Vision Transformer (ViT) applied to structural magnetic resonance images has demonstrated success in the diagnosis of Alzheimer's disease (AD) and mild cognitive impairment (MCI). However, three key challenges have yet to be well addressed: 1) ViT requires a large labeled dataset to mitigate overfitting while most of the current AD-related sMRI data fall short in the sample sizes. 2) ViT neglects the within-patch feature learning, e.g., local brain atrophy, which is crucial for AD diagnosis. 3) While ViT can enhance capturing local features by reducing the patch size and increasing the number of patches, the computational complexity of ViT quadratically increases with the number of patches with unbearable overhead. To this end, this paper proposes a 3D-convolutional neural network (CNN) Enhanced Multiscale Progressive ViT (3D-CNN-MPVT). First, a 3D-CNN is pre-trained on sMRI data to extract detailed local image features and alleviate overfitting. Second, an MPVT module is proposed with an inner CNN module to explicitly characterize the within-patch interactions that are conducive to AD diagnosis. Third, a stitch operation is proposed to merge cross-patch features and progressively reduce the number of patches. The inner CNN alongside the stitch operation in the MPTV module enhances local feature characterization while mitigating computational costs. Evaluations using the Alzheimer's Disease Neuroimaging Initiative dataset with 6610 scans and the Open Access Series of Imaging Studies-3 with 1866 scans demonstrated its superior performance. With minimal preprocessing, our approach achieved an impressive 90% accuracy and 80% in AD classification and MCI conversion prediction, surpassing recent baselines.

Functional magnetic resonance imaging (fMRI) enables non-invasive brain disorder classification by capturing blood-oxygen-level-dependent (BOLD) signals. However, most existing methods rely on functional connectivity (FC) via Pearson correlation, which reduces 4D BOLD signals to static 2D matrices-discarding temporal dynamics and capturing only linear inter-regional relationships. In this work, we benchmark state-of-the-art temporal models (e.g., time-series models: PatchTST, TimesNet, TimeMixer) on raw BOLD signals across five public datasets. Results show these models consistently outperform traditional FC-based approaches, highlighting the value of directly modeling temporal information such as cycle-like oscillatory fluctuations and drift-like slow baseline trends. Building on this insight, we propose DeCI, a simple yet effective framework that integrates two key principles: (i) Cycle and Drift Decomposition to disentangle cycle and drift within each ROI (Region of Interest); and (ii) Channel-Independence to model each ROI separately, improving robustness and reducing overfitting. Extensive experiments demonstrate that DeCI achieves superior classification accuracy and generalization compared to both FC-based and temporal baselines. Our findings advocate for a shift toward end-to-end temporal modeling in fMRI analysis to better capture complex brain dynamics. The code is available at https://github.com/Levi-Ackman/DeCI.

Diffusion-weighted imaging (DWI) enables non-invasive characterization of tissue microstructure, yet acquiring densely sampled q-space data remains time-consuming and impractical in many clinical settings. Existing deep learning methods are typically constrained by fixed q-space sampling, limiting their adaptability to variable sampling scenarios. In this paper, we propose a Q-space Guided Multi-Modal Translation Network (Q-MMTN) for synthesizing multi-shell, high-angular resolution DWI (MS-HARDI) from flexible q-space sampling, leveraging commonly acquired structural data (e.g., T1- and T2-weighted MRI). Q-MMTN integrates the hybrid encoder and multi-modal attention fusion mechanism to effectively extract both local and global complementary information from multiple modalities. This design enhances feature representation and, together with a flexible q-space-aware embedding, enables dynamic modulation of internal features without relying on fixed sampling schemes. Additionally, we introduce a set of task-specific constraints, including adversarial, reconstruction, and anatomical consistency losses, which jointly enforce anatomical fidelity and signal realism. These constraints guide Q-MMTN to accurately capture the intrinsic and nonlinear relationships between directional DWI signals and q-space information. Extensive experiments across four lifespan datasets of children, adolescents, young and older adults demonstrate that Q-MMTN outperforms existing methods, including 1D-qDL, 2D-qDL, MESC-SD, and Q-GAN in estimating parameter maps and fiber tracts with fine-grained anatomical details. Notably, its ability to accommodate flexible q-space sampling highlights its potential as a promising toolkit for clinical and research applications. Our code is available at https://github.com/Idea89560041/Q-MMTN.

