Development of Mathematical Methods for Next Generation Stent Design

该项目致力于下一代支架设计数学方法的全面发展。支架是网状的管子，用来撑开病变的动脉。迄今为止，已经设计了几代支架。目前使用的支架是药物洗脱支架和新一代裸金属支架。尽管支架植入术的有益效果，持续的高并发症率，如支架内再狭窄和晚期支架血栓形成要求新的方法来支架设计。基于纳米工程支架的最新想法似乎特别有前途。它们包括：（1）纳米工程支架，其是覆盖有纳米工程表面的支架，其促进功能性内皮的加速恢复，并提供无药物方法以保持支架长期专利;以及（2）铁磁支架，其具有用于改善动脉壁愈合的抗血栓形成药物的磁性增强纳米颗粒药物递送。该项目将致力于开发新的数学方法，以指导和帮助下一代支架的生物工程设计。这些方法是基于偏微分方程，粒子基动力学方法，和人工智能为基础的优化方法。数学和计算结果将在UCSF的治疗微技术和纳米技术实验室进行实验测试。两名学生和一名博士后将参与该项目，这项研究的主题将在加州大学伯克利分校的一个新的跨学科课程中提出，交叉列出三个不同的部门（数学，生物工程和机械工程）。将特别关注为高中女生组织夏季研讨会，并促进妇女参与STEM研究。该项目旨在开发一个统一的平台，用于基于新的数学，计算，生物工程和实验方法的跨学科，协同方法的下一代支架设计。数学方法联合收割机宏观尺度和微观（纳米）尺度方法来建模：（1）覆盖有工程纳米管阵列的纳米工程支架表面;（2）铁磁纳米颗粒药物递送;（3）支架拓扑结构、几何形状和机械性能的优化设计，以最大限度地减少动脉组织损伤;以及（4）药物洗脱支架的涂层策略设计。数学模型将与高性能计算相结合，并在UCSF的治疗微技术和纳米技术实验室进行实验验证。数学方法包括涉及多层多孔弹性介质的流体-结构相互作用模型来模拟动脉壁，基于降维的1D双曲线网络模型描述支架的几何和机械特性，以及铁磁纳米颗粒流体-结构相互作用模型。计算方法将基于宏观尺度连续模型的有限元方法近似和微/纳米尺度颗粒模型的平滑颗粒流体动力学近似的组合。不确定性量化和人工智能（深度神经网络）将用于研究解决方案对问题中参数的依赖性，并研究最佳支架设计。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project addresses a comprehensive development of mathematical methods for next generation stent design. Stents are mesh-like tubes which are used to prop diseased arteries open. Several generations of stents have been designed to date. The currently used stents are drug eluting stents, and new generations of bare metal stents. Despite the beneficial effects of stenting, persistent high rates of complications such as in-stent restenosis and late stent thrombosis call for novel approaches to stent design. Recent ideas based on nano-engineered stents seem to be particularly promising. They include: (1) nano-engineered stents, which are stents covered with nano-engineered surface that promotes accelerated restoration of functional endothelium and provides a drug-free approach to keeping stents patent long-term; and (2) ferromagnetic stents with magnet-enhanced nano-particle drug delivery of anti-thrombogenic drugs for improved arterial wall healing. This project will addresses the development of new mathematical methods to guide and aid the bioengineering design of next generation stents. The methods are based on partial differential equations, particle-base kinetic methods, and artificial intelligence-based optimization methods. The mathematical and computational results will be experimentally tested in the Therapeutic Microtechnology and Nanotechnology Lab at UCSF. Two students and a postdoc will be involved in the project, and topics from this research will be presented in a new, interdisciplinary class at UC Berkeley, cross-listed in three different departments (Mathematics, Bioengineering, and Mechanical Engineering). Special attention will be paid to organizing a Summer Workshop for High School Girls, and to promoting inclusion of women in STEM research.This project addresses the development of a unified platform for interdisciplinary, synergistic approaches to next generation stent design based on novel mathematical, computational, bioengineering, and experimental methods. The mathematical methods combine macro-scale and micro(nano)-scale approaches to the modeling of: (1) nanoengineered stents' surfaces covered with engineered nano-tube arrays; (2) ferromagnetic nano-particle drug delivery; (3) optimal design of stent's topology, geometry, and mechanical properties to minimize arterial tissue injury; and (4) design of coating strategies for drug-eluting stents. The mathematical models will be combined with high performance computing, and with experimental validation in the Therapeutic Microtechnology and Nanotechnology Lab at UCSF. The mathematical methods include a fluid-structure interaction model involving multi-layered poroelastic media to model arterial walls, a dimension reduction-based 1D hyperbolic net model describing stents' geometric and mechanical properties, and a ferromagnetic nano-particle fluid-structure interaction model. The computational methods will be based on a combination of Finite Element Method approximations of the macro-scale continuum models, and on Smoothed Particle Hydrodynamics approximations of the micro/nano-scale particle models. Uncertainty Quantification and Artificial Intelligence (Deep Neural Networks) will be used to study solution dependence on the parameters in the problem, and to study optimal stent design.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.