Resting-State Connectivity Dynamics in the Human Brain Using High-Speed Fmri Kishore Vakamudi

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8-25-2016 Resting-state Connectivity Dynamics in the Human Brain using High-speed fMRI Kishore Vakamudi

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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

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

freedom, reason, and truth

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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 Sincere thanks to the departments of Physics and Astronomy, and Neurology, University of New Mexico, Albuquerque, for the and Astronomy and financial support. Neurology iv

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.

and to my parents For everything they are. Suseela and Late Sobhanachalam

Vakamudi

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.

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.

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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

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

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

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

xii

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

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.

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.

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.

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

│S⃗ │ = 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) 5

The energy of a spin system placed in a magnetic field 퐵⃗ is given by

E = -µ·퐵⃗ (2.4) where µ is the magnetic moment. It is proportional to the spin angular momentum,

µ=γ푆 (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 (퐵⃗ ·푆 )

Hz= -γħBzSz (2.6)

Solving the Schrödinger equation of this Hamiltonian for the energy eigenstate, we get

H│푚⃗⃗ s˃ = E│푚⃗⃗ s˃

E = -γħBzms (2.7)

The change in energy of a proton as a result of transition between two spin states (±1/2),

E 1 − E 1 훾 ΔE = −2 +2 = ħBz (2.8)

This transition is accompanied by emission or absorption of a photon with frequency ν0

ΔE = γħBz = hν0 (2.9)

γ B B⃗⃗⃗⃗ = B ẑ where ν0 = 2π Z. For a constant field z 0 ,

ω0 = 훾B0 (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.

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 ∆E +1 2 = eκBT (2.11) P 1 −2

-23 ∆퐸 where 휅퐵 = 1.3806x10 J/K and T is the absolute temperature. Since 휅퐵 is very small ( ≪ 1), 휅퐵푇 Eq. 2.11 can be approximated as

P +1 ∆E 2 ≈ 1 + (2.12) P 1 κBT −2

푃 1 + 푃 1 = 1 (푃 1 − 푃 1 Using +2 −2 , we calculate the excess number of spins +2 −2) that are parallel to the magnetic field as

∆E P+1 − P−1 ≈ (2.13) 2 2 2κBT

∆퐸 A small sample of any biological tissue contains N excess proton spins, where N is Avogadro 2휅퐵푇 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.

2.4. Classical Equations for NMR

2.4.1. Precession

The equation of motion of a magnetic moment vector (M⃗⃗⃗ ), placed in a magnetic field (B⃗⃗ ) is

dM⃗⃗⃗ = γM⃗⃗⃗ x B⃗⃗ dt (2.14)

̂ For a static magnetic field, B⃗⃗ = B0k, the solution of this equation can be written as

M⃗⃗⃗ (t) = Mx0(x̂ cos ωt − ŷ sin ωt) + My0(x̂ sin ωt + ŷ cos ωt) + 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.

Fig. 2.1. Precession of a magnetization vector M⃗⃗⃗ , in a magnetic field B⃗⃗ 0 directed along Z- axis with an angular frequency ω.

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 8

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 B⃗⃗⃗⃗1 (t) = B1(x̂ cos ωt − ŷ sin ωt) is applied along with the static magnetic field B⃗⃗ = B0ẑ, 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:

dM⃗⃗⃗ 1 1 = γM⃗⃗⃗ x B⃗⃗ + (M⃗⃗⃗⃗⃗0 − M⃗⃗⃗⃗⃗z ) − (M⃗⃗⃗⃗⃗x + M⃗⃗⃗⃗⃗y ) (2.16) dt T1 T2

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

dM⃗⃗⃗ = γM⃗⃗⃗ x B⃗⃗ eff dt (2.17) Ω B⃗⃗ eff = B⃗⃗ + . where γ

Fig. 2.2. Laboratory and rotatory frames of reference. The XY plane of a laboratory frame is

rotated by an angular frequency Ω = –γ퐵0.

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 ⃗⃗M⃗⃗ is along the direction of the applied magnetic field

퐵⃗ . This is called the equilibrium magnetization M⃗⃗⃗⃗⃗0 , which contains only the Z component, known

o as longitudinal magnetization M⃗⃗⃗⃗⃗z . After a 90 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,

dM (M −M ) z = − z 0 (2.18) dt T1

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.

