Probabilistic multi-tensor estimation using the tensor distribution function

Diffusion weighted magnetic resonance (MR) imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of 6 directions, second-order tensors can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve crossing fiber tracts. Recently, a number of high-angular resolution schemes with greater than 6 gradient directions have been employed to address this issue. In this paper, we introduce the Tensor Distribution Function (TDF), a probability function defined on the space of symmetric positive definite matrices. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the diffusion orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function.

White matter integrity measured by fractional anisotropy correlates poorly with actual individual fiber anisotropy

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. High-angular resolution diffusion imaging (HARDI) can resolve more complex diffusion geometries than standard DTI, including fibers crossing or mixing. The tensor distribution function (TDF) can be used to reconstruct multiple underlying fibers per voxel, representing the diffusion profile as a probabilistic mixture of tensors. Here we found that DTIderived mean diffusivity (MD) correlates well with actual individual fiber MD, but DTI-derived FA correlates poorly with actual individual fiber anisotropy, and may be suboptimal when used to detect disease processes that affect myelination. Analysis of the TDFs revealed that almost 40% of voxels in the white matter had more than one dominant fiber present. To more accurately assess fiber integrity in these cases, we here propose the differential diffusivity (DD), which measures the average anisotropy based on all dominant directions in each voxel.

Automatic clustering and population analysis of white matter tracts using maximum density paths

We introduce a framework for population analysis of white matter tracts based on diffusion-weighted images of the brain. The framework enables extraction of fibers from high angular resolution diffusion images (HARDI); clustering of the fibers based partly on prior knowledge from an atlas; representation of the fiber bundles compactly using a path following points of highest density (maximum density path; MDP); and registration of these paths together using geodesic curve matching to find local correspondences across a population. We demonstrate our method on 4-Tesla HARDI scans from 565 young adults to compute localized statistics across 50 white matter tracts based on fractional anisotropy (FA). Experimental results show increased sensitivity in the determination of genetic influences on principal fiber tracts compared to the tract-based spatial statistics (TBSS) method. Our results show that the MDP representation reveals important parts of the white matter structure and considerably reduces the dimensionality over comparable fiber matching approaches.

Investigating brain connectivity heritability in a twin study using diffusion imaging data

Heritability of brain anatomical connectivity has been studied with diffusion-weighted imaging (DWI) mainly by modeling each voxel's diffusion pattern as a tensor (e.g., to compute fractional anisotropy), but this method cannot accurately represent the many crossing connections present in the brain. We hypothesized that different brain networks (i.e., their component fibers) might have different heritability and we investigated brain connectivity using High Angular Resolution Diffusion Imaging (HARDI) in a cohort of twins comprising 328 subjects that included 70 pairs of monozygotic and 91 pairs of dizygotic twins. Water diffusion was modeled in each voxel with a Fiber Orientation Distribution (FOD) function to study heritability for multiple fiber orientations in each voxel. Precision was estimated in a test-retest experiment on a sub-cohort of 39 subjects. This was taken into account when computing heritability of FOD peaks using an ACE model on the monozygotic and dizygotic twins. Our results confirmed the overall heritability of the major white matter tracts but also identified differences in heritability between connectivity networks. Inter-hemispheric connections tended to be more heritable than intra-hemispheric and cortico-spinal connections. The highly heritable tracts were found to connect particular cortical regions, such as medial frontal cortices, postcentral, paracentral gyri, and the right hippocampus.

Neuroimaging and genetics: Exploring, searching, and finding

This issue on the genetics of brain imaging phenotypes is a celebration of the happy marriage between two of science's highly interesting fields: neuroscience and genetics. The articles collected here are ample evidence that a good deal of synergy exists in this marriage. A wide selection of papers is presented that provide many different perspectives on how genes cause variation in brain structure and function, which in turn influence behavioral phenotypes (including psychopathology). They are examples of the many different methodologies in contemporary genetics and neuroscience research. Genetic methodology includes genome-wide association (GWA), candidate-gene association, and twin studies. Sources of data on brain phenotypes include cortical gray matter (GM) structural/volumetric measures from magnetic resonance imaging (MRI); white matter (WM) measures from diffusion tensor imaging (DTI), such as fractional anisotropy; functional- (activity-) based measures from electroencephalography (EEG), and functional MRI (fMRI). Together, they reflect a combination of scientific fields that have seen great technological advances, whether it is the single-nucleotide polymorphism (SNP) array in genetics, the increasingly high-resolution MRI imaging, or high angular resolution diffusion imaging technique for measuring WM connective properties.

