifactual connectivity, further enhancing the confound tolerance of wSCA, and decrease
the extent of true-positive connectivity, reducing the intra- and inter-RSN connectivity strength
measured with wSCA in comparison to cSCA. Neither scrubbing nor despiking were used in this
study, which might differentially affect the confound suppression of conventional and windowed
SCA approaches. Adding motion covariates to the correlation analysis, along with scrubbing and
despiking will be investigated in a future study. The low resolution partial brain images acquired
in this study limit the precision of spatial normalization and the delineation of seed regions in gray
matter, WM, and CSF. Like any seed-based approach, wSCA is highly sensitive to the choice of
the seed locations, therefore, seeds were carefully chosen to avoid the edges of the MEVI slabs,
where respiratory artifacts primarily manifest.
61
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Chapter 5 Functional Connectomics
5.1. Introduction
Although resting-state fMRI is being increasingly used to map the functional connectomics,
variability inherent in the choice of the data analysis methods (e.g., SCA, ICA, graph theory) and
processing parameters, and subject-specific seed selection have limited reliability [1,2]. This can
impair the comparison across studies. Efforts of parcellating RSN connectivity in single subjects
have sought to overcome the shortcomings of spatial normalization and variability due to
structured noise sources by using multiscale clustering, dictionary based learning and related
approaches [3-7]. Standardization of seed selection and brain parcellation are of considerable
interest for increasing the clinical utility of resting-state fMRI [8,9].
This chapter presents the framework in which wSCA is implemented offline to map whole-brain
inter-regional connectivity (IRC) across 140 Brodmann and subcortical areas and inter-network
connectivity (INC) among 28 RSNs using single- and multi-region seeds. IRC and INC enable
comparison of sensitivity and specificity of mapping resting-state connectomics in single subjects
and across a group of subjects.
5.2. Statistical Hierarchy
Multi-level statistics implemented in the wSCA were shown in Fig. 5.1. The hierarchy consists of
three levels of statistics: single-voxel, region/single-subject, and subject group, resulting in
temporal, spatial, and group statistics respectively. The mean and SD of the Pearson’s correlation
coefficients [ρt] were calculated for each voxel at every TR (t – temporal), resulting in single-voxel
level meta-statistics (meta-mean [μt], meta-SD [σt]) which correspond to the temporal
information. Spatial means and SDs of the [μt] and [σt] were computed across brain regions using
segmentation based on a modified Talairach Daemon Database [10,11] that encompasses 140
bilateral brain regions from the Talairach atlas in the left and right hemispheres (see Table 4.2),
resulting in the region/single-subject level meta-statistics ([μ1s], [σ
1s], [μ2
s ], and [σ2s]) which
correspond to spatial information (s – spatial). The [μ2s ] maps were a measure of temporal
fluctuations of correlations within each brain region. The group information was obtained by
computing the mean and SD across subjects ([μ1g], [σ
1g], [μ2
g], and [σ2g]) (g – group). The [μ1
g]
68
corresponds to the strength of the correlations across the subjects and the [σ1g] measures the inter-
subject variability of the meta-mean correlations within each brain region. The [μ2g] corresponds
to the average temporal fluctuations within each brain region across subjects and the [σ2g] measures
the variability in temporal fluctuations in each brain region across subjects.
Fig. 5.1. Statistical hierarchy. Computation of cumulative meta-statistics (running mean and
SD) on Pearson’s correlations [ρt] for every voxel at each TR (temporal statistics) results in
meta-mean [μt] and meta-SD [σt] maps at the end of the scan. The red dotted squares depict
two positions of a moving sliding-window of width ‘w’. The spatial mean and SD across the
voxels within the functional brain regions (spatial statistics) yields [μ1s]/[σ
1s] and
[μ2s ]/[σ
2s] maps. The mean and SD across subjects (group statistics) provides group level maps
[μ1g]/[σ
1g] and [μ2
g]/[σ2g]. Notation: μ-principal mean, σ-principal SD; subscripts: 1-derived
mean, 2-derived SD; superscripts: t-temporal, s-spatial, and g-group.
69
5.3. Seed Selection
Single-region seeds Single-region seeds were selected as described in chapter 4 (4.3.1).
Multi-region seed clusters The 28 multi-region seed clusters (multiple voxels in multiple
regions) were derived from the 100 nodes of the 28 RSNs described in Allen et al., 2011 [12].
Spatially distributed voxels corresponding to the nodes of each of the above mentioned RSNs were
linked together to form a compound seed cluster consisting of 1-7 voxels. The motivation for
choosing these multi-region seed clusters was to encompass all the nodes of a given network to
probe the total spatial extent of connectivity and to investigate the interplay of the nodes for
mapping whole-brain connectivity. The MNI coordinates of all 100 nodes can be found in [12].
5.4. Resting-state Networks with Multi-region Seeds
The 28 resting-state networks were mapped using multi-region seeds, similar to the single-region
seeds as described in chapter 4 (see 4.8). In this chapter, the 28 wSCA generated RSNs using both
the single- and multi-region seeds were compared with the 28 RSN patterns shown in Fig. 4A of
the group-ICA study [12]. As a result of the optimization of processing parameters, a 15 s sliding-
window and a 2 s moving average temporal low-pass filter were selected, resulting in an RSN
frequency bandwidth of 0.06-0.5 Hz. Representative axial meta-mean ([μt]) correlation maps in a
single-subject are shown in Fig. 5.2. The thresholded meta-mean correlation maps display [μt]
values in the range of 0.6 to 1.0. The single-region seeds (ATN - IC55, IC60; SMN - IC38, IC56;
and VSN - IC39, IC46, IC64) generate more widely distributed connectivity patterns that extend
into the contralateral hemisphere, compared with the ICA derived RSNs. The majority of the
connectivity patterns generated by the multi-region seeds (ATN – IC52, IC55, IC72; AUN17,
DMN – IC25, IC68; FRN - IC42, IC47; SMN - IC23, IC24, IC38, IC56; and VSN - IC39, IC46,
IC64) show spatially extensive ipsi- and contra- lateral connectivity patterns that extend across
multiple functional brain regions in contrast to the single-region seed connectivity patterns. Some
of the multi-region seeds (ATN - IC34; BGN - IC21; DMN - IC43, IC50; FRN - IC20; SMN -
IC29; and VSN - IC67) generate connectivity patterns that are similar to the ICA derived RSNs. A
few single- and multi-region seeds (e.g., ATN - IC71, SMN - IC074, VSN - IC59) generate less
extensive connectivity patterns compared to the ICA derived RSNs.
