Multi-resolutional brain network filtering and analysis via wavelets on non-Euclidean space

Association of longitudinal white matter degeneration and cerebrospinal fluid biomarkers of neurodegeneration, inflammation and Alzheimer's disease in late-middle-aged adults

Alzheimer's disease (AD) is characterized by substantial neurodegeneration, including both cortical atrophy and loss of underlying white matter fiber tracts. Understanding longitudinal alterations to white matter may provide new insights into trajectories of brain change in both healthy aging and AD, and fluid biomarkers may be particularly useful in this effort. To examine this, 151 late-middle-aged participants enriched with risk for AD with at least one lumbar puncture and two diffusion tensor imaging (DTI) scans were selected for analysis from two large observational and longitudinally followed cohorts. Cerebrospinal fluid (CSF) was assayed for biomarkers of AD-specific pathology (phosphorylated-tau/Aβ42 ratio), axonal degeneration (neurofilament light chain protein, NFL), dendritic degeneration (neurogranin), and inflammation (chitinase-3-like protein 1, YKL-40). Linear mixed effects models were performed to test the hypothesis that biomarkers for AD, neurodegeneration, and inflammation, or two-year change in those biomarkers, would be associated with worse white matter health overall and/or progressively worsening white matter health over time. At baseline in the cingulum, phosphorylated-tau/Aβ42 was associated with higher mean diffusivity (MD) overall (intercept) and YKL-40 was associated with increases in MD over time. Two-year change in neurogranin was associated with higher mean diffusivity and lower fractional anisotropy overall (intercepts) across white matter in the entire brain and in the cingulum. These findings suggest that biomarkers for AD, neurodegeneration, and inflammation are potentially important indicators of declining white matter health in a cognitively healthy, late-middle-aged cohort.

Associations Between Positron Emission Tomography Amyloid Pathology and Diffusion Tensor Imaging Brain Connectivity in Pre-Clinical Alzheimer's Disease

Characterizing Alzheimer's disease (AD) at pre-clinical stages is crucial for initiating early treatment strategies. It is widely accepted that amyloid accumulation is a primary pathological event in AD. Also, loss of connectivity between brain regions is suspected of contributing to cognitive decline, but studies that test these associations using either local (i.e., individual edges) or global (i.e., modularity) connectivity measures may be limited. In this study, we utilized data acquired from 139 cognitively unimpaired participants. Sixteen gray matter (GM) regions known to be affected by AD were selected for analysis. For each of the 16 regions, the effect of amyloid burden, measured using Pittsburgh Compound B (PiB) positron emission tomography, on each of the 1761 brain network connections derived from diffusion tensor imaging (DTI) connecting 162 GM regions, was investigated. Applying our unique multiresolution statistical analysis called the Wavelet Connectivity Signature (WaCS), this study demonstrates the relationship between amyloid burden and structural brain connectivity as assessed with DTI. Our statistical analysis using WaCS shows that in 15 of 16 GM regions, statistically significant relationships between amyloid burden in those regions and structural connectivity networks were observed. After applying multiple testing correction, 10 unique structural brain connections were found to be significantly associated with amyloid accumulation. For 7 of those 10 network connections, the decrease in their network connection strength indexed by fractional anisotropy was, in turn, associated with lower cognitive function, providing evidence that AD-related structural connectivity loss is a correlate of cognitive decline.

Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks

There is a great deal of interest in using large scale brain imaging studies to understand how brain connectivity evolves over time for an individual and how it varies over different levels/quantiles of cognitive function. To do so, one typically performs so-called tractography procedures on diffusion MR brain images and derives measures of brain connectivity expressed as graphs. The nodes correspond to distinct brain regions and the edges encode the strength of the connection. The scientific interest is in characterizing the evolution of these graphs over time or from healthy individuals to diseased. We pose this important question in terms of the Laplacian of the connectivity graphs derived from various longitudinal or disease time points - quantifying its progression is then expressed in terms of coupling the harmonic bases of a full set of Laplacians. We derive a coupled system of generalized eigenvalue problems (and corresponding numerical optimization schemes) whose solution helps characterize the full life cycle of brain connectivity evolution in a given dataset. Finally, we show a set of results on a diffusion MR imaging dataset of middle aged people at risk for Alzheimer's disease (AD), who are cognitively healthy. In such asymptomatic adults, we find that a framework for characterizing brain connectivity evolution provides the ability to predict cognitive scores for individual subjects, and for estimating the progression of participant's brain connectivity into the future.