Diffusion-weighted imaging (DWI) is a key modality for studying brain microstructure, but its signals are highly susceptible to noise due to the thermal motion of water molecules and interactions with tissue microarchitecture, leading to significant signal attenuation and a low signal-to-noise ratio (SNR). In this paper, we propose a novel approach, a Cycle-Conditional Diffusion Model (Cycle-CDM) using unpaired data learning, aimed at improving DWI quality and reliability through noise correction. Cycle-CDM leverages a cycle-consistent translation architecture to bridge the domain gap between noise-contaminated and noise-free DWIs, enabling the restoration of high-quality images without requiring paired datasets. By utilizing two conditional diffusion models, Cycle-CDM establishes data interrelationships between the two types of DWIs, while incorporating synthesized anatomical priors from the cycle translation process to guide noise removal. In addition, we introduce specific constraints to preserve anatomical fidelity, allowing Cycle-CDM to effectively learn the underlying noise distribution and achieve accurate denoising. Our experiments conducted on simulated datasets, as well as children and adolescents' datasets with strong clinical relevance. Our results demonstrate that Cycle-CDM outperforms comparative methods, such as U-Net, CycleGAN, Pix2Pix, MUNIT and MPPCA, in terms of noise correction performance. We demonstrated that Cycle-CDM can be generalized to DWIs with head motion when they were acquired using different MRI scannsers. Importantly, the denoised DWI data produced by Cycle-CDM exhibit accurate preservation of underlying tissue microstructure, thus substantially improving their medical applicability.

Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and $k$k-simplices, enabling the definition of graph-structured data on any $k$k-simplex. We design a novel Hodge-Laplacian heterogeneous graph attention network (HL-HGAT) to learn heterogeneous signal representations across $k$k-simplices. The HL-HGAT incorporates three key components: HL convolutional filters (HL-filters), simplicial projection (SP), and simplicial attention pooling (SAP) operators, applied to $k$k-simplices. HL-filters leverage the unique topology of $k$k-simplices encoded by the Hodge-Laplacian (HL) operator, operating within the spectral domain of the $k$k-th HL operator. To address computation challenges, we introduce a polynomial approximation for HL-filters, exhibiting spatial localization properties. Additionally, we propose a pooling operator to coarsen $k$k-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices. The HL-HGAT is comprehensively evaluated across diverse graph applications, including NP-hard problems, graph multi-label and classification challenges, and graph regression tasks in logistics, computer vision, biology, chemistry, and neuroscience. The results demonstrate the model's efficacy and versatility in handling a wide range of graph-based scenarios.

The linear mixed-effects model is commonly utilized to interpret longitudinal data, characterizing both the global longitudinal trajectory across all observations and longitudinal trajectories within individuals. However, characterizing these trajectories in high-dimensional longitudinal data presents a challenge. To address this, our study proposes a novel approach, Unsupervised Orthogonal Mixed-Effects Trajectory Modeling (UOMETM), that leverages unsupervised learning to generate latent representations of both global and individual trajectories. We design an autoencoder with a latent space where an orthogonal constraint is imposed to separate the space of global trajectories from individual trajectories. We also devise a cross-reconstruction loss to ensure consistency of global trajectories and enhance the orthogonality between representation spaces. To evaluate UOMETM, we conducted simulation experiments on images to verify that every component functions as intended. Furthermore, we evaluated its performance and robustness using longitudinal brain cortical thickness from two Alzheimer's disease (AD) datasets. Comparative analyses with state-of-the-art methods revealed UOMETM's superiority in identifying global and individual longitudinal patterns, achieving a lower reconstruction error, superior orthogonality, and higher accuracy in AD classification and conversion forecasting. Remarkably, we found that the space of global trajectories did not significantly contribute to AD classification compared to the space of individual trajectories, emphasizing their clear separation. Moreover, our model exhibited satisfactory generalization and robustness across different datasets. The study shows the outstanding performance and potential clinical use of UOMETM in the context of longitudinal data analysis.

