Connectome Analysis: Characterization, Methods, and Analysis

Connectome Analysis: Characterization, Methods, and Analysis is a comprehensive companion for the analysis of brain networks, or connectomes. The book provides sources of constituent structural and functional MRI signals, network construction and practices for analysis, cutting-edge methods that address the latest challenges in neuroscience, and the fundamentals of network theory in the context of giving practical methods for building connectomes for analysis. Emphasis is placed on quality control of the individual analysis steps. Subsequent chapters discuss networks in neuroscience in clinical and general populations, including how findings are related to underlying neurophysiology and neuropsychology.

This book is aimed at students and early-career researchers in brain connectomics and neuroimaging who have a background in computer science, mathematics and physics, as well as more broadly to neuroscientists and psychologists who want to start incorporating connectomics into their research.

• Provides practical recommendations on how to construct, assess and analyze brain networks
• Gives an understanding of all the technical methods for connectome analysis
• Presents the basic network theoretical principles typically used in neuroscience
• Covers the latest tools and data repositories that are freely available for the reader to carry out connectomic analyses

• Language: English
• Publisher: Academic Press
• Release date: Jun 30, 2023
• ISBN: 9780323852814

Book preview

Introduction

Markus D. Schirmer¹, Tomoki Arichi² and Ai Wern Chung³ 1 Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, MA, United States 2 Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom 3 Fetal-Neonatal Neuroimaging and Developmental Science Center, Division of Newborn Medicine, Boston Children's Hospital, Harvard Medical School, Boston, MA, United States

Understanding how the human brain is put together and how it works represents one of the most fascinating and important endeavors of our time. This is a huge challenge, as the human brain is a highly complex system containing approximately 86 billion neurons [1]. Critically, it is becoming increasingly clear that it is the interaction within such a complex system, rather than integrity or activity of the individual units, which makes human life and behavior possible [2,3]. This has many parallels with other life science disciplines such as genetics; where it is has become apparent that sequencing the entire human genome [4] was only the start for unpicking how genes influence life, and that in most cases, a true understanding will likely only be possible through characterizing and modeling systems-level effects beyond mapping single genes.

The intuitive mapping of the human brain as a network, or graph, of connections between distinct regions originated at the end of the 19th century, in which aphasia (a disorder characterized by a patient’s inability to communicate with language) was described as a disconnection syndrome [5]. Since then and through a variety of different methods, scientists have continually strived to identify and characterize the underlying connectivity profile (commonly referred to as the connectome) in both human and nonhuman brains [6–8]. In neuroscience, it is common to differentiate between functional and structural connectivity between brain regions, where structural connectivity describes the constituent anatomical pathways and functional connectivity describes the relationships between their neural activity [9]. While interrelated through their possible influence on each other’s development as early as in utero, these distinct forms of connectivity also have unique characteristics and thus can describe different aspects about the brain’s functioning and intrinsic organization [10].

Many approaches have been used to characterize both connectivity profiles through the years, starting with neuroanatomical tracer studies as early as the 19th century [11]. These postmortem studies first identified connections between brain regions by following individual axonal pathways within the white matter. However, while such pioneering studies provided definitive information about fiber pathways through direct visualization, they required large numbers of samples which makes studying the human brain, and particularly nonprevalent diseases, incredibly difficult. In addition, this approach relies on dissections through the postmortem brain, which prevents longitudinal study of dynamic processes (i.e., plasticity, degeneration), and exploration of the relationships between structural pathways and functional activity.

With the advent of safe, noninvasive imaging technologies, including magnetic resonance imaging (MRI), in vivo studies of brain connectivity have become feasible [12]. MRI, in particular, is ideally suited for the combined study of structural and functional connectomes and has become the most prevalent assessment modality across the field of connectomics. Here, structural and functional connectivity profiles are most commonly defined through diffusion [13–15] and functional MRI [16,17] using specific sequences that are sensitized to capture the regional properties of water diffusion and temporal fluctuations of the blood oxygen level dependent (BOLD) signal, respectively. Over the years, these methods have enabled a wealth of connectivity studies to characterize the brain’s fundamental architecture and begun to reveal many key aspects of how it is established in early development, alters over the life span, and its role in explaining the pathological processes underlying neurological and psychiatric diseases.