Solving for 푀푧,

t −T Mz = M0(1 − e 1 ) (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,

t −T Mz = M0(1 − 2e 1 ) (2.19b)

 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 Mx dMy My = My. γB − and = −Mx. γB − (2.20) dt T2 dt T2

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,

t −T −iωt Mxy = Mxy0e 2 . e (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. 12

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 B⃗⃗⃗⃗0 . These gradient fields, when combined with the static magnetic field B⃗⃗⃗⃗0 (directed along the scanner axis), generate an effective field B⃗⃗ 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.

퐵⃗ (t) = 퐵⃗⃗⃗⃗0 + Gx(t) 푥̂ + Gy(t) 푦̂+ Gz(t) 푧̂ (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 = 훾B in Eq. 2.21, the transverse magnetization at a given location and time is given by,

t t −T −iγBot −iγ ∫ (Gx(t)x+Gy(t)y+Gz(t)z)dt Mxy(x, y, z, t) = Mxy0(x, y, z)e 2 . e e 0 (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 휏 and is given by,

τ) = M (x, y, z)dx dy dz S( ∭x,y,z xy (2.24)

Substituting Mxy from Eq. 2.23 into 2.24, we get,

t −t −iγ ∫ (G (t)x+G (t)y+G (t)z)dt τ) = M (x, y, z)e T2 . e−iγBot e 0 x y z dx dy dz S( ∭x,y,z xy0 (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 퐵표, 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.

2.5.1. Zeugmatography and Slice Selection

The principle of encoding space using magnetic field gradients is called Zeugmatography [12],

−t introduced by Nobel Laureate Lauterbur in 1972 [13]. The term e T2 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.

t −iγ ∫ (G (t)x+G (t)y+G (t)z)dt S(τ) = M (x, y, z)e 0 x y z dx dy dz ∭x,y,z xy0 (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.

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,

∆휔 푇퐻 = 푟푓 훾Gz (2.27)

The magnetization within the slice depends only on X and Y, and Eq. 2.26 is reduced to

t −iγ ∫ (G (t)x+G (t)y)dt τ) = M(x, y)e 0 x y dx dy S( ∬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).

γ t k (t) = ∫ G (τ)dτ x 2π 0 x (2.29a)

γ t k (t) = ∫ G (τ)dτ y 2π 0 y (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

Fig. 2.6. The relationship between image space and k-space through the two-dimensional Fourier transform of a brain image. 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

τ) = M(x, y)e−i2πkx(t)xe−i2πky(t)ydx dy S( ∬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. 16

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.

TR TR TR TR − − − − T T T T CAB = M0A (1 − e 1A ) e 2A – M0B (1 − e 1B ) e 2B (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 TR − T contrast should be minimized using short TE. For TE << T2 (e 2  1), Eq. 2.31 becomes

TR TR − − T T CAB = M0A (1 − e 1A ) − M0B (1 − e 1B ) (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 푇푅 − 푇 optimal T2 contrast, TR should be long so that T1 contrast is minimal. For TR >> T1 (푒 1  0), Eq. 2.32 becomes,

TR TR − − T T CAB = M0Ae 2A – M0Be 2B (2.33)

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 1 1 ∗ = + ′ (2.34) T2 T2 T2

* ′ * 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 TR − as, S ~ e 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 18

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 o sequence with a 90 radiofrequency (RF) excitation pulse, slice selection gradient (Gx), frequency

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).

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).

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.

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

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,

√3 Ta ∗ FWHMTTz = ∗ ∆x (2.36) π Tz

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,

∗ t ∆Tz t −( ) ∗ Tz Tz ∆S(t) = S0 ∗ e (2.37) Tz

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

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.

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

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 (n⃗ ) using Euler rotation matrices, projecting the position vector P⃗⃗ onto n, and adjusting a half-slice offset to account for the digitization of the slices:

D = RL cos α sin β − AP sin α + HF cos α cos β − 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.

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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).

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.

tα1−1 tα2−1 β1t β2t ℋ(t, θ) = c1 e + c2 e (3.1) Γ(α1) Γ(α2)

6 where Γ(훼푖) is the Gamma function, c1 ≥ c2 and θ = [c1, α1, β1, c2, α2, β2] ϵ ℝ . The schematic representation of HDR is shown in Fig. 3.1.

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).

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

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]. 30

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.

 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

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.

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.

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.