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5.5. Inter-Regional Connectivity (IRC)
The meta-statistics ([μt], [σt]) in single subjects were computed for the 28 single- and 28 multi-
region seeds and the resulting whole-brain meta-statistics maps were segmented into 140 brain
regions in standardized MNI space, in reference to the Talairach Daemon database [10,11]
comprising both the left and right hemispheres. The [μt], and [σt] were then parsed using custom
PERL scripts, resulting in region-wise meta-statistics for each seed region in single subjects ([μ1s],
[σ1s], [μ2
s ], and [σ2s]). The group level region-wise meta-statistics were obtained by averaging
across the subjects ([μ1g], [σ
1g], [μ2
g], and [σ2g]). IRC matrices (IRCMs) at the single-subject and
Fig. 5.2. Representative RSN patterns in a single-subject. The meta-mean correlation maps ([μt])
from seven major classes of networks (ATN, AUN, BGN, DMN, FRN, SMN, and VSN) using
a) 28 single- and b) 28 multi-region seeds, displayed using the most informative slice locations
(Z-coordinates) in neurological orientation for comparison with Fig. 4A of the group-ICA study
by Allen et al., 2011. The maps are thresholded at 0.6.
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group level, which plot the region-wise meta-statistics across 28 single-, and 28 multi-region seeds
and 140 functional brain regions, were generated using custom MATLAB scripts. The following
IRCMs were computed separately for left and right hemispheres to quantify inter-hemispheric
differences: (a) the meta-mean correlation coefficients were plotted as a measure of functional
connectivity among the atlas-based functional brain regions at the single-subject ([μ1s]) and the
group levels ([μ1g]). (b) The meta-SDs were plotted as a measure of temporal fluctuations among
the atlas-based functional brain regions both at the single-subject ([σ1s]) and the group levels ([σ
1g]).
(c) The SDs of the meta-mean correlation coefficients ([μ2g] and the SD of meta-SDs [σ
2g] across
subjects were plotted as a measure of inter-subject variability of functional connectivity and inter-
subject variability of temporal fluctuations within each functional brain region. Global
connectivity metrics for groups of seed regions that correspond to six of the seven major classes
of RSN seeds were computed by averaging across all 140 brain regions for each of these IRCMs.
5.5.1. Single-subject Connectomics The functional connectivity ([μ1
s]) IRCMs in single subjects exhibit widely distributed seed region-
specific connectivity patterns across left cortical and subcortical brain regions as shown in the
example in Fig. 5.3A. Single-region seeds are associated with stronger inter-regional differences
in connectivity, both positive and negative (Fig. 5.3A, a), compared with multi-region seeds (Fig.
5.3A, b). Negative [μ1s] correlations are predominantly seen across the subcortical regions (Fig.
5.3A, a), particularly with FRN and SMN seeds and are also measured in a small number of cortical
regions, e.g., the strongest negative [μ1s] correlation between the DMN seed (DMN - IC25) and
BA33 in this subject is -0.55 (Fig. 5.3A, a). The multi-region seeds (Fig. 5.3A, b) show much
smaller negative [μ1s] correlations (the strongest in this subject being -0.24 in Fig. 5.3A, b) and
stronger positive connectivity that is more uniform across brain regions compared with single-
region seeds. Similar connectivity characteristics are observed in the right brain regions for single-
and multi-region seeds.
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Fig. 5.3. Single-subject connectomics – Functional connectivity and temporal fluctuation inter-
regional connectivity matrices (IRCMs). (A) Functional connectivity ([μ1s]) IRCM among 28 seed
regions and 70 left-hemispheric atlas-based brain regions for: (a) single-region seeds; and (b)
multi-region seeds. (B) Temporal fluctuation ([σ1s]) IRCM among 28 seed regions and 70 left-
hemispheric atlas-based brain regions for: (a) single-region seeds; and (b) multi-region seeds. (C)
Maximum negative- (anti) and positive- [μ1s] correlations for each subject (S1-S8) and the group
average (Avg) across the whole-brain for single- (light and dark blue bars) and multi-region
(orange and green bars) seeds, respectively. (D) Minimum and maximum [σ1s] for each subject
(S1-S8) and the group average (Avg) for single- (light and dark blue bars) and multi-region
(orange and green bars) seeds, respectively. The error bars in both the maps indicate the standard
errors in the [μ1s] and the [σ
1s].
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The single-subject temporal fluctuation ([σ1s]) IRMCs (Fig. 5.3B) display particularly strong
fluctuations for subsets of the ATN, DMN, FRN, SMN and VSN seeds. Single-region seeds (Fig.
5.3B, a), display stronger fluctuations across left brain regions compared with multi-region seeds
(Fig. 5.3B, b), in particular for the ATN and DMN seeds. The fluctuations in BAs 3-7 for multi-
region seeds are among the smallest across all brain regions (< 0.25 on average in Fig. 5.3B, b),
whereas fluctuations in the subcortical regions are considerably stronger (on the order of 0.45 for
ATN seeds in Fig. 5.3B, b). Overall, BAs 3-7, 20, 38, 39 and dentate show the smallest temporal
fluctuations with both seed types. The global connectivity metrics shown in Fig. 5.3C emphasize
the consistency of the positive [μ1s] correlations across subjects for both single- and multi-region
seeds. The negative [μ1s] correlations are more variable across subjects, in particular for multi-
region seeds. The range of positive [μ1s] correlations in single subjects is from 0.71 to 0.93 for the
left hemisphere, 0.78 to 0.92 for the right hemisphere in the case of single-region seeds, and
between 0.72 and 0.91 for the left hemisphere, and 0.73 to 0.92 for the right hemisphere in the case
of multi-region seeds. Negative [μ1s] correlations in single subjects are in the range from -0.57 to -
0.01 for the left hemisphere and from -0.66 to -0.24 for the right hemisphere in the case of single-
region seeds, and in the range of -0.69 to 0.03 for the left hemisphere and from -0.65 to -0.11 for
temporal fluctuations ([σ1s]) are more consistent across the subjects (range: 0.4 to 0.55) than the
[μ1s] correlations. The [σ
1s] in the case of single-region seeds ranged from a minimum of 0.02 (left
hemisphere) and 0.01 (right hemisphere), to a maximum of 0.53 (left hemisphere) and 0.54 (right
hemisphere). For multi-region seeds the [σ1s] range from a minimum of 0.02 (left and right
hemispheres) to a maximum of 0.52 (left hemisphere) and 0.55 (right hemisphere).
