Buried deep in a cerebral vessel lies a forest — an endlessly dense, infinitely delicate network of branches, roots, and leaves, choking the very surrounding space with their effervescent expansion. Born of 100 billion simultaneously- planted seeds, this web of wonders ultimately faces an inescapable death.
Mortal, moral, and marinated with morale — oft-majestic and peppered with mephitic nodes — this forest is anything, everything, nothing. Every triumph and every struggle, every leap and every plunge, every pledge and every deception, every romance and every heartbreak — all stems from the forest.
Perhaps it is then surprising that this corporeal forest — no longer in size than a paper map — lives inside your skull. Dubbed “the connectome” in deliberate analogy to an organism’s full complement of genetic information (the genome), this forest comprises the complete description of the structural connectivity of neurons in the brain. Connectomics (the study of the connectome) therefore represents an attempt to produce a comprehensive map of these neural connections — an effort to comprehend the totality of this forest.
“All of our hopes, desires, beliefs and experiences are encoded in the brain as patterns of neural firings.” − Daniel J. Levitin
A Worm’s Mind
In general, a network’s function is critically dependent on the pattern of its interconnections. In spite of intense efforts to elucidate the structure and function of the brain — which, after all, is just an example of such a complex network — and its neural systems, we do not currently have a comprehensive map of the network connectivity structure of the brain of any species, with all but one notable exception: the nematode C. elegans.
Daunted by the human brain’s considerable complexity, many neuroscientists selected animals with drastically fewer neurons than ourselves. With the goal of creating a complete wiring diagram of all 302 neurons in the C. elegans nervous system as well as the 7,000 synapses (connections between neurons), scientists in 1986 published a partially comprehensive draft of the worm’s connectome — one honed to completion by scientists in 2019 in a major step towards an understanding of how a brain’s function emerges from its form.
The following diagram depicts the neural connectivity of the C. elegans adult hermaphrodite, with the inset (top right) showing the sex muscles and worm diagrams (bottom left) indicating the locations of cell nuclei, where the layout of the vertices in the graph representation (central) was determined by an algorithm that clusters cell pairs with heavier connectivity:
More recently, researchers have endeavored to map out the physical wiring of of Drosophila melanogaster: the common fruit fly. After spending no less than 12 years charting a region approximately 250 micrometers across (about the thickness of two strands of hair), scientists released a wiring diagram of the fly’s hemibrain containing 25,000 neurons and the 20 million connections between them, representing around ⅓ of the total fly brain and encompassing several critical regions responsible for memory, learning, and navigation:
“The reconstruction is no doubt a technical marvel. It will not in itself answer pressing scientific questions; but it might throw up some interesting mysteries.” − Mark Humphries
The Human Connectome
In 1909, German neurologist Korbinian Brodmann detailed a human brain parcellation based on anatomical and cellular structure of the brain’s surface, diving our brains into around 47 parts. This familiar model is depicted below:
However, just as a world map does little to explain the intricate interrelationships and interactions between countries and cultures, the Brodmann map does little to yield a robust understanding of more complex neurological functions. In particular, the model has a limited offering with respect to interactions between areas of the brain — the very interactions responsible for comprehension and emotion, or when compromised, neurological disorders and differences such as depression and schizophrenia. Furthermore, while, say, street navigation technologies have grown exponentially in capability and accessibility, the Brodmanian toolkit for navigation of the brain has seen little modernization.
“The method by which the Brodmann map identified functional areas of the brain was unlikely to be completely accurate — just like the examination of the earth’s surface alone does not meaningfully assist in drawing country, state, and city boundaries.” − Mike Sughrue
Think of the human brain as a modern-day company — one operating with multiple departments, each containing various teams of employees working together on specific projects. These departments represent the brain’s main networks, while the company’s employees correspond to the individual nodes in the brain’s parcellation — each with a specific, primary function which contributes to a larger, coordinated operation. For too long, neuroscience has classified individual nodes based on the tasks they handle, breeding a misunderstanding of how these nodes act in unison, just as an attempt to categorize a firm based on the day-to-day routines of a randomly selected spoonful of employees is unlikely to engender an accurate representation.