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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 36

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 multiband 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

R e stin g - Coordinates sta te Independent in M N I F u n c tio n a l B r o d m a n n N e tw o r k C o m p o n e n t te m p la te Brain Region A r e a ATN IC 3 4 * (-4 7 , -5 7 , 3 9 )* Left inferior parietal lobule B A 4 0 Right inferior parietal IC 6 0 (4 2 , -5 6 , 4 2 ) lo b u le B A 4 0 IC 5 2 (-3 3 , -6 4 , 3 1 ) Left angular gyrus B A 3 9 IC 7 2 (0 , -5 3 , 6 1 ) Bilateral precuneus B A 0 7 Right superior temporal IC 7 1 (5 7 , -4 4 , 1 1 ) g y ru s B A 4 0 IC 5 5 (0, 22, 45) Bilateral cingulate gyrus B A 4 0 Left superior te m p o ra l AUN IC 1 7 * (-5 1 , -1 8 , 7 )* g y ru s B A 2 2 BGN IC 2 1 (2 5 , -1 , 0 ) Right putamen DMN IC 5 0 * (1 , -6 4 , 4 3 )* Bilateral precuneus B A 0 7 Bilateral posterior cingulate IC 5 3 (0 , -5 2 , 2 2 ) c o rte x B A 2 3 Bilateral anterior cingulate IC 2 5 (0 , 4 1 , 4 ) c o rte x B A 3 2 IC 6 8 (-26, 26, 42) Left middle frontal gyrus B A 0 8 FRN IC 4 2 * (5 0 , -2 3 , 2 )* Right inferior frontal gyrus B A 4 5 IC 2 0 (-5 5 , 2 2 , 7 ) Left inferior frontal gyrus B A 2 3 IC 4 7 (-48, 17, 29) Left middle frontal gyrus B A 0 9 IC 4 9 (31, 55, 7) Right middle frontal gyrus B A 1 0 SMN IC 0 7 * (-5 2 , -9 , 3 1 )* Left precentral gyrus B A 0 6 IC 2 3 (-3 5 , -2 7 , 5 4 ) Left precentral gyrus B A 0 4 IC 2 4 (3 7 , -2 5 , 5 3 ) Right precentral gyrus B A 0 4 IC 2 9 (1 , -2 8 , 6 1 ) Bilateral para -central lobule B A 0 6 IC 3 8 (-5 5 , -3 4 , 3 7 ) Left supramarginal gyrus B A 0 2 Bilateral supplementary IC 5 6 (1 , -3 , 6 1 ) m o to r a re a B A 0 6 VSN IC 4 6 * (1 , -8 7 , -2 )* Bilateral lingual gyrus B A 1 7 , 1 8 IC 6 4 (1 , -7 1 , 1 3 ) Bilateral calcarine gyrus B A 1 7 , 1 8 IC 6 7 (-1 5 , -5 6 , -8) Left lingual gyrus B A 1 8 IC 4 8 (2 9 , -7 6 , -8) R ig h t lingual gyrus B A 1 8 , 1 9 Right inferior temporal IC 3 9 (4 8 , -6 3 , -8) g y ru s B A 3 7 IC 5 9 (2 , -8 4 , 2 8 ) Bilateral cuneus B A 1 9

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*).

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 39

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).

1 B A 0 1 15 B A 1 9 29 B A 3 4 43 A m yg d a la 57 Mammillary Body 2 B A 0 2 16 B A 2 0 30 B A 3 5 44 A n te rio r 58 M edial Dorsal Nucleus Commissure 3 B A 0 3 17 B A 2 1 31 B A 3 6 45 Anterior Nucleus 59 Medial Geniculum Body 4 B A 0 4 18 B A 2 2 32 B A 3 7 46 Caudate Body 60 M edial Globus Pallidus 5 B A 0 5 19 B A 2 3 33 B A 3 8 47 Caudate Head 61 Midline Nucleus 6 B A 0 6 20 B A 2 4 34 B A 3 9 48 Caudate Tail 62 P u lv in a r 7 B A 0 7 21 B A 2 5 35 B A 4 0 49 Corpus Callosum 63 P u ta m e n 8 B A 0 8 22 B A 2 7 36 B A 4 1 50 D e n ta te 64 Red Nucleus 9 B A 0 9 23 B A 2 8 37 B A 4 2 51 Hippocampus 65 Substania Nigra 10 B A 1 0 24 B A 2 9 38 B A 4 3 52 Hypothalamus 66 Subthalamic Nucleus 11 B A 1 1 25 B A 3 0 39 B A 4 4 53 Lateral Dorsal 67 Ventral Anterior Nucleus N u c le u s 12 B A 1 3 26 B A 3 1 40 B A 4 5 54 L a te ra l 68 Ventral Lateral Nucleus Geniculum Body 13 B A 1 7 27 B A 3 2 41 B A 4 6 55 Lateral Globus 69 Ventral Posterior Lateral P a llid u s N u c le u s 14 B A 1 8 28 B A 3 3 42 B A 4 7 56 Lateral Posterior 70 Ventral Posterior M edial N u c le u s N u c le u s

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).