5.5.2. Group Connectomics a) The group functional connectivity IRCM ([μ
1
g]) in Fig. 5.4 (only left-hemispheric regions
shown) displays higher contrast between regions and on average lower mean compared with
the single-subject IRCMs (Fig. 5.3), both for single- (Fig. 5.4a) and for multi-region (Fig. 5.4b)
74
Fig. 5.4. Group averaged connectomics - Functional connectivity inter-regional connectivity
matrices (IRCMs). [μ1g] correlations among 28 seed regions and 70 left-hemispheric atlas-
based brain regions for: (a) single-region seeds, and (b) multi-region seeds. (c) Group
averaged global (140 regions) functional connectivity (Z-scores of [μ1g] correlations) of 6
major classes of single- and multi-region RSN seeds (ATN, AUN, DMN, FRN, SMN, and
VSN). The error bars represent the standard error in the [μ1g] correlations.
75
Fig. 5.6. Inter-subject variability of connectomics – Spatial inter-regional connectivity
matrices (IRCMs). [μ2g] correlation among 28 seed regions and 70 left-hemispheric atlas-based
brain regions: (a) single-region seeds, and (b) multi-region seeds. (c) Inter-subject variability
in global (140 regions) functional network connectivity (Z-scores of the [μ2g] correlation) of 6
major classes of single- and multi-region RSN seeds (ATN, AUN, DMN, FRN, SMN, and
VSN). The error bars represent the standard error in the [μ2g] correlations.
76
Fig. 5.5. Group averaged connectomics - Temporal fluctuation inter-regional connectivity
matrices (IRCMs). [σ1g] among 28 seed regions and 70 left-hemispheric atlas-based brain
regions for: (a) single-region seeds, and (b) multi-region seeds. (c) Group averaged global
(140 regions) temporal fluctuations in functional connectivity (Z-scores of meta-SD) of 6
major classes of single- and multi-region RSN seeds (ATN, AUN, DMN, FRN, SMN, and
VSN). The error bars represent the standard error in the [σ1g].
77
seeds. Single-region seeds show mostly low positive [μ1g] correlations (0-0.1) across the
majority of regions, particularly across the BAs 20-47 and subcortical regions. The maximum
negative [μ1g] correlation seen with single-region seeds is -0.03 for the left hemisphere and -
0.05 for the right hemisphere. BGN, DMN, and FRN seeds are the least positively correlated
throughout the brain whereas the subsets of other RSNs (ATN, AUN, SMN, and VSN) are
strongly correlated with their associated brain regions (e.g., SMN seeds are highly correlated
with BAs 01-07). The maximum positive [μ1g] correlations seen with single-region seeds are
0.69 for the left hemisphere and 0.75 for the right hemisphere.
The multi-region seeds (Fig. 5.4b), not only show strong connectivity with the regions that are
associated with the networks, but also extend over a larger number of regions. The ATN, AUN,
SMN, and VSN seeds show strong [μ1g] correlations with most of the 140 regions, whereas the
DMN and BGN seeds show smaller [μ1g] correlations. The maximum negative [μ1
g] correlations
seen with multi-region seeds are -0.03 for the left hemisphere and -0.01 for the right
hemisphere. The maximum positive [μ1g] correlations are 0.60 for the left hemisphere, 0.63 for
the right hemisphere. Similar connectivity characteristics are seen in right hemispheric brain
regions for both seeds. The group global connectivity statistics across the whole-brain and
subjects presented in Fig. 5.4c show that the multi-region seed clusters have 26% overall higher
connectivity strength compared to the single-region seeds. The average global [μ1g] correlation
across the networks, with single- and multi-region seeds is 0.23 and 0.29, respectively.
b) The temporal fluctuation IRCMs ([σ1g]) show that the single-region seeds (Fig. 5.5a) exhibit
slightly higher temporal fluctuations compared to the multi-region seeds (Fig. 5.5b). The [σ1g]
correlations vary from a minimum of 0.17/0.18 to a maximum of 0.43/0.40 in the case of
single/multi-region seeds, respectively. Apart from the slightly higher [σ1g] correlations seen in
the case of single-region seeds, the global connectivity patterns are similar between the single-
and multi-region seeds: the fluctuations in the frontal, visual, and posterior cingulate (PCC)
cortices are higher compared to the auditory, and sensorimotor cortices; BAs 20, 28, 35, 36, 38
and dentate show meta-SD of the order of 0.25. The global [σ1g] temporal fluctuations (Fig.
5.5c) are higher for ATN, FRN, and SMN with single-region seeds compared to the multi-
region seeds. The average global [σ1g] temporal fluctuations with single/multi-region seeds are
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0.33/0.32, respectively, across the networks. Similar results are seen in the case of right brain
IRCMs.
c) The inter-subject variability of functional connectivity ([μ2g]) displayed in Fig. 5.6 for single-
(Fig. 5.6a), and multi-region seeds (Fig. 5.6b) show that the ATN, AUN, DMN, FRN and SMN
seeds exhibit a small spatial variability in most cortical areas, in particular in BAs 01-32, in
contrast to the BAs 33-35 and 43-44, for both types of seeds. The subcortical regions, including
amygdala, dentate, lateral dorsal nucleus, midline nucleus, red nucleus, display particularly
high variability across the subjects. The inter-subject variability graph in Fig. 5.6c shows that,
except for the AUN seed, all the other seeds show significant global variability. The global
inter-subject variability is higher for the AUN, DMN, SMN and VSN seeds compared to the
ATN and FRN seeds. The average global inter-subject variability with single/multi-region
seeds is 0.16/0.17 respectively, across the whole-brain.
