Emerging Trends in The Social and Behavioral Sciences

How Form Constrains Function in the Human Brain

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How Form Constrains Function in the Human Brain

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How Form Constrains Function
in the Human Brain
TIMOTHY D. VERSTYNEN

Abstract
In neural systems, form and function are intimately linked; the communication
dynamics across networked areas depends on the organization and integrity
of the connections between them (i.e., axons and tracts). With the growth of
diffusion-weighted imaging (DWI) and fiber tractography tools over the past
decade, it has become possible to visualize the physical architecture of the human
brain at an unprecedented resolution. This information has provided the first
glimpses into the component circuitry supporting cognition, presenting a unique
opportunity for cognitive neuroscientists. For the first time we can visualize the
connections in the living brain, allowing us to measure individual differences in
anatomical connectivity, relate this connectivity to brain function, and gain insights
into the link between white matter architecture and behavior. In many ways, this
technology is still in its infancy and its full potential has not yet been realized.
Here, I outline the importance of understanding neuroanatomical connectivity as a
hard constraint on neural computation. Beginning with an overview of the typical
patterns of connectivity seen in neural systems, I go on to show how current neuroimaging tools can visualize several different types of connectivity in the brain. By
highlighting recent findings showing how neuroanatomical organization and brain
function are related during cognitive tasks, I emphasize the utility that structural
brain mapping approaches can have for the broader social and behavioral sciences.

BACKGROUND
Two decades ago, in a commentary to the journal Nature, Francis Crick and
Edward Jones threw down the proverbial gauntlet to the human neuroscience community. Highlighting the work being done to map the physical
connections in the macaque brain, Crick and Jones lamented that the lack
of such methods in humans fundamentally limits how much we can truly
understand about the brain:
“Without [knowing anatomical connectivity] there is little hope of understanding how our brains work in the crudest way.” (Crick & Jones, 1993).
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Indeed, the organization of white matter pathways within the brain defines
the essential wiring diagram that acts as a hard constraint on neural processing (Felleman & Van Essen, 1991; Passingham, Stephan, & Kötter, 2002). Without the knowledge of how the different brain areas are connected together, it
is impossible to truly understand how specific neural computations can lead
to specific cognitive processes.
However, magnetic resonance (MR) physics was already working on a technology that would end up answering their challenge to map the physical
connections in vivo. In fact, 3 years earlier, Michael Moseley and colleagues
had published a series of studies showing how a new form of MRI (magnetic resonance imaging) called diffusion-weighted imaging (DWI; Bihan et al.,
1985) could be used to detect directionally dependent water diffusion in the
cat brain (Moseley et al., 1990). Subsequent work would go on to show that
this water is constrained mostly within axons and could be used as a proxy
to describe the geometry of underlying white matter pathways. Thus, by the
time of Crick and Jones’s commentary in Nature, physicists and radiologists
were already working on methods to noninvasively capture the structural
connections in the brain.
Over the past 20 years, DWI has grown to become arguably one of the most
valuable tools in cognitive neuroscience. The increased popularity of DWI
methods is most evident in the steadily increasing number of publications
reporting DWI results over the past decade. According to Pubmed, the number of publications reporting on results using diffusion tensor imaging (DTI),
the most popular DWI technique in cognitive neuroscience, has risen from
138 publications in 2003 to 1590 publications in 2013.
This accelerated adoption of DWI has led to a number of significant discoveries over the past decade. For example, DWI has been used to identify novel
white matter pathways within human brain, such as the connectivity of the
middle longitudinal fasciulus (Makris et al., 2009; Wang et al., 2012) and the
existence of the frontal aslant tract (Catani et al., 2012, 2013). When integrated
with functional magnetic resonance imaging (fMRI), DWI is being used to
map the human connectome and reveal fundamental properties of neural
connectivity in our brains (Bullmore & Sporns, 2009). Clinically, DWI represents one of the most promising approaches to identifying diffuse axonal
injury from head trauma such as concussion and traumatic brain injury (TBI;
(Huisman et al., 2004)) mainly due to its sensitivity to the directional motion
of water, which is disturbed by axonal injury, rather than the density of water,
which is measured by typical clinical MRI scans and not affected by axonal
injury.
The most common way that DWI is used in cognitive neuroscience is in the
evaluation of the microstructural integrity of underlying white matter pathways through measures such as fractional anisotropy (FA). These measures

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provide local estimates of the diffusion of water molecules at fixed points in
space, called voxels (short for “volumetric pixels” and reflect the spatial sampling of MRI-based imaging methods), with more restrictive water diffusion
in a specific direction being used as a proxy for the health and integrity of
underlying white matter. As a measure of integrity, these metrics appear to
provide a good index of the health of axons and myelin when examined in
animal studies (Budde, Xie, Cross, & Song, 2009; Klawiter et al., 2011; Song
et al., 2005). Cross-sectional differences in FA are associated with group differences in physical health (Bolzenius et al., 2013; Mueller et al., 2011; Stanek
et al., 2011; Verstynen, Weinstein, et al., 2012; Verstynen et al., 2013), neurological pathologies (Bihan et al., 2001; Dyrba et al., 2013), and even broader social
factors such as socioeconomic status (Gianaros, Marsland, Sheu, Erickson,
& Verstynen, 2012). But these associations with behavior are not just limited to predicting differences across individuals. Longitudinal changes in FA
have been associated with learning (Keller & Just, 2009; Sampaio-Baptista
et al., 2013; Scholz, Klein, Behrens, & Johansen-Berg, 2009). These promising findings, along with the relative conceptual and methodological ease of
voxel-wise measures such as FA, these white matter integrity measures are
quite appealing for a wide variety of applications in the social and behavioral
sciences.
However, DWI allows for more than just a local estimate of white matter
integrity. With the increased application of tractography methods to DWI
data (for a review of tractography, see Jbabdi & Johansen-Berg, 2011), it has
become possible to map a subset of the physical point-to-point connections in
the human brain (Figure 1). This connectivity information is equally important to the behavioral scientist as integrity measures such as FA, if not more
so. This is because connectivity analysis allows for visualization of the component circuitry of neural systems that regulate a vast number of cognitive
processes (Passingham et al., 2002). As tractography methods continue to
improve, they will be used to ask some of the most fundamental questions
about the human brain and its relation to cognition. In what follows, I highlight some of the most promising avenues of this structural mapping method
for understanding the biological basis of human cognition.
STRUCTURAL CONNECTIVITY AND NEURAL COMPUTATION
In order to conceptualize the utility of neuroanatomical mapping approaches
for social and behavioral sciences, it is important to understand that the
physical wiring of brain circuits is a hard (i.e., nonmodifiable) constraint on
how information flows through the network. There are two specific ways
that anatomical connectivity can constrain function. First, the organization of
connections between sets of neurons will determine the flow of information

