Synopsis
This paper will introduce the concept of connectivity and how it can be measured using MRI data. Potential pitfalls will also be reviewed
Target Audience
Scientists and Clinicians
willing to apply concepts and measures of brain connectivity to the study of
the healthy and diseased brain. The Audience will be expected to be familiar
with basic concepts of diffusion MRI.
Outcomes and Objectives
This talk aims at
clarifying the differing meanings of the term “connectivity”, and how to
measure it. It will also described some of the basic concepts of graph theory,
and what are the main pitfalls and limitations associated with MRI-based
measures of connectivity.
Background
Connectivity: In recent years the
concept of connectivity has become increasingly central to Neuroscience and
related fields, with the effort of mapping brain circuits and structures often
being the focus of big research initiatives. When applied to the brain, the
term connectivity refers to several different and interrelated aspects of brain
organization [1]. It can be defined as a
pattern of anatomical links ("anatomical/structural connectivity"),
of statistical dependencies ("functional connectivity") or of causal
interactions ("effective connectivity") between distinct units within
a nervous system. Brain connectivity can be described at several levels of
scale: the microscale, with individual neurons linked by individual synaptic
connections; the mesoscale, with networks connecting neuronal populations, and
the macroscale level, characterized by fiber pathways connecting brain regions
[2]. During this talk we will focus on the macroscale and on structural connectivity
although some concepts can be applied to other types of connectivity.
The
importance of connectivity in the clinical context: It is becoming increasingly recognized
that many behavioral manifestations of neurological and psychiatric diseases
are not solely the result of abnormality in one isolated region but represent
alterations in brain networks and connectivity [3]. Thus, the improved
characterization of brain networks can have an enormous relevance in
discovering the basis of common disorders of the brain, response to recovery
from brain injury, individual differences, heritability, normal development and
aging.
How to measure connectivity in humans
Although other approaches
are possible, the term structural connectivity has relied predominantly on
diffusion MRI (dMRI) techniques, such as Diffusion Tensor Imaging (DTI), which
are able to characterize the main white matter tracts of the brain in vivo. Thanks
to its ability to infer tissue orientation and thus to enable the
reconstruction of the main white matter tracts with tractography [4], dMRI
provides a unique insight into physical connections between anatomically
segregated areas of the brain. In order to develop appropriate tools to measure
connectivity one should first define precisely what a quantification of
structural connectivity should express. Depending on the context, “decreased/increased
connectivity” is meant to indicate differing concepts. It may indicate a reduced/increased
number of connections, thinner/thicker connections, or less/more efficient connections. It is
not always clear which of this aspects of connectivity is the most relevant. Since
the early days of diffusion, researchers have attempted to interpret changes to
indices derived from DTI, such as fractional anisotropy (FA), as measures of
connectivity. However, it should be remembered that FA is affected by many
factors that do not reflect any of the properties of connections that we
contemplate under the connectivity umbrella.
As tractography reconstructs streamlines which are believed to reflect existing white
matter pathways, it is an ideal candidate to provide information about
physical connections in the brain. Early attempts to build quantitative indices
of connectivity from tractography include anatomical connectivity mapping [5]
and track density imaging [6]. More recently, however, a popular approach is the one at the intersection between neuroscience and the rising
field of network science and graph theory. In order to apply these concepts to the
study of the brain, it is possible to use a topological representation where
the entities of a network are modelled as nodes and their interactions as
edges, reducing the problem to the analysis of a mathematical graph.How to build a graph
In order to build a graph
from a set of dMRI data, one first has to define the nodes. An obvious choice
as a node would be the smallest measurable unit, i.e. a voxel in the case of
MRI. Although offering such a unique definition, this method has limits. In the
case of MRI, each voxel can contain up to 100000 neurons, and it’s not possible
to assess if such neurons form a meaningful unit or not [7]. A common node
definition method relies instead on the parcellation of the brain gray matter by
means of atlases and then the estimation of structural or functional
connectivity between each pair of parcellated regions [8].
As for nodes, also
defining edges is not univocal. Counting the number of the tracts (NOS) between
each possible pair of nodes, (i.e., the corresponding grey matter regions)
results in building the weighted connectivity matrix and representing the
structural network [9]. The number of reconstructed streamlines, however, is
affected by several factors that do not reflect connectivity (e.g., the
shape/geometry of the white matter tracts, orientational dispersion, noise, and
distance); alternative approaches, while still relying on tractography to
reconstruct the connections, use other indices to weight the edges of the
graphs. Such indices can be other quantities derived from dMRI (E.g. FA), or be
derived from other modalities, believe for example, to reflect the degree of
myelination of the specified connections. The rationale is that myelin enables fast
signal transmission, and therefore has a role in supporting connectivity.Concepts from graph theory
Any complex system of any
nature (biological, technological, social) can be represented as a network,
composed of its basic elements and their interactions. From a mathematical
point of view, such representation is equivalent to a graph G, defined as a
pair of sets G=(V,E), where V is a set of elements called nodes or vertices,
and E is a set of pairs of different nodes called edges or links [10]. An edge
(i,j) connects two nodes.
The graph is directed if
the set of edges is ordered, and undirected if such set is unordered,
reflecting the presence or absence of directionality in the modelled
relationships. Moreover, if there is a weight wi,j associated with
each edge (i,j) the graph is defined as weighted, and it models further
properties of the edges themselves. In the opposite case, the graph is
unweighted or binary, representing the presence or absence of connections.
This structure can be conveniently
defined by means of a matrix representation [11], the so-called adjacency
matrix. A number of graph measures that can be used to characterize the network.
Broadly they can be classified as measures of either integration or segregation.Limitations and Pitfalls
Extracting meaningful
data from dMRI can be challenging [12] and the available options for
acquisition parameters, data preprocessing, diffusion model to fit and
tractography algorithm are so numerous to make an informed choice difficult.
Data quality is ultimately the most important factor in determining the output,
and caution should be exercised when interpreting graphs derived from
sub-optimal datasets. Tractography is known to be prone to be both false
negatives and false positives [13]. When weighting the connections using an MRI
proxy of tissue microstructure, the potential errors and limitations associated
with the specific MRI modality must also be considered. In this case the main
danger in the overinterpretation of such indices in terms of underlying
biology.
A different problem is
related to the use of network modelling itself on brain structure and function.
A broad set of studies has applied graph theory concepts to brain analysis
limiting to comparison of conventional metrics used in collateral fields [14].
Despite finding significant and potentially useful results, the interpretation
issue has not received the right attention and such studies did forget about
the context.Acknowledgements
No acknowledgement found.References
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