5.5.3. Spatio-temporal Stability of Inter-Regional Connectivity A dual threshold technique was applied at the group level meta-statistics using functional
connectivity, temporal fluctuation and inter-subject variability IRCMs for both seed types using
custom MATLAB scripts. A spatial stability map was obtained by applying the first threshold on
the [μ1g] IRCM (group averaged functional connectivity) and by applying a second threshold, based
on the [μ2g] IRCM (inter-subject variability of functional connectivity). Similarly, a temporal
stability map was obtained by applying the first threshold to the [σ1g] IRCM (group averaged
temporal fluctuations) and by applying a second threshold based on the [σ2g] IRCM (inter-subject
variability of temporal fluctuations). Upper and lower thresholds were determined by histogram
analysis of each of the IRCMs at a 20 % cut-off level, resulting in four combinations of dual
thresholds: (i) high-mean, high-SD, (ii) high-mean, low-SD, (iii) low-mean, high-SD, and (iv) low-
mean, low-SD. The same thresholds were applied to temporal fluctuation maps. Among these
combinations of thresholds, maps (ii) and (iii) were of particular interest, as they identify strong
and stable connectivity, and weak and unstable connectivity, respectively. The percentages of
functional brain regions passing the dual threshold were calculated to quantify the whole-brain
spatio-temporal stability.
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The spatial stability of the functional brain regions across subjects (Fig. 5.7A) shows that the
single-region seed IRCM (Fig. 5.7A, a) exhibits a smaller number of spatially stable regions
compared to the multi-region seeds (Fig. 5.7A, c) for a given threshold. The BAs 01-07 are among
the most stable regions identified by the selected thresholds for both seed types (Fig. 5.7Aa, c)
apart from the subsets of the VSN, DMN, and ATN seeds, particularly in the case of multi-region
seeds. Connectivity in subcortical regions is less stable compared to the cortical regions, as seen
using single-region seeds (Fig. 5.7A, b). Multi-region seeds show a smaller number of unstable
regions both in cortical and subcortical regions (Fig. 5.7A, d).
A similar analysis on the temporal stability IRCMs (Fig. 5.7B) shows that BA08, 09 show the
lowest temporal stability (SD of 0.4) with FRN, SMN, and VSN single-region seeds (Fig. 5.7B, a)
compared to smaller number of unstable regions with multi-region seeds (Fig. 5.7B, c). Also,
considerable number of functional regions beyond BA19 show higher temporal stability (SD of
0.3) (Fig. 5.7 B b, d), across higher Brodmann areas (BA20-47) and dentate which shows strikingly
significant fluctuations across all the RSN seeds, with both the seed types. The percentage of
functional regions passing a given combination of the dual threshold is listed in Table 5.1 for both
spatial and temporal stability maps. More number of regions show spatio-temporal stability with
multi-region seeds comparison to the single-region seeds.
Regions passing the dual threshold (%) Single-region seeds Multi-region seeds
Spatial stability (Fig 5.6A)
Stable (a) 2.10 Stable (c) 4.03 Unstable (b) 4.13 Unstable (d) 0.30
Temporal stability (Fig 5.6B)
Unstable (a) 3.16 Unstable (c) 1.27 Stable (b) 7.09 Stable (d) 4.23
Table 5.1. The percentage of functional brain regions passing the dual threshold in the spatio-
temporal stability maps in Fig. 5.7.
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Fig. 5.7. Group averaged connectomics – Spatio-temporal stability inter-regional connectivity matrices (IRCMs) of left brain regions obtained with a dual threshold technique based on the [μ1
g]/[μ2g] (spatial) and [σ
1g]/[σ
2g] (temporal). The lower and upper thresholds of these meta-
statistics are selected at a 20% cut-off determined from a histogram analysis. (A) Thresholded spatial stability IRCMs for (a) regions that show higher spatial stability and (b) regions that show lower spatial stability using single-region seeds; (c) regions that show higher spatial stability and (d) regions that show lower spatial stability using multi-region seeds. (B) Thresholded temporal stability IRCMs for (a) regions that show lower temporal stability and (b) regions that show higher temporal stability using single-region seeds; (c) regions that show lower temporal stability and (d) regions that show higher temporal stability using multi-region seeds. The percentage of the functional left brain regions passing the dual threshold for each of the above maps are shown in Table 5.1.
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5.6. Inter-Network Connectivity (INC)
Single-subject meta-maps for single-region seeds were masked individually with each of the 28
single-region seeds and spatially averaged within the mask to compute a seed region averaged [μ1s]
INC using TurboFIRE and custom MATLAB scripts. The same procedure was implemented for
multi-region seed maps. In addition to the single-subject INC, the group [μ1g] was also computed
to compare the resulting wSCA based connectivity map with the ICA-based connectivity map. The
seed region averaged meta-means were arranged in the form of a color-coded inter- network
connectivity matrix (INCM), similar to the functional network connectivity matrix (FNCM)
presented as Fig. 4B in the ICA-based group study [12]. Global metrics of group averaged INC
and inter-subject variability in INC were computed.
Inter-network connectivity matrices (Fig. 5.8) for: single-subject single-region seeds – [μ1s] (Fig.
5.8 a), single-subject multi-region seeds – [μ1s] (Fig. 5.8b), group average single-region seeds –
[μ1g] (Fig. 5.8c), and group average multi-region seeds – [μ1
g] (Fig. 5.8d) display seed vs. seed
connectivity compared to the seed vs. brain region connectivity (IRCMs) described in previous
sections. The group averaged single-region seed INCM (Fig. 5.8c) is found to have the most similar
connectivity patterns to the FNCM presented in the group-ICA study [12].
The strongest correlations (blocks of high connectivity across the principal diagonal) are seen
among the intra-RSNs (sub-networks that belong the same major class), both in the single subjects
and in group results, a characteristic feature also observed in the FNCM presented in the group-
ICA study. Single-subject INCMs (Fig. 5.8a, b) display stronger anti-correlations across DMN and
VSN seeds than the group INCM (Fig. 5.8c, d), in both seed analyses. The group averaged meta-
statistics (Fig. 5.8c, d) show predominantly positive correlations. The SMN seed shows strong
positive correlations with the ATN seed and weaker correlations with the VSN seed, in both single-,
and multi-region seed analyses. The DMN seed is less strongly correlated with the rest of task
positive RSN seeds, as expected. Fig. 5.8e shows that multi-region seeds have higher global
connectivity strength and lower inter-subject variability relative to the single-region seeds.
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Fig. 5.8. Single-subject and group averaged inter-network connectivity matrices (INCMs).