In recent years, deep learning has gained momentum in computer-aided Alzheimer's Disease (AD) diagnosis. This study introduces a novel approach, Monte Carlo Ensemble Vision Transformer (MC-ViT), which develops an ensemble approach with Vision transformer (ViT). Instead of using traditional ensemble methods that deploy multiple learners, our approach employs a single vision transformer learner. By harnessing Monte Carlo sampling, this method produces a broad spectrum of classification decisions, enhancing the MC-ViT performance. This novel technique adeptly overcomes the limitation of 3D patch convolutional neural networks that only characterize partial of the whole brain anatomy, paving the way for a neural network adept at discerning 3D inter-feature correlations. Evaluations using the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset with 7199 scans and Open Access Series of Imaging Studies-3 (OASIS-3) with 1992 scans showcased its performance. With minimal preprocessing, our approach achieved an impressive 90% accuracy in AD classification, surpassing both 2D-slice CNNs and 3D CNNs.

We develop a deep learning framework, spatio-temporal directed acyclic graph with attention mechanisms (ST-DAG-Att), to predict cognition and disease using functional magnetic resonance imaging (fMRI). This ST-DAG-Att framework comprises of two neural networks, (1) spatio-temporal graph convolutional network (ST-graph-conv) to learn the spatial and temporal information of functional time series at multiple temporal and spatial graph scales, where the graph is represented by the brain functional network, the spatial convolution is over the space of this graph, and the temporal convolution is over the time dimension; (2) functional connectivity convolutional network (FC-conv) to learn functional connectivity features, where the functional connectivity is derived from embedded multi-scale fMRI time series and the convolutional operation is applied along both edge and node dimensions of the brain functional network. This framework also consists of an attention component, i.e., functional connectivity-based spatial attention (FC-SAtt), that generates a spatial attention map through learning the local dependency among high-level features of functional connectivity and emphasizing meaningful brain regions. Moreover, both the ST-graph-conv and FC-conv networks are designed as feed-forward models structured as directed acyclic graphs (DAGs). Our experiments employ two large-scale datasets, Adolescent Brain Cognitive Development (ABCD, n=7693) and Open Access Series of Imaging Study-3 (OASIS-3, n=1786). Our results show that the ST-DAG-Att model is generalizable from cognition prediction to age prediction. It is robust to independent samples obtained from different sites of the ABCD study. It outperforms the existing machine learning techniques, including support vector regression (SVR), elastic net's mixture with random forest, spatio-temporal graph convolution, and BrainNetCNN.

Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate numerical scheme to solve heat diffusion on surface meshes. This is achieved by approximating the heat kernel convolution using high degree orthogonal polynomials in the spectral domain. We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve heat diffusion on a manifold for the first time. The proposed fast polynomial approximation scheme avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large mesh size, and the numerical instability associated with the finite element method based diffusion solvers. The proposed method is applied in localizing the male and female differences in cortical sulcal and gyral graph patterns obtained from MRI in an innovative way. The MATLAB code is available at http://www.stat.wisc.edu/~mchung/chebyshev.

We present a set of multiscale frame-based kernels that can be used to construct diffeomorphic transformation in the large deformation diffeomorphic metric mapping (LDDMM) framework. We construct multiscale kernels via compact wavelet frames that are equipped with the hierarchical multiresolution analysis. We show that these kernels under certain conditions can form reproducing kernel Hilbert spaces of smooth velocity fields and hence can be used to generate multiscale diffeomorphic transformation for LDDMM. As a proof of concept, we incorporate these kernels in the LDDMM framework. We show the improvement of whole brain mapping accuracy using the LDDMM with frame-based kernels in comparison to that obtained using the LDDMM with Gaussian kernels. Moreover, we evaluate whole brain mapping accuracy of the LDDMM with frame-based kernels against that obtained from the 14 brain mapping methods given by Klein et al.. Our results suggest that the LDDMM with frame-based kernels has the potential to outperform the 14 brain mapping methods for whole brain mapping.

Brain surface registration is an important tool for characterizing cortical anatomical variations and understanding their roles in normal cortical development and psychiatric diseases. However, surface registration remains challenging due to complicated cortical anatomy and its large differences across individuals. In this paper, we propose a fast coarse-to-fine algorithm for surface registration by adapting the large diffeomorphic deformation metric mapping (LDDMM) framework for surface mapping and show improvements in speed and accuracy via a multiresolution analysis of surface meshes and the construction of multiresolution diffeomorphic transformations. The proposed method constructs a family of multiresolution meshes that are used as natural sparse priors of the cortical morphology. At varying resolutions, these meshes act as anchor points where the parameterization of multiresolution deformation vector fields can be supported, allowing the construction of a bundle of multiresolution deformation fields, each originating from a different resolution. Using a coarse-to-fine approach, we show a potential reduction in computation cost along with improvements in sulcal alignment when compared with LDDMM surface mapping.

