Efficient computation of N-point correlation functions in D dimensions.

We present efficient algorithms for computing the N-point correlation functions (NPCFs) of random fields in arbitrary D-dimensional homogeneous and isotropic spaces. Such statistics appear throughout the physical sciences and provide a natural tool to describe stochastic processes. Typically, algorithms for computing the NPCF components have [Formula: see text] complexity (for a dataset containing n particles); their application is thus computationally infeasible unless N is small. By projecting the statistic onto a suitably defined angular basis, we show that the estimators can be written in a separable form, with complexity [Formula: see text] or [Formula: see text] if evaluated using a Fast Fourier Transform on a grid of size [Formula: see text]. Our decomposition is built upon the D-dimensional hyperspherical harmonics; these form a complete basis on the [Formula: see text] sphere and are intrinsically related to angular momentum operators. Concatenation of [Formula: see text] such harmonics gives states of definite combined angular momentum, forming a natural separable basis for the NPCF. As N and D grow, the number of basis components quickly becomes large, providing a practical limitation to this (and all other) approaches: However, the dimensionality is greatly reduced in the presence of symmetries; for example, isotropic correlation functions require only states of zero combined angular momentum. We provide a Julia package implementing our estimators and show how they can be applied to a variety of scenarios within cosmology and fluid dynamics. The efficiency of such estimators will allow higher-order correlators to become a standard tool in the analysis of random fields.

Semi-analytic three-shell forward calculation for magnetoencephalography.

In previous studies, the magnetic lead field theorem in the quasi-static approximation was derived and used for the development of a method for the forward problem of MEG. It was applied and tested on a single-shell model of the human head and the question whether one shell is adequate enough for the calculation of the magnetic field is the main reason for this study. This forward method is based on the fundamental concept that one can calculate the lead field for MEG by decomposing it into two parts: the lead field of an arbitrary volume conductor that is already known and the gradient of basis functions that have to be harmonic, here derived from spherical harmonics. The problem then is reduced to evaluating the coefficients found in the basis functions. In this research we aim to improve the accuracy of the forward model, hence improving the localization accuracy in inverse methods by introducing a more detailed realistic head model. We here generalize the algorithm developed for a single-shell volume conductor to a three-shell volume conductor representing the brain, the skull and the skin with homogenous and isotropic conductivities in realistic ratios. The expansion to three shells could be tested as the three-shell algorithm is approaching the single-shell with high accuracy in special cases where three-shell solutions can also be calculated using a single-shell solution, especially for higher levels of expansion. The deviation in the calculation of the lead field is also evaluated when using three shells with realistic conductivities. The magnetic field turned out to differ to an important measurable extend in particular for deeper sources, making the three-shell algorithm substantially more accurate for these dipole locations.

On Difference Pattern Synthesis for Spherical Sensor Arrays.

An innovative method for synthesizing optimum difference patterns of the spherical sensor array is introduced, along with a sidelobe tapering technique. Firstly, we suggest employing the spherical harmonics of degree ±1 to synthesize the spherical array difference pattern; secondly, we study the mapping relationship between the difference pattern of the spherical sensor array and the difference pattern of the uniformly spaced linear array (ULA) with odd-numbered elements; finally, we enhance the Zolotarev difference pattern, which is a counterpart to the Dolph-Chebyshev sum pattern that traditionally allows synthesis only for ULA with even-numbered elements. Our modification extends its applicability to synthesize difference patterns for ULA with odd-numbered elements. Leveraging the optimal difference pattern, a generalized Bayliss difference pattern synthesis method designed for the ULA with odd-numbered elements is further proposed. To illustrate the effectiveness of our approach, we present several design examples through experimental simulation.

Shim coils tailored for correcting B0 inhomogeneity in the human brain (SCOTCH): Design methodology and 48-channel prototype assessment in 7-Tesla MRI.