RSN seed vs RSN seed [μ1s] correlation maps of the 28 networks listed in Table 4.1 for (a)
single-subject single-region seeds ([μ1s]); (b) single-subject multi-region seeds ([μ1
s]); (c) group
averaged single-region seeds ([μ1g]); (d) group averaged multi-region seeds ([μ1
g]). (e) Group
averaged global functional connectivity ([μ1g]) and inter-subject variability ([μ2
g]) of INC. The
error bars represent the standard errors of the [μ1g] and [μ2
g].
83
5.7. Atlas-based Functional Connectomics
The wSCA approach developed in this study takes advantage of the enhanced sensitivity offered
by high-speed fMRI acquisition to map RSNs across 140 functional regions in the entire brain,
which provides an unparalleled richness of information about the spatio-temporal dynamics of
intra- and inter-network connectivity in single subjects to create a connectome fingerprint (see
Chapter 6). Quantitative mapping of inter-subject variability in functional connectivity across
groups of subjects using the dual threshold technique based on the group statistics at a given
threshold, reveals distinct domains of stable connectivity and enabled segmentation of the regions
that exhibit strong fluctuations. The IRCMs generated in this study (that mapped connectivity
among the RSN seeds and whole-brain), are complementary to the spatially sparser INCMs or
FNCMs, and illustrate the connectivity across the whole-brain. The INCMs display anti-
correlations in the connectivity between RSNs at the single-subject level without the use of global
signal regression (GSR), which is consistent with several recent studies [13,14]. The single-region
seed INCMs shown in Fig. 5.7a, c are symmetric (in the absence of post-correlation filters), since
the masking of the meta-map to generate the single-region seed INCM is equivalent to the
multiplication of identity matrices whose product is commutative. In contrast, the multi-region
seed INCMs Fig. 5.7b, d are not symmetric, since the masking of the meta-maps to generate the
multi-region seed INCMs have different spatial configurations in terms of voxel locations resulting
in the multiplication of two non-identity matrices whose product is not commutative, hence the
asymmetry.
The developed wSCA approach represents an initial implementation of a generalized framework
for mapping whole-brain connectivity in individual networks and in clusters of networks that
expands current SCA approaches. While the current wSCA employs equal weights for the nodes
of the individual networks, an expansion of this approach using a weighted combination of seed
region time courses will provide further flexibility for hypothesis-driven analysis of whole-brain
inter-regional connectivity dynamics. The extension of this approach to a higher number of
seeds/dimensions will enhance the parcellation of spatio-temporal features of RSN connectivity.
This high dimensional INCM approach lends itself in training a spatially aggregated classifier [15]
to characterize the spatio-temporal dynamics of functional networks [16]. When comparing the
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INCMs with ICA-based FNCMs [12,17], the single-region seed group results show more similar
patterns of connectivity but with higher and more positive correlations and reduced contrast among
networks, which may reflect the greater segregation of RSNs of the ICA algorithm relative to SCA
and the much smaller number of subjects in the present study. ICA can perform spatial filtering by
separation of spatially overlapping components, and segregation of confounding signal changes
[18] resulting in high contrast FNCMs.
85
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12. Allen, E. A., Erhardt, E. B., Damaraju, E., Gruner. W., Segall, J. M., Silva, R. F., Calhoun, V. D., et al, 2011. A baseline for the multivariate comparison of resting-state networks. Front. Syst. Neurosci. 5:2. doi: 10.3389/fnsys.2011.00002.
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13. Chai, X. J., Castanon, A. N., Ongur, D., Whifield-Gabriell, S., 2012. Anti-correlations in resting-state networks without global signal regression. Neuroimage. 2012 January 16; 59(2): 1420-1428 doi: 10.1016/j.neuroimage.2011.08.048.
14. Liu, X., and Duyn, J. H., 2013. Resting-state fMRI signal anti-correlation exists in absence of global signal regression. Proc. Intl. Soc. Mag. Reson. Med. 21, 2013.
15. Zheng, W., Ackley, E. S., Martinez-Ramon, M., and Posse, S., 2012. Spatially aggregated multiclass pattern classification in functional MRI using optimally selected functional brain areas. Magn. Reson. Imaging 31, 247-261. doi: 101016/j.mri.2012.07.010.
16. Hansen, E. C. A., Battaglia, D., Spiegler, A., Deco, G., Jirsa, V. K., 2015. Functional connectivity dynamics: Modeling the switching behavior of the resting-state. NeuroImage 105 (2015) 525-535. http://dx.doi.org/10.1016/j.neuroimage.2014.11.001.
17. Allen, E. A., Damaraju, E., Plis, S. M., Erhardt, E. B., Eichele, T., Calhoun, V. D., 2012. Tracking the whole-brain connectivity dynamics in the resting-state. Cerebral cortex, November 11, 2012. doi:10.1093/cercor/bhs352.
18. Calhoun, V. D., Adali, T., Pekar, J. J., 2004. A method for comparing group fMRI data using independent component analysis: application to visual, motor and visuomotor tasks. Mag. Res. Imaging 22 (2004) 1181-1191 doi: 10.1016/j.mri.2004.09.004.
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Chapter 6 High Dimensional Connectomics
6.1. Introduction
Functional connectomics using resting-state fMRI (rsfMRI) is a rapidly expanding task-free
approach which has significant clinical impact. There is a growing need for seed-based
connectivity mapping tools with improved tolerance to confounding signal changes that enable
whole-brain connectomics in single subjects. One of the ways to achieve this is via an unbiased,
automated seed selection method in combination with wSCA. This chapter presents a novel atlas-
based connectomics study to map the connectivity across the entire brain in a single-subject. This
is an extension of the inter-network connectivity maps discussed in Chapter 5, with no a priori
knowledge of seed locations or correlation thresholds. Functional connectivity across the 140
bilateral brain regions from the Talairach Daemon database were computed using the wSCA
approach and presented as a connectome fingerprint.
6.2. Materials and Methods
High-speed resting-state echo-volumar imaging data (TR/TE 136/35 ms, 5 min scan, Siemens 3T
scanner) was collected in a single-subject with informed consent [1]. Data were analyzed in
TurboFIRE v5.14.5.1 [2]. Preprocessing steps included motion correction, spatial normalization
into MNI atlas and mapping into Talairach Daemon database, spatial smoothing using 8 mm3
Gaussian filter, and a 4 s temporal moving average low-pass filter to suppress the physiological
noise [3]. The entire functional brain region is selected as an ROI from Talairach Daemon database
[4]. Seed time courses were extracted from each of the voxels in the region and non-thresholded
correlation statistics were computed with all 24,682 voxels in the brain. These statistics were then
averaged across the brain region over the time of the scan. A 30 s sliding-window was used coupled
with meta-statistics [5] for effective confound tolerance [6]. The meta-statistics were plotted using
PERL scripts and MATLAB toolboxes to represent the underlying functional connectivity
signature in the resting brain. The connectivity is then mapped across the hemispheres using
Talairach Daemon database (Table 4.2) and subsequently segregated into 12 major functional
systems.
