Characterizing age-related alterations in brain networks is crucial for understanding aging trajectories and identifying deviations indicative of neurodegenerative disorders, such as Alzheimer's disease. In this study, we developed a Fully Hyperbolic Neural Network (FHNN) to embed functional brain connectivity graphs derived from magnetoencephalography (MEG) data into low dimensions on a Lorentz model of hyperbolic space. Using this model, we computed hyperbolic embeddings of the MEG brain networks of 587 individuals from the Cambridge Centre for Ageing and Neuroscience (Cam-CAN) dataset. Notably, we leveraged a unique metric-the radius of the node embeddings-which effectively captures the hierarchical organization of the brain, to characterize subtle hierarchical organizational changes in various brain subnetworks attributed to the aging process. Our findings revealed that a considerable number of subnetworks exhibited a reduction in hierarchy during aging, with some showing gradual changes and others undergoing rapid transformations in the elderly. Moreover, we demonstrated that hyperbolic features outperform traditional graph-theoretic measures in capturing age-related information in brain networks. Overall, our study represents the first evaluation of hyperbolic embeddings in MEG brain networks for studying aging trajectories, shedding light on critical regions undergoing significant age-related alterations in the large cohort of the Cam-CAN dataset.

An expansive area of research focuses on discerning patterns of alterations in functional brain networks from the early stages of Alzheimer's disease, even at the subjective cognitive decline (SCD) stage. Here, we developed a novel hyperbolic MEG brain network embedding framework for transforming high-dimensional complex MEG brain networks into lower-dimensional hyperbolic representations. Using this model, we computed hyperbolic embeddings of the MEG brain networks of two distinct participant groups: individuals with SCD and healthy controls. We demonstrated that these embeddings preserve both local and global geometric information, presenting reduced distortion compared to rival models, even when brain networks are mapped into low-dimensional spaces. In addition, our findings showed that the hyperbolic embeddings encompass unique SCD-related information that improves the discriminatory power above and beyond that of connectivity features alone. Notably, we introduced a unique metric-the radius of the node embeddings-which effectively proxies the hierarchical organization of the brain. Using this metric, we identified subtle hierarchy organizational differences between the two participant groups, suggesting increased hierarchy in the dorsal attention, frontoparietal, and ventral attention subnetworks among the SCD group. Last, we assessed the correlation between these hierarchical variations and cognitive assessment scores, revealing associations with diminished performance across multiple cognitive evaluations in the SCD group. Overall, this study presents the first evaluation of hyperbolic embeddings of MEG brain networks, offering novel insights into brain organization, cognitive decline, and potential diagnostic avenues of Alzheimer's disease.

Identifying heterogeneous cognitive impairment markers at an early stage is vital for Alzheimer's disease diagnosis. However, due to complex and uncertain brain connectivity features in the cognitive domains, it remains challenging to quantify functional brain connectomic changes during non-pharmacological interventions for amnestic mild cognitive impairment (aMCI) patients. We present a quantitative method for functional brain network analysis of fMRI data based on the multi-graph unsupervised Gaussian embedding method (MG2G). This neural network-based model can effectively learn low-dimensional Gaussian distributions from the original high-dimensional sparse functional brain networks, quantify uncertainties in link prediction, and discover the intrinsic dimensionality of brain networks. Using the Wasserstein distance to measure probabilistic changes, we discovered that brain regions in the default mode network and somatosensory/somatomotor hand, fronto-parietal task control, memory retrieval, and visual and dorsal attention systems had relatively large variations during non-pharmacological training, which might provide distinct biomarkers for fine-grained monitoring of aMCI cognitive alteration. An important finding of our study is the ability of the new method to capture subtle changes for individual patients before and after short-term intervention. More broadly, the MG2G method can be used in studying multiple brain disorders and injuries, e.g., in Parkinson's disease or traumatic brain injury (TBI), and hence it will be useful to the wider neuroscience community.

Manually labeled landmark sets are often required as inputs for landmark-based image registration. Identifying an optimal subset of landmarks from a training dataset may be useful in reducing the labor intensive task of manual labeling. In this paper, we present a new problem and a method to solve it: given a set of N landmarks, find the k(< N) best landmarks such that aligning these k landmarks that produce the best overall alignment of all N landmarks. The resulting procedure allows us to select a reduced number of landmarks to be labeled as a part of the registration procedure. We apply this methodology to the problem of registering cerebral cortical surfaces extracted from MRI data. We use manually traced sulcal curves as landmarks in performing inter-subject registration of these surfaces. To minimize the error metric, we analyze the correlation structure of the sulcal errors in the landmark points by modeling them as a multivariate Gaussian process. Selection of the optimal subset of sulcal curves is performed by computing the error variance for the subset of unconstrained landmarks conditioned on the constrained set. We show that the registration error predicted by our method closely matches the actual registration error. The method determines optimal curve subsets of any given size with minimal registration error.

Detection of small lesions in fluorodeoxyglucose (FDG) positron emission tomography (PET) is limited by image resolution and low signal to noise ratio. We have previously described a matched subspace detection method that uses the time activity curve to distinguish tumors from background in dynamic FDG PET. Applying this algorithm on a voxel by voxel basis throughout the dynamic image produces a test statistic image or "map" which on thresholding indicates the potential locations of secondary or metastatic tumors. In this paper, we describe a thresholding method that controls familywise error rate (FWER) for the matched subspace detection statistical map. The method involves three steps. First, the PET image is segmented into several homogeneous regions. Then, the statistical map is normalized to a zero mean unit variance Gaussian random field. Finally, the images are thresholded at a fixed FWER by estimating their spatial smoothness and applying a random field theory maximum statistic approach. We evaluate this thresholding method using digital phantoms generated from clinical dynamic images. We also present an application of the proposed approach to clinical PET data from a breast cancer patient with metastatic disease.