Increased static field inhomogeneities are a burden for human brain MRI at Ultra-High-Field. In particular they cause enhanced Echo-Planar image distortions and signal losses due to magnetic susceptibility gradients at air-tissue interfaces in the subject's head. In the past decade, Multi-Coil Arrays (MCA) have been proposed to shim the field in the brain better than the 2nd or 3rd order Spherical Harmonic (SH) coils usually offered by MRI manufacturers. Here we present a novel MCA, named SCOTCH, optimized for whole brain shimming. Based on a cylindrical structure, it features several layers of small coils whose shape, size and location are found from a principal component analysis of ideal stream functions computed from an internal 100-brain fieldmap database. From an Open-Access external database of 126 brains, our SCOTCH implementation is shown to be equivalent to a partial 7th-order SH system with unlimited power, outperforming all known existing MCA prototypes. This result is further confirmed by a low-cost  30-cm diameter SCOTCH prototype built with 48 coils on 3 layers, and tested on 7 volunteers at 7T with a parallel-transmit RF coil made to be inserted in SCOTCH. Echo-Planar images of the subject brains before and after SCOTCH shimming show large signal recoveries, especially in the prefrontal cortex.

Multi-band- and in-plane-accelerated diffusion MRI enabled by model-based deep learning in q-space and its extension to learning in the spherical harmonic domain.

PURPOSE: To propose a new method for the recovery of combined in-plane- and multi-band (MB)-accelerated diffusion MRI data. METHODS: Combining MB acceleration with in-plane acceleration is crucial to improve the time efficiency of high (angular and spatial) resolution diffusion scans. However, as the MB factor and in-plane acceleration increase, the reconstruction becomes challenging due to the heavy aliasing. The new reconstruction utilizes an additional q-space prior to constrain the recovery, which is derived from the previously proposed qModeL framework. Specifically, the qModeL prior provides a pre-learned representation of the diffusion signal space to which the measured data belongs. We show that the pre-learned q-space prior along with a model-based iterative reconstruction that accommodate multi-band unaliasing, can efficiently reconstruct the in-plane- and MB-accelerated data. The power of joint reconstruction is maximally utilized by using an incoherent under-sampling pattern in the k-q domain. We tested the proposed method on single- and multi-shell data, with high/low angular resolution, high/low spatial resolution, healthy/abnormal tissues, and 3T/7T field strengths. Furthermore, the learning is extended to the spherical harmonic basis, to provide a rotational invariant learning framework. RESULTS: The qModeL joint reconstruction is shown to simultaneously unalias and jointly recover DWIs with reasonable accuracy in all the cases studied. The reconstruction error from 18-fold accelerated multi-shell datasets was <3%. The microstructural maps derived from the accelerated acquisitions also exhibit reasonable accuracy for both healthy and abnormal tissues. The deep learning (DL)-enabled reconstructions are comparable to those derived using traditional methods. CONCLUSION: qModeL enables the joint recovery of combined in-plane- and MB-accelerated dMRI utilizing DL.

Comparing and combining sliding semilandmarks and weighted spherical harmonics for shape analysis.

Quantifying morphological variation is critical for conducting anatomical research. Three-dimensional geometric morphometric (3D GM) landmark analyses quantify shape using homologous Cartesian coordinates (landmarks). Setting up a high-density landmark set and placing it on all specimens, however, can be a time-consuming task. Weighted spherical harmonics (SPHARM) provides an alternative method for analyzing the shape of such objects. Here we compare sliding semilandmark and SPHARM analyses of the calcaneus of Gorilla gorilla gorilla (n = 20), Pan troglodytes troglodytes (n = 20), and Homo sapiens (n = 20) to determine whether the SPHARM and sliding semilandmark analyses capture comparable levels of shape variation. We also compare both the sliding semilandmark and SPHARM analyses to a novel combination of the two methods, here termed SPHARM-sliding. In SPHARM-sliding, the vertices of the surface models produced from the SPHARM analysis (that are the same in number and relative location) are used as the starting landmark positions for a sliding semilandmark analysis. Calcaneal shape variation quantified by all three analyses was summarized using separate principal components analyses. Results were compared using the root mean square (RMS) and maximum distance between surface models of species averages scaled (up) to centroid size created from each analysis. The average RMS was 0.23 mm between sliding semilandmark and SPHARM average surface models, 0.19 mm between SPHARM and SPHARM sliding average surface models, and 0.22 mm between sliding semilandmark and SPHARM sliding average surface models. Although results indicate that all three analyses are comparable methods for 3D shape analysis, there are advantages and disadvantages to each. While the SPHARM analysis is less time-intensive, it is unable to capture the same level of detail around the sharp edges of articular facets on average surface models as the sliding semilandmark analysis. The SPHARM analysis also does not allow for individual articular facets to be analyzed in isolation. SPHARM-sliding, however, captures the same level of detail as the sliding semilandmark analysis, and (as in the sliding semilandmark analysis) allows for the evaluation of individual portions of bone. SPHARM is a comparable method to a 3D GM analysis for small, irregularly shaped bones, such as the calcaneus, and SPHARM-sliding allows for an expedited set up process for a sliding semilandmark analysis.