In the beginning, connectomics relied on developments in the field of graph theory and related areas. Graph theory was specifically developed as a mathematical framework to characterize complex systems. Historically, its roots can be traced back to Leonhard Euler, who used it to solve the Seven Bridges of Königsberg problem in the early 18th century [18], which consisted of devising a walk through the city of Königsberg that would cross each of seven bridges once and only once. Since these early days, many methodological advancements have been and continue to be made in graph theory, with widespread application across all fields seeking to understand relationships within complex systems. However, the data-rich connectome is a network like no other, calling for the amalgamation of traditional and innovative methods to unearth new insights into brain connectivity and function. The exciting world of connectomics has further opened the door to neuroscience and imaging, attracting researchers from diverse disciplines who have brought new perspectives and pushed the field forward at an exponential rate. However, while incredibly exciting, we feel that this rapid rate of innovation has understandably led to a lack of practical how-tos which ultimately are necessary to keep the field moving forward.

Connectome analysis is a comprehensive companion for analyzing connectomes. It will guide the reader from the sources of the constituent structural and functional MRI data, network construction, and practices for analysis, through to cutting-edge methods embracing connectomes to address the latest challenges in neuroscience and disease.

This book is divided into three sections. The first section, Fundamentals of connectomics, will take the reader from the biology of the human brain through to how it is studied using MRI methods, the practicalities of building connectomes, and the basics of network theory towards analysis. The second section, Advanced concepts and methods explains principles of network topology in connectomics, and dives deeper into how to exploit these data-rich networks through advanced statistical, graph theoretical, and artificial intelligence–based frameworks. The final section, Applications in the human brain, will provide the reader with context of networks applied to neuroscience research in clinical and general populations, with discussions on how findings are related to the underlying neurophysiology, neuropsychology, and genetics. Readers can expect an overview of applications in human life span and disease populations, as well as potential areas ripe for exploration with connectomics.

References

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5. Wernicke, C. Der aphasische Symptomencomplex: eine psychologische Studie auf anatomischer Basis. (Cohn., 1874).

6. Sporns O. The human connectome: a complex network. Ann N Y Acad Sci. 2011;1224:109–125.

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18. Euler L. Solutio problematis ad geometriam situs pertinentis. Comment Acad Sci Petropolitanae 1741;:128–140.

Section I

Fundamentals of connectomics

Outline

Chapter 1 Neurobiology and the connectome

Chapter 2 Structural network construction using diffusion MRI

Chapter 3 Functional network construction using functional MRI

Chapter 4 Network nodes in the brain

Chapter 5 Network measures and null models

Chapter 6 Hubs and rich clubs

Chapter 7 Community detection in network neuroscience

Chapter 8 Network comparisons and their applications in connectomics

Chapter 1

Neurobiology and the connectome

Judit Ciarrusta¹ and Tomoki Arichi²,    ¹Center for Brain and Cognition, Pompeu Fabra University, Barcelona, Spain,    ²Centre for the Developing Brain, School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom

Abstract

In this chapter, the key neurobiological concepts that underlie the connectome are reviewed and a possible framework of how to integrate microscale and macroscale findings into studies is introduced. This includes an overview of the key historical findings about neuronal morphology, cytoarchitecture, synaptic mechanisms, and network dynamics that provided the neuroscience foundation for the connectome era. This includes description of the characteristics of the different cell types that compose the brain, first from a morphological point of view and then considering the basic electrophysiological mechanisms of signal propagation related to different cell types and neural circuits on the mesoscale. Neuroimaging-based connectomic studies are largely on the macroscale level, and therefore a primer is presented about how the different tissue types and properties observed using magnetic resonance imaging (MRI) methods might relate to specific parcellation approaches used to further segment the brain. Lastly, the association between the signal derived from diffusion and functional MRI with the underlying neurobiology is explored.

Keywords

Brain cells; synaptic mechanisms; circuits; diffusion; BOLD

1.1 Introduction

Over the last 200 years, neuroscience has witnessed an exponential increase in scientific publications that have contributed to our understanding of the constituent parts and processes (i.e., different cell types, cell assemblies, cytoarchitectonic organization, activity patterns, metabolic processes, etc.) within the central nervous system (CNS). In more recent years, advances in magnetic resonance imaging (MRI) have allowed studies of the brain in vivo and presented the possibility of investigating connectivity in the living human brain at a macroscopic level. Importantly, it has also enabled the translation of knowledge gained from detailed animal neuroscience studies to humans. In this context, the brain connectome represents a model with which to investigate how brain structure defined by the connections between neural elements provides the scaffolding for brain function [1] across species (e.g., comparative connectomics [2]), in developmental neuroscience [3], in pathology [4], and even for individual identification (e.g., fingerprinting [5]). The connectome and its broad contributions to neuroscience will be thoroughly discussed throughout this book. However, to be able to ask the right questions and interpret the results of connectome studies on the macroscale, a grounding in the underlying neurobiological concepts on the microscale is in our view, also essential (Fig. 1.1). In this chapter, we describe the key neurobiological findings and concepts that preceded the connectome, consider that structural and functional neurobiological aspects are captured in neuroimaging defined models of the connectome, and consider that are not, as well as summarize the wide range of techniques that are available today to build and study the connectome from microscale to macroscale.

