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Advances in neuroimaging acquisition protocols and denoising techniques, along with increasing magnetic field strengths, have dramatically improved the temporal signal‐to‐noise ratio (tSNR) in functional magnetic resonance imaging (fMRI). This permits spatial resolution with submillimeter voxel sizes and ultrahigh temporal resolution and opens a route toward performing precision fMRI in the brains of individuals. Yet ultrahigh spatial and temporal resolution comes at a cost: it reduces tSNR and, therefore, the sensitivity to the blood oxygen level‐dependent (BOLD) effect and other functional contrasts across the brain. Here we investigate the potential of various smoothing filters to improve BOLD sensitivity while preserving the spatial accuracy of activated clusters in single‐subject analysis. We introduce adaptive‐weight smoothing with optimized metrics (AWSOM), which addresses this challenge extremely well. AWSOM employs a local inference approach that is as sensitive as cluster‐corrected inference of data smoothed with large Gaussian kernels, but it preserves spatial details across multiple tSNR levels. This is essential for examining whole‐brain fMRI data because tSNR varies across the entire brain, depending on the distance of a brain region from the receiver coil, the type of setup, acquisition protocol, preprocessing, and resolution. We found that cluster correction in single subjects results in inflated family‐wise error and false positive rates. AWSOM effectively suppresses false positives while remaining sensitive even to small clusters of activated voxels. Furthermore, it preserves signal integrity, that is, the relative activation strength of significant voxels, making it a valuable asset for a wide range of fMRI applications. Here we demonstrate these features and make AWSOM freely available to the research community for download. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of the study is to identify differences between axisymmetric diffusion kurtosis imaging (DKI) and standard DKI, their consequences for biophysical parameter estimates, and the protocol choice influence on parameter estimation. Methods: Noise‐free and noisy, synthetic diffusion MRI human brain data is simulated using standard DKI for a standard and the fast "199" acquisition protocol. First the noise‐free "baseline" difference between both DKI models is estimated and the influence of fiber complexity is investigated. Noisy data is used to establish the signal‐to‐noise ratio at which the baseline difference exceeds noise variability. The influence of protocol choices and denoising is investigated. The five axisymmetric DKI tensor metrics (AxTM), the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor are used to compare both DKI models. Additionally, the baseline difference is also estimated for the five parameters of the WMTI‐Watson model. Results: The parallel and perpendicular kurtosis and all of the WMTI–Watson parameters had large baseline differences. Using a Westin or FA mask reduced the number of voxels with large baseline difference, that is, by selecting voxels with less complex fibers. For the noisy data, precision was worsened by the fast "199" protocol but adaptive denoising can help counteract these effects. Conclusion: For the diffusivities and mean of the kurtosis tensor, axisymmetric DKI with a standard protocol delivers similar results as standard DKI. Fiber complexity is one main driver of the baseline differences. Using the "199" protocol worsens precision in noisy data but adaptive denoising mitigates these effects. [ABSTRACT FROM AUTHOR]

The article "Oh yes - research data management" emphasizes the importance of research data management in mathematics. Mathematical data such as literature, articles, proofs, and code must be carefully curated to make them accessible to other mathematicians. The MaRDI guide for research data management provides a framework for this. Various tools and services are introduced for publishing and archiving data, such as GitHub, GitLab, arXiv, and Zenodo. The FAIR principles play an important role in preparing mathematical data. The MaRDI consortium is working on building a national research data infrastructure for mathematics in Germany. [Extracted from the article]

In this paper we discuss the notion of research data for the field of mathematics and report on the status quo of research-data management and planning. A number of decentralized approaches are presented and compared to needs and challenges faced in three use cases from different mathematical subdisciplines. We highlight the importance of tailoring research-data management plans to mathematicians’ research processes and discuss their usage all along the data life cycle. [ABSTRACT FROM AUTHOR]

Purpose: To compare the estimation accuracy of axisymmetric diffusion kurtosis imaging (DKI) and standard DKI in combination with Rician bias correction (RBC). Methods: Axisymmetric DKI is more robust against noise‐induced variation in the measured signal than standard DKI because of its reduced parameter space. However, its susceptibility to Rician noise bias at low signal‐to‐noise ratios (SNR) is unknown. Here, we investigate two main questions: first, does RBC improve estimation accuracy of axisymmetric DKI?; second, is estimation accuracy of axisymmetric DKI increased compared to standard DKI? Estimation accuracy was investigated on the five axisymmetric DKI tensor metrics (AxTM): the parallel and perpendicular diffusivity and kurtosis and mean of the kurtosis tensor, using a noise simulation study based on synthetic data of tissues with varying fiber alignment and in‐vivo data focusing on white matter. Results: RBC mainly increased accuracy for the parallel AxTM in tissues with highly to moderately aligned fibers. For the perpendicular AxTM, axisymmetric DKI without RBC performed slightly better than with RBC. However, the combination of axisymmetric DKI with RBC was the overall best performing algorithm across all five AxTM in white matter and axisymmetric DKI itself substantially improved accuracy in axisymmetric tissues with low fiber alignment. Conclusion: Combining axisymmetric DKI with RBC facilitates accurate DKI parameter estimation at unprecedented low SNRs (≈15$$ \approx 15 $$) in white matter, possibly making it a valuable tool for neuroscience and clinical research studies where scan time is a limited resource. The tools used here are available in the open‐source ACID toolbox for SPM. [ABSTRACT FROM AUTHOR]