A morphometric analysis of early Eocene Euprimate tarsals from Gujarat, India.

Early Eocene primate postcranial bones from the Vastan lignite mine of Gujarat, India, have proven useful for understanding the haplorhine and strepsirrhine divergence. Previous analyses of material assigned to Asiadapidae supported interpretations that these primates were generalized arboreal quadrupeds, while the omomyid Vastanomys was likely to have been more proficient leaper than asiadapids. More recent examinations of long bone cross-sectional properties and calcaneal elongation have complicated the behavioral interpretations of these fossils. This study examines whole talar and calcaneal morphology of the Vastan material to refine the locomotor reconstructions of these fossils. A comparative sample of extant primate species representing various locomotor behaviors was obtained by accessing surface models from MorphoSource.org. Surface models of fossil specimens attributed to Asiadapis cambayensis, Marcgodinotius indicus, and Vastanomys major were generated from micro-computed tomography scans. A morphological analysis was carried out using weighted spherical harmonics, a Fourier-based method that represents surfaces using coefficients associated with a common set of spherical harmonic functions. The coefficients describing each surface were then used as shape variables in a principal components analysis. Significant differences between locomotor groups were assessed using nonparametric tests. Results from extant comparative samples show that locomotor behavior can be predicted from both talar and calcaneal morphology when phylogenetic relationships are known. Consistent with previous analyses, our results indicate that Asiadapis cambayensis and Marcgodinotius indicus were likely arboreal quadrupeds with some leaping capabilities. Vastanomys major is reconstructed as an arboreal quadruped with greater leaping proficiency than its asiadapid counterparts based on its talar morphology.

Physical limits to human brain B0 shimming with spherical harmonics, engineering implications thereof.

OBJECTIVE: As the MRI main magnetic field rises for improved signal-to-noise ratio, susceptibility-induced B0-inhomogeneity increases proportionally, aggravating related artifacts. Considering only susceptibility disparities between air and biological tissue, we explore the topological conditions for which perfect shimming could be performed in a Region of Interest (ROI) such as the human brain or part thereof. MATERIALS AND METHODS: After theoretical considerations for perfect shimming, spherical harmonic (SH) shimming simulations of very high degree are performed, based on a 100-subject database of 1.7-mm-resolved brain fieldmaps acquired at 3T . In addition to the whole brain, shimmed ROIs include slabs targeting the prefrontal cortex, both or single temporal lobes, or spheres in the frontal brain above the nasal sinus. RESULTS AND DISCUSSION: We show "perfect" SH shimming is possible only if the ROI can be contained in a sphere that does not enclose sources of magnetic field inhomogeneity, which are gathered at the air-tissue interface. We establish a [Formula: see text]Hz inhomogeneity hard shim limit at 7T for whole brain SH shimming, that can only be attained at shimming degree higher than 90. On the other hand, under limited power and SH degree resources, 3D region-specific shimming is shown to greatly improve homogeneity in critical zones such as the prefrontal cortex and around ear canals.

Solid waste shape description and generation based on spherical harmonics and probability density function.