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(b) Map of water diffusion models

(c) Fiber tractography

Figure 1 An outline of a typical fiber tractography analysis. (a) Water trapped in axons diffuses primarily along the length of the
axon (axial diffusivity) and less so in the orthogonal direction (radial diffusivity). (b) This directionally dependent diffusion signal is
measured with DWI and modeled at each volumetric pixel, called a voxel. The map shows a distribution of orientation distribution
functions in MNI template space (Yeh & Tseng, 2011). (c) The whole-brain map of water diffusion at each voxel is then explored using
automated tractography algorithms to produce a map of connections throughout the brain. (d) Brain areas can then be segmented
into a set of regions of interest (ROI) using a number of approaches (anatomical segmentation is shown here). (e) The connectivity
between each ROI pair is then estimated, providing a structural connectivity map.

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(e) Connectivity to each ROI

Radial diffusion

Axial diffusion

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across the circuit and define the tuning properties (e.g., directional tuning,
receptive fields) of connected units. Second, the integrity of the connections
between two nodes can influence the strength of information transfer within
the circuit. Here, I focus on the utility of organizational patterns in neural
circuits to explain the functional processing related to cognition.
Before going into too much detail about the computational utility of
anatomical connectivity, it is important to first know the general classes of
connections that are seen in the brain. Work in animal systems has revealed
several common connection patterns seen in neural circuits (for an excellent
review of this work, see Thivierge & Marcus, 2007). These patterns include
the following:
Convergence. Many-to-one connections (e.g., corticostriatal systems)
Divergence. One-to-many-connections (e.g., pedunculopontine efferents)
Reciprocity. Symmetrically looped connections (e.g., thalamicocortical
loops)
Lateral Connectivity. Mutual connections within a layer (e.g., retinal ganglion cells)
Topography. Point-to-point mappings that preserve spatial and functional
arrangements (e.g., retinotopy of projections from the lateral geniculate
nucleus to the primary visual cortex).
Each of these connectivity patterns contributes to a specific class of computations (Figure 2). For example, neural network models have shown how convergent inputs allow for networks to perform information integration from
multiple inputs, such as what happens during sensory integration across
sensory modalities (Denève, Duhamel, & Pouget, 2007; Deneve, Latham, &
Pouget, 2001). On the other hand, lateral connectivity within a layer allows
for stability in local computations (Deneve, Latham, & Pouget, 1999; Deneve,
Pouget, & Latham, 1999; Ma, Beck, Latham, & Pouget, 2006) and provides a
physical architecture that allows for adaptive plasticity within a local circuit
(Verstynen & Sabes, 2011; Wu, Amari, & Nakahara, 2002; Wu & Amari, 2005;
Wu, Chen, Niranjan, & Amari, 2003). Finally, topography constrains the way
that information is represented as it passes from one region to the next and
thus defines the representational structure of the system (Jbabdi, Sotiropoulos, & Behrens, 2013). The complete class of functional computations that are
constrained by each connectivity pattern is still unknown. Nor is it certain
that this is even an exhaustive list of connectivity patterns (see also Thivierge
& Marcus, 2007). What is certain, however, is that the properties of network
computations are fundamentally limited by how the system is wired together
(Passingham et al., 2002).

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Supported function

Connectivity

Integration

Divergent

Segregation

Topographic

Representation

Lateral

Stability & estimation

Visible with tractography

Convergent

Figure 2 An example of some of the most common connectivity patterns seen in
neural circuits [see Thivierge and Marcus (2007) for a more detailed description of
these patterns]. The patterns highlighted in the box show patterns that can be
detected using DWI methods.

With the advent of DWI-based fiber tractography algorithms, it has become
possible to virtually map the underlying white matter pathways in the living
human brain and capture some of these connectivity patterns (for a complete
review of DWI, see Hagmann et al., 2006). These algorithms use the geometry
of water diffusion in the brain that is measured with DWI and iteratively
map the likelihood, either probabilistically or deterministically, that any two
voxels in the brain are connected.
While these tools have shown great promise in mapping underlying white
matter pathways, current DWI-based methods can only resolve a subset of
the overall connectivity patterns in the brain. This is largely due to the spatial
resolution of DWI (i.e., millimeters) and the inability to identify the directionality of connections (i.e., it is not possible to tell if a detected connection emits
from point A to point B or vice versa or both). Nonetheless, fiber tractography
approaches are already providing key insights about brain–behavior associations linked to two general connectivity patterns: convergence/divergence
connectivity and topography. The functional utility of each pattern is considered in turn.
INTEGRATION AND SEGREGATION
With current DWI-based tractography methods it is impossible to tell
whether a connection between any three regions reflects a divergent set of
connections, a convergent set of connections, or both. Considered together,
convergence and divergence patterns describe the integration and segregation of information within a circuit. With the adoption of graph-analytic
methods to describe neural connectivity, we now know a lot about the