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Fig. 6.1a. The high dimensional, single-subject connectome fingerprint between 70 left
hemisphere and whole-brain.
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Fig. 6.1b. The high dimensional single-subject connectome fingerprint between 70 right
hemisphere and whole-brain.
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Fig. 6.2. The abridged functional connectivity map with brain regions segregated according to functional networks. Motor cortex – BA01-07; Frontal cortex – BA13,14; Visual cortex – BA17 -19; Attention areas – BA20-22; Wernicke’s area – BA39, 40; Auditory cortex – BA41, 42; Broca’s area – BA44,45; Caudate – Caudate Body (CB), Caudate Head (CH), Caudate Tail (CT); Central brain regions – Anterior Commissure (AC), Anterior Nucleus (AN), Corpus Callosum (CC), Dendate, Hypothalamus, Lateral Dorsal Nucleus (LDN), Lateral Geniculum Body (LGB), Lateral Globus Pallidus (LGP), Lateral Posterior Nucleus (LPN), Mammillary Body (MB), Medial Dorsal Nucleus (MDN), Medial Geniculum Body (MGB), Medial Globus Pallidus (MGP), Midline Nucleus (MN), Putamen, Pulvinar, Red Nucleus (RN), Substantia Nigra, Subthalamic Nucleus (SN), Ventral Anterior Nucleus (VAN), Ventral Lateral Nucleus (VL), Ventral Posterior Lateral Nucleus (VP), Ventral Posterior Medial Nucleus (VPM). The numbers 1-47 represents the corresponding Brodmann areas BA01-47. Meta mean correlation scale: -0.3 to +0.9.
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The whole-brain connectome fingerprint, based on meta-mean correlations across the two
hemispheres in a single-subject, is shown in Fig. 6.1. a & b. As each seed ROI (brain region)
consists of extended functional brain regions, the resulting connectivity matrix was not symmetric
and had a non-unitary diagonal. Using the motor, frontal, and visual cortices as seed regions, the
strength of the connectivity is maximum across the central brain regions. Anti-correlations were
observed between the auditory cortex and the rest of the brain. Functional connectivity patterns
were similar across hemispheres, but left hemisphere showed higher anti-correlations across the
auditory cortex relative to the right hemisphere. The whole-brain connectivity fingerprint is
abridged to represent the 12 major functional systems across the 140 brain regions (Fig. 6.2). The
insular and visual cortices showed lower connectivity strength, whereas amygdala and
hippocampus showed higher connectivity strength. In general, the central brain regions showed
overall higher connectivity strength across the 12 systems.
6.3. Whole-brain Connectivity Fingerprints
This method facilitates quantification of the functional connectomics at whole-brain level which
does not require a priori knowledge of seed locations. These connectome fingerprints can be
extended from functional brain region level (140×140 matrix) to single-voxel level (e.g.,
24,682×24,682 matrix). The major time delay during online processing is due to the image
reconstruction on the scanner itself, particularly at high temporal resolutions, therefore, such high
dimensional mapping during an ongoing scan requires enormous computational power and
accumulates significant delay in real-time processing. These higher dimensional connectomics
have potential applications in mapping the global information processing by providing a
visualization tool for probing connectivity dynamics. The method enables mapping of anti-
correlations in single subjects without global signal regression, as shown in a previous study [7].
Using pattern classification algorithms [8] in real-time, this method can segregate different
functional connectivity states known in healthy brain and disease related abnormalities, improving
individualized diagnosis in patients with neurological and psychiatric disorders. We are currently
investigating novel brain parcellation [9] and individualized seed optimization methods to improve
the computational efficiency of wSCA for generating the connectome fingerprints.
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References
1. Posse, S., Ackley, E., Mutihac, R., Rick, J., Shane, M., Murray-Krezan, C., et al. (2012). Enhancement of temporal resolution and BOLD sensitivity in real-time fMRI using multi-slab echo-volumar imaging. Neuroimage 61, 115-130. doi: 10.1016/j.neuroimage.2012.02.059.
2. Gembris, D., Taylor, G. J., Schor, S., Frings, W., Suter, D., and Posse, S (2000). Functional Magnetic Resonance Imaging in Real-Time (FIRE): Sliding-Window Correlation Analysis and Reference Vector Optimization, Mag. Reson. Med. 43:259-268.
3. Lin, F. H., Nummenmaa, A., Witzel, T., Polimeni, J. R., Zeffiro, T. A., Wang, F. N., et al. (2011). Physiological noise reduction using volumetric functional magnetic resonance inverse imaging. Hum. Brain. Mapp. 33, 2815-2830. doi:10.1002/hbm.21403.
4. Lancaster JL, Woldorff MG, Parsons LM, Liotti M, Freitas CS, Rainey L, Kochunov PV, Nickerson D, Mikiten SA, Fox PT, "Automated Talairach Atlas labels for functional brain mapping". Human Brain Mapping 10:120-131, 2000.
5. Posse, S., Ackley, E., Mutihac, R., Zhang, T., Hummatov, R., Akhtari, M., Chohan, M., Fisch, B., and Yonas, H (2013). High-speed real-time fMRI using multi-slab echo-volumar imaging. Front. Hum. Neurosci. 7:479. doi:10.3389/fnhum.2013.00479.
6. Vakamudi, K., Ackley, E., Posse, S (2014). Resting-state connectivity dynamics in real-time fMRI using a novel seed-based approach, Proceedings of the 20th Annual Meeting of the OHBM. June 2014 Sub. No. 3916.
7. Chai, X. J., Castanon, A. N., Ongur, D., Whifield-Gabriell, S (2011). Anti-correlations in resting-state networks without global signal regression. Neuroimage. 2012 January 16; 59(2): 1420-1428. doi: 10.1016/j.neuroimage.2011.08.048.
8. Zheng, W., Ackley, E. S., Martinez-Ramon, M., and Posse, S (2013). Spatially aggregated multiclass pattern classification in functional MRI using optimally selected functional brain areas. Magn. Reson. Imaging 31, 247-261. doi: 10.1016/j.mri.2012.07.010.