Changes in white matter connectivity following therapy for anomia post stroke

Background. The majority of studies investigating the neural mechanisms underlying treatment-induced recovery in aphasia have focused on the cortical regions associated with language processing. However, the integrity of the white matter connecting these regions may also be crucial to understanding treatment mechanisms. Objective. This study investigated the integrity of the arcuate fasciculus (AF) and uncinate fasciculus (UF) before and after treatment for anomia in people with aphasia. Method. Eight people with aphasia received 12 treatment sessions to improve naming; alternating between phonologically-based and semantic-based tasks, with high angular resolution diffusion imaging conducted pre and post treatment. The mean generalized fractional anisotropy (GFA), a measure of fiber integrity, and number of fibers in the AF and UF were compared pre and post treatment, as well as with a group of 14 healthy older controls. Results. Pre treatment, participants with aphasia had significantly fewer fibers and lower mean GFA in the left AF compared with controls. Post treatment, mean GFA increased in the left AF to be statistically equivalent to controls. Additionally, mean GFA in the left AF pre and post treatment positively correlated with maintenance of the phonologically based treatment. No differences were found in the right AF, or the UF in either hemisphere, between participants with aphasia and controls, and no changes were observed in these tracts following treatment. Conclusions. Anomia treatments may improve the integrity of the white matter connecting cortical language regions. These preliminary results add to the understanding of the mechanisms underlying treatment outcomes in people with aphasia post stroke.

Brain network efficiency and topology depend on the fiber tracking method: 11 tractography algorithms compared in 536 subjects

As connectivity analyses become more popular, claims are often made about how the brain's anatomical networks depend on age, sex, or disease. It is unclear how results depend on tractography methods used to compute fiber networks. We applied 11 tractography methods to high angular resolution diffusion images of the brain (4-Tesla 105-gradient HARDI) from 536 healthy young adults. We parcellated 70 cortical regions, yielding 70×70 connectivity matrices, encoding fiber density. We computed popular graph theory metrics, including network efficiency, and characteristic path lengths. Both metrics were robust to the number of spherical harmonics used to model diffusion (4th-8th order). Age effects were detected only for networks computed with the probabilistic Hough transform method, which excludes smaller fibers. Sex and total brain volume affected networks measured with deterministic, tensor-based fiber tracking but not with the Hough method. Each tractography method includes different fibers, which affects inferences made about the reconstructed networks.

A novel measure of fractional anisotropy based on the tensor distribution function

Fractional anisotropy (FA), a very widely used measure of fiber integrity based on diffusion tensor imaging (DTI), is a problematic concept as it is influenced by several quantities including the number of dominant fiber directions within each voxel, each fiber's anisotropy, and partial volume effects from neighboring gray matter. With High-angular resolution diffusion imaging (HARDI) and the tensor distribution function (TDF), one can reconstruct multiple underlying fibers per voxel and their individual anisotropy measures by representing the diffusion profile as a probabilistic mixture of tensors. We found that FA, when compared with TDF-derived anisotropy measures, correlates poorly with individual fiber anisotropy, and may sub-optimally detect disease processes that affect myelination. By contrast, mean diffusivity (MD) as defined in standard DTI appears to be more accurate. Overall, we argue that novel measures derived from the TDF approach may yield more sensitive and accurate information than DTI-derived measures.

Multiple sulfur isotope analyses support a magmatic model for the volcanogenic massive sulfide deposits of the Teutonic Bore volcanic complex, Yilgarn Craton, Western Australia

