Development of Mathematical Methods for Next Generation Stent Design

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

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.