Transport and separation processes of solid waste can only be modelled successfully with discrete element methods in case the shape of the particles can be described accurately. The existing techniques for morphological data acquisition, such as computed tomography, laser scanning technique, optical interferometer, stereo photography and structured light technique, are laborious and require a large amount of realistic solid waste samples. Therefore, there is a pressing need for an alternative method to describe the shape of solid waste particles and to generate multiple variations of particles with almost similar shapes. In this paper, a new method to describe solid waste particles is proposed that is frequency-based and uses spherical harmonics (SHs). Additionally, a new shape generation method is introduced that uses the shape description of a single particle to generate an array of related shapes based on a probability density function with a dimensionless control factor η. The newly proposed methods were successfully applied to describe the complex shapes of pieces of metal and plastic scrap. The shapes of these pieces of scrap can be described adequately with 15° of SH expansion and the overall divergence is within 0.1 mm. Five different values for η were tested, which generated shapes with the same distribution as the original particle. Rising levels of η cause the morphological variation of the generated particles to increase. These new methods improve the modelling of transportation and separation processes.

Dynamic B0 shimming for multiband imaging using high order spherical harmonic shims.

PURPOSE: To describe and implement a strategy for dynamic slice-by-slice and multiband B0 shimming using spherical harmonic shims in the human brain at 7T. THEORY: For thin axial slices, spherical harmonic shims can be divided into pairs of shims (z-degenerate and non-z-degenerate) that are spatially degenerate, such that only ½ of the shims (non-z-degenerate) are required for single slice optimizations. However, when combined, the pairs of shims can be used to simultaneously generate the same in-plane symmetries but with different amplitudes as a function of their z location. This enables multiband shimming equivalent to that achievable by single slice-by-slice optimization. METHODS: All data were acquired at 7T using a spherical harmonic shim insert enabling shimming up through 4th order with two additional 5th order shims (1st-4th+). Dynamic shim updating was achieved using a 10A shim power supply with 2 ms ramps and constrained optimizations to minimize eddy currents. RESULTS: In groups of eight subjects, we demonstrated that: 1) dynamic updating using 1st-4th+ order shims reduced the SD of the B0 field over the whole brain from 32.4 ± 2.6 and 24.9 ± 2 Hz with 1st-2nd and 1st-4th+ static global shimming to 15.1 ± 1.7 Hz; 2) near equivalent performance was achieved when dynamically updating only the non-z-degenerate shims (14.3 ± 1.5 Hz), or when a using multiband shim factor of 2, MBs = 2, and all shims (14.4 ± 2.0 Hz). CONCLUSION: High order spherical harmonics provide substantial improvements over static global shimming and enable dynamic multiband shimming with near equivalent performance to that of dynamic slice-by-slice shimming. This reduces distortion in echo planar imaging.

Cross-scanner and cross-protocol multi-shell diffusion MRI data harmonization: Algorithms and results.

Cross-scanner and cross-protocol variability of diffusion magnetic resonance imaging (dMRI) data are known to be major obstacles in multi-site clinical studies since they limit the ability to aggregate dMRI data and derived measures. Computational algorithms that harmonize the data and minimize such variability are critical to reliably combine datasets acquired from different scanners and/or protocols, thus improving the statistical power and sensitivity of multi-site studies. Different computational approaches have been proposed to harmonize diffusion MRI data or remove scanner-specific differences. To date, these methods have mostly been developed for or evaluated on single b-value diffusion MRI data. In this work, we present the evaluation results of 19 algorithms that are developed to harmonize the cross-scanner and cross-protocol variability of multi-shell diffusion MRI using a benchmark database. The proposed algorithms rely on various signal representation approaches and computational tools, such as rotational invariant spherical harmonics, deep neural networks and hybrid biophysical and statistical approaches. The benchmark database consists of data acquired from the same subjects on two scanners with different maximum gradient strength (80 and 300 â€‹mT/m) and with two protocols. We evaluated the performance of these algorithms for mapping multi-shell diffusion MRI data across scanners and across protocols using several state-of-the-art imaging measures. The results show that data harmonization algorithms can reduce the cross-scanner and cross-protocol variabilities to a similar level as scan-rescan variability using the same scanner and protocol. In particular, the LinearRISH algorithm based on adaptive linear mapping of rotational invariant spherical harmonics features yields the lowest variability for our data in predicting the fractional anisotropy (FA), mean diffusivity (MD), mean kurtosis (MK) and the rotationally invariant spherical harmonic (RISH) features. But other algorithms, such as DIAMOND, SHResNet, DIQT, CMResNet show further improvement in harmonizing the return-to-origin probability (RTOP). The performance of different approaches provides useful guidelines on data harmonization in future multi-site studies.