Figure 1.1 Brain scales: from the macroscale to synapse.

(A) On the macroscale, the brain can be seen to have multiple gyri and sulci along the occipital, parietal, frontal, and temporal cortices. (B) This provides a larger surface area to accommodate multiple cortical columns that can be observed at the mesoscale. Cortical columns vary widely along the cortex, but they all have six cortical layers. (C) At a single cortical layer, synaptic circuitry at the microscale can be visualized.

1.2 A brief history of what preceded the connectome era

Experiments at the end of the 19th century and beginning of the 20th century first identified key concepts, such as the neuron (the nerve cells that represent the building blocks of the CNS) and the synapse (the clasp between neurons that provides a communication link between them). Although the term neuron was first coined by von Waldeyer-Hartz, it was primarily the work of Ramon y Cajal during this period that established the modern neuron theory which we continue to use today. This theory states that a nerve cell is the unit of neural structure and that individual nerve cells communicate through cell-to-cell contact, but without direct continuity between them [6]. When defending the neuron theory in 1889 [7], Ramon y Cajal presented a vision that perhaps can be considered the beginning of network analysis:

We have made careful investigations of the course and connections of nerve fibres in the cerebral and cerebellar convolutions of man, monkey, dog, etc., and we have never seen an anastomosis between the ramifications of the two different protoplasmic expansions, nor have we observed them between the filaments emanating from the same expansions of Deiters; the fibres intermingle in a most complex manner, producing a thick and intricate plexus but never a net. The observations which we have just explained, concerning the structure of the avian cerebellum, also support this viewpoint; it could be said that each element is an absolutely autonomous physiological canton

Santiago Ramon y Cajal—Neuron theory or reticular theory, 1954, p. 8.

Of key relevance to the modern study of connectomics, is the statement that we have never seen an anastomosis between the ramifications of the two different protoplasmic expansions (i.e., cells are connected but never fused together) and reference to the expansions of Deiters, which represent what we now refer to as axons. These descriptions were later fundamental for the work of Sherrington, which culminated in a seminal book The Integrative Action of the Nervous System, published in the same year that Ramon y Cajal was awarded a Nobel Prize in 1906. Here, Sherrington coined the term synapse from the Greek word for clasp and proposed the fundamental premise that synapses provide a unidirectional communication point for nerve conductance, thus offering the framework for all research into neural communication via synaptic transmission [8]. This was accompanied in 1902 by the membrane hypothesis of Julius Bernstein, which established that nerve cells have a high intracellular concentration of potassium ions (K+) and a negative intracellular potential. Upon stimulation, the nerve cell becomes permeable to other ions, creating what we currently refer to as an action potential and eliciting a propagation of electric impulses between cells. The combination of Bernstein’s and Sherrington’s work at the turn of the 20th century therefore formed the basis of electrophysiological studies of neural activity through inventions of intracellular microelectrodes and voltage-clamp recordings. This enabled John Eccle, a student of Sherrington who worked on spinal motor neurons, together with Alan Hodgkin and Andrew Huxley working primarily with giant squid axons, to share the Nobel Prize in 1963 for their discoveries around excitatory and inhibitory synaptic mechanisms. For a thorough review on the history of electrophysiology and the characterization of electrical conductance between nerve cells in the 20th century, refer to [9].

The combination of these exciting discoveries together with increasingly available methods with which to study them led to an exponential growth in the field of brain science in the 1960s, which aimed to map how the connections within and between brain systems resulted in behavior. Therefore, while the term connectome came into use relatively recently, the network maps and brain models from the last 60 years which preceded this have been fundamental to establish the era of connectomics.