Given these impediments, neuroscientists have explored digital mapping the structural and functional neural connections in the human brain — and all its 86 billion neurons and 100 trillion synapses. Indeed, with a map of the brain and its connections, neuroscientists would be well-equipped to understand how differences between brains underlie differences in behaviour — in doing so, the field procures the prospect of understanding cognitive disorders having a connectomic basis, and revealing an evolutionary progression in candidate pathways by identify common synaptic circuits in different species.
Maps Across Magnitudes
In an attempt to model the brain as a whole large-scale network, mapping neurons and synapses at the neuron level maximizes the likeness between the connectome produced and our own brains. This approach is encapsulated in the example below, in which scientists extracted a microscopic chunk of brain in order to map a single neuron’s detailed anatomical structure (shown in orange) across different slices of the cube, and the synapses (shown in blue) connecting it with another neuron:
Indeed, researchers at Google and the Lichtman Lab at Harvard released a similar model of a miniscule section of human brain just 2 months ago (June 2021). The resulting H01 dataset (the most comprehensive map of the human brain compiled to data) contains 50,000 cells and 130 million synapses in a file 1.4 petabytes large — approximately equivalent to 2 to the 50th power of bytes. The following illustration puts the monstrous size of a measure of data storage capacity as colossal as 1.4 petabytes in perspective:
The graphic below depicts a small section of this already miniature dataset (left), alongside a subgraph of the neurons within this sample (right), highlighting excitatory neurons in green and inhibitory neurons in red:
The kicker? In their study, the researchers detail how this sample — widely considered unprecedented in the extent of its coverage — represents just one millionth of the volume of the full human brain. In fact, current modeling technologies remain incapable of accurately capturing the whole-brain connectome, with all its billions of neurons and trillions of synapses, at the neuron level; tracking connections at the mesoscale, which entails the use of light microscopy to identify single axons, or the microscale, in which serial electron microscopy unveils synaptic connections between nerve cells, both represent unviable avenues to mapping the whole-brain connectome.
These microscopic approaches are typically achieved by extracting the brain, perfusing it with a fixative such as formaldehyde and slicing it up as many times as possible, before finally analyzing these slices structurally in order to locate individual neurons and trace their paths. Of course, crucial to this technique is the preservation of the extracted brain insofar as the connectome is almost perfectly maintained before it’s sliced up. However, without oxygen-rich blood flow, the brain’s cells experience a marked drop in metabolic activity, causing irreversible structural damage within just 5 minutes.
Beyond the painstaking requirement to maintain the brain’s physical form, mapping the connectome at the neuron level would necessarily entail processing many zettabytes (millions of petabytes) worth of raw data — a task today’s classical computers are simply unequipped to handle.
“The world is not yet ready for the million-petabyte data set the human brain would be. But it will be.” − Dr. Jeff Lichtman
Accordingly, researchers apply imaging techniques which depict how large bundles of axon fibres are connected across the brain at a macroscopic level, eliminating the need to extract and preserve the brain, or handle an inordinate amount of data. This is accomplished with MRI— a non-invasive imaging technique with the ability to procure a variety of sequences, each conveying different chunks of brain-related information.
For instance, T1-weighted scans give insight into how much grey matter volume a patient has. Furthermore, functional MRI measures brain activity by detecting changes associated with blood flow and diffusion tensor imaging uses anisotropic diffusion to estimate the brain’s axonal (white matter) organisation. Collectively, these sequences accrue a significant amount of macroscopic detail.
Graph Theoretic Analysis
Complementing magnetic resonance imaging in the pursuit of procuring a comprehensive map of neural connectivity is graph theory; a brain graph theory network is a mathematical representation of the real brain architecture consisting of a set of nodes (vertices) and edges (links) interposed between them. Whilst the nodes conventionally represent brain regions, edges can correspond to anatomical, functional, or effective connections.
The basic processing pipeline for graph theoretic analysis of MRI data foremost entails the acquisition of imaging data. Subsequently, the brain must be parcellated into distinct regions to act as the network nodes. Typically, the nodes are defined through one of 3 methods: using anatomical landmarks such as the brain sulci and gyri (as used by the Harvard-Oxford atlas), through division by functional role (as used by the Craddock atlas), or with a random parcellation of equivalent size (as used in Wang et al., 2016):
The next step involves defining some measure of connectivity between nodes (this straddles how close they are, how they interact, and how frequently they do so), which is to represent the edges of the brain network. With diffusion MRI, inter-regional connectivity can be measured using tractography, while structural connectivity is indirectly measured using inter-subject covariations in gray matter morphometry with T1-weighted scans and functional connectivity is measured as a statistical dependence between regional time series with fMRI.