3D rigid-body motion information from spherical Lissajous navigators at small k-space radii: A proof of concept.

PURPOSE: To demonstrate, for the first time, the feasibility of obtaining low-latency 3D rigid-body motion information from spherical Lissajous navigators acquired at extremely small k-space radii, which has significant advantages compared with previous techniques. THEORY AND METHODS: A spherical navigator concept is proposed in which the surface of a k-space sphere is sampled on a 3D Lissajous curve at a radius of 0.1/cm. The navigator only uses a single excitation and is acquired in less than 5 ms. Rotation estimations were calculated with an algorithm from computer vision that exploits a rotation theorem of the spherical harmonics transform and has minimal computational cost. The effectiveness of the concept was investigated with phantom and in vivo measurements on a commercial 3T MRI scanner. RESULTS: Scanner-induced in vivo motion was measured with maximum absolute errors of 0.58° and 0.33 mm for rotations and translations, respectively. In the case of real, in vivo motion, the proposed method showed good agreement with motion information from FSL image registrations (mean/maximum deviations of 0.37°/1.24° and 0.44 mm/1.35 mm). In addition, phantom measurements indicated precisions of 0.014° and 0.013 mm. The computations for complete motion information took, on average, 24 ms on an ordinary laptop. CONCLUSIONS: This work demonstrates a proof of concept for obtaining accurate motion information from small-radius spherical navigators. The method has the potential to overcome several previously reported problems and could help increase the utility of navigator-based motion correction both in research and in the clinic.

Comparative analysis of the shape and size of the middle ear cavity of turtles reveals no correlation with habitat ecology.

The middle ear of turtles differs from other reptiles in being separated into two distinct compartments. Several ideas have been proposed as to why the middle ear is compartmentalized in turtles, most suggesting a relationship with underwater hearing. Extant turtle species span fully marine to strictly terrestrial habitats, and ecomorphological hypotheses of turtle hearing predict that this should correlate with variation in the structure of the middle ear due to differences in the fluid properties of water and air. We investigate the shape and size of the air-filled middle ear cavity of 56 extant turtles using 3D data and phylogenetic comparative analysis to test for correlations between habitat preferences and the shape and size of the middle ear cavity. Only weak correlations are found between middle ear cavity size and ecology, with aquatic taxa having proportionally smaller cavity volumes. The middle ear cavity of turtles exhibits high shape diversity among species, but we found no relationship between this shape variation and ecology. Surprisingly, the estimated acoustic transformer ratio, a key functional parameter of impedance-matching ears in vertebrates, also shows no relation to habitat preferences (aquatic/terrestrial) in turtles. We suggest that middle ear cavity shape may be controlled by factors unrelated to hearing, such as the spatial demands of surrounding cranial structures. A review of the fossil record suggests that the modern turtle ear evolved during the Early to Middle Jurassic in stem turtles broadly adapted to freshwater and terrestrial settings. This, combined with our finding that evolutionary transitions between habitats caused only weak evolutionary changes in middle ear structure, suggests that tympanic hearing in turtles evolved as a compromise between subaerial and underwater hearing.

Sensitivity Analysis of Leakage Correction of GRACE Data in Southwest China Using A-Priori Model Simulations: Inter-Comparison of Spherical Harmonics, Mass Concentration and In Situ Observations.