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general patterns of integration and segmentation within the human brain
(Bullmore & Sporns, 2009; Leergaard, Hilgetag, & Sporns, 2012). These
machine learning analytics summarize how easily information can travel
across brain areas by looking at the paths it takes to get from one area
to the next (Sporns, 2013). These descriptive topology metrics have been
used to identify differences in connectivity patterns in clinical neurological
and psychiatric conditions such as multiple sclerosis, schizophrenia, and
Alzheimer’s disease (for a review of these findings and limitations of clinical
connectometry, see Griffa et al., 2013).
One major limitation of this approach is that it is not clear how these graph
metrics aid our understanding of neural function or map onto cognitive
abilities.
What does a more modular structural network mean for the function of
the system or behavior? How does altered structural connectivity between
groups, for example, sex differences, provide a mechanism for the altered
computations that lead to any behavioral differences seen in these groups?
Metrics of “small worldness” are excellent at providing summary statistics of
network structure, but they are generally agnostic with regard to the underlying functions of the network itself.
However, that is not to say that measures of convergence and divergence
have no utility for understanding brain function. In fact, measures of
structural convergence have recently been shown to be useful for predicting
functional activity during face processing (Saygin et al., 2011). While participants passively viewed a series of faces, Zeynep Saygin and colleagues
recorded hemodynamic responses across the entire brain using fMRI. They
then estimated the structural connectivity between the fusiform face area
(FFA; a region on the fusiform gyrus with selective responses to faces) and
the rest of the brain using a probabilistic form of tractography that was
applied to DTI data. The pattern of task-related responses in the FFA was
then modeled as a function of the activity in the other brain regions, with
the amount of influence of each brain region determined by the amount of
connectivity they had with the FFA. Compared to several null models, Saygin and her colleagues found that a portion of the variance in FFA responses
could be explained by the structural connectivity with other brain areas. This
intriguing finding alludes to the possibility that the degree of convergent
(or reciprocal divergent/convergent pathways) might have some predictive
utility for explaining task-related activity, at least in sensory regions.
TOPOGRAPHY
While convergence and divergence describe the path that information travels across a brain network, topography describes the way that information

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is represented as it travels from region to region. Recently, there has been
a growing interest in resolving topographic patterns of structural connectivity in the human brain. Over the past few years, my colleagues and I, as
well as other researchers, have shown how DWI-based tractography methods can resolve fine topographic patterns in the human brain. For example,
using diffusion spectrum imaging (DSI), a high-angular resolution form of
DWI, we have shown how it is possible to visualize the somatotopic organization of corticospinal pathways using DSI (Verstynen, Jarbo, Pathak, &
Schneider, 2011). These pathways are particularly difficult to resolve as they
pass through the midbrain and because they compact into an area of space
about 5 mm2 in diameter. Yet, it is still possible to detect the general somatotopic organization of these fibers using tractography on DSI data (Figure 3a).
More recently, we have shown how this approach can capture both global
(centimeters) and local (millimeters) topographic patterns in corticostriatal
pathways (Verstynen et al., 2012) (Figure 3b). This type of topographic analysis is not particularly specialized to DSI imaging approaches. Work from Iona
Fine’s laboratory has shown how tractography on DTI data can reveal the
retinotopy of the interhemispheric connections in the splenium that connect
the two primary visual cortices (Bock et al., 2013; Saenz & Fine, 2010). This
organization of the callosal pathways only encompasses a few voxels (i.e., a
few millimeters) of tissue space, but event at this small distance, tractography
approaches can detect these general patterns. Taken together, these findings
illustrate the utility of DWI-based methods at capturing fine topologies at the
macroscopic level in the human brain.
But what informative value does topography have for understanding brain
function or cognition? In functional activity, understanding the topography
of different functional responses can provide clues as to the nature of processing that an area does (see Schlerf, Verstynen, Ivry, & Spencer, 2010 for an
example of this in the cerebellum). Recently, Jbabdi and colleagues argued
that similar principles apply when looking at the structural organization
of brain networks (Jbabdi et al., 2013), that is, knowing how information is
organized as it projects from one area to the next can provide insights into
network-level representations.
My colleagues and I looked at how the organization of connections from the
intraparietal sulcus (IPS) could explain patterns of attentional modulation of
the early visual cortex (Greenberg et al., 2012). Using functional localizers, we
mapped out the boundaries of V1, V2, and V3, as well as the topographic representation of spatial attention in the IPS. Using tractography on DSI data, we
then mapped the structural connections between these functionally defined
regions. With a fairly high resolution we were able to confirm that regions of
the posterior IPS that were selective for attending to a specific area of space
were most strongly connected to early visual areas that also attended to that

How Form Constrains Function in the Human Brain

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Figure 3 (a) Somatotopic organization of the corticospinal projections from the
central sulcus for a single subject. Top inset shows organization of fiber start
points at the cortex and bottom image shows organization of fiber positions in the
crus cerebri of the midbrain. Reprinted from Verstynen et al. (2011). (b)
Organization of corticostriatal projections that originate in the middle frontal gyrus
for a single subject. Coloring reflects position of the fiber start point in the cortex,
with more rostral fibers shown in cooler colors and more caudal fibers shown in
warmer colors. Upper inset shows the fiber start points along the sagittal plane in
the cortex and lower inset shows fiber end points along the sagittal plane in the
striatum. Reprinted from Verstynen, Badre, et al. (2012).

