Figure 1.
Identifying structure-function relationships in task-related networks.
(a) In both representative and subject-specific brain networks, we identify brain regions that belong to the task-positive and task-negative network described in [7], and we label all remaining regions as “other” regions. There are six possible types of couplings between these three types of regions. We focus on three of these couplings: those between two task-negative regions (), between two task-positive regions (
), and between a task-positive and a task-negative region (
). These couplings are highlighted in the axial view of the representative brain network. (b) We compute measures of structural (SC) and functional (FC) connectivity between each pair of regions by measuring the number of white matter streamlines linking two regions (SC) and the task-dependent strength of functional correlation between BOLD time series measured within regions (FC). The pie chart shows the decomposition of all structural connections into those that link two task-positive (
), two task-negative (
), one task-positive and one task-negative (
), and all other regions (
). (c) We assess variations
in these number densities as we bias toward increasingly strong functional correlations. This relationship is illustrated here for the representative brain network, where variations
,
, and
are shown as a function of the resting-state threshold
. This can be understood as computing the change in composition of the pie chart shown in (b) while incrementally biasing toward strongly-correlated region pairs with functional correlations above the threshold value
. Inset: complementary cumulative distribution function (cCDF) of FCR computed for
,
, and
couplings, where the
) measures the probability of finding
for every value of
. The variable threshold
selects the subset of connections with
. (d) The changes in
,
, and
densities can be compactly represented by comparing the degree of within-network coupling, quantified by the relative change in
versus
densities (
), with the degree of between-network coupling, quantified by the change in
density (
). This representation reveals that strong resting-state FC is supported by strong local coupling within the task-negative network, represented by the increase in
relative to
density, and weak coupling between task-positive and task-negative networks, represented by the decrease in
density.
Figure 2.
State-space mapping of structure-function relationships.
Density of between-network couplings () versus within-network couplings (
) are shown as a function of the increasing functional threshold
in the representative brain network for the resting (circular markers), attention (square markers), and memory (triangular markers) states. Comparison of these network couplings reveals a large degree of separation between rest, attention, and memory states, with the degree of separation increasing as a function of
. The resting state is characterized by an increased density of
relative to
connections and a decreased density of
contributions. In comparison, the attention state is characterized by an increased density of
relative to
connections. The memory state shares features of both the resting and attention states, showing an increased density of
relative to
connections and an increased density of
connections.
Figure 3.
Individual variability in state-space relationships.
Subject-specific relationships between resting (), attention (
), and memory (
) states shown for a single subject (upper row) and for the entire set of subjects (lower row). (a) Subject-specific brain networks can each be described by a state-space of network couplings, quantified by
versus
, that is analogous to the state space shown in Figure 2 for the representative brain network. Each subject can then be compactly described by a triad of points, one each for resting (circular marker), attention (square marker), and memory (triangular marker) states, that marks the distribution averages
and
for each cognitive state. (b) The separation between two states can be quantified by the angular separation
between distribution averages, with
. (c) To isolate the angular separation between states, we perform a remapping of the state space in which we represent each individual by a triangle whose vertices are defined by cyclical permutations of
. Each vertex is visually indicated by the superposition of markers that denote the two cognitive states related by
(e.g.
is denoted by the superposition of a circular (
) and square (
) marker). This remapping reveals a high degree of inter-subject consistency in the relative separation between states, as noted by the clusters of markers of a given type and the highly overlapping triangles linking these clusters. (d) Subjects can be grouped according to the rank order of angular separations. This method naturally isolates one primary group of subjects who show the smallest separation between attention and memory states. The subject shown in the upper row falls into this primary group, as indicated by the proximity of
(superposition of triangular and square markers) to the vertical dotted line marking
. The remaining two secondary groups show the smallest separation between rest and memory (
closest to
) and between attention and memory (
closest to
).
Figure 4.
Behavioral performance of primary versus secondary groups.
Absolute () and relative (
) differences in performance measures
for attention (
) and memory (
) tasks, where
denotes the group average value of
. Performance differences are reported as means and standard errors for subjects within the primary (gray) and secondary (red) groups. (a) The secondary groups show larger absolute differences in reaction time (RT) for both attention and memory tasks. (b) The secondary groups show larger relative differences between attention and memory tasks for both the criterion switch score (CS) and the d-prime (
) score.