1.3 Microscale neurobiology

1.3.1 Neuronal diversity and classification

Neurons constitute the essential cellular units of the CNS. In addition to their cell body, neurons have dendrites to receive information, axons to output information, and use synapses for communication (Fig. 1.2). The adult human brain contains approximately 86 (range: 79–95) billion neurons [10] and 164 trillion synapses, with over a third of them found in the frontal cortices and an average of 278 million synapses per cubic mm [11]. The number of neurons varies widely across the six layers that comprise the cortex and also between different brain structures, such as the cerebellum or subcortical regions (e.g., striatum, thalamus, or hippocampus). In addition, cell morphology varies not only between brain regions but also across species suggesting that these relationships are complex. For example, the dendritic length of human pyramidal neurons in layers 2/3 of the temporal cortex is threefold larger than those seen in mice, while dendritic branching in the macaque monkey more closely resembles the mouse than a human, thus suggesting the mass of dendritic arborization (branching) is not linearly related to cortical thickness across species [12]. Of interest, diversity in cellular morphology has been shown to have direct implications for brain function, while dendritic arborization density is not only highly correlated with cortical thickness but also IQ in humans [13].

Figure 1.2 Neuron, glia cell types, and capillaries.

Neurons, depicted with a white cell body, have large metabolic requirements that are fulfilled by astrocytes (a type of glial cell), shown in dark gray, that deliver nutrients and oxygen transported by blood vessels. Oligodendrocytes, depicted in lighter gray, are another type of glia cell that forms myelin sheaths to protect axons and to ensure faster and more efficient signal transmission between cells. The smallest type of glia are microglia depicted in the lightest gray, which are responsible for immune processes, cleaning of residuals, and pruning among other functions.

The simplest classification of neurons is to consider them either as excitatory projection neurons (which are larger with dendrites and axons that can travel over large distances) and inhibitory interneurons (which are smaller and often restricted to cover very small areas) [14]. The neocortex forms the outermost layer of the brain’s neural tissue and contains six horizontal layers (with layer 1 being the most superficial and layer 6 the deepest) defined predominately by the distinctive cell types and connections within them across the lifespan. Thus anatomically, excitatory neurons in the cerebral cortex can be further classified for example into layer 2/3 intra-telencephalic neurons (projecting to the striatal system in the center of the brain), layer 4 spiny stellate or star pyramidal cells (enabling local circuit feedback and signal integration), layer 5 pyramidal tract neurons (projecting down to the spinal cord to carry descending motor signals), layer 6 cortico-thalamic neurons (projecting to the central thalamic nuclei), and layer 6b (containing remnants of the subplate neurons which are thought to play a key role in early brain development). Inhibitory interneurons can be further subgrouped into parvalbumin-expressing cells, somatostatin-expressing cells, vasoactive intestinal peptide-expressing cells, and cells that express 5-hydroxytryptamine receptor 3A [15].

Beyond excitatory and inhibitory cell types that release either glutamate or gamma aminobutyric acid (GABA), respectively (described in more detail later in the chapter), there are also neuromodulator cells mostly located in subcortical regions, such as the brain stem. These cells have long projections that can modulate the activity of large neuronal populations and are classified based on the neurotransmitters they produce, the most abundant being dopaminergic cells [16], serotoninergic cells [17], and cholinergic cells [18].

It is important to additionally note that neuronal classification can vary based on transcriptomics, physiology and other factors (detailed information on approximately 200 different cell types can be found at http://celltypplymouthes.brain-map.org). The spatial expression and the characteristics of all these cell types have direct implications for trying to understand not only signal propagation but also both structural and functional connectivities. For example, synaptic protein expression has been used in recent years to create a microscale connectivity map between different cell types, called the synaptome, which is highly correlated with the macroscale functional connectome [19]. Thus in the next section, we will delve into how neurons enable signal propagation resulting in connectivity patterns that can be captured at macroscale.

1.3.2 Neuronal electrophysiology

Upon stimulation, an action potential is triggered, which represents the nervous system’s main form of signal propagation. While it can vary between cells, on average, neurons have a negative resting membrane potential of −60 mV, which rises to +40 mV upon depolarization. Depolarization primarily occurs due to an influx of positively charged sodium ions (Na+) through specific voltage gated ion permeable channels in the postsynaptic membrane, resulting in a change in the electrochemical gradient across the cell membrane. When the membrane potential surpasses a specific threshold level, an action potential is triggered through opening of all available ion channels, resulting in a rapid rise in the membrane potential. With the reversal of the plasma membrane polarity, the channels close thus blocking a further influx of Na+. The subsequent opening of potassium (K+) channels results in an efflux of K+ ions from the cell, resulting in a return of the membrane potential toward its resting state. As there is a delay in K+ channel closure, an undershoot with an intracellular negative potential is seen (commonly referred to as the "refractory period") before re-establishment at the resting level of −60 mV [20,21]. The generated action potential then propagates through the dendrite, toward the soma (cell body) and out through the axon. In addition to this unidirectional signal propagation, there is polarized transport of proteins toward presynaptic terminals which in contrast can be bidirectional in dendrites and axons and can vary depending on where the action potential takes place and cell type [22].

