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Fluid-structure interaction (FSI) simulation of biological systems presents significant computational challenges, particularly for applications involving large structural deformations and contact mechanics, such as heart valve dynamics. Traditional arbitrary Lagrangian-Eulerian methods encounter fundamental difficulties with such problems due to mesh distortion, motivating immersed techniques. This work presents a novel open-source immersed FSI framework that strategically couples two mature finite element libraries: MFEM, a GPU-ready and scalable library with state-of-the-art parallel performance developed at Lawrence Livermore National Laboratory, and FEBio, a nonlinear finite element solver with sophisticated solid mechanics capabilities designed for biomechanics applications developed at the University of Utah and Columbia University. This coupling creates a unique synergy wherein the fluid solver leverages MFEM's distributed-memory parallelization and pathway to GPU acceleration, while the immersed solid exploits FEBio's comprehensive suite of hyperelastic and viscoelastic constitutive models and advanced solid mechanics modeling targeted for biomechanics applications. FSI coupling is achieved using a fictitious domain/distributed Lagrange multiplier methodology with variational multiscale stabilization for enhanced accuracy on under-resolved grids expected with unfitted meshes used in immersed FSI. A fully implicit, monolithic scheme provides robust coupling for strongly coupled fluid-solid interactions characteristic of cardiovascular applications. The framework's modular architecture facilitates straightforward extension to additional physics and element technologies. Several test problems are considered to demonstrate the capabilities of the proposed framework, including a three-dimensional semilunar heart valve simulation. This platform addresses a critical need for open-source immersed FSI software combining advanced biomechanics modeling with high-performance computing infrastructure.

Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as the square root of time. These sublinear fronts preserve an invariant shape, with an effective diffusion constant that diverges at the transition to linear spreading. The model applies to dense cellular aggregates of nonmotile cells consuming a diffusible nutrient. The sublinear spread results from biomass redistribution slowing due to nutrient depletion, a phenomenon supported experimentally but often neglected. Our results provide a potential explanation for the linear rather than quadratic increase of colony area with time, which has been observed for many microbes.

Magnetic Resonance Fingerprinting (MRF) enables fast quantitative imaging, yet reconstructing high-resolution 3D data remains computationally demanding. Non-Cartesian reconstructions require repeated non-uniform FFTs, and the commonly used Locally Low Rank (LLR) prior adds computational overhead and becomes insufficient at high accelerations. Learned 3D priors could address these limitations, but training them at scale is challenging due to memory and runtime demands. We propose SPUR-iG, a fully 3D deep unrolled subspace reconstruction framework that integrates efficient data consistency with a progressive training strategy. Data consistency leverages implicit GROG, which grids non-Cartesian data onto a Cartesian grid with an implicitly learned kernel, enabling FFT-based updates with minimal artifacts. Training proceeds in three stages: (1) pretraining a denoiser with extensive data augmentation, (2) greedy per-iteration unrolled training, and (3) final fine-tuning with gradient checkpointing. Together, these stages make large-scale 3D unrolled learning feasible within a reasonable compute budget. On a large in vivo dataset with retrospective undersampling, SPUR-iG improves subspace coefficient maps quality and quantitative accuracy at 1-mm isotropic resolution compared with LLR and a hybrid 2D/3D unrolled baseline. Whole-brain reconstructions complete in under 15-seconds, with up to $times$111 speedup for 2-minute acquisitions. Notably, $T_1$ maps with our method from 30-second scans achieve accuracy on par with or exceeding LLR reconstructions from 2-minute scans. Overall, the framework improves both accuracy and speed in large-scale 3D MRF reconstruction, enabling efficient and reliable accelerated quantitative imaging.

Purpose: Aortic valve (AV) biomechanics play a critical role in maintaining normal cardiac function. Pathological variations, particularly in bicuspid aortic valves, alter leaflet loading, increase strain, and accelerate disease progression. Accurate patient-specific characterization of valve geometry and deformation is therefore essential for predicting disease progression and guiding durable repair. However, existing imaging and computational methods often fail to capture rapid valve motion and complex patient-specific features, limiting precise biomechanical assessment.