We report sensitive high mass resolution ion microprobe, stable isotopes (SHRIMP SI) multiple sulfur isotope analyses (32S, 33S, 34S) to constrain the sources of sulfur in three Archean VMS deposits—Teutonic Bore, Bentley, and Jaguar—from the Teutonic Bore volcanic complex of the Yilgarn Craton, Western Australia, together with sedimentary pyrites from associated black shales and interpillow pyrites. The pyrites from VMS mineralization are dominated by mantle sulfur but include a small amount of slightly negative mass-independent fractionation (MIF) anomalies, whereas sulfur from the pyrites in the sedimentary rocks has pronounced positive MIF, with ∆33S values that lie between 0.19 and 6.20‰ (with one outlier at −1.62‰). The wall rocks to the mineralization include sedimentary rocks that have contributed no detectable positive MIF sulfur to the VMS deposits, which is difficult to reconcile with the leaching model for the formation of these deposits. The sulfur isotope data are best explained by mixing between sulfur derived from a magmatic-hydrothermal fluid and seawater sulfur as represented by the interpillow pyrites. The massive sulfide lens pyrites have a weighted mean ∆33S value of −0.27 ± 0.05‰ (MSWD = 1.6) nearly identical with −0.31 ± 0.08‰ (MSWD = 2.4) for pyrites from the stringer zone, which requires mixing to have occurred below the sea floor. We employed a two-component mixing model to estimate the contribution of seawater sulfur to the total sulfur budget of the two Teutonic Bore volcanic complex VMS deposits. The results are 15 to 18% for both Teutonic Bore and Bentley, much higher than the 3% obtained by Jamieson et al. (2013) for the giant Kidd Creek deposit. Similar calculations, carried out for other Neoarchean VMS deposits give value between 2% and 30%, which are similar to modern hydrothermal VMS deposits. We suggest that multiple sulfur isotope analyses may be used to predict the size of Archean VMS deposits and to provide a vector to ore deposit but further studies are needed to test these suggestions.

The tensor distribution function

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Complex crystallization dynamics in amorphous germanium observed with dynamic transmission electron microscopy

Crystallization of amorphous germanium (a-Ge) by laser or electron beam heating is a remarkably complex process that involves several distinct modes of crystal growth and the development of intricate microstructural patterns on the nanosecond to ten microsecond time scales. Here we use dynamic transmission electron microscopy (DTEM) to study the fast, complex crystallization dynamics with 10 nm spatial and 15 ns temporal resolution. We have obtained time-resolved real-space images of nanosecond laser-induced crystallization in a-Ge with unprecedentedly high spatial resolution. Direct visualization of the crystallization front allows for time-resolved snapshots of the initiation and roughening of the dendrites on submicrosecond time scales. This growth is followed by a rapid transition to a ledgelike growth mechanism that produces a layered microstructure on a time scale of several microseconds. This study provides insights into the mechanisms governing this complex crystallization process and is a dramatic demonstration of the power of DTEM for studying time-dependent material processes far from equilibrium.

MEG Adaptation resolves the spatiotemporal characteristics of face-sensitive brain responses

An unresolved goal in face perception is to identify brain areas involved in face processing and simultaneously understand the timing of their involvement. Currently, high spatial resolution imaging techniques identify the fusiform gyrus as subserving processing of invariant face features relating to identity. High temporal resolution imaging techniques localize an early latency evoked component—the N/M170—as having a major generator in the fusiform region; however, this evoked component is not believed to be associated with the processing of identity. To resolve this, we used novel magnetoencephalographic beamformer analyses to localize cortical regions in humans spatially with trial-by-trial activity that differentiated faces and objects and to interrogate their functional sensitivity by analyzing the effects of stimulus repetition. This demonstrated a temporal sequence of processing that provides category-level and then item-level invariance. The right fusiform gyrus showed adaptation to faces (not objects) at ∼150 ms after stimulus onset regardless of face identity; however, at the later latency of ∼200–300 ms, this area showed greater adaptation to repeated identity faces than to novel identities. This is consistent with an involvement of the fusiform region in both early and midlatency face-processing operations, with only the latter showing sensitivity to invariant face features relating to identity.