Estimation of learning curves is ubiquitously based on proportions of correct responses within moving trial windows. Thereby, it is tacitly assumed that learning performance is constant within the moving windows, which, however, is often not the case. In the present study we demonstrate that violations of this assumption lead to systematic errors in the analysis of learning curves, and we explored the dependency of these errors on window size, different statistical models, and learning phase. To reduce these errors in the analysis of single-subject data as well as on the population level, we propose adequate statistical methods for the estimation of learning curves and the construction of confidence intervals, trial by trial. Applied to data from an avoidance learning experiment with rodents, these methods revealed performance changes occurring at multiple time scales within and across training sessions which were otherwise obscured in the conventional analysis. Our work shows that the proper assessment of the behavioral dynamics of learning at high temporal resolution can shed new light on specific learning processes, and, thus, allows to refine existing learning concepts. It further disambiguates the interpretation of neurophysiological signal changes recorded during training in relation to learning. [ABSTRACT FROM AUTHOR]

Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis for which there is no strong evidence for containing true alternatives. We show control of the family-wise error rate at this first stage of testing. Then, at the second stage, we proceed to test the hypotheses within each non-excluded family and obtain asymptotic control of the FDR within each family at this second stage. Our main mathematical result is that this two-stage strategy implies asymptotic control of the FDR with respect to all hypotheses. In simulations we demonstrate the increased power of this new procedure in comparison with established procedures in situations with highly unbalanced families. Finally, we apply the proposed method to simulated and to real fMRI data. [ABSTRACT FROM AUTHOR]

Background: Common symptoms of multiple sclerosis (MS) such as gait ataxia, poor coordination of the hands, and intention tremor are usually the result of dysfunctionality in the cerebellum. Magnetic resonance imaging (MRI) has frequently failed to detect cerebellar damage in the form of inflammatory lesions in patients presenting with symptoms of cerebellar dysfunction. Objective: To detect microstructural cerebellar tissue alterations in early MS patients with a “normal appearing” cerebellum using diffusion tensor imaging (DTI). Methods: A total of 68 patients with relapsing–remitting MS (RRMS) and without cerebellar lesions and 26 age-matched healthy controls were admitted to high-resolution MRI and DTI to assess microstructure and volume of the cerebellar white matter (CBWM). Results: We found cerebellar fractional anisotropy (FA) and CBWM volume reductions in the group of 68 patients. Interestingly, a subgroup of these patients that was derived by including only patients with early and mild MS (N=23, median age 30 years, median Expanded Disability Status Scale =1.5, median duration 28 months) showed already cerebellar FA but no CBWM volume reductions. FA reductions were correlated with disability, atrophy, and disease duration. Conclusion: “Normal appearing” cerebellar white matter can be damaged in a very early stage of RRMS. DTI seems to be a sensitive tool for detecting this hidden cerebellar damage. [ABSTRACT FROM AUTHOR]

Diffusion Kurtosis Imaging (DKI) is more sensitive to microstructural differences and can be related to more specific micro-scale metrics (e.g., intra-axonal volume fraction) than diffusion tensor imaging (DTI), offering exceptional potential for clinical diagnosis and research into the white and gray matter. Currently DKI is acquired only at low spatial resolution (2-3mm isotropic), because of the lower signal-to-noise ratio (SNR) and higher artifact level associated with the technically more demanding DKI. Higher spatial resolution of about 1mm is required for the characterization of fine white matter pathways or cortical microstructure. We used restricted-field-of-view (rFoV) imaging in combination with advanced post-processing methods to enable unprecedented high-quality, high-resolution DKI (1.2mm isotropic) on a clinical 3T scanner. Post-processing was advanced by developing a novel method for Retrospective Eddy current and Motion ArtifacT Correction in High-resolution, multi-shell diffusion data (REMATCH). Furthermore, we applied a powerful edge preserving denoising method, denoted as multi-shell orientation-position-adaptive smoothing (msPOAS). We demonstrated the feasibility of high-quality, high-resolution DKI and its potential for delineating highly myelinated fiber pathways in the motor cortex. REMATCH performs robustly even at the low SNR level of high-resolution DKI, where standard EC and motion correction failed (i.e., produced incorrectly aligned images) and thus biased the diffusion model fit. We showed that the combination of REMATCH and msPOAS increased the contrast between gray and white matter in mean kurtosis (MK) maps by about 35% and at the same time preserves the original distribution of MK values, whereas standard Gaussian smoothing strongly biases the distribution. [ABSTRACT FROM AUTHOR]