The connectivity between these pairs of brain regions can subsequently be represented as a connectivity matrix based on the associations between the previously defined nodes. MRI analyses typically yield weighted and symmetric matrices, which can subsequently be thresholded to emphasize the strongest links in the network, as portrayed in the example below:
This connectivity matrix can then be used to generate a graph-based representation of the brain network, before the network parameters of this constructed graph are ultimately finalized and calculated. The complete aforementioned pipeline for graph theoretic analysis is captured below:
“Graphs provide useful models of brain networks — a unified framework for representing multiscale organization.” − Alex Fornito
Functional Connectivity
The structural and functional connectivity between cells correspond to the 2 means by which edges are defined. The former corresponds to a measure of the correlations in activity over time between brain regions. When any area of the brain is engaged, the electrical activity therein tends to increase — network changes which can be modelled at a macroscopic scale (millimetre resolution) with non-invasive neuroimaging methods, notably including functional MRI (fMRI), although novel approaches such as Dynamic Regional Phase Synchrony (DRePS) are in development.
fMRI-based studies in particular quantify functional connectivity through changes in cerebral blood flow, the magnetic properties of which can be detected by MRI; through a statistical analysis of fMRI time-series from healthy patients and subjects with psychiatric disorders, the functional biomarkers of neurological diseases can be identified. For instance, the following graphic depicts the discernible abnormalities of functional whole-brain connectomes in depression, ADHD, and schizophrenia.
The illustration below outlines the process by which functional connectivity between nodes is computed — in this particular example, as the level of correlation between their resting-state fMRI and blood oxygenation level dependent (BOLD) time series. In the association matrix produced, significantly polarized (positive or negative) correlation values are identified. Finally, the functional brain network features nodes located according to their centroid stereotaxic coordinates and edges coded based on the intensity of their correlation.
“[Functional connectivity] concurs with the intuitive notion that when two things happen together, these two things should be related to each other.” − S.B. Eickhoff, V.I. Müller
Structural Connectivity
The second major approach with which edges in brain networks can be defined is structural connectivity, which generally involves the use of tractography (a 3D modeling technique) to model data collected with MRI-based diffusion tensor imaging (DTI). This technique enables the detection of white matter tracts based on the direction and relative magnitude of the diffusion of water molecules in the brain; these connective nerve tracts indicate the physical wiring of the brain’s different regions.
More specifically, inferring a macro-connectome from diffusion MRI (dMRI) images entails node delineation and edge mapping, where nodes represent distinct cortical and subcortical gray matter regions defined either geometrically, functionally or cyto/myelo-architectonically, while edges correspond to the white matter fiber bundles that interconnect pairs of regions. dMRI and tractography techniques can probe these white matter connections and estimate relative weights, as illustrated in the figure below:
Collectively, these acquisition techniques accrue a colossal amount of data, insofar as big data processing is required to combine functional and structural mapping in the creation of a comprehensive model of the human brain.
“When it comes to defining the edges…the most straightforward of these options is using the Y matter fibres or anatomical connections.” − Joana Pereira
Tackling Mental Disorders
Three brains are depicted in the picture below— on the left is a healthy individual’s brain, while the brain in the middle has a clear abnormality — a tumor (upper right). Finally, although the brain on the right looks healthy, this patient has generalized anxiety disorder. Could you tell?
Neurologists typically can’t. With almost a quarter of people globally set to face some form of mental illness during their life and hundreds of thousands of likely preventable suicides occurring annually, the world’s mental health crisis remains as pressing and cloaked an issue as ever.
In order to detect these psychiatric disorders earlier and treat them with greater efficacy, it is imperative that we uncover how they affect brain connectivity patterns — in doing so with advanced fMRI scans, neurologists can transform the diagnosis of these mental illnesses into a data problem. Opportunely, machine learning capabilities can applied in the connectomic domain to classify symptoms based on patterns of brain network dysfunction.