Oxygen reduction and proton translocation by cytochrome c oxidase

Energy conversion by living organisms is central dogma of bioenergetics. The effectiveness of the energy extraction by aerobic organisms is much greater than by anaerobic ones. In aerobic organisms the final stage of energy conversion occurs in respiratory chain that is located in the inner membrane of mitochondria or cell membrane of some aerobic bacteria. The terminal complex of the respiratory chain is cytochrome c oxidase (CcO) - the subject of this study. The primary function of CcO is to reduce oxygen to water. For this, CcO accepts electrons from a small soluble enzyme cytochrome c from one side of the membrane and protons from another side. Moreover, CcO translocates protons across the membrane. Both oxygen reduction and proton translocation contributes to generation of transmembrane electrochemical gradient that is used for ATP synthesis and different types of work in the cell. Although the structure of CcO is defined with a relatively high atomic resolution (1.8 Å), its function can hardly be elucidated from the structure. The electron transfer route within CcO and its steps are very well defined. Meanwhile, the proton transfer roots were predicted from the site-specific mutagenesis and later proved by X-ray crystallography, however, the more strong proof of the players of the proton translocation machine is still required. In this work we developed new methods to study CcO function based on FTIR (Fourier Transform Infrared) spectroscopy. Mainly with use of these methods we answered several questions that were controversial for many years: [i] the donor of H+ for dioxygen bond splitting was identified and [ii] the protolytic transitions of Glu-278 one of the key amino acid in proton translocation mechanism was shown for the first time.

Coastal environmental gradients – Key to reproduction habitat mapping of freshwater fish in the Baltic Sea

Habitat requirements of fish are most strict during the early life stages, and the quality and quantity of reproduction habitats lays the basis for fish production. A considerable number of fish species in the northern Baltic Sea reproduce in the shallow coastal areas, which are also the most heavily exploited parts of the brackish marine area. However, the coastal fish reproduction habitats in the northern Baltic Sea are poorly known. The studies presented in this thesis focused on the influence of environmental conditions on the distribution of coastal reproduction habitats of freshwater fish. They were conducted in vegetated littoral zone along an exposure and salinity gradient extending from the innermost bays to the outer archipelago on the south-western and southern coasts of Finland, in the northern Baltic Sea. Special emphasis was placed on reed-covered Phragmites australis shores, which form a dominant vegetation type in several coastal archipelago areas. The main aims of this research were to (1) develop and test new survey and mapping methods, (2) investigate the environmental requirements that govern the reproduction of freshwater fish in the coastal area and (3) survey, map and model the distribution of the reproduction habitats of pike (Esox lucius) and roach (Rutilus rutilus). The white plate and scoop method with a standardized sampling time and effort was demonstrated to be a functional method for sampling the early life stages of fish in dense vegetation and shallow water. Reed-covered shores were shown to form especially important reproduction habitats for several freshwater fish species, such as pike, roach, other cyprinids and burbot, in the northern Baltic Sea. The reproduction habitats of pike were limited to sheltered reed- and moss-covered shores of the inner and middle archipelago, where suitable zooplankton prey were available and the influence of the open sea was low. The reproduction habitats of roach were even more limited and roach reproduction was successful only in the very sheltered reed-covered shores of the innermost bay areas, where salinity remained low (< 4‰) during the spawning season due to freshwater inflow. After identifying the critical factors restricting the reproduction of pike and roach, the spatial distribution of their reproduction habitats was successfully mapped and modelled along the environmental gradients using only a few environmental predictor variables. Reproduction habitat maps are a valuable tool promoting the sustainable use and management of exploited coastal areas and helping to maintain the sustainability of fish populations. However, the large environmental gradients and the extensiveness of the archipelago zone in the northern Baltic Sea demand an especially high spatial resolution of the coastal predictor variables. Therefore, the current lack of accurate large-scale, high-resolution spatial data gathered at exactly the right time is a considerable limitation for predictive modelling of shallow coastal waters.

A Low-Complexity Near-ML Performance Achieving Algorithm for Large MIMO Detection

In this paper, we present a low-complexity, near maximum-likelihood (ML) performance achieving detector for large MIMO systems having tens of transmit and receive antennas. Such large MIMO systems are of interest because of the high spectral efficiencies possible in such systems. The proposed detection algorithm, termed as multistage likelihood-ascent search (M-LAS) algorithm, is rooted in Hopfield neural networks, and is shown to possess excellent performance as well as complexity attributes. In terms of performance, in a 64 x 64 V-BLAST system with 4-QAM, the proposed algorithm achieves an uncoded BER of 10(-3) at an SNR of just about 1 dB away from AWGN-only SISO performance given by Q(root SNR). In terms of coded BER, with a rate-3/4 turbo code at a spectral efficiency of 96 bps/Hz the algorithm performs close to within about 4.5 dB from theoretical capacity, which is remarkable in terms of both high spectral efficiency as well as nearness to theoretical capacity. Our simulation results show that the above performance is achieved with a complexity of just O(NtNt) per symbol, where N-t and N-tau denote the number of transmit and receive antennas.