The talk will cover various aspects of processing and
analysis of diffusion data, from the perspective of hypotheses associated with population
studies. Specifically it will discuss (1) connectome creation - atlas and structure-based parcellation, tracking and choice of connectivity measures; (2) connectomic
analysis – edge-based statistics, extraction of meso-scale structures
(subnetworks and core-periphery), and their application to discriminative and
regressive hypotheses; (3) tract-based analysis - automated tract extraction
that does not require the placement of ROIs; and (4) biomarker creation. In
addition to describing the protocol for cross-sectional studies, we will also
discuss the extension of these methods to longitudinal studies.
A connectome is mathematically described as
a graph G=(V,E), consisting of nodes V representing brain regions, and a set of
edges E, representing connection between these regions, weighted with a
connectivity measure [1, 2]. A matrix representation of this graph is
used for all methodological derivations. Connectomes (Fig. 1) are created by
parcellating the brain into regions, tracking between regions, and deriving a
measure based on the tracking that will quantify connectivity strength. As
there is no consensus in literature on methods to build the connectome, as a
pre-processing step, we will discuss several types of connectomes by varying
parcellation, tractography and connectivity measures. Namely (A) Parcellation: Atlas-based and
structural-connectivity based; (B) Tracking algorithm: probabilistic
tractography (probtrackx from FSL [3]) and deterministic tracking (Trackvis [4, 5]), comparison based on the density of the
connectome [3, 6]. (C)
Connectivity Measure is the number assigned to each edge representing
connectivity strength. We will use (1) Binary where weights of edges are set to 1 or 0,
based on whether there is at least one streamline connecting the regions; (2)
Streamline count: number of streamlines between regions; (3)
Incorporating ROI volume by
normalizing the streamline count with the sum of region volumes. This
accounts for the fact that due to the non-uniform sizes of parcellated
regions, bigger regions may have a higher probability of being touched by a
streamline; and (4) Incorporating fiber length: due to the possible
distal bias in tractography, that is, the number of fibers between two regions
decreases with distance [7, 8], as a larger number of propagation steps
need to be traversed, streamline count will be normalized by the average
inter-regional fiber length. These measures can be used to create an n x n (n
is the number of regions used in parcellation) matrix representation of the
connectome. The pros and cons of the measures will be discussed.
We will begin
with a description of edge-based analysis [9]. Connectomes are created by parcellating
the WM/GM boundary of the brain into “regions” and tracking between them using
a fiber tracking algorithm, with connectivity measures created by averaging
connectivity in each region, producing a network representation of the brain. Thus
the study of networks predicates on the ability of methods in succinctly
extracting meaningful representative connectivity information from these
connectomes at the subject and population level. We will briefly review the
considerable amount of work that has been done in extracting local and global network
features [2,
10-12].
We will the focus on describing meso-scale structures, which are groupings of
nodes and their communication patterns that characterize the dominant
organizational structure (communities/ subnetwork) of the brain, as well as its
auxiliary characteristics (core-periphery). Identification of meso-scale
structures can reveal how the network manages an interplay of the seemingly
competing principles of functional segregation and integration, which in turn
lead to a complex behavioral repertoire. We will describe methods that can
extract underlying network patterns (meso-scale structures) that characterize
the connectivity variation in a population with separate components components
pertaining to each source of variation, while also capturing variations at the
subject-specific level [13-17]. The
decomposition maintains the interpretation of each component as a subnetwork
and the coefficients associated with these components as the weight of the
subnetwork, while providing a succinct low dimensional representation of the
population amenable to statistical analysis. In addition to determining the
connectivity patterns of variability, the projection of the subject networks
into the basis set, provides a low dimensional representation of it that teases
apart different sources of variation in the sample, facilitating
variation-specific statistical analysis, as well as the ability to monitor
subject-specific changes in longitudinal studies. We will also discuss a unified
formulation for the algorithmic detection and analysis of hybrid meso-scale structures
that captures the interplay between multiple meso-scale structures and
statistical comparison of competing structures [13]. These methods have been applied to ASD, TBI and
developmental populations [14,
15,
17-20].
Advances in diffusion
imaging and tractography techniques have led to an increasing interest in
tract-based analysis. Statistical analyses over white matter tracts can
contribute greatly towards understanding structural mechanisms of the brain
since tracts are representative of the connectivity pathways. Automated
extraction of eloquent tracts is of crucial importance in neurosurgical
planning, which requires the knowledge of placement of tracts with regards to
the tumor. The main challenge with tract-based studies is the extraction of
tracts in a consistent and comparable manner over a large group of individuals
without drawing the inclusion and exclusion regions of interest, or using shape
based tract features that may alter in the presence of pathology like tumors. We
will describe a framework for automated extraction of WM tracts, in which
connectivity signatures are created for each fiber [21] using
probabilistic tracking [3] from each voxel to parcelleted
regions of subject’s brain [22].
A group-wise clustering of these fibers on healthy controls is used to
generate a fiber bundle atlas. Finally, Adaptive Clustering incorporates the
previously generated clustering atlas as a prior, to cluster the fibers of a
new subject automatically. By alleviating the seed selection or
inclusion/exclusion ROI drawing requirements that are usually handled by
trained radiologists, this framework expands the range of possible
clinical applications, especially surgical planning [23], and establishes the ability to
perform tract-based analysis with large samples, which will be discussed in the
talk.
Connectomes and tracts are imaging features that provide
non-invasive insight into brain mechanisms. However, univariate statistical analysis
in which each feature (e.g. mean subnetwork
connectivity) was treated individually, without accounting for multivariate
interactions between features, do not accurately represent complex (non-linear)
developmental patterns in a developing brain [24]. Linear and non-linear
classification approaches like kernel support vector machine (SVM) [25, 26] and deep learning (DL) [27-29]
are now routinely used to create population markers by learning complex
multivariate relationships between features and finding high-dimensional brain
patterns representative of disorder-induced alterations. These assign a quantitative
subject-wise score that can be correlated with age or diagnostic/behavioral
measures and can help in assessing treatment and disease progression. Analogously,
Support Vector Regression (SVR) can learn brain patterns to predict continuous
variables like age and diagnostic/behavioral measures. Imaging-based markers of
pathology [30-38]
(using structural imaging [30-33],
and more recently DTI [35-38]),
and brain age [39] have been created. We will
discuss non-linear machine learning approaches for creating network-based
biomarkers.
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