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ABSTRACT Microfluidic devices (MDs) present a novel method for detecting circulating tumor cells (CTCs), enhancing the process through targeted techniques and visual inspection. However, current approaches often yield heterogeneous CTC populations, necessitating additional processing for comprehensive analysis and phenotype identification. These procedures are often expensive, time‐consuming, and need to be performed by skilled technicians. In this study, we investigate the potential of a cost‐effective and efficient hyperuniform micropost MD approach for CTC classification. Our approach combines mathematical modeling of fluid–structure interactions in a simulated microfluidic channel with machine learning techniques. Specifically, we developed a cell‐based modeling framework to assess CTC dynamics in erythrocyte‐laden plasma flow, generating a large dataset of CTC trajectories that account for two distinct CTC phenotypes. Convolutional neural network (CNN) and recurrent neural network (RNN) were then employed to analyze the dataset and classify these phenotypes. The results demonstrate the potential effectiveness of the hyperuniform micropost MD design and analysis approach in distinguishing between different CTC phenotypes based on cell trajectory, offering a promising avenue for early cancer detection. 

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. 

We give a brief survey of the recent progress in the area of mathematical well-posedness for moving boundary problems describing fluid-structure interaction between incompressible, viscous fluids and elastic, viscoelastic, and rigid solids. 

The article describes novel mathematics developed within the past 20 years to study optimal design of vascular stents. 

The biological response of a coronary artery can be assessed measuring the radial stress of the arterial wall, which depend on the location, arterial tortuosity, and cardiac cycle. We sought to study the radial stress and investigate which geometric distribution of stent struts is associated with favorable biologic response in tortuous coronary arteries.