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 40

(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

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.

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

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 44

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.

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.

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.

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).

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). 49

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).

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 50

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 51

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,

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).

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.

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).

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.

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.

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 ~ 57

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 58

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 59

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. 60

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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), s s s s resulting in the region/single-subject level meta-statistics ([μ1], [σ1], [μ2], and [σ2]) which s correspond to spatial information (s – spatial). The [μ2] maps were a measure of temporal fluctuations of correlations within each brain region. The group information was obtained by g g g g g computing the mean and SD across subjects ([μ1], [σ1], [μ2], and [σ2]) (g – group). The [μ1] 67

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 s s voxels within the functional brain regions (spatial statistics) yields [μ1]/[σ1] and s s [μ2]/[σ2] maps. The mean and SD across subjects (group statistics) provides group level maps g g g g [μ1]/[σ1] and [μ2]/[σ2]. Notation: μ-principal mean, σ-principal SD; subscripts: 1-derived mean, 2-derived SD; superscripts: t-temporal, s-spatial, and g-group.

g corresponds to the strength of the correlations across the subjects and the [σ1] measures the inter- g subject variability of the meta-mean correlations within each brain region. The [μ2] corresponds g to the average temporal fluctuations within each brain region across subjects and the [σ2] measures the variability in temporal fluctuations in each brain region across subjects.

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 contralateral 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.

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.

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 s PERL scripts, resulting in region-wise meta-statistics for each seed region in single subjects ([μ1], s s s [σ1], [μ2], and [σ2]). The group level region-wise meta-statistics were obtained by averaging g g g g across the subjects ([μ1], [σ1], [μ2], and [σ2]). IRC matrices (IRCMs) at the single-subject and 70

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 s connectivity among the atlas-based functional brain regions at the single-subject ([μ1]) and the g group levels ([μ1]). (b) The meta-SDs were plotted as a measure of temporal fluctuations among s g the atlas-based functional brain regions both at the single-subject ([σ1]) and the group levels ([σ1]). g g (c) The SDs of the meta-mean correlation coefficients ([μ2] and the SD of meta-SDs [σ2] 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

s The functional connectivity ([μ1]) 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. s 5.3A, b). Negative [μ1] 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 s regions, e.g., the strongest negative [μ1] 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 s smaller negative [μ1] 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.

Fig. 5.3. Single-subject connectomics – Functional connectivity and temporal fluctuation inter- s regional connectivity matrices (IRCMs). (A) Functional connectivity ([μ1]) IRCM among 28 seed regions and 70 left-hemispheric atlas-based brain regions for: (a) single-region seeds; and (b) s multi-region seeds. (B) Temporal fluctuation ([σ1]) IRCM among 28 seed regions and 70 left- hemispheric atlas-based brain regions for: (a) single-region seeds; and (b) multi-region seeds. (C) s Maximum negative- (anti) and positive- [μ1] 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 s (orange and green bars) seeds, respectively. (D) Minimum and maximum [σ1] 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 s s errors in the [μ1] and the [σ1].

s The single-subject temporal fluctuation ([σ1]) 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 s the consistency of the positive [μ1] correlations across subjects for both single- and multi-region s seeds. The negative [μ1] correlations are more variable across subjects, in particular for multi- s region seeds. The range of positive [μ1] 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 s of multi-region seeds. Negative [μ1] 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 s temporal fluctuations ([σ1]) are more consistent across the subjects (range: 0.4 to 0.55) than the s s [μ1] correlations. The [σ1] 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 s hemisphere). For multi-region seeds the [σ1] 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

g μ a) The group functional connectivity IRCM ([ 1]) 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)

Fig. 5.4. Group averaged connectomics - Functional connectivity inter-regional connectivity g matrices (IRCMs). [μ1] 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 g averaged global (140 regions) functional connectivity (Z-scores of [μ1] correlations) of 6 major classes of single- and multi-region RSN seeds (ATN, AUN, DMN, FRN, SMN, and g VSN). The error bars represent the standard error in the [μ1] correlations.