Characterization of Aspartate Kinase from Corynebacterium pekinense and the Critical Site of Arg169

Aspartate kinase (AK) is the key enzyme in the biosynthesis of aspartate-derived amino acids. Recombinant AK was efficiently purified and systematically characterized through analysis under optimal conditions combined with steady-state kinetics study. Homogeneous AK was predicted as a decamer with a molecular weight of ~48 kDa and a half-life of 4.5 h. The enzymatic activity was enhanced by ethanol and Ni²⁺. Moreover, steady-state kinetic study confirmed that AK is an allosteric enzyme, and its activity was inhibited by allosteric inhibitors, such as Lys, Met, and Thr. Theoretical results indicated the binding mode of AK and showed that Arg169 is an important residue in substrate binding, catalytic domain, and inhibitor binding. The values of the kinetic parameter V_max of R169 mutants, namely, R169Y, R169P, R169D, and R169H AK, with l-aspartate as the substrate, were 4.71-, 2.25-, 2.57-, and 2.13-fold higher, respectively, than that of the wild-type AK. Furthermore, experimental and theoretical data showed that Arg169 formed a hydrogen bond with Glu92, which functions as the entrance gate. This study provides a basis to develop new enzymes and elucidate the corresponding amino acid production.

Multi-resolution statistical analysis of brain connectivity graphs in preclinical Alzheimer's disease

There is significant interest, both from basic and applied research perspectives, in understanding how structural/functional connectivity changes can explain behavioral symptoms and predict decline in neurodegenerative diseases such as Alzheimer's disease (AD). The first step in most such analyses is to encode the connectivity information as a graph; then, one may perform statistical inference on various 'global' graph theoretic summary measures (e.g., modularity, graph diameter) and/or at the level of individual edges (or connections). For AD in particular, clear differences in connectivity at the dementia stage of the disease (relative to healthy controls) have been identified. Despite such findings, AD-related connectivity changes in preclinical disease remain poorly characterized. Such preclinical datasets are typically smaller and group differences are weaker. In this paper, we propose a new multi-resolution method for performing statistical analysis of connectivity networks/graphs derived from neuroimaging data. At the high level, the method occupies the middle ground between the two contrasts - that is, to analyze global graph summary measures (global) or connectivity strengths or correlations for individual edges similar to voxel based analysis (local). Instead, our strategy derives a Wavelet representation at each primitive (connection edge) which captures the graph context at multiple resolutions. We provide extensive empirical evidence of how this framework offers improved statistical power by analyzing two distinct AD datasets. Here, connectivity is derived from diffusion tensor magnetic resonance images by running a tractography routine. We first present results showing significant connectivity differences between AD patients and controls that were not evident using standard approaches. Later, we show results on populations that are not diagnosed with AD but have a positive family history risk of AD where our algorithm helps in identifying potentially subtle differences between patient groups. We also give an easy to deploy open source implementation of the algorithm for use within studies of connectivity in AD and other neurodegenerative disorders.

Spectral Laplace-Beltrami wavelets with applications in medical images

The spectral graph wavelet transform (SGWT) has recently been developed to compute wavelet transforms of functions defined on non-Euclidean spaces such as graphs. By capitalizing on the established framework of the SGWT, we adopt a fast and efficient computation of a discretized Laplace-Beltrami (LB) operator that allows its extension from arbitrary graphs to differentiable and closed 2-D manifolds (smooth surfaces embedded in the 3-D Euclidean space). This particular class of manifolds are widely used in bioimaging to characterize the morphology of cells, tissues, and organs. They are often discretized into triangular meshes, providing additional geometric information apart from simple nodes and weighted connections in graphs. In comparison with the SGWT, the wavelet bases constructed with the LB operator are spatially localized with a more uniform "spread" with respect to underlying curvature of the surface. In our experiments, we first use synthetic data to show that traditional applications of wavelets in smoothing and edge detectio can be done using the wavelet bases constructed with the LB operator. Second, we show that multi-resolutional capabilities of the proposed framework are applicable in the classification of Alzheimer's patients with normal subjects using hippocampal shapes. Wavelet transforms of the hippocampal shape deformations at finer resolutions registered higher sensitivity (96%) and specificity (90%) than the classification results obtained from the direct usage of hippocampal shape deformations. In addition, the Laplace-Beltrami method requires consistently a smaller number of principal components (to retain a fixed variance) at higher resolution as compared to the binary and weighted graph Laplacians, demonstrating the potential of the wavelet bases in adapting to the geometry of the underlying manifold.

MULTI-RESOLUTION STATISTICAL ANALYSIS ON GRAPH STRUCTURED DATA IN NEUROIMAGING

Statistical data analysis plays a major role in discovering structural and functional imaging phenotypes for mental disorders such as Alzheimer's disease (AD). The goal here is to identify, ideally early on, which regions in the brain show abnormal variations with a disorder. To make the method more sensitive, we rely on a multi-resolutional perspective of the given data. Since the underlying imaging data (such as cortical surfaces and connectomes) are naturally represented in the form of weighted graphs which lie in a non-Euclidean space, we introduce recent work from the harmonics literature to derive an effective multi-scale descriptor using wavelets on graphs that characterize the local context at each data point. Using this descriptor, we demonstrate experiments where we identify significant differences between AD and control populations using cortical surface data and tractography derived graphs/networks.