Diffusion tensor imaging (DTI) measures variations in the local microstructure of brain tissue. Microstructural variations alter the diffusion of water molecules in the brain, which can in turn be measured via magnetic resonance techniques. In the absence of microstructural tissue variations, this diffusive process would be random and would not exhibit a preferential diffusion gradient. However, because the rate of water diffusion varies within different types of brain tissue, preferential diffusion gradients can be observed at tissue boundaries.
This diffusion anisotropy is particularly useful for identifying the boundaries of white matter tracts in the brain. These tracts consist of bundles of myelinated axons along which water diffuses more rapidly than it would in an orthogonal direction. DTI measurements infer the direction and degree of net diffusion within individual voxels (volume pixels) of tissue, which can then be used to reconstruct anatomical fiber pathways.
The diffusive properties of molecules can be measured by applying a pulsed magnetic field gradient that aligns nuclear spins in the transverse plane and causes precession at different rates. The application of a second pulsed field gradient can then be used to realign the spins. If water molecules have moved in time between the first and second pulses, this realignment will be imperfect, resulting in a detectable MR signal. Strongly preferential diffusive processes, such as those along while matter tracts, produce strong local signals that can be used to map tract boundaries.
If diffusion gradients in two adjacent voxels are largely overlapping, the assumption is made that the axon boundary extends between voxels along this gradient direction. Tractography, a computational method that searches for significant gradient overlap, can be used to reconstruct large-scale white matter pathways linking different regions of the brain from voxel-wise measurements of water diffusion.
Functional MRI (fMRI) measures local changes in blood oxygenation, which are in turn thought to reflect local changes in neural activity.
Active brain cells require more energy, in the form of glucose and oxygen, than inactive brain cells. This energy is delivered to cells in the form of oxygenated blood, which results in a local (2-3mm) increase in blood flow, a local expansion of blood vessels, and a local net increase in oxygenated hemoglobin (the oxygen carrier in blood). Changes in neural activity can therefore by characterized by changes in oxygenated blood flow to localized brain regions.
Changes in blood oxygenation are detectable by MRI measurements due to the differences in magnetic properties between oxygenated and deoxygenated blood. Deoxygenated blood (deoxyhemoglobin, dHB) is paramagnetic, while oxygenated blood (hemoglobin, Hb) is diamagnetic. dHB interacts with and distorts the local magnetic field such that nuclear spins decohere more quickly in the presence of dHB than in the presence of Hb. As a result, regions with higher Hb content produce stronger MR signals, enabling the mapping of local changes in blood oxygen content.
Magnetic resonance imaging measurements, described in the previous sections, can be used to measure the local properties of brain tissue. Variations in these properties can be related to underlying structural inhomogeneities, such as the physical boundaries between axons and their surrounding tissue, that affect the translational motion of molecules. Similarly, local tissue properties can reflect functional responses, such as the degree of energy consumption, that affect the local density of different types of molecules. Our goal is to use these local measurements to gain an understanding of the large scale structural and functional properties of the human brain.
Structural Connectivity: DTI techniques can resolve both the number and length of white matter tracts that link different brain regions. This gives both a binary measurement (was there a connection or not) and a weighted measurement (how many connections, or how long) of structural connectivity. It is reasonable to assume that these measures are stable over time, although changes in local tissue microstructure (which can occur, e.g., during learning) can occur over the timescale of weeks.
Functional Connectivity: fMRI techniques can resolve time-dependent changes in activity within brain regions. Functional connectivity is commonly commonly measured by the strength of correlation between time series measured in different regions. Functional connectivity measures are task-dependent, meaning that they vary in strength depending on the activity being performed by subjects during MRI scanning (e.g. staring blankly versus recalling a memory).
We use network approaches for studying relationships between structural and functional brain connectivity. In the network representation, localized brain regions are represented as nodes, and the strengths of interaction (structural or functional) between brain regions are represented by weighted, undirected connections between nodes.
In addition to direct connectivity measures, such as the length and number of white matter tracts or the degree of correlation between time series, there is a myriad of higher-order measures that can be used to assess connectivity patterns in complex networks (degree distribution, hierarchy, modularity, and clustering coefficient, toname a few...). These can be used to measure static network properties, or they can be used to evaluate changes in functional connectivity over time (of course, functional connectivity itself is measured from correlated changes in activity, so these dynamics deal with changes in changes in activity...). While these measures provide useful metrics for comparing networks, they can also obscure differences in connectivity that could be important for distinguishing between two networks. Some of our work focuses on distinguishing between these two cases by exploring regimes in which dissimilar networks can be characterized by similar metrics.
The anatomical scaffolding of the brain exhibits significant variability in the number, length, and spatial distribution of structural pathways. We are interested in understanding how these structural variations shape correlated neural actvity, and how these relationships change during different tasks.
We recently showed that the length and number inter- versus intra-hemispheric connections differentially shape functional connectivity (FC) in a task-dependent manner. In resting state, inter-hemispheric and dense intra-hemispheric connections support strong FC, while long intra-hemispheric connections support relatively weak FC. Interestingly, these long intra-hemispheric connections supported the greatest changes in correlated activity during tasks relative to rest, suggesting that these connections help integrate information from spatially distant regions of the brain to facilitate task performance.
The brain is neither fixed in structure nor static in function. Anatomical pathways can differ between individuals, as can the manner by which these pathways are utilized for different cognitive functions. Furthermore, structure can be altered during development, learning, and aging, and it can be disrupted by neurological disorders. Each of these can have significant functional consequences.
To explore these consequences, we combine inferred models of network connectivity (as discussed here) with forward network models in which we can manipulate specific features of the structural or functional architecture. For more information on these forward modeling projects, see the Artificial Networks page.
Ultimately, we are interested in understanding how the structural properties of the brain shape cognitive function. To this end, we explore how relationships between structural and functional connectivity shape behavioral performance during different tasks.
In recent work, we assessed connectivity within and between known task-relevant brain networks. By comparing inter- and intra-network connectivity across different task states, we were able to measure a "degree of separation" between different states. We showed that this separation, defined in terms of brain network organization, relates to a measure of behavioral separation in the performance of different tasks.