9. Blumensath, T., Jbabdi, S., Glasser, M. F., Van Essen, D. C., Ugurbil, K., Behrens, T. E., and Smith, S. M. (2013). Spatially constrained hierarchical parcellation of the brain with resting-state fMRI. Neuroimage, vol. 76, pp. 313-324, 2013, 3758955.
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Chapter 7 Real-time Neurofeedback
7.1. Introduction
Self-regulation of functional networks using real-time fMRI has recently been demonstrated using
ROI-based approaches [1-3], however, neurofeedback based modulation of signal correlation
within and among the resting-state networks (RSNs) has not yet been studied. Seed-based
connectivity analysis (SCA) is suitable for real-time connectivity analysis, but it is sensitive to
head movement and confounding signal sources [4] as discussed in previous chapters.
Furthermore, it is desirable to use high-speed fMRI acquisition methods, which have been shown
to increase sensitivity for detecting resting-state connectivity [5,6]. This chapter presents a novel
whole-brain SCA approach to study the RSN connectivity dynamics in real-time using ultra-high-
speed fMRI in the context of neurofeedback. The process flow of the proposed neurofeedback
experiment is as shown in Fig. 7.1. The methodology enables sensitive mapping of connectivity
changes in RSNs at time scales as short as 10-15s.
Fig. 7.1. A comprehensive process flow for neurofeedback using TurboFIRE and its integration
with the scanner.
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Fig. 7.2. Intra-, Inter-RSN connectivity dynamics displaying distinct connectivity patterns
characteristics of high positive connectivity (red circle), high negative connectivity (blue
circle) and combination of positive and negative connectivity (green circle), captured at
every 4 s of the scan.
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7.2. Real-time Windowed SCA
Six ROIs were selected to display a 6x6 correlation coefficient matrix in real-time. Resting-state
data (eyes open) in 9 healthy controls were collected on a 3 T scanner using ultra-high-speed echo-
volumar imaging (TR/TE 136/35 ms, 5 min scan) [7]. Data were analyzed in TurboFIRE [8,9]
using a 2 s moving average temporal low-pass filter [10], spatial normalization, sliding-windows
(range: 1–120 s), and cumulative meta-statistics [7]. Real-time monitoring of intra- and inter-
network connectivity in 6 RSNs (attention ATN, auditory AUN, default-mode DMN, frontal FRN,
sensorimotor SMN and visual VSN) was performed using seeds from Allen et al., 2011 [11].
Analysis of 28 RSNs was performed offline. Inter-network NxN correlation matrices were
computed, where N is the number of ROIs being investigated.
7.3. Connectivity Dynamics of Resting-state Networks
The real-time wSCA revealed RSNs in time frames as short as 20-30 s using sliding-windows as
short as 4 s (Fig.7.2). Cumulative meta-statistics reduced spurious correlations in non-gray matter
areas to the noise level after approximately 90 s.
Fig. 7.3. a) The inter-RSN real-time meta-statistics among six major RSNs; b) the
corresponding connectivity states throughout the same scan, showing distinct dynamical
connectivity patterns.
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7.4. Pattern Classification and Brain States
Mapping of RSN connectivity dynamics in real-time using a set of six seed regions enable intra-,
inter-RSN connectivity dynamics for networks of interest. An inter-network connectivity pattern
among six resting-state seed regions is shown in Fig. 7.3a. Such dynamically changing
connectivity patterns can be monitored throughout the ongoing scan in TurboFIRE, showing
distinct transient periods of hyper- and hypo-connectivity. Additionally, it shows periods of strong
anti-correlations between RSNs, which self-repeat over the time scales of minutes, as shown in
Fig.7.3b. The wSCA is shown to be a highly sensitive approach (Chapter 4) for mapping the RSN
connectivity dynamics in individual subjects in real-time. Generating intra- and inter-RSN
functional connectivity matrices during an ongoing resting-state fMRI scan enables sensitive
detection of network connectivity dynamics. Inter-and intra-RSN connectivity allows for
characterization of brain state dynamics, novel self-regulation [12,13], and neuro-feedback
methods [14].
7.5. Real-time Neurofeedback
We demonstrate the feasibility of real-time mapping of intra- and inter-network connectivity
dynamics at time scales of seconds using ultra-high-speed fMRI in an exploratory study. Six seed
regions of DMN were selected as ROIs and the resulting connectivity matrix was shown to the
subject on the scanner computer screen over regular intervals of time (4 s). This enabled the subject
to attempt regulation of the DMN by modulating their attention, as shown in Fig. 7.4. We
Fig. 7.4. Real-time neurofeedback circuit.
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encountered a lag between the real-time streaming of the images from the scanner and the
computation of connectivity matrix in TurboFIRE, which increased with time. However, this
approach enables sensitive detection of FNC dynamics in individual subjects and may lead to novel
neurofeedback approaches, which are currently under investigation to mitigate the scanner
hardware and computational limitations. This approach is also suitable for monitoring data quality
in resting-state fMRI, e.g. to assess artifacts due to head motion, for which there are no currently
available tools.
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References
1. Emmert, K., Breimhorst, M., BAuermann, T., Birklein, F., Van De Ville, D., Haller, S. (2014). Comparison of anterior vs. insular cortex as targets for real-time fMRI regulation during pain stimulation. Front. Beh. Neurosci. Vol 8, 350, doi: 10.3389/fnbeh.2014.00350.
2. Hinds, O., Thompson, T. W., Ghosh, S., Yoo, J. J., Whitfield-Gabrieli, S., Triantafyllou, C., et al., 2013. Roles of default-mode network and supplementary motor area in human vigilance performance: evidence from real-time fMRI. J Neurophysiol 109: 1250 –1258.
3. Shen, J., Zhang, G., Yao, L., Zhao, X. (2015). Real-time fMRI training-induced changes in regional connectivity mediating verbal working memory behavioral performance. Neuroscience 289 (2015) 114-152. http://dx.doi.org/10.1016/j.neuroscience.2014.12.071.
4. Power, J. D., Mitra, A., Laumann, T. O., Snyder, A. Z., Schlagger, et al., 2014. Methods to detect, characterize, and remove motion artifact in resting-state fMRI. NI, 84 320-341.
