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Publication Numerical approximation techniques for a fully nonlinear Schrödinger equation: nonlinear waves and shocks(Colorado School of Mines. Arthur Lakes Library, 2025-04)In this project, we study three numerical methods: the Finite Difference (FD) Method, a Finite Volume (FV) Scheme with an Osher-Solomon Riemann Problem Approximator, and the Entropy Viscosity Method. These methods are applied to a fully nonlinear partial differential equation (PDE) of Schrödinger type, which is suspected to produce shocks in finite time. Our goal is to identify which terms in the PDE drive shock formation and to develop a stability-preserving scheme for approximating solutions to the resulting balance law. The theory of stability-preserving methods, e.g., entropy-viscosity method, is primarily developed for hyperbolic conservation laws. Therefore, we also explore potential reformulations of the model PDE to recast it as a hyperbolic system of PDEs. Finally, we validate our methods by solving Burgers' equation, which has a known analytical solution.Publication Age and limb effects on sit-to-stand ground reaction forces(Colorado School of Mines. Arthur Lakes Library, 2025-04)The sit-to-stand (STS) movement is an important activity of daily living, but it can be a challenge for older adults. Examining vertical ground reaction forces (VGRFs) between limbs and across the lifespan can provide an understanding of task mechanics. Fourteen younger and fourteen older participants completed three STS trials. Vertical ground reaction force (VGRF) was normalized to body weight and integrated over time to determine impulse. We compared peak VGRFs, impulses, and completion time between age groups with an unpaired t-test (α=0.05), and between limbs with a paired t-test (α=0.05). Variability in VGRF peak and impulse was compared across groups and limbs using an F-test (α=0.05). Completion time was defined as the instant when VGRF on the foot increased 5% from the seated value until the local VGRF minimum prior to static standing. STS completion time was not different between the younger (1.601±0.284s) and older groups (1.686±0.258s). Healthy adults generally had symmetric VGRFs across the lifespan, with two exceptions. Peak VGRF (p=0.028) and vertical impulse (p=0.002) were greater on the dominant limb for younger adults. Variance in impulse was not different between groups on the dominant limb but was greater in older adults on the non-dominant limb (p=0.039). This variance may explain why differences between limbs were not observed in older adults. Overall, few differences were observed between limbs and across groups, suggesting that these healthy participant groups were effective at completing this submaximal task. Peak VGRFs and impulse variability can provide insight into movement strategies during STS with aging.Publication Improving CMR ventricular volume estimation in rodents under limited data conditions(Colorado School of Mines. Arthur Lakes Library, 2025-04)Accurate ventricular volume estimation from cardiac magnetic resonance imaging (CMR) in rodents is often limited by reduced short-axis (SA) coverage due to anesthesia duration, subject health, or slice planning constraints. This study (1) evaluated how reduced SA coverage impacts volume estimates and (2) compared the performance of three reconstruction methods under these constraints: the standard Simpson’s Disk Summation (SD), a short-axis alpha-shape method (SAα), and a combined long-axis plus short-axis alpha-shape method (LA+SAα). The SAα and LA+SAα approaches are novel techniques that use alpha-meshing and Monte Carlo volume estimation to address the geometric limitations of SD. We analyzed CMR data from nine rodents (five Sham, four Pulmonary-Artery-Banded) and compared volume estimates computed with all three methods under full SA coverage (7–8 slices) and reduced coverage (5–6 slices). Incorporating a single long-axis image and mesh-based reconstruction notably improved volume accuracy, particularly for the right ventricle. These findings demonstrate that combining orthogonal imaging views with advanced volumetric estimation enhances the reliability of ventricular volume calculations under constrained imaging conditions. This approach supports more accurate preclinical cardiac assessments and provides a practical solution when full short-axis acquisition is not feasible.Publication 3D modeling of mouse dorsiflexor muscles(Colorado School of Mines. Arthur Lakes Library, 2025-04)The accurate 3D modeling of musculoskeletal structures is essential for understanding mechanical stimuli in biomechanics. This study focuses on developing a 3D model of the tibialis anterior (TA), tibia, extensor digitorum longus (EDL), and internal tendon of a mouse limb to analyze responses to electrical stimulation. The experimental setup involves sending electrical signals through the TA of a restrained mouse leg, necessitating precise anatomical modeling for future biomechanical simulations. High-resolution micro-CT scans were obtained and imported into 3D Slicer for segmentation, outlining cross-sections of the tibia, TA, EDL, and internal tendon. Segmentation produced a high facet count making files too large to import into other software. MeshLab was used for mesh simplification, reducing computational complexity while preserving accuracy. For modeling and refinement, SolidWorks, Blender, and Cubit were tested. SolidWorks was the most effective despite lofting challenges, a technique used to create a 3D model with smooth transitions between cross-sectional profiles. Blender provided superior smoothing but lacked precise parametric control, while Cubit excelled in meshing yet had a steep learning curve due to its reliance on command-based operations. Future work will focus on applying Finite Element Analysis (FEA) using FEBio, a biomechanics simulation software, to study the mechanical responses of the musculoskeletal system under electrical stimulation. The objective is to simulate how muscle tissue deforms and reacts to external forces, providing valuable insights for biomechanical research. Validation and verification will be conducted by comparing simulation results with experimental data from similar studies. This research lays the foundation for advanced biomechanical modeling by optimizing micro-CT scan processing, mesh simplification, and software selection, ultimately improving simulations of muscle response to external stimuli.Publication Pre-filtering micrograph data to train machine learning algorithms to optimize medical metals(Colorado School of Mines. Arthur Lakes Library, 2025-04)Slip band analysis plays a crucial role in understanding material deformation and failure. Our research focuses on developing a program to automate the measurement of average slip band spacing within metal grains. The goal is to create a filtering algorithm that differentiates individual grains and identifies the average distance between slip bands within each grain. Our current approach involves image preprocessing using the Frangi filter, pixel equalization, scaling, thresholding, and then applying the Canny filter to isolate slip bands. We then apply the Hough Line detection algorithm to identify slip bands and compute their angles relative to the x-axis. By determining the grain width perpendicular to the average slip band angle and counting the slip bands, we estimate their average spacing. While this method has been successfully implemented for a single grain, further validation is required across multiple grains before conclusive analysis can be performed. Initial tests with alternative edge detection techniques, such as Sobel and Canny filters, revealed that Frangi filtering provides the most effective segmentation. A key challenge remains in defining crystal boundaries, as slip bands within a single grain align consistently, but outlining grain boundaries is complex. To address this, we are exploring blurring, labeling, thresholding, and masking techniques to enhance boundary detection. This research has broader implications for materials science, particularly in predicting metal failure and optimizing biocompatible materials. Our findings can apply to another project on our research team focused on improving metal/human tissue interfaces for medical applications.