Structurally segregated and functionally specialized regions of the human cerebral cortex are interconnected by a dense network of cortico-cortical axonal pathways. By using diffusion spectrum imaging, we noninvasively mapped these pathways within and across cortical hemispheres in individual human participants. An analysis of the resulting large-scale structural brain networks reveals a structural core within posterior medial and parietal cerebral cortex, as well as several distinct temporal and frontal modules. Brain regions within the structural core share high degree, strength, and betweenness centrality, and they constitute connector hubs that link all major structural modules. The structural core contains brain regions that form the posterior components of the human default network. Looking both within and outside of core regions, we observed a substantial correspondence between structural connectivity and resting-state functional connectivity measured in the same participants. The spatial and topological centrality of the core within cortex suggests an important role in functional integration.

In the cerebral cortex, the activity levels of neuronal populations are continuously fluctuating. When neuronal activity, as measured using functional MRI (fMRI), is temporally coherent across 2 populations, those populations are said to be functionally connected. Functional connectivity has previously been shown to correlate with structural (anatomical) connectivity patterns at an aggregate level. In the present study we investigate, with the aid of computational modeling, whether systems-level properties of functional networks-including their spatial statistics and their persistence across time-can be accounted for by properties of the underlying anatomical network. We measured resting state functional connectivity (using fMRI) and structural connectivity (using diffusion spectrum imaging tractography) in the same individuals at high resolution. Structural connectivity then provided the couplings for a model of macroscopic cortical dynamics. In both model and data, we observed (i) that strong functional connections commonly exist between regions with no direct structural connection, rendering the inference of structural connectivity from functional connectivity impractical; (ii) that indirect connections and interregional distance accounted for some of the variance in functional connectivity that was unexplained by direct structural connectivity; and (iii) that resting-state functional connectivity exhibits variability within and across both scanning sessions and model runs. These empirical and modeling results demonstrate that although resting state functional connectivity is variable and is frequently present between regions without direct structural linkage, its strength, persistence, and spatial statistics are nevertheless constrained by the large-scale anatomical structure of the human cerebral cortex.computational model ͉ diffusion MRI ͉ neuroanatomy ͉ cerebral cortex ͉ brain networks P opulations of neurons in the mammalian cerebral cortex are continuously active during purposeful behavior, as well as during resting and sleep (1). Activity levels are modulated across time by the internal dynamics of each neuronal population and by signals received from cortical, subcortical, and peripheral elements of the nervous system. In the past decade, there has been intense interest in the patterns of correlated activity [''functional connectivity'' (2)] in the human brain, because these patterns are believed to reflect the patterns of interaction between neuronal populations. A set of functionally connected regions is referred to as a ''functional network.'' Some functional networks are most commonly detected when participants are not performing any demanding task (in the resting state); others are observed in the context of taskfocused behavior; and some networks persist across both behavioral states (3-6). A set of regions including posterior medial, anterior medial, and lateral parietal cortices comprise the default mode network (DMN) (7, 8), a functional network that is particularly robust across participants...

Methods are presented to map complex fiber architectures in tissues by imaging the 3D spectra of tissue water diffusion with MR. First, theoretical considerations show why and under what conditions diffusion contrast is positive. Using this result, spin displacement spectra that are conventionally phase-encoded can be accurately reconstructed by a Fourier transform of the measured signal's modulus. Second, studies of in vitro and in vivo samples demonstrate correspondence between the orientational maxima of the diffusion spectrum and those of the fiber orientation density at each location. In specimens with complex muscular tissue, such as the tongue, diffusion spectrum images show characteristic local heterogeneities of fiber architectures, including angular dispersion and intersection. Cerebral diffusion spectra acquired in normal human subjects resolve known white matter tracts and tract intersections. Over the past decade, MRI methods have been developed that can nondestructively map the structural anisotropy of fibrous tissues in living systems by mapping the diffusion tensor (DT) of tissue water (for review see Ref. 1). Such methods have been used to elucidate the fiber architecture and functional dynamics of the myocardium (2,3) and skeletal muscle (4). They have also been used in the nervous system to identify and map the trajectories of neural white matter tracts and infer neuroanatomic connectivity (for review see Ref. 5).Notwithstanding this progress, the DT paradigm has notable limitations. Because the distances resolved by MRI are far larger than the diffusion scale, each 3D resolution element (voxel) represents many distinct diffusional environments. This provides a complicated diffusion signal that in general is underspecified by the six degrees of freedom of the DT model. An example of particular interest occurs when a tissue has a composite fiber structure, such that each small region may contain fibers of multiple orientations corresponding to distinct diffusion anisotropies (6).The present study describes a model-free MRI methodology called diffusion spectrum imaging (DSI). This method affords the capacity to resolve intravoxel diffusion heterogeneity of compartments with sufficient angular separation and anisotropy by measuring its diffusion density spectra estimator. In describing this method, we will show that DSI generalizes the analysis of diffusion spectra by demonstrating that the Fourier transform of the diffusion spectrum must be positive. We also discuss how the DSI method encompasses existing alternate analyses of MRI diffusion contrast, and present examples of diffusion contrast in biological tissues analyzed with DSI. THEORY Measuring the Diffusion SpectrumWe consider the classical Stejskal-Tanner experiment (7). It allows the phase-encoding of spin displacements by embedding a strong pulse gradient of duration ␦ and intensity ͉g͉ on each side of the RF-pulse of a conventional spin-echo sequence. In such a manner the MR signal is made proportional to the voxel average (͗ ⅐ ͘) deph...