The Gravity Recovery and Climate Experiment (GRACE) level-2 spherical harmonic (SH) solutions are noisy and thus require filtering. Filtering reduces noise but affects signal quality via signal leakage. Generally, a leakage correction is required for GRACE applications to remove leakage signal and recover the true signal. Forward modelling based on some a priori information is a widely used approach for leakage correction of GRACE data. The a priori information generally relies on global hydrological model simulations. There are many global hydrological models and therefore it is of interest to explore how different global hydrology model simulations influence leakage correction results. This study investigated the sensitivity of three leakage correction methods (additive method, scaling factor method and multiplicative method) to five global hydrology model simulations (four models from the Global Land Data Assimilation System (GLDAS) and the WaterGAP Global Hydrology Model (WGHM)). The sensitivity analysis was performed with observational data in Southwest China and one sub-region, Guangxi. Results show that although large differences were identified among the five global model simulations, the additive and scaling factor methods are less affected by the choice of a priori model in comparison to the multiplicative approach. For the additive and scaling factor methods, WGHM outperforms the other four GLDAS models in leakage correction of GRACE data. GRACE data corrected with the multiplicative method shows the highest amount of error, indicating this method is not applicable for leakage correction in the study area. This study also assessed the level-3 mascon (mass concentration) solutions of GRACE data. The mascon-based results are nearly as good as the leakage corrected results based on SH solutions.

A New Relatively Simple Approach to Multipole Interactions in Either Spherical Harmonics or Cartesians, Suitable for Implementation into Ewald Sums.

We present a novel derivation of the multipole interaction (energies, forces and fields) in spherical harmonics, which results in an expression that is able to exactly reproduce the results of earlier Cartesian formulations. Our method follows the derivations of Smith (W. Smith, CCP5 Newsletter 1998, 46, 18.) and Lin (D. Lin, J. Chem. Phys. 2015, 143, 114115), who evaluate the Ewald sum for multipoles in Cartesian form, and then shows how the resulting expressions can be converted into spherical harmonics, where the conversion is performed by establishing a relation between an inner product on the space of symmetric traceless Cartesian tensors, and an inner product on the space of harmonic polynomials on the unit sphere. We also introduce a diagrammatic method for keeping track of the terms in the multipole interaction expression, such that the total electrostatic energy can be viewed as a 'sum over diagrams', and where the conversion to spherical harmonics is represented by 'braiding' subsets of Cartesian components together. For multipoles of maximum rank n, our algorithm is found to have scaling of n 3.7 vs. n 4.5 for our most optimised Cartesian implementation.

Bayesian Inference for Acoustic Direction of Arrival Analysis Using Spherical Harmonics.

This work applies two levels of inference within a Bayesian framework to accomplish estimation of the directions of arrivals (DoAs) of sound sources. The sensing modality is a spherical microphone array based on spherical harmonics beamforming. When estimating the DoA, the acoustic signals may potentially contain one or multiple simultaneous sources. Using two levels of Bayesian inference, this work begins by estimating the correct number of sources via the higher level of inference, Bayesian model selection. It is followed by estimating the directional information of each source via the lower level of inference, Bayesian parameter estimation. This work formulates signal models using spherical harmonic beamforming that encodes the prior information on the sensor arrays in the form of analytical models with an unknown number of sound sources, and their locations. Available information on differences between the model and the sound signals as well as prior information on directions of arrivals are incorporated based on the principle of the maximum entropy. Two and three simultaneous sound sources have been experimentally tested without prior information on the number of sources. Bayesian inference provides unambiguous estimation on correct numbers of sources followed by the DoA estimations for each individual sound sources. This paper presents the Bayesian formulation, and analysis results to demonstrate the potential usefulness of the model-based Bayesian inference for complex acoustic environments with potentially multiple simultaneous sources.

Fully Bayesian spectral methods for imaging data.