These trained algorithms can subsequently form predictions about symptom severity or make comparisons between standard and subject-specific datasets to diagnose patients with familiar symptoms. Moreover, with a connectomic approach, neurosurgeons can pinpoint the effect of specific brain incisions to a greater degree of certainty, and accordingly perform surgery in such a way that preserves the highest amount of meaningful brain function.
The figure above outlines a design schematic for a particular study where a connectome approach was leveraged in a psychiatric context — one in which network topological changes in patients with mild cognitive impairment no dementia (CIND) and moderate CIND compared to healthy controls were studied. In this particular experiment, while the subject-level structural connectome was derived from diffusion MRI data using probabilistic fiber tracking based, the subject-level functional connectome originated from task-free fMRI data based on pairwise Pearson’s correlations between the very same regions of interests.
Subsequent to the computation of graph theoretical global-wise and nodal-wise metrics for both connectomes, the alterations in structural and functional network topology metrics can be compared across groups and associated with cognitive performance. By characterizing brain functional architecture as such, graph theoretical analysis can be applied to these brain networks; through calculation of global-wise metrics (global and local efficiency) and nodal-wise metrics (nodal degree centrality and nodal efficiency), group differences in these metrics can be identified, alongside the associations between them and cognitive performance.
“To better understand, diagnose, and treat psychiatric disorders, it is crucial to obtain deeper insights into brain circuits in health and disease and in humans and animal models.” − David C. Van Essen, Deanna M. Barch
Application Beyond Psychiatry
In addition to diagnosing and treating neurological deficits, connectomic techniques have the capability of delivering valuable insight into our own minds, from enhancing cognitive function to crystalizing appreciation of individual brain strengths.
Although significant development remains necessary to fully realize these applications, studies have increasingly served to translate brain enhancement-related possibilities from the realm of science fiction to promising, real-world results. For instance, based on fMRI data, repetitive transcranial magnetic stimulation (rTMS), which entails targeted stimulation of certain key brain areas, has already been demonstrated to improve cognitive function for everything from working memory and cognitive control to executive task processing and skill acquisition.
Furthermore, a notable recent study on the the effects of high-frequency rTMS over the left DLPFC on cognitive control in young healthy participants exhibited marked increases in reaction time and faster conflict resolution.
The results above depict that under both congruent and incongruent conditions, multiple sessions of rTMS can decrease reaction time.
“Magnetic stimulation of the brain improves working memory, offering a new potential avenue of therapy for individuals living with Alzheimer’s disease and other forms of dementia.” − Duke Department of Neurology
The Human Connectome Project
Naturally, in order to furnish such psychiatric and other benefits, researchers must first dedicate their attention to mapping the entirety of the human connectome at cellular resolution, and by extension, understanding the complete details of neural connectivity.
One effort at the forefront of this lofty objective is the Human Connectome Project (HCP) — the first large scale-attempt to to collect and share data of a scope and detail sufficient to begin the process of addressing deeply fundamental questions about human connectional anatomy and variation. The project’s proximate goal is to construct a network map of the complete structural and functional neural connections in vivo within and across individuals, as well as to produce a body of data that will facilitate research into brain disorders, such as Alzheimer’s disease and schizophrenia.
The HCP is considered to have made substantial improvements in data acquisition, analysis, and sharing — advances in the aggregate which constitute a neuroimaging paradigm with 7 core tenets, as outlined here:
With the rapidly growing number of publications acknowledging the use of HCP data in excess of 140, the scope and diversity of the project’s emerging discoveries continues to grow; indeed, from functional connectivity correlating with gene expression patterns in post-mortem human cortex to models linking resting-state fMRI measurements to task activations, the impacts of the project’s research are far-reaching within the field.
“[We aim] to provide an unparalleled compilation of neural data, an interface to graphically navigate this data and the opportunity to achieve never before realized conclusions about the living human brain.” − The Human Connectome Project
Closing Thoughts
Connectomics is on the verge of significantly advancing our understanding of how functional brain states emerge from their underlying structural substrates, and providing novel mechanistic insights regarding deficits in the brain’s function if this substrate is disrupted. By mapping and analyzing the vast, intricate forests embedded in skulls across the world, the field is not only set to procure psychiatric benefits for millions of patients with neurological disorders, but also well-equipped to conquer the final frontier: our very own brains.
“I am more than my genes! What am I? I am my connectome.” − Sebastian Seung