Methods: To address these limitations, we developed an image registration framework coupled with the finite element method (FEM) to improve AV tracking and biomechanical evaluation. Patient-specific valve geometries derived from 4D echocardiography and CT were used to simulate AV closure and generate intermediate deformation states. These FEM-generated states facilitated leaflet tracking, while image registration corrected misalignment between simulations and imaging data.

Results: In 20 patients, FEM-augmented registration improved tracking accuracy by 40% compared with direct registration. This improvement enabled more reliable strain estimation by measuring leaflet deformation directly from imaging and reducing uncertainties associated with boundary conditions and material assumptions. Using the improved tracking results, areal, Green-Lagrange, and deviatoric strains were quantified in adult trileaflet and bicuspid valves, as well as pediatric patients, revealing distinct deformation patterns across valve groups. Convergence in mean deviatoric strain between adult trileaflet and pediatric valves suggests volumetric deformation underlies age- and size-related differences in AV mechanics.

Conclusion: Overall, this FEM-augmented registration framework enhances geometric tracking and biomechanical evaluation accuracy, providing clinically relevant insights into patient-specific AV deformation to support individualized medical and intervention planning.

Integrating multi-omics data, such as DNA methylation, mRNA expression, and microRNA (miRNA) expression, offers a comprehensive view of the biological mechanisms underlying disease. However, the high dimensionality of multi-omics data, the heterogeneity across modalities, and the lack of reliable biological interaction networks make meaningful integration challenging. In addition, many existing models rely on handcrafted similarity graphs, are vulnerable to class imbalance, and often lack built-in interpretability, limiting their usefulness in biomedical applications. We propose Multi-Omics integration with Tree-generated Graph Neural Network (MOTGNN), a novel and interpretable framework for binary disease classification. MOTGNN employs eXtreme Gradient Boosting (XGBoost) for omics-specific supervised graph construction, followed by modality-specific Graph Neural Networks (GNNs) for hierarchical representation learning, and a deep feedforward network for cross-omics integration. Across three real-world disease datasets, MOTGNN outperforms state-of-the-art baselines by 5-10% in accuracy, ROC-AUC, and F1-score, and remains robust to severe class imbalance. The model maintains computational efficiency through the use of sparse graphs and provides built-in interpretability, revealing both top-ranked biomarkers and the relative contributions of each omics modality. These results highlight the potential of MOTGNN to improve both predictive accuracy and interpretability in multi-omics disease modeling.

Universal approximation theorems establish the expressive capacity of neural network architectures. For dynamical systems, existing results are limited to finite time horizons or systems with a globally stable equilibrium, leaving multistability and limit cycles unaddressed. We prove that Neural ODEs achieve $\epsilon -\delta$ closeness-trajectories within error $\epsilon$ except for initial conditions of measure $<\delta$ -over the infinite time horizon $[0,\infty )$ for three target classes: (1) Morse-Smale systems (a structurally stable class) with hyperbolic fixed points, (2) Morse-Smale systems with hyperbolic limit cycles via exact period matching, and (3) systems with normally hyperbolic continuous attractors via discretization. We further establish a temporal generalization bound: $\epsilon -\delta$ closeness implies $L^p$ error $\le {\epsilon }^p+\delta \cdot D^p$ for all $t\ge 0$ , bridging topological guarantees to training metrics. These results provide the first universal approximation framework for multistable infinite-horizon dynamics.

Integration and analysis of multi-omics data provide valuable insights for improving cancer subtype classification. However, such data are inherently heterogeneous, high-dimensional, and exhibit complex intra- and inter-modality dependencies. Graph neural networks (GNNs) offer a principled framework for modeling these structures, but existing approaches often rely on prior knowledge or predefined similarity networks that produce undirected or unweighted graphs and fail to capture task-specific directionality and interaction strength. Interpretability at both the modality and feature levels also remains limited. To address these challenges, we propose TF-DWGNet, a novel Graph Neural Network framework that combines tree-based Directed Weighted graph construction with Tensor Fusion for multiclass cancer subtype classification. TF-DWGNet introduces two key innovations: (i) a supervised tree-based strategy that constructs directed, weighted graphs tailored to each omics modality, and (ii) a tensor fusion mechanism that captures unimodal, bimodal, and trimodal interactions using low-rank decomposition for computational efficiency. Experiments on three real-world cancer datasets demonstrate that TF-DWGNet consistently outperforms state-of-the-art baselines across multiple metrics and statistical tests. In addition, the model provides biologically meaningful insights through modality-level contribution scores and ranked feature importance. These results highlight that TF-DWGNet is an effective and interpretable solution for multi-omics integration in cancer research.