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Scaled connectedness

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Contralateral attention BOLD signal change

Figure 4 (a) Position of fiber endpoints (dots) that terminate in functionally
defined regions of the intraparietal sulcus, at the cortical surfus. Colors reflect
functionally defined regions based on a spatial attention mapping paradigm:
attention to upper visual field, blue; attention to lateral visual field, red; attention to
lower visual field, green. (b) Percent BOLD signal change due to attentional
modulation, in six extra striate regions, plotted relative to the number of
anatomical connections from three topographically organized regions in the
anterior intraparietal sulcus (aIPS) and posterior intraparietal sulcus (pIPS). Both
panels reprinted from Greenberg et al. (2012).

area of space. Thus, there was a consistent topography of spatial information
between visual areas in the occipital lobe and attention areas in the parietal
lobe (Figure 4a). More importantly, however, we showed that this topography of connectedness positively correlated with the degree of attentional
modulation seen in early visual cortex (Figure 4b). Therefore, the efficiency of
point-to-point organization of connections from the posterior IPS to the early
visual cortex could reflect a potential mechanism for attentional modulation
in the primary visual cortex.
LIMITATIONS
Thus far I have outlined the emerging utility of DWI-based imaging tools
for understanding how the physical architecture of connections in the brain
might constrain brain function. However, there are several important limitations that are, as of yet, unresolved with these DWI approaches.
Bias. In many cases, the tractography output from DWI data is biased
toward detecting connections between gyri (the folds of cortical tissue),
with substantial loss in connectivity to sulcal regions (the wrinkles of
cortical tissue). This significantly limits the scope of connectivity that can be
estimated within the brain.
Artifacts. Just like its cousin method fMRI, there are many sources of noise
in the DWI signal. Many of these sources can bias results toward a spurious
finding between groups. For example, it was recently shown that spurious

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head motion can introduce a change in the FA signal that resembles what
is also seen in demyelination (Yendiki, Koldewyn, Kakunoori, Kanwisher, &
Fischl, 2013). For a comprehensive review of noise sources in DWI, see Jones
& Cercignani, 2010.
Directionality. Currently it is not possible to tell the direction mapped
connections from the DWI signal, that is, if axons are going from region A
to region B or vice versa. Thus, any inferences made from DWI data are
restricted to undirected graphs and networks.
Spatial Resolution. Being an MRI-based method means that the spatial resolution of DWI is on the order of millimeters and centimeters. This is an order
of magnitude higher than the spatial range of individual neurons. As with
the directionality problem, any models or inferences made from DWI data
are restricted to large networks of millions of neurons, rather than local networks of dozens of neurons or less.
Mapping to Function. Where possible I tried to highlight findings linking
white matter architecture to either brain function or cognition. However, the
precise mapping between these measures of white matter and functional
properties of brain systems remains elusive. For example, in an integrated
DWI and transcranial magnetic stimulation (TMS) study, DWI-based measures of corticospinal tract integrity, including FA, were not correlated with
the conduction excitability of the corticospinal pathways when stimulated
with TMS (Hübers, Klein, Kang, Hilker, & Ziemann, 2012). Thus, variability
in FA did not predict individual differences in how signals are propagated
from the motor cortex to the spinal motor neurons. While it is difficult to
make an inference from this null result, it does suggest that the precise
mapping between structure and function using DWI based methods is still
ambiguous.
Validation. Until more studies are done incorporating histological or
microdissection methods with DWI results, it is difficult to know the
false-positive or false-negative rates of tractography data or how measures
such as FA relate to the true number of underlying axons in a voxel.
Despite these limitations, some of which are shared with other neuroimaging methods, DWI still represents the best available tool for mapping white
matter pathways in humans and understanding how they relate to cognition.
PUTTING IT TOGETHER
While DWI is most widely used to measure the integrity of white matter
pathways, tractography approaches are just beginning to allow us to explore
deeper questions about principles of neural organization and how the
specific organization of brain pathways leads to behavior. Current studies
are just beginning to get a handle on the phenomenological relationships

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between structural connections and brain function. One day it may be
possible to go beyond characterizing specific white matter–behavior relationships and identify the fundamental principles regarding how certain
connection patterns (e.g., convergence, topography) constrain information
processing in neural networks. Knowing these principles can provide a
deeper understanding of the mechanisms by which neural circuits give rise
to cognition.
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doi:10.1016/j.neuroimage.2013.11.027

TIMOTHY D. VERSTYNEN SHORT BIOGRAPHY
Timothy D. Verstynen received his bachelors in Psychology at the University
of New Mexico in 2001 and a PhD in Psychology at the University of California, Berkeley in 2006. He went on to do postdoctoral training in theoretical

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

neurobiology at the University of California, San Francisco and in cognitive
neuroscience at the University of Pittsburgh. In 2012, Dr. Verstynen started
as an Assistant Professor at Carnegie Mellon University in the Department
of Psychology and the Center for the Neural Basis of Cognition.
As the director of the Cognitive Axon (CoAx) Laboratory, Dr. Verstynen
is interested in how white matter architecture influences brain function
on behavior, focusing mainly on sensorimotor learning and executive
control. He uses a combination of behavioral testing, neuroimaging, and
computational modeling to explore the statistical dynamics of learning and
decision making. His work has been sponsored by many agencies including
the Department of Defense, NSF, NIH, the Sandler Foundation and the
Swartz Foundation. Outside the laboratory, Dr. Verstynen is also very active
in science outreach, including giving public lectures about neuroscience,
a blogging at Psychology Today (White Matter Matters), and collaborating
on a podcast about the interface of psychology and philosophy (Axons and
Axioms). His latest outreach project is a book that teaches the history of
neurology and neuroscience principles by diagnosing the brains of horror
movie zombies. Website: www.cognitiveaxon.com
RELATED ESSAYS
Spatial Attention (Psychology), Kyle R. Cave
Resource Limitations in Visual Cognition (Psychology), Brandon M. Liverence
and Steven L. Franconeri