The CNS contains two types of synapses: electrical and chemical (Fig. 1.3). Electrical synapses have a very narrow synaptic gap or cleft due to connexin hemichannels, which directly connect the pre- and postsynaptic terminals for quick signal propagation (Fig. 1.3B) [23]. These types of synapses are also commonly referred to as gap junctions and are particularly important in very early development when they enable quick synchronous signal propagation and close coupling of cells leading to the formation of the first neuronal ensembles [24,25]. In the adult brain, electrical synapses are additionally thought to have an important modulatory role on chemical synapses [26].

Figure 1.3 Electrical and chemical synapses in neuronal cell types.

(A) A chemical synapse is characterized by a vesicle recycling system in the presynapse that releases neurotransmitters into the synaptic cleft, a slightly wider synaptic cleft, and a postsynapse packed with different types of receptors, such as ion channels (NMDA, AMPA, etc.) and mGluR that are sustained on the surface thanks to the PSD proteins. (B) Electrical synapses are characterized by a very narrow synaptic cleft, and connexin hemichannels that form gap junctions to allow transmission of electrical currents. mGluR, Metabotropic receptors; PSD, postsynaptic density.

Chemical synapses require the release of a neurotransmitter through vesicle release from a presynaptic terminal [27] that then binds to specific receptors in the postsynaptic membrane to regulate the influx and efflux of different ions and thus alter the membrane potential (Fig. 1.3A). While a detailed explanation of all chemical neurotransmission is beyond the scope of this chapter, an understanding of the key concepts and in particular, the key role of excitatory and inhibitory processes in neuronal signaling is important, particularly when developing biophysical models of connectome level brain activity. Here, we describe a brief description of the two most abundant excitatory (glutamate) and inhibitory (GABA) systems to give a representative overview.

1.3.2.1 Glutamate (excitatory)

The most abundant types of cells in the neocortex are excitatory neurons, which secrete the neurotransmitter glutamate via vesicles released into the synaptic cleft (70%–80%) [28]. Released glutamate primarily binds to N-methyl-D-aspartate (NMDA) receptors and/or α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors in the postsynaptic terminal. Although both specifically bind to glutamate, these receptor types have distinct structures and mechanisms of action, with AMPA receptors enabling a rapid influx of Na+ and an efflux of K+ ions to generate an excitatory postsynaptic current (EPSC) and action potential [29]. NMDA receptors additionally allow an influx of calcium ions (Ca²+) resulting in a far wider range of actions including enzyme activation, regulating the opening of other ion channels, and even altering gene expression. In contrast to the rapid response of AMPA receptors, responses in NMDA receptors are slower given that they have a voltage-dependent magnesium block, which is only released once an EPSC has already started [30]. Of interest, although NMDA receptors are not as abundant as AMPA receptors in the adult brain, the opposite is observed in the maturing brain when slow oscillations mediated by calcium are highly prevalent [31,32]. In addition to the AMPA and NMDA ionotropic receptors (due to their integral ion transport channel), there are metabotropic glutamate receptors (mGluR). These G-protein-coupled receptors are found in both the pre- and postsynaptic membrane and glia cells and have a modulatory role through eliciting a cascade of protein changes. An important distinction from ionotropic receptors is that glutamate binding with mGluR receptors does not directly initiate any form of trans-membrane transport [33].

1.3.2.2 GABA or gamma aminobutyric acid (inhibitory)

The second most common neurotransmitter in the human CNS is GABA, which has an inhibitory role in the adult brain. Inhibitory interneurons that release both glycine and GABA account for 20%–30% of neurons in the neocortex [28]. These interneurons can be readily identified because they all contain the enzyme glutamic acid decarboxylase, which converts glutamate into GABA. The inhibitory action of GABA-gated ion channels is due to their permeability to chloride (Cl−), with an influx resulting in hyperpolarization in direct contrast to the depolarizing action of glutamate.

Of importance, receptors in a chemical synapse are not fixed but are highly dynamic, with many different types of ion channels and other receptor types appearing and disappearing through modulation by diverse activity mechanisms. Action potentials can also elicit activity with different frequency patterns onto different neighboring synapses, making signal propagation extremely complex [34]. Thus rather than thinking of a single synapse as an isolated unit, signal propagation can be better conceptualized as a net effect of different inputs and outputs of a cell [35]. For further information on electrophysiological properties of different cell types, refer to https://neuroelectro.org/neuron/index [36].