Tabular datasets are commonly visualized as heatmaps, where data values are represented as color intensities in a matrix to reveal patterns and correlations. However, modern omics technologies increasingly generate matrices so large that existing visual exploration tools require downsampling or filtering, risking loss of biologically important patterns. Additional barriers arise from tools that require command-line expertise, or fragmented workflows for downstream biological interpretation. We present ClusterChirp, a web-based platform for real-time, interactive exploration of large-scale data matrices enabled by GPU-accelerated rendering and parallelized hierarchical clustering using multiple CPU cores. Built on deck.gl and multi-threaded clustering algorithms, ClusterChirp supports on-the-fly clustering, multi-metric sorting, feature search, and adjustable visualization parameters for interactive explorations. Uniquely, a natural language interface powered by a Large Language Model helps users perform complex operations and build reproducible workflows from conversational commands. Furthermore, users can select clusters to explore interactive within-cluster correlation networks in 2D or 3D, or perform functional enrichment through biological knowledge bases. Developed with iterative user feedback and adhering to FAIR4S principles, ClusterChirp empowers researchers to extract insights from high-dimensional omics data with unprecedented ease and speed. This website is freely available at clusterchirp.mssm.edu, with no login required.

Understanding how cells escape from embedded spheroids requires a mechanical framework linking stress generation within cells, across cells, and between cells and the surrounding extracellular matrix (ECM). We develop such a framework by coupling a 3D vertex model of a spheroid to a fibrous ECM network and deriving a 3D Cauchy stress tensor for deformable polyhedral cells, enabling direct cell-level stress quantification in three dimensions. We analyze maximum shear stress in solid-like and fluid-like spheroids: solid-like spheroids exhibit broader stress distributions and radial stress gradients, while fluid-like spheroids show lower stresses with weak spatial organization. Cell shape anisotropy is not generically aligned with principal stress directions, indicating that morphology alone is an unreliable proxy for mechanical state. We further demonstrate strain stiffening at the single-cell level, where elongation produces nonlinear increases in maximum shear stress, allowing boundary cells in otherwise low-stress, fluid-like spheroids to transiently generate forces sufficient to remodel the matrix. To connect strain-induced stress amplification to invasion modes, we introduce an extended 3D vertex model with explicit, tunable cell-cell adhesion springs. In this minimal mechanical framework, single-cell breakout results from strain stiffening combined with reduced adhesion, whereas multi-cell streaming additionally requires anisotropic adhesion strengthened along the elongation axis and weakened orthogonally. Together, these results identify distinct mechanical pathways coupling cell strain, stress amplification, and adhesion organization to spheroid invasion.

This study demonstrates the feasibility of a novel fabrication technique for high spatial resolution CsI: Tl scintillation detectors tailored for single photon emission computed tomography (SPECT) systems. Building upon our previously developed laser induced optical barrier (LIOB) method, which achieved high spatial resolution, excellent sensitivity, and 100% fabrication yield in CsI: Tl detectors, we extend this approach to a converging-pixel architecture. A CsI: Tl crystal array with converging pixels was designed and fabricated, featuring entrance-face pixels of 1.6x1.6 mm2 and photodetector side pixels of 2x2 mm2. To localize gamma-ray interactions, both the center of gravity (CoG) algorithm and a maximum-likelihood (ML) based decoding method were implemented. A custom built four axis motion platform was developed to deliver a finely collimated pencil beam at precisely controlled positions and angles across the array, enabling generation of a comprehensive dataset for prior knowledge and validation. The results demonstrate an energy resolution of 11.79+/-0.53% (collimated experiment) and a position localization accuracy of 1.00+/-0.42 mm (nearest neighbor interpolation), confirming that the proposed converging-pixel architecture, combined with statistical decoding algorithms, provides a promising path toward the development of high-performance SPECT detectors.