How Form Constrains Function
in the Human Brain
TIMOTHY D. VERSTYNEN

Abstract
In neural systems, form and function are intimately linked; the communication
dynamics across networked areas depends on the organization and integrity
of the connections between them (i.e., axons and tracts). With the growth of
diffusion-weighted imaging (DWI) and fiber tractography tools over the past
decade, it has become possible to visualize the physical architecture of the human
brain at an unprecedented resolution. This information has provided the first
glimpses into the component circuitry supporting cognition, presenting a unique
opportunity for cognitive neuroscientists. For the first time we can visualize the
connections in the living brain, allowing us to measure individual differences in
anatomical connectivity, relate this connectivity to brain function, and gain insights
into the link between white matter architecture and behavior. In many ways, this
technology is still in its infancy and its full potential has not yet been realized.
Here, I outline the importance of understanding neuroanatomical connectivity as a
hard constraint on neural computation. Beginning with an overview of the typical
patterns of connectivity seen in neural systems, I go on to show how current neuroimaging tools can visualize several different types of connectivity in the brain. By
highlighting recent findings showing how neuroanatomical organization and brain
function are related during cognitive tasks, I emphasize the utility that structural
brain mapping approaches can have for the broader social and behavioral sciences.

BACKGROUND
Two decades ago, in a commentary to the journal Nature, Francis Crick and
Edward Jones threw down the proverbial gauntlet to the human neuroscience community. Highlighting the work being done to map the physical
connections in the macaque brain, Crick and Jones lamented that the lack
of such methods in humans fundamentally limits how much we can truly
understand about the brain:
“Without [knowing anatomical connectivity] there is little hope of understanding how our brains work in the crudest way.” (Crick & Jones, 1993).
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

1

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Indeed, the organization of white matter pathways within the brain defines
the essential wiring diagram that acts as a hard constraint on neural processing (Felleman & Van Essen, 1991; Passingham, Stephan, & Kötter, 2002). Without the knowledge of how the different brain areas are connected together, it
is impossible to truly understand how specific neural computations can lead
to specific cognitive processes.
However, magnetic resonance (MR) physics was already working on a technology that would end up answering their challenge to map the physical
connections in vivo. In fact, 3 years earlier, Michael Moseley and colleagues
had published a series of studies showing how a new form of MRI (magnetic resonance imaging) called diffusion-weighted imaging (DWI; Bihan et al.,
1985) could be used to detect directionally dependent water diffusion in the
cat brain (Moseley et al., 1990). Subsequent work would go on to show that
this water is constrained mostly within axons and could be used as a proxy
to describe the geometry of underlying white matter pathways. Thus, by the
time of Crick and Jones’s commentary in Nature, physicists and radiologists
were already working on methods to noninvasively capture the structural
connections in the brain.
Over the past 20 years, DWI has grown to become arguably one of the most
valuable tools in cognitive neuroscience. The increased popularity of DWI
methods is most evident in the steadily increasing number of publications
reporting DWI results over the past decade. According to Pubmed, the number of publications reporting on results using diffusion tensor imaging (DTI),
the most popular DWI technique in cognitive neuroscience, has risen from
138 publications in 2003 to 1590 publications in 2013.
This accelerated adoption of DWI has led to a number of significant discoveries over the past decade. For example, DWI has been used to identify novel
white matter pathways within human brain, such as the connectivity of the
middle longitudinal fasciulus (Makris et al., 2009; Wang et al., 2012) and the
existence of the frontal aslant tract (Catani et al., 2012, 2013). When integrated
with functional magnetic resonance imaging (fMRI), DWI is being used to
map the human connectome and reveal fundamental properties of neural
connectivity in our brains (Bullmore & Sporns, 2009). Clinically, DWI represents one of the most promising approaches to identifying diffuse axonal
injury from head trauma such as concussion and traumatic brain injury (TBI;
(Huisman et al., 2004)) mainly due to its sensitivity to the directional motion
of water, which is disturbed by axonal injury, rather than the density of water,
which is measured by typical clinical MRI scans and not affected by axonal
injury.
The most common way that DWI is used in cognitive neuroscience is in the
evaluation of the microstructural integrity of underlying white matter pathways through measures such as fractional anisotropy (FA). These measures

How Form Constrains Function in the Human Brain

3

provide local estimates of the diffusion of water molecules at fixed points in
space, called voxels (short for “volumetric pixels” and reflect the spatial sampling of MRI-based imaging methods), with more restrictive water diffusion
in a specific direction being used as a proxy for the health and integrity of
underlying white matter. As a measure of integrity, these metrics appear to
provide a good index of the health of axons and myelin when examined in
animal studies (Budde, Xie, Cross, & Song, 2009; Klawiter et al., 2011; Song
et al., 2005). Cross-sectional differences in FA are associated with group differences in physical health (Bolzenius et al., 2013; Mueller et al., 2011; Stanek
et al., 2011; Verstynen, Weinstein, et al., 2012; Verstynen et al., 2013), neurological pathologies (Bihan et al., 2001; Dyrba et al., 2013), and even broader social
factors such as socioeconomic status (Gianaros, Marsland, Sheu, Erickson,
& Verstynen, 2012). But these associations with behavior are not just limited to predicting differences across individuals. Longitudinal changes in FA
have been associated with learning (Keller & Just, 2009; Sampaio-Baptista
et al., 2013; Scholz, Klein, Behrens, & Johansen-Berg, 2009). These promising findings, along with the relative conceptual and methodological ease of
voxel-wise measures such as FA, these white matter integrity measures are
quite appealing for a wide variety of applications in the social and behavioral
sciences.
However, DWI allows for more than just a local estimate of white matter
integrity. With the increased application of tractography methods to DWI
data (for a review of tractography, see Jbabdi & Johansen-Berg, 2011), it has
become possible to map a subset of the physical point-to-point connections in
the human brain (Figure 1). This connectivity information is equally important to the behavioral scientist as integrity measures such as FA, if not more
so. This is because connectivity analysis allows for visualization of the component circuitry of neural systems that regulate a vast number of cognitive
processes (Passingham et al., 2002). As tractography methods continue to
improve, they will be used to ask some of the most fundamental questions
about the human brain and its relation to cognition. In what follows, I highlight some of the most promising avenues of this structural mapping method
for understanding the biological basis of human cognition.
STRUCTURAL CONNECTIVITY AND NEURAL COMPUTATION
In order to conceptualize the utility of neuroanatomical mapping approaches
for social and behavioral sciences, it is important to understand that the
physical wiring of brain circuits is a hard (i.e., nonmodifiable) constraint on
how information flows through the network. There are two specific ways
that anatomical connectivity can constrain function. First, the organization of
connections between sets of neurons will determine the flow of information