1.3.3 Nonneuronal cells

The human brain contains almost the same number of neurons and nonneuronal cells, with an average of 84.6 billion nonneuronal cells in the adult brain [10]. While not captured (or generally modeled) in the connectome, these support cells sustain and modulate the brain’s structure and function. The majority of these are glial cells, which are subgrouped as astrocytes, oligodendrocytes, or microglia. Their crucial importance is emphasized by a marked pathological impact if malfunctioning (Fig. 1.2). The other nonneuronal cell types are the ependymal cells, which are more abundant in early development (remaining only in some parts of the surface of the adult ventricular system) and provide metabolic support to progenitor cells and a line of defense against potential CNS pathogens [37].

The most abundant glial cell type is the astrocyte, which plays a key role in neural physiology, blood flow regulation, and energy metabolism. The CNS has at least nine different types of astrocytes, with many showing high regional specificity with diverse modulatory roles in distinct neural circuits [38]. The most common are protoplasmic astrocytes, which are found only in gray matter (GM) predominately in layers 3 and 4, and fibrous astrocytes, which are found only in the white matter (WM). Protoplasmic astrocytes have several branches and a circular shape, with a single astrocyte supporting between 270,000 and 2 million synapses and many capillaries. In contrast, fibrous astrocytes only make contact with axons through the nodes of Ranvier (nonmyelinated axonal openings; see Fig. 1.2) in WM [39]. Although astrocytes also have ion channels, unlike neurons they do not fire or propagate action potentials and instead experience a form of excitability through an increase in intracellular calcium in association with neural activity [40]. This fulfills the purpose of regulating calcium signaling. Moreover, astrocytes produce molecules that can increase or decrease local blood vessel diameter (see Section 1.5.2), express transporters that can clear neurotransmitters from the synaptic space to be recycled, and can store glycogen in areas with high synaptic density to promote neuronal activity [41]. Astrocytes therefore play a key role in the neurovascular coupling cascade that links neural activity to the vascular provision of its metabolic substrates, which underlies the Blood Oxygenation Level Dependent (BOLD) response measured by functional MRI (refer to Section 1.5.2 and Chapter 3) and is used to estimate the functional connectome. Last, but not least, astrocytes can also take a role in injury response and neuroinflammatory processes [42].

Oligodendrocytes are the second most common type of glial cells and are responsible for producing the myelin sheaths which wrap around axons. These cells therefore are seen predominately in WM once myelination begins in early development and can be further classified into subgroups depending on the type of axons (size and orientation). Oligodendrocyte precursor cells migrate to different regions along WM tracts and settle next to axons with a diameter of greater than 0.2 µm (which is generally considered to be the size threshold for myelination). Once it receives the necessary signal to differentiate into an oligodendrocyte and begins proliferation, it can generate myelin sheaths in just 5 hours. A single oligodendrocyte can generate between 20 and 60 myelinating processes with each of them varying in length from 20 to 200 µm and up to 100 membrane turns, making them the cells with the largest surface area in any living organism. After myelination is complete, these cells also cause an accumulation of K+ channels in the nodes of Ranvier, the only unmyelinated axonal segments (Fig. 1.4) [43,44]. Importantly, oligodendrocyte precursor cells’ migration and differentiation are stimulated by neural activity and therefore myelin sheath thickness is increased within active circuits [45]. Like oligodendrocytes, Schwann cells also produce myelin to wrap around axons but are only found in the peripheral nervous system, covering axons that expand to all nerve terminals. Of interest, Schwann cells have been shown to migrate to the CNS and aid or replace oligodendrocyte function in cases of WM injury [46].

Figure 1.4 Myelin and water diffusion, proxy measures of axon structure.

(A) Layers upon layers of myelin sheaths wrap around axons except for occasional unwrapped gaps, known as nodes of Ranvier. (B) At the microscale, although very long, most axons are narrow and can be packed tightly. This picture shows an electron microscope capture of a 3D section of a mouse CC and the 3D reconstruction of the axons within this block. While the image resolution in a MRI scanner can vary, 1 mm isotropic is considered high resolution. If all axons in that cube are facing the same direction, the modeled orientation distribution function will look like the one shown in the image, because the myelin in the axons will make the water content flow in a single direction. This image aims to highlight the number of axons that can fit in a single MRI voxel [47]. CC, Corpus callosum; MRI, magnetic resonance imaging. Images reproduced and adapted from: (B) Lee HH, Yaros K, Veraart J, Pathan JL, Liang FX, et al. Along-axon diameter variation and axonal orientation dispersion revealed with 3D electron microscopy: implications for quantifying brain white matter microstructure with histology and diffusion MRI. Brain Structure Funct 2019;224(4):1469–88. https://doi.org/10.1007/s00429-019-01844-6.