5. Feinberg, D. A., Moeller, S., Smith, S. M., Auerbach, E., Ramanna, S., et al, 2010. Multiplexed echo-planar imaging for sub-second whole-brain fMRI and fast diffusion imaging. PLoS ONE 5(12): e 15710. doi: 10.1371/journal.pone.0015710.
6. Posse, S., Ackley, E., Mutihac, R., Rick, J., Shane, M., Murray-Krezan, C., et al, 2012. Enhancement of temporal resolution and BOLD sensitivity in real-time fMRI using multi-slab echo-volumar imaging. NeuroImage 61, 115-130.
7. Posse, S., Ackley, E., Mutihac, R., Zhang, T., Hummatov, R., Akhtari, M., Chohan, M., Fisch, B., and Yonas, H., 2013. High-speed real-time fMRI using multi-slab echo-volumar imaging. Front. Hum. Neurosci. 7:479. doi:10.3389/fnhum.2013.00479.
8. Gao, K., and Posse, S., 2004. TurboFIRE: Real-time fMRI with online generation of reference vectors. Proceedings of the 10th Annual Meeting of the Organization for Human Brain Mapping (Budapest: Organization for Human Brain Mapping), WE177.
9. Gembris, D., Taylor, G. J., Schor, S., Frings, W., Suter, D., and Posse, S., 2000. Functional Magnetic Resonance Imaging in Real-Time (FIRE): Sliding-Window Correlation Analysis and Reference Vector Optimization. Mag. Reson. Med. 43:259-268.
10. Lin, F. H., Nummenmaa, A., Witzel, T., Polimeni, J. R., Zeffiro, T. A., Wang, F. N., et al, 2011. Physiological noise reduction using volumetric functional magnetic resonance inverse imaging. Hum. Brain. Mapp. 33, 2815-2830. doi:10.1002/hbm.21403.
11. Allen, E. A., Erhardt, E. B., Damaraju, E., Gruner. W., Segall, et al, 2011. A baseline for the multivariate comparison of resting-state networks. Front. Syst. Neurosci. 5:2.
12. Weiskopf, N., Sitaram, R., Josephs, O., Veit, R., Scharnowski, F., et al, 2007. Real-time functional magnetic resonance imaging: methods and applications. Mag. Reso. Imaging 25 (2007) 989-1003. doi: 10.1016/j.mri.2007.02.007.
13. Sitaram, R., Lee, S., Ruiz, S., & Birbaumer, N. 2011. Real-time regulation and detection of brain states from fMRI signals. In R. Coben, & J. Evans (Eds.), Neurofeedback and neuromodulation techniques and applications (pp. 227–253). London: Elsevier Inc.
14. Koush, Y., Rosa, M. J., Robineau, F., Heinen, K., Rieger, S. W et al., 2013. Connectivity-based neurofeedback: Dynamic causal modeling for real-time fMRI. NeuroImage 81, 422-430. http://dx.doi.org/10.1016/j.neuroimage.2013.05.010.
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Chapter 8 Conclusions and Future Directions
8.1. Conclusions
The wSCA approach provides a flexible framework for probing the spatial-temporal dynamics of
whole-brain connectivity in individual networks and in clusters of networks at time scales as short
as 10-20 s. It has been demonstrated that the confound suppression performance of wSCA for
mapping RSN connectivity dynamics compares with that of conventional SCA using regression,
and serves as an alternative to the existing real-time fMRI approaches. This study benefits from
the higher temporal resolution provided by high-speed fMRI in order to improve the detection of
connectivity and dynamic changes thereof, as shown in several recent studies [1-3]. The
methodology developed in this study provides unprecedented sensitivity for mapping the dynamics
of the functional connectome in single subjects at time scales as short as 30 s. The wSCA enables
highly specific mapping of connectivity in single networks, as well as long-range connectivity in
spatially distributed clusters of networks. The identification of regions with pathology related
alterations in RSN connectivity in neurological and psychiatric patient populations is expected to
be facilitated by combining dual thresholding of connectivity maps (see 5.5.3) and pattern
classification. The application of this automated wSCA in patients with brain lesions complements
task-based pre-surgical mapping of eloquent brain regions. The interpretation of RSN connectivity
measured with this method will benefit from multi-modal integration with other functional
imaging techniques that map resting-state connectivity, such as EEG, MEG and fNIRS [3]. This
will ultimately lead to a novel approach to understand the neurophysiological mechanisms that
govern dynamic RSN fluctuations and their effect on brain function.
8.2. Future Directions
Automated seed selection methods
Although wSCA is largely automated, this study relied on previous studies for the selection of
seed regions. The seeds adopted from the group-ICA study [4] do not account for the inter-subject
variability of anatomy. Thus, we are working on novel automated seed identification methods that
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account for the anatomy of an individual subject, thereby maximizing the functional connectivity
measures.
Integrated windowed-regression SCA approach
The aim of this study is to combine the current wSCA approach with the conventional regression-
based approaches for offline analysis of the fMRI data. This is expected to provide a more accurate
mapping of functional connectivity without the loss of the advantages offered by the wSCA.
Pattern classification and neurofeedback
Further development of pattern classification based approaches to investigate the functional
connectivity dynamics from the perspective of brain states. This will allow for the assessment of
the modulation and regulation of brain function through real-time neurofeedback.
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References 1. Feinberg, D. A., Moeller, S., Smith, S. M., Auerbach, E., Ramanna, S., et al, 2010.
Multiplexed echo-planar imaging for sub-second whole-brain fMRI and fast diffusion imaging. PLoS ONE 5(12): e 15710. doi: 10.1371/journal.pone.0015710.
2. Posse, S., Ackley, E., Mutihac, R., Rick, J., Shane, M., et al, 2012. Enhancement of temporal resolution and BOLD sensitivity in real-time fMRI using multi-slab echo-volumar imaging. NeuroImage 61, 115-130. doi: 10.1016/j.neuroimage.2012.02.059.
3. Smith, S. M., 2012. The future of fMRI connectivity. NeuroImage 62 (2012) 1257-1266. doi: 10.1016/j.neuroimage.2012.01.022.
4. Allen, E. A., Erhardt, E. B., Damaraju, E., Gruner. W., Segall, J. M., Silva, R. F., Calhoun, V. D., et al, 2011. A baseline for the multivariate comparison of resting-state networks. Front. Syst. Neurosci. 5:2. doi: 10.3389/fnsys.2011.00002.