Medical imaging data with thousands of spatially correlated data points are common in many fields. Methods that account for spatial correlation often require cumbersome matrix evaluations which are prohibitive for data of this size, and thus current work has either used low-rank approximations or analyzed data in blocks. We propose a method that accounts for nonstationarity, functional connectivity of distant regions of interest, and local signals, and can be applied to large multi-subject datasets using spectral methods combined with Markov Chain Monte Carlo sampling. We illustrate using simulated data that properly accounting for spatial dependence improves precision of estimates and yields valid statistical inference. We apply the new approach to study associations between cortical thickness and Alzheimer's disease, and find several regions of the cortex where patients with Alzheimer's disease are thinner on average than healthy controls.

Reconstructing anatomy from electro-physiological data.

Here we show how it is possible to make estimates of brain structure based on MEG data. We do this by reconstructing functional estimates onto distorted cortical manifolds parameterised in terms of their spherical harmonics. We demonstrate that both empirical and simulated MEG data give rise to consistent and plausible anatomical estimates. Importantly, the estimation of structure from MEG data can be quantified in terms of millimetres from the true brain structure. We show, for simulated data, that the functional assumptions which are closer to the functional ground-truth give rise to anatomical estimates that are closer to the true anatomy.

Complexity analysis of cortical surface detects changes in future Alzheimer's disease converters.

Alzheimer's disease (AD) is a neurological disorder that creates neurodegenerative changes at several structural and functional levels in human brain tissue. The fractal dimension (FD) is a quantitative parameter that characterizes the morphometric variability of the human brain. In this study, we investigate spherical harmonic-based FD (SHFD), thickness, and local gyrification index (LGI) to assess whether they identify cortical surface abnormalities toward the conversion to AD. We study 33 AD patients, 122 mild cognitive impairment (MCI) patients (50 MCI converters and 29 MCI nonconverters), and 32 healthy controls (HC). SHFD, thickness, and LGI methodology allowed us to perform not only global level but also local level assessments in each cortical surface vertex. First, we found that global SHFD decreased in AD and future MCI converters compared to HC, and in MCI converters compared to MCI nonconverters. Second, we found that local white matter SHFD was reduced in AD compared to HC and MCI mainly in medial temporal lobe. Third, local white-matter SHFD was significantly reduced in MCI converters compared to MCI nonconverters in distributed areas, including the medial frontal lobe. Thickness and LGI metrics presented a reduction in AD compared to HC. Thickness was significantly reduced in MCI converters compared to healthy controls in entorhinal cortex and lateral temporal. In summary, SHFD was the only surface measure showing differences between MCI individuals that will convert or remain stable in the next 4 years. We suggest that SHFD may be an optimal complement to thickness loss analysis in monitoring longitudinal changes in preclinical and clinical stages of AD. Hum Brain Mapp 38:5905-5918, 2017. © 2017 Wiley Periodicals, Inc.

Terrestrial Water Storage in African Hydrological Regimes Derived from GRACE Mission Data: Intercomparison of Spherical Harmonics, Mass Concentration, and Scalar Slepian Methods.

Spherical harmonics (SH) and mascon solutions are the two most common types of solutions for Gravity Recovery and Climate Experiment (GRACE) mass flux observations. However, SH signals are degraded by measurement and leakage errors. Mascon solutions (the Jet Propulsion Laboratory (JPL) release, herein) exhibit weakened signals at submascon resolutions. Both solutions require a scale factor examined by the CLM4.0 model to obtain the actual water storage signal. The Slepian localization method can avoid the SH leakage errors when applied to the basin scale. In this study, we estimate SH errors and scale factors for African hydrological regimes. Then, terrestrial water storage (TWS) in Africa is determined based on Slepian localization and compared with JPL-mascon and SH solutions. The three TWS estimates show good agreement for the TWS of large-sized and humid regimes but present discrepancies for the TWS of medium and small-sized regimes. Slepian localization is an effective method for deriving the TWS of arid zones. The TWS behavior in African regimes and its spatiotemporal variations are then examined. The negative TWS trends in the lower Nile and Sahara at -1.08 and -6.92 Gt/year, respectively, are higher than those previously reported.