Microglia represent 10%–15% of glial cells and are essential in early development as they release several trophic factors that support the formation and survival of neural circuits. They also play a key role in programmed cell death and the removal of cellular debris through the lymphatic and vascular system. Microglia also promote and sustain synaptic plasticity, as well as eliminate defective synapses, and thus are fundamental to the processes involved in activity-dependent synaptic pruning. Their malfunction has therefore been associated with several neurodevelopmental disorders and psychiatric disorders [48–50]. Due to their crucial role in homeostasis and local support system, there is a great diversity of microglia density and function across the brain [51], and they can also elicit astrocyte and oligodendrocyte activity during inflammatory or injury processes [52].

In summary, while glial cells are frequently not directly considered when investigating brain connectivity, there is no doubt that they play a critical role in regulating it and thus considering or modeling their influence is an important future direction [53].

1.4 Mesoscale columns and circuits

1.4.1 Cortical columns and tissue types

To understand the architecture of the brain, one must keep in mind that neurons do not function as individual elements, but rather gather into larger functional units. Across the neocortex, neurons from layers 4 to 2 are arranged into vertical columns, forming the most basic processing units of the brain. Although these cortical columns were first described in 1957 in the cat somatosensory cortex [54], the first 3D morphological reconstruction (based on neurons that had been labeled in vivo in the rat brain) was not achieved until some 50 years later [55]. As with the aforementioned different cell types, cortical columns also vary widely based on their cellular composition and distribution, overall size, signaling properties, etc. [56]. The width and the organization level of the column are associated to the complexity of the processing, with columns involved in unimodal sensory input appearing to be narrower, while those involved in higher-order processing, such as multimodal sensory input, are wider and more distributed (details about the classification of cortical columns can be found in [57]). With the increasing availability and resultant advances in ultra-high field MRI, acquiring human in vivo structural imaging at the level of the cortical column (i.e., at the mesoscale level between micro and macro) has become more of a reality. This enables the characterization of the columnar connectome, which could model functional specificity within cortical columns and provide deeper insight into brain architecture [58]. Fig. 1.1 shows a schematic representation of the differences in scale for the different brain components currently studied in neuroscience from a cortical column to a small synaptic circuit.

1.4.2 Neural circuits

Lorente de Nó, a disciple of Ramon y Cajal, introduced the laws that represent the basis of functional neuronal connectivity in 1930. The key premise that this work proposed was that the brain is a composite of closed neural circuits. Within this schema, the law of plurality described that a single cell can have connections with another cell multiple times via a third neuron or set of neurons; and the law of reciprocity explained that for a given neuron A, it can both receive an axon from another neuron B and also have its own axon forming a connection to create a feedback loop. A further key component of this framework is the importance of the balance between excitation and inhibition together with modulatory synaptic weights, which together produce a functional network output [59]. This work inspired Hebb’s research and led to the publication of The Organization of Behavior in 1949, in which he described that repeated activity between two cells would lead to an increasing association between the two, thus making their connection more durable. This forms the basis of synaptic plasticity (or Hebbian plasticity), which represents the neurophysiological mechanism thought to underlie perception, learning, and memory. Hebb also introduced the term cell assembly to refer to a group of neurons that have become connected to each other by the process of perceptual learning and temporally organized neural activity patterns, which are now recognized in nearly all processing from primary sensory perception to higher-level cognitive processing [60].