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.

We first propose a large deformation diffeomorphic metric mapping algorithm to align multiple b-value diffusion weighted imaging (mDWI) data, specifically acquired via hybrid diffusion imaging (HYDI). We denote this algorithm as LDDMM-HYDI. We then propose a Bayesian probabilistic model for estimating the white matter atlas from HYDIs. We adopt the work given in Hosseinbor et al. (2013) and represent the q-space diffusion signal with the Bessel Fourier orientation reconstruction (BFOR) signal basis. The BFOR framework provides the representation of mDWI in the q-space and the analytic form of the emsemble average propagator (EAP) reconstruction, as well as reduces memory requirement. In addition, since the BFOR signal basis is orthonormal, the L(2) norm that quantifies the differences in the q-space signals of any two mDWI datasets can be easily computed as the sum of the squared differences in the BFOR expansion coefficients. In this work, we show that the reorientation of the q-space signal due to spatial transformation can be easily defined on the BFOR signal basis. We incorporate the BFOR signal basis into the LDDMM framework and derive the gradient descent algorithm for LDDMM-HYDI with explicit orientation optimization. Additionally, we extend the previous Bayesian atlas estimation framework for scalar-valued images to HYDIs and derive the expectation-maximization algorithm for solving the HYDI atlas estimation problem. Using real HYDI datasets, we show that the Bayesian model generates the white matter atlas with anatomical details. Moreover, we show that it is important to consider the variation of mDWI reorientation due to a small change in diffeomorphic transformation in the LDDMM-HYDI optimization and to incorporate the full information of HYDI for aligning mDWI. Finally, we show that the LDDMM-HYDI outperforms the LDDMM algorithm with diffusion tensors generated from each shell of HYDI.

In this paper, we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images (HARDI) characterized by orientation distribution functions (ODFs). Our proposed algorithm seeks an optimal diffeomorphism of large deformation between two ODF fields in a spatial volume domain and at the same time, locally reorients an ODF in a manner such that it remains consistent with the surrounding anatomical structure. To this end, we first review the Riemannian manifold of ODFs. We then define the reorientation of an ODF when an affine transformation is applied and subsequently, define the diffeomorphic group action to be applied on the ODF based on this reorientation. We incorporate the Riemannian metric of ODFs for quantifying the similarity of two HARDI images into a variational problem defined under the large deformation diffeomorphic metric mapping framework. We finally derive the gradient of the cost function in both Riemannian spaces of diffeomorphisms and the ODFs, and present its numerical implementation. Both synthetic and real brain HARDI data are used to illustrate the performance of our registration algorithm.

We present a new diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Unlike existing LDDMM approaches, this new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorphic shape space is represented by a linear space of initial momenta of diffeomorphic geodesic flows from a fixed template. In addition, for the first time, the diffeomorphic mapping is formulated within a decision-theoretic scheme based on Bayesian modeling in which an empirical shape prior is characterized by a low dimensional Gaussian distribution on initial momentum. This is achieved using principal component analysis (PCA) to construct the eigenspace of the initial momentum. A likelihood function is formulated as the conditional probability of observing surfaces given any particular value of the initial momentum, which is modeled as a random field of vector-valued measures characterizing the geometry of surfaces. We define the diffeomorphic mapping as a problem that maximizes a posterior distribution of the initial momentum given observable surfaces over the eigenspace of the initial momentum. We demonstrate the stability of the initial momentum eigenspace when altering training samples using a bootstrapping method. We then validate the mapping accuracy and show robustness to outliers whose shape variation is not incorporated into the shape prior.

Brain extraction is an important preprocessing step for further processing (e.g., registration and morphometric analysis) of brain MRI data. Due to the operator-dependent and time-consuming nature of manual extraction, automated or semi-automated methods are essential for large-scale studies. Automatic methods are widely available for human brain imaging, but they are not optimized for rodent brains and hence may not perform well. To date, little work has been done on rodent brain extraction. We present an extended pulse-coupled neural network algorithm that operates in 3-D on the entire image volume. We evaluated its performance under varying SNR and resolution and tested this method against the brain-surface extractor (BSE) and a level-set algorithm proposed for mouse brain. The results show that this method outperforms existing methods and is robust under low SNR and with partial volume effects at lower resolutions. Together with the advantage of minimal user intervention, this method will facilitate automatic processing of large-scale rodent brain studies.