Fig. 5.6. Inter-subject variability of connectomics – Spatial inter-regional connectivity g matrices (IRCMs). [μ2] 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 g in global (140 regions) functional network connectivity (Z-scores of the [μ2] correlation) of 6 major classes of single- and multi-region RSN seeds (ATN, AUN, DMN, FRN, SMN, and g VSN). The error bars represent the standard error in the [μ2] correlations.

Fig. 5.5. Group averaged connectomics - Temporal fluctuation inter-regional connectivity g matrices (IRCMs). [σ1] 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 g VSN). The error bars represent the standard error in the [σ1].

g seeds. Single-region seeds show mostly low positive [μ1] correlations (0-0.1) across the majority of regions, particularly across the BAs 20-47 and subcortical regions. The maximum g negative [μ1] 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 g with BAs 01-07). The maximum positive [μ1] 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, g SMN, and VSN seeds show strong [μ1] correlations with most of the 140 regions, whereas the g g DMN and BGN seeds show smaller [μ1] correlations. The maximum negative [μ1] correlations seen with multi-region seeds are -0.03 for the left hemisphere and -0.01 for the right g hemisphere. The maximum positive [μ1] 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 g connectivity strength compared to the single-region seeds. The average global [μ1] correlation across the networks, with single- and multi-region seeds is 0.23 and 0.29, respectively. g b) The temporal fluctuation IRCMs ([σ1]) show that the single-region seeds (Fig. 5.5a) exhibit g slightly higher temporal fluctuations compared to the multi-region seeds (Fig. 5.5b). The [σ1] correlations vary from a minimum of 0.17/0.18 to a maximum of 0.43/0.40 in the case of g single/multi-region seeds, respectively. Apart from the slightly higher [σ1] 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 g and dentate show meta-SD of the order of 0.25. The global [σ1] temporal fluctuations (Fig. 5.5c) are higher for ATN, FRN, and SMN with single-region seeds compared to the multi- g region seeds. The average global [σ1] temporal fluctuations with single/multi-region seeds are 77

0.33/0.32, respectively, across the networks. Similar results are seen in the case of right brain IRCMs. g c) The inter-subject variability of functional connectivity ([μ2]) 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 g the [μ1] IRCM (group averaged functional connectivity) and by applying a second threshold, based g on the [μ2] IRCM (inter-subject variability of functional connectivity). Similarly, a temporal g stability map was obtained by applying the first threshold to the [σ1] IRCM (group averaged g temporal fluctuations) and by applying a second threshold based on the [σ2] 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.

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 Stable (a) 2.10 Stable (c) 4.03 (Fig 5.6A) Unstable (b) 4.13 Unstable (d) 0.30 Temporal stability Unstable (a) 3.16 Unstable (c) 1.27 (Fig 5.6B) 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.

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 g g g g [μ1]/[μ2] (spatial) and [σ1]/[σ2] (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.

5.6. Inter-Network Connectivity (INC) Single-subject meta-maps for single-region seeds were masked individually with each of the 28 s single-region seeds and spatially averaged within the mask to compute a seed region averaged [μ1] INC using TurboFIRE and custom MATLAB scripts. The same procedure was implemented for g multi-region seed maps. In addition to the single-subject INC, the group [μ1] 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. s Inter-network connectivity matrices (Fig. 5.8) for: single-subject single-region seeds – [μ1] (Fig. s 5.8 a), single-subject multi-region seeds – [μ1] (Fig. 5.8b), group average single-region seeds – g g [μ1] (Fig. 5.8c), and group average multi-region seeds – [μ1] (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.

Fig. 5.8. Single-subject and group averaged inter-network connectivity matrices (INCMs). s RSN seed vs RSN seed [μ1] correlation maps of the 28 networks listed in Table 4.1 for (a) s s single-subject single-region seeds ([μ1]); (b) single-subject multi-region seeds ([μ1]); (c) group g g averaged single-region seeds ([μ1]); (d) group averaged multi-region seeds ([μ1]). (e) Group g g averaged global functional connectivity ([μ1]) and inter-subject variability ([μ2]) of INC. The g g error bars represent the standard errors of the [μ1] and [μ2].

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

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.

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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.

Fig. 6.1a. The high dimensional, single-subject connectome fingerprint between 70 left hemisphere and whole-brain.

Fig. 6.1b. The high dimensional single-subject connectome fingerprint between 70 right hemisphere and whole-brain.

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.

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. 91

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.

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.

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.

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.

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. 96

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.

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. 98

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

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.

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