Abstract: Increasing the spatial resolution in functional Magnetic Resonance Imaging (fMRI) inherently lowers the signal-to-noise ratio (SNR). In order to still detect functionally significant activations in high-resolution images, spatial smoothing of the data is required. However, conventional non-adaptive smoothing comes with a reduced effective resolution, foiling the benefit of the higher acquisition resolution. We show how our recently proposed structural adaptive smoothing procedure for functional MRI data can improve signal detection of high-resolution fMRI experiments regardless of the lower SNR. The procedure is evaluated on human visual and sensory–motor mapping experiments. In these applications, the higher resolution could be fully utilized and high-resolution experiments were outperforming normal resolution experiments by means of both statistical significance and information content. [Copyright &y& Elsevier]

In the field of quantitative imaging, the image information at a pixel or voxel in an underlying domain entails crucial information about the imaged matter. This is particularly important in medical imaging applications, such as quantitative magnetic resonance imaging (qMRI), where quantitative maps of biophysical parameters can characterize the imaged tissue and thus lead to more accurate diagnoses. Such quantitative values can also be useful in subsequent, automatized classification tasks in order to discriminate normal from abnormal tissue, for instance. The accurate reconstruction of these quantitative maps is typically achieved by solving two coupled inverse problems which involve a (forward) measurement operator, typically ill‐posed, and a physical process that links the wanted quantitative parameters to the reconstructed qualitative image, given some underlying measurement data. In this review, by considering qMRI as a prototypical application, we provide a mathematically‐oriented overview on how data‐driven approaches can be employed in these inverse problems eventually improving the reconstruction of the associated quantitative maps. [ABSTRACT FROM AUTHOR]

The reconstruction of geometric properties of semiconductor quantum dots (QDs) from imaging of bulk‐like samples (thickness 100‐300 nm) by transmission electron microscopy (TEM) is a difficult problem. A direct reconstruction by solving the tomography problem is not feasible due to the limited image resolution (0.5‐1 nm), the highly nonlinear behavior of the dynamic electron scattering, nonlocal effects due to strain and strong stochastic influences due to uncertainties in the experiment. We present a mathematical model for the numerical simulation of TEM images. This includes elasticity theory to obtain the strain profile coupled with the Darwin‐Howie‐Whelan equations, describing the propagation of the electron wave through the sample. Furthermore, we introduce a novel concept for 3D model‐based geometry reconstruction of QDs from TEM images. The approach includes a geometric model for the QD configuration in real space, a database of simulated TEM images and a statistical procedure for the estimation of the geometric properties and the classification of QD types. [ABSTRACT FROM AUTHOR]

The generation and processing of research data for modeling and simulation is an important part of the scientific work at WIAS. Together with scientific software it plays an essential role for the transfer of mathematical research results to industry or to other scientific disciplines. In the face of the emerging digital science agenda research data is now more and more recognized as an essential foundation for scientific work. The importance of research data is also emphasized by the recent adoption of the 'DFG Guidelines on the Handling of Research Data' by the Deutsche Forschungsgemeinschaft and the Open Data Pilot within the EU Horizon 2020 programme. In this contribution we present our definition of research data in mathematical modeling and simulation and requirements for its management. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Introduction The underlying pathophysiology of neurological complications in patients with hemolytic–uremic syndrome (HUS) remains unclear. It was recently attributed to a direct cytotoxic effect of Shiga toxin 2 (Stx2) in the thalamus. Conventional MRI of patients with Stx2-caused HUS revealed – despite severe neurological symptoms – only mild alterations if any, mostly in the thalamus. Against this background, we questioned: Does diffusion tensor imaging (DTI) capture the thalamic damage better than conventional MRI? Are neurological symptoms and disease course better reflected by thalamic alterations as detected by DTI? Are other brain regions also affected? Methods Three women with serious neurological deficits due to Stx2-associated HUS were admitted to MRI/DTI at disease onset. Two of them were longitudinally examined. Fractional anisotropy (FA) and mean diffusivity were computed to assess Stx2-caused microstructural damage. Results Compared to 90 healthy women, all three patients had significantly reduced thalamic FA. Thalamic mean diffusivity was only reduced in two patients. DTI of the longitudinally examined women demonstrated slow normalization of thalamic FA, which was paralleled by clinical improvement. Conclusion Whereas conventional MRI only shows slight alterations based on subjective evaluation, DTI permits quantitative , objective , and longitudinal assessment of cytotoxic cerebral damage in individual patients. [ABSTRACT FROM AUTHOR]