Atlas-driven morphometric analysis has received great attention for studying anatomical shape variation across clinical populations in neuroimaging research as it provides a local coordinate representation for understanding the family of anatomic observations. We present a procedure for generating atlas of subcortical and ventricular structures, including amygdala, hippocampus, caudate, putamen, globus pallidus, thalamus, and lateral ventricles, using the large deformation diffeomorphic metric atlas generation algorithm. The atlas was built based on manually labeled volumes of 41 subjects randomly selected from the database of Open Access Series of Imaging Studies (OASIS, 10 young adults, 10 middle-age adults, 10 healthy elders, and 11 patients with dementia). We show that the estimated atlas is representative of the population in terms of its metric distance to each individual subject in the population. In the application of detecting shape variations, using the estimated atlas may potentially increase statistical power in identifying group shape difference when comparing with using a single subject atlas. In shape-based classification, the metric distances between subjects and each of within-class estimated atlases construct a shape feature space, which allows for performing a variety of classification algorithms to distinguish anatomies.

Functional and structural maps, such as a curvature, cortical thickness, and functional magnetic resonance imaging (MRI) maps, indexed over the local coordinates of the cortical manifold play an important role in neuropsychiatric studies. Due to the highly convoluted nature of the cerebral cortex and image quality, these functions are generally uninterpretable without proper methods of association and smoothness onto the local coordinate system. In this paper, we generalized the spline smoothing problem (Wahba, 1990) from a sphere to any arbitrary two-dimensional (2-D) manifold with boundaries. We first seek a numerical solution to orthonormal basis functions of the Laplace-Beltrami (LB) operator with Neumann boundary conditions for a 2-D manifold M then solve the spline smoothing problem in a reproducing kernel Hilbert space (r.k.h.s.) of real-valued functions on manifold M with kernel constructed from the basis functions. The explicit discrete LB representation is derived using the finite element method calculated directly on the manifold coordinates so that finding discrete LB orthonormal basis functions is equivalent to solving an algebraic eigenvalue problem. And then smoothed functions in r.k.h.s can be represented as a linear combination of the basis functions. We demonstrate numerical solutions of spherical harmonics on a unit sphere and brain orthonormal basis functions on a planum temporale manifold. Then synthetic data is used to quantify the goodness of the smoothness compared with the ground truth and discuss how many basis functions should be incorporated in the smoothing. We present applications of our approach to smoothing sulcal mean curvature, cortical thickness, and functional statistical maps on submanifolds of the neocortex.

The human cerebral cortex is a laminar structure about 3 mm thick, and is easily visualized with current magnetic resonance (MR) technology. The thickness of the cortex varies locally by region, and is likely to be influenced by such factors as development, disease and aging. Thus, accurate measurements of local cortical thickness are likely to be of interest to other researchers. We develop a parametric stochastic model relating the laminar structure of local regions of the cerebral cortex to MR image data. Parameters of the model include local thickness, and statistics describing white, gray and cerebrospinal fluid (CSF) image intensity values as a function of the normal distance from the center of a voxel to a local coordinate system anchored at the gray/white matter interface. Our fundamental data object, the intensity-distance histogram (IDH), is a two-dimensional (2-D) generalization of the conventional 1-D image intensity histogram, which indexes voxels not only by their intensity value, but also by their normal distance to the gray/white interface. We model the IDH empirically as a marked Poisson process with marking process a Gaussian random field model of image intensity indexed against normal distance. In this paper, we relate the parameters of the IDH model to the local geometry of the cortex. A maximum-likelihood framework estimates the parameters of the model from the data. Here, we show estimates of these parameters for 10 volumes in the posterior cingulate, and 6 volumes in the anterior and posterior banks of the central sulcus. The accuracy of the estimates is quantified via Cramer-Rao bounds. We believe that this relatively crude model can be extended in a straightforward fashion to other biologically and theoretically interesting problems such as segmentation, surface area estimation, and estimating the thickness distribution in a variety of biologically relevant contexts.