100

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(d) Segmentation of region
of interest (ROI)

(b) Map of water diffusion models

(c) Fiber tractography

Figure 1 An outline of a typical fiber tractography analysis. (a) Water trapped in axons diffuses primarily along the length of the
axon (axial diffusivity) and less so in the orthogonal direction (radial diffusivity). (b) This directionally dependent diffusion signal is
measured with DWI and modeled at each volumetric pixel, called a voxel. The map shows a distribution of orientation distribution
functions in MNI template space (Yeh & Tseng, 2011). (c) The whole-brain map of water diffusion at each voxel is then explored using
automated tractography algorithms to produce a map of connections throughout the brain. (d) Brain areas can then be segmented
into a set of regions of interest (ROI) using a number of approaches (anatomical segmentation is shown here). (e) The connectivity
between each ROI pair is then estimated, providing a structural connectivity map.

600

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(e) Connectivity to each ROI

Radial diffusion

Axial diffusion

(a) Water molecules trapped axons

ROI i

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How Form Constrains Function in the Human Brain

5

across the circuit and define the tuning properties (e.g., directional tuning,
receptive fields) of connected units. Second, the integrity of the connections
between two nodes can influence the strength of information transfer within
the circuit. Here, I focus on the utility of organizational patterns in neural
circuits to explain the functional processing related to cognition.
Before going into too much detail about the computational utility of
anatomical connectivity, it is important to first know the general classes of
connections that are seen in the brain. Work in animal systems has revealed
several common connection patterns seen in neural circuits (for an excellent
review of this work, see Thivierge & Marcus, 2007). These patterns include
the following:
Convergence. Many-to-one connections (e.g., corticostriatal systems)
Divergence. One-to-many-connections (e.g., pedunculopontine efferents)
Reciprocity. Symmetrically looped connections (e.g., thalamicocortical
loops)
Lateral Connectivity. Mutual connections within a layer (e.g., retinal ganglion cells)
Topography. Point-to-point mappings that preserve spatial and functional
arrangements (e.g., retinotopy of projections from the lateral geniculate
nucleus to the primary visual cortex).
Each of these connectivity patterns contributes to a specific class of computations (Figure 2). For example, neural network models have shown how convergent inputs allow for networks to perform information integration from
multiple inputs, such as what happens during sensory integration across
sensory modalities (Denève, Duhamel, & Pouget, 2007; Deneve, Latham, &
Pouget, 2001). On the other hand, lateral connectivity within a layer allows
for stability in local computations (Deneve, Latham, & Pouget, 1999; Deneve,
Pouget, & Latham, 1999; Ma, Beck, Latham, & Pouget, 2006) and provides a
physical architecture that allows for adaptive plasticity within a local circuit
(Verstynen & Sabes, 2011; Wu, Amari, & Nakahara, 2002; Wu & Amari, 2005;
Wu, Chen, Niranjan, & Amari, 2003). Finally, topography constrains the way
that information is represented as it passes from one region to the next and
thus defines the representational structure of the system (Jbabdi, Sotiropoulos, & Behrens, 2013). The complete class of functional computations that are
constrained by each connectivity pattern is still unknown. Nor is it certain
that this is even an exhaustive list of connectivity patterns (see also Thivierge
& Marcus, 2007). What is certain, however, is that the properties of network
computations are fundamentally limited by how the system is wired together
(Passingham et al., 2002).

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Supported function

Connectivity

Integration

Divergent

Segregation

Topographic

Representation

Lateral

Stability & estimation

Visible with tractography

Convergent

Figure 2 An example of some of the most common connectivity patterns seen in
neural circuits [see Thivierge and Marcus (2007) for a more detailed description of
these patterns]. The patterns highlighted in the box show patterns that can be
detected using DWI methods.

With the advent of DWI-based fiber tractography algorithms, it has become
possible to virtually map the underlying white matter pathways in the living
human brain and capture some of these connectivity patterns (for a complete
review of DWI, see Hagmann et al., 2006). These algorithms use the geometry
of water diffusion in the brain that is measured with DWI and iteratively
map the likelihood, either probabilistically or deterministically, that any two
voxels in the brain are connected.
While these tools have shown great promise in mapping underlying white
matter pathways, current DWI-based methods can only resolve a subset of
the overall connectivity patterns in the brain. This is largely due to the spatial
resolution of DWI (i.e., millimeters) and the inability to identify the directionality of connections (i.e., it is not possible to tell if a detected connection emits
from point A to point B or vice versa or both). Nonetheless, fiber tractography
approaches are already providing key insights about brain–behavior associations linked to two general connectivity patterns: convergence/divergence
connectivity and topography. The functional utility of each pattern is considered in turn.
INTEGRATION AND SEGREGATION
With current DWI-based tractography methods it is impossible to tell
whether a connection between any three regions reflects a divergent set of
connections, a convergent set of connections, or both. Considered together,
convergence and divergence patterns describe the integration and segregation of information within a circuit. With the adoption of graph-analytic
methods to describe neural connectivity, we now know a lot about the

