A comprehensive mathematical and computational framework for next generation stent design

University Of California-Berkeley, Berkeley CA

Investigators

Abstract

Stents are mesh-like tubes which hold blood vessels and air passages open. There are many types of stents, including bare metal stents, drug eluting stents (DES), airway stents, and stents that anchor bioartifical heart valves in transcatheter (aortic) valve replacement procedures. DES is a metallic mesh platform coated with an anti-inflammatory pharmacologic agent (drug) to reduce re-blocking (restenosis) of coronary arteries and allow normal blood supply to the heart muscle. Implantation of DES continues to be the method of choice in the treatment of patients with symptomatic coronary artery disease. The FDA first approved the use of 3D-printed airway stents in 2020. With the rapid development of 3D printing technology, it is only a matter of time until 3D printed vascular stent are slated for FDA approval. This is what makes this research pressing and timely. This project aims to deliver a comprehensive unified mathematical and computational framework for optimal stent design, producing digital stents ready for 3D printing, tailored to specific uses and patient geometries. In addition to developing novel mathematical and computational approaches, which will influence the field of mathematics, this project will produce tools for designing patient-specific digital stents. Furthermore, it will provide a platform for interdisciplinary mentoring of students and postdoctoral researchers by the main investigators, who include a mathematician, an engineer, and an interventional cardiologist. The mathematical framework to be developed in this project, consists of three modules: 1. A reduced model optimization module for optimal design of mesh-like structures. This stent optimization algorithm outperforms classical engineering and ad hoc optimization approaches in terms of speed and accuracy, since it relies on sophisticated mathematical approaches rooted in dimension reduction modeling and optimization. This is the first stent optimization model (and a computational scheme) that is based on reduced, 1D network modeling of stents. A comparison with a Genetic Algorithm, Proper Orthogonal Decomposition, and Deep Autoencoder Neural Networks approaches will be performed. The stent prototypes will be 3D printed and mechanically tested in a Biomechanics Lab at Berkeley. Medical oversight will