Through the measurement of light and knowledge of the specific properties of photons, optical imaging can be used to record activity from multiple neural cells simultaneously and provide noninvasive anatomical characterization of cell firing. This is typically achieved using a voltage-sensitive dye, which binds to specific molecules in the extra- or intracellular cell layer. This dye then transmits different wavelengths of light as action potentials or other forms of signal propagation occur, thereby effectively acting as transducers of the membrane potential to a measurable optical signal [61]. The temporal and spatial resolution of these methods significantly improved in the 1990s with the introduction of two-photon laser microscopy and ion-sensitive dyes, such as calcium [62]. In the case of the latter, cell activity and signal propagation can therefore be measured by measuring the degree of change in fluorescence when cells are activated or an action potential is generated and calcium channels are opened [63–65]. This allows detailed investigation of neuronal circuitry and has provided marked new insight into their control. Visualization of higher numbers of dendritic spines, for example, has been shown to allow more distributed connectivity patterns, regulation of excitatory inputs, and connections to be independently plastic [66]. This strategy is summarized in the following text:

Allow for connections to be as promiscuous as possible, with a secondary step where activity-driven learning rules could first prune and later, alter the synaptic weight matrix, adapting it to the computational task at hand. The final wiring would therefore reflect an initial random selection, followed by a subsequent activity-dependent synapse pruning and modification. This secondary refinement step would provide the circuit with the specificity and selectivity it needs to perform a particular computation.

Yuste [66].

In addition to two-photon microscopy calcium imaging, advanced techniques in single- and multiunit electrophysiological recordings [67], as well as other novel methods to manipulate and investigate network physiology (such as optogenetics [68]) have exponentially expanded our knowledge about both the organization and function of neural circuitry. In the visual cortices, for example, orientation-tuning neurons are seen to be stable over weeks and somatosensory columns show sparse coding with only a few cells stably responding to activity [69]. A layer-specific distribution of inhibitory cells (known as a disinhibition circuit) can also be seen in the primary somatosensory cortex, which can regulate excitatory cells and thus modulate active and passive behavior [70]. Similar functional organization and mechanisms have been described in frontal executive networks [71]. As much of the aforementioned studies are only possible in invasive studies with animal models, a major (and important) neuroscientific challenge is therefore to understand how these findings about neural circuitry translate to in vivo human studies.

1.5 Assembling the brain from microscale to macroscale connectivity

1.5.1 Anatomical segmentation and major connectivity pathways

In broad terms, connectomic studies typically consider the functional processing units in the brain to be contained within the GM tissue of the neocortex across the surface of the brain where the neuron cell bodies, cortical layers, and columns reside. Lying below the GM cortical surface is the WM, which contains the aforementioned oligodendrocytes and axon fibers, and is generally considered in connectome studies to make up the brain’s framework of structural connectivity.

The WM takes its name because of the high lipid content of the fatty myelin sheath surrounding axons as insulation to increase signal transmission speed (Fig. 1.4A). While axons additionally exist in the GM, they are relatively short and less myelinated in contrast to the long-distance connections below the cortical layers. In the adult human brain, approximately 58%–66% of WM is composed of lipid, while GM contains only 36%–40% lipid [72]. This network of WM connections is extensive: on average, a 20-year-old human has a total equivalent of 162,500 km of myelinated fibers declining to 89,600 km by the time they reach 80 years of age [73]. The amount of cortical myelin is region specific, with the primary motor and sensory areas appearing more densely myelinated in comparison to associative areas [74,75]. Interest in myeloarchitecture has increased in recent years because high-resolution imaging is more sensitive to myelin than to cell bodies [76,77]. As one might expect, regional myelin density is strongly associated with axonal diameter and length. Thus the distribution of axonal diameters across the brain is an essential feature of network topology, ranging from 0.16 to 9 µm, with the majority averaging below 1 µm [78]. This axonal diameter is largely preserved across mammals, with studies combining electron microscopy and diffusion MRI in rodents highlighting the importance of validating MRI data with histology to better understand axonal diameter, shape, and orientation [47]. For example, it is important to note that diffusion MRI acquisition parameters have an impact on the estimation of axon diameter, which can differ significantly from what is observed under the microscope [47]. However, recent advances in high gradient diffusion imaging now allow modeling of axonal diameter within major WM tracts using MRI data. Results from this model are consistent with histological findings indicating that the corticospinal tract followed by the superior longitudinal fasciculus in the temporal lobe has the largest axon diameters, while more anterior tracts like the forceps minor have smaller axon diameters [79]. It is important to keep in mind that axonal diameter estimation and most structural connectivity maps are based on the probabilistic tractography of WM fiber bundles derived from diffusion MRI at a millimeter resolution (see also Chapter 2). Thus combining micro- and macroscale structural information would result in not only a more detailed but also perhaps more accurate connectome [80,81], which can resolve the possible limitations and/or assumptions imposed by the resolution and modeling methods associated with diffusion MRI (Fig. 1.4). While the accuracy of estimating axonal count, orientation, and density continues to be explored, a good introduction to major white matter tracts defined with diffusion MRI can be found in Ref.