Search for: All records

Recent data across the globe indicates a decline in stem competency among secondary education students. Despite persistent interest in STEM fields this decrease in preparedness could yield detrimental effects for both future scientists and engineers. To address this current trend, a collaborative partnership between a university and high school commenced. The goal was to create an advanced experiential engineering course focused primarily on ophthalmology principles, research, and hands-on solutions. Twenty-one high school students (grades 9-12) enrolled in the course. Their objective was to investigate research questions involving ocular physiology. These ranged from surveying intraocular pressure measurement methods, examining the nature of vitreous humor properties, and investigating the inherent connection between blood flow and fluid dynamics. Furthermore, students engaged in hands-on experimentation that resulted in a hydraulics-based model which attempted to link the correlation between blood pressure and intraocular pressure involved in glaucoma progression. Post-course interviews revealed three major themes: i) an increased appreciation for the utility of mathematics and its real-world use; ii) the importance of the mentor-mentee relationship and professional networking; and iii) increased access to resources beyond what is traditionally found in a high school classroom. These findings suggest that incorporating research into a high school classroom can foster positive outcomes and spark students’ interest in ophthalmology research and in STEM more broadly. This course can serve as a model in future development of project-based engineering curriculum and help broaden participation in STEM. 

In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. In this paper, we propose a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of fluid flows through deformable porous media equations is coupled with a systemic, 0D, lumped model of the remainder of the circulation, where the fluid flow through a vascular network is described via its analog with a current flowing through an electric circuit. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the surrounding circulatory system. This PDE/ODE coupling leads to interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales, and careful consideration is taken to address this interface mismatch. The resulting system involves PDEs of mixed type with interface conditions depending on nonlinear ODEs. A new result on local existence of solutions for this multiscale interface coupling is provided in this article. 

Many real-life applications require mathematical models at multiple scales, defined in domains with complex structures, some of which having time dependent boundaries. Mathematical models of this type are encountered in seemingly disparate areas e.g., flow and deformation in the subsurface or beneath the ocean floor, and in processes of clinical relevance. While the areas are different, the structure of the models and the challenges are shared: the analysis and simulation must account for the evolution of the domain due to the many coupled processes in the multi-scale context. The key theme and focus of the workshop were novel ideas in the mathematical modeling, analysis, and numerical simulation, which are cross-cutting between the two application areas mentioned above. The talks have covered the mathematical treatment of such problems, as well as the development of efficent numerical discretization schemes and of solvers for large-scale problems.