How Form Constrains Function in the Human Brain

7

general patterns of integration and segmentation within the human brain
(Bullmore & Sporns, 2009; Leergaard, Hilgetag, & Sporns, 2012). These
machine learning analytics summarize how easily information can travel
across brain areas by looking at the paths it takes to get from one area
to the next (Sporns, 2013). These descriptive topology metrics have been
used to identify differences in connectivity patterns in clinical neurological
and psychiatric conditions such as multiple sclerosis, schizophrenia, and
Alzheimer’s disease (for a review of these findings and limitations of clinical
connectometry, see Griffa et al., 2013).
One major limitation of this approach is that it is not clear how these graph
metrics aid our understanding of neural function or map onto cognitive
abilities.
What does a more modular structural network mean for the function of
the system or behavior? How does altered structural connectivity between
groups, for example, sex differences, provide a mechanism for the altered
computations that lead to any behavioral differences seen in these groups?
Metrics of “small worldness” are excellent at providing summary statistics of
network structure, but they are generally agnostic with regard to the underlying functions of the network itself.
However, that is not to say that measures of convergence and divergence
have no utility for understanding brain function. In fact, measures of
structural convergence have recently been shown to be useful for predicting
functional activity during face processing (Saygin et al., 2011). While participants passively viewed a series of faces, Zeynep Saygin and colleagues
recorded hemodynamic responses across the entire brain using fMRI. They
then estimated the structural connectivity between the fusiform face area
(FFA; a region on the fusiform gyrus with selective responses to faces) and
the rest of the brain using a probabilistic form of tractography that was
applied to DTI data. The pattern of task-related responses in the FFA was
then modeled as a function of the activity in the other brain regions, with
the amount of influence of each brain region determined by the amount of
connectivity they had with the FFA. Compared to several null models, Saygin and her colleagues found that a portion of the variance in FFA responses
could be explained by the structural connectivity with other brain areas. This
intriguing finding alludes to the possibility that the degree of convergent
(or reciprocal divergent/convergent pathways) might have some predictive
utility for explaining task-related activity, at least in sensory regions.
TOPOGRAPHY
While convergence and divergence describe the path that information travels across a brain network, topography describes the way that information

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

is represented as it travels from region to region. Recently, there has been
a growing interest in resolving topographic patterns of structural connectivity in the human brain. Over the past few years, my colleagues and I, as
well as other researchers, have shown how DWI-based tractography methods can resolve fine topographic patterns in the human brain. For example,
using diffusion spectrum imaging (DSI), a high-angular resolution form of
DWI, we have shown how it is possible to visualize the somatotopic organization of corticospinal pathways using DSI (Verstynen, Jarbo, Pathak, &
Schneider, 2011). These pathways are particularly difficult to resolve as they
pass through the midbrain and because they compact into an area of space
about 5 mm2 in diameter. Yet, it is still possible to detect the general somatotopic organization of these fibers using tractography on DSI data (Figure 3a).
More recently, we have shown how this approach can capture both global
(centimeters) and local (millimeters) topographic patterns in corticostriatal
pathways (Verstynen et al., 2012) (Figure 3b). This type of topographic analysis is not particularly specialized to DSI imaging approaches. Work from Iona
Fine’s laboratory has shown how tractography on DTI data can reveal the
retinotopy of the interhemispheric connections in the splenium that connect
the two primary visual cortices (Bock et al., 2013; Saenz & Fine, 2010). This
organization of the callosal pathways only encompasses a few voxels (i.e., a
few millimeters) of tissue space, but event at this small distance, tractography
approaches can detect these general patterns. Taken together, these findings
illustrate the utility of DWI-based methods at capturing fine topologies at the
macroscopic level in the human brain.
But what informative value does topography have for understanding brain
function or cognition? In functional activity, understanding the topography
of different functional responses can provide clues as to the nature of processing that an area does (see Schlerf, Verstynen, Ivry, & Spencer, 2010 for an
example of this in the cerebellum). Recently, Jbabdi and colleagues argued
that similar principles apply when looking at the structural organization
of brain networks (Jbabdi et al., 2013), that is, knowing how information is
organized as it projects from one area to the next can provide insights into
network-level representations.
My colleagues and I looked at how the organization of connections from the
intraparietal sulcus (IPS) could explain patterns of attentional modulation of
the early visual cortex (Greenberg et al., 2012). Using functional localizers, we
mapped out the boundaries of V1, V2, and V3, as well as the topographic representation of spatial attention in the IPS. Using tractography on DSI data, we
then mapped the structural connections between these functionally defined
regions. With a fairly high resolution we were able to confirm that regions of
the posterior IPS that were selective for attending to a specific area of space
were most strongly connected to early visual areas that also attended to that

How Form Constrains Function in the Human Brain

(a)

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D
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Figure 3 (a) Somatotopic organization of the corticospinal projections from the
central sulcus for a single subject. Top inset shows organization of fiber start
points at the cortex and bottom image shows organization of fiber positions in the
crus cerebri of the midbrain. Reprinted from Verstynen et al. (2011). (b)
Organization of corticostriatal projections that originate in the middle frontal gyrus
for a single subject. Coloring reflects position of the fiber start point in the cortex,
with more rostral fibers shown in cooler colors and more caudal fibers shown in
warmer colors. Upper inset shows the fiber start points along the sagittal plane in
the cortex and lower inset shows fiber end points along the sagittal plane in the
striatum. Reprinted from Verstynen, Badre, et al. (2012).

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Scaled connectedness

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Figure 4 (a) Position of fiber endpoints (dots) that terminate in functionally
defined regions of the intraparietal sulcus, at the cortical surfus. Colors reflect
functionally defined regions based on a spatial attention mapping paradigm:
attention to upper visual field, blue; attention to lateral visual field, red; attention to
lower visual field, green. (b) Percent BOLD signal change due to attentional
modulation, in six extra striate regions, plotted relative to the number of
anatomical connections from three topographically organized regions in the
anterior intraparietal sulcus (aIPS) and posterior intraparietal sulcus (pIPS). Both
panels reprinted from Greenberg et al. (2012).

area of space. Thus, there was a consistent topography of spatial information
between visual areas in the occipital lobe and attention areas in the parietal
lobe (Figure 4a). More importantly, however, we showed that this topography of connectedness positively correlated with the degree of attentional
modulation seen in early visual cortex (Figure 4b). Therefore, the efficiency of
point-to-point organization of connections from the posterior IPS to the early
visual cortex could reflect a potential mechanism for attentional modulation
in the primary visual cortex.
LIMITATIONS
Thus far I have outlined the emerging utility of DWI-based imaging tools
for understanding how the physical architecture of connections in the brain
might constrain brain function. However, there are several important limitations that are, as of yet, unresolved with these DWI approaches.
Bias. In many cases, the tractography output from DWI data is biased
toward detecting connections between gyri (the folds of cortical tissue),
with substantial loss in connectivity to sulcal regions (the wrinkles of
cortical tissue). This significantly limits the scope of connectivity that can be
estimated within the brain.
Artifacts. Just like its cousin method fMRI, there are many sources of noise
in the DWI signal. Many of these sources can bias results toward a spurious
finding between groups. For example, it was recently shown that spurious

How Form Constrains Function in the Human Brain

11

head motion can introduce a change in the FA signal that resembles what
is also seen in demyelination (Yendiki, Koldewyn, Kakunoori, Kanwisher, &
Fischl, 2013). For a comprehensive review of noise sources in DWI, see Jones
& Cercignani, 2010.
Directionality. Currently it is not possible to tell the direction mapped
connections from the DWI signal, that is, if axons are going from region A
to region B or vice versa. Thus, any inferences made from DWI data are
restricted to undirected graphs and networks.
Spatial Resolution. Being an MRI-based method means that the spatial resolution of DWI is on the order of millimeters and centimeters. This is an order
of magnitude higher than the spatial range of individual neurons. As with
the directionality problem, any models or inferences made from DWI data
are restricted to large networks of millions of neurons, rather than local networks of dozens of neurons or less.
Mapping to Function. Where possible I tried to highlight findings linking
white matter architecture to either brain function or cognition. However, the
precise mapping between these measures of white matter and functional
properties of brain systems remains elusive. For example, in an integrated
DWI and transcranial magnetic stimulation (TMS) study, DWI-based measures of corticospinal tract integrity, including FA, were not correlated with
the conduction excitability of the corticospinal pathways when stimulated
with TMS (Hübers, Klein, Kang, Hilker, & Ziemann, 2012). Thus, variability
in FA did not predict individual differences in how signals are propagated
from the motor cortex to the spinal motor neurons. While it is difficult to
make an inference from this null result, it does suggest that the precise
mapping between structure and function using DWI based methods is still
ambiguous.
Validation. Until more studies are done incorporating histological or
microdissection methods with DWI results, it is difficult to know the
false-positive or false-negative rates of tractography data or how measures
such as FA relate to the true number of underlying axons in a voxel.
Despite these limitations, some of which are shared with other neuroimaging methods, DWI still represents the best available tool for mapping white
matter pathways in humans and understanding how they relate to cognition.
PUTTING IT TOGETHER
While DWI is most widely used to measure the integrity of white matter
pathways, tractography approaches are just beginning to allow us to explore
deeper questions about principles of neural organization and how the
specific organization of brain pathways leads to behavior. Current studies
are just beginning to get a handle on the phenomenological relationships

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between structural connections and brain function. One day it may be
possible to go beyond characterizing specific white matter–behavior relationships and identify the fundamental principles regarding how certain
connection patterns (e.g., convergence, topography) constrain information
processing in neural networks. Knowing these principles can provide a
deeper understanding of the mechanisms by which neural circuits give rise
to cognition.
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TIMOTHY D. VERSTYNEN SHORT BIOGRAPHY
Timothy D. Verstynen received his bachelors in Psychology at the University
of New Mexico in 2001 and a PhD in Psychology at the University of California, Berkeley in 2006. He went on to do postdoctoral training in theoretical

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neurobiology at the University of California, San Francisco and in cognitive
neuroscience at the University of Pittsburgh. In 2012, Dr. Verstynen started
as an Assistant Professor at Carnegie Mellon University in the Department
of Psychology and the Center for the Neural Basis of Cognition.
As the director of the Cognitive Axon (CoAx) Laboratory, Dr. Verstynen
is interested in how white matter architecture influences brain function
on behavior, focusing mainly on sensorimotor learning and executive
control. He uses a combination of behavioral testing, neuroimaging, and
computational modeling to explore the statistical dynamics of learning and
decision making. His work has been sponsored by many agencies including
the Department of Defense, NSF, NIH, the Sandler Foundation and the
Swartz Foundation. Outside the laboratory, Dr. Verstynen is also very active
in science outreach, including giving public lectures about neuroscience,
a blogging at Psychology Today (White Matter Matters), and collaborating
on a podcast about the interface of psychology and philosophy (Axons and
Axioms). His latest outreach project is a book that teaches the history of
neurology and neuroscience principles by diagnosing the brains of horror
movie zombies. Website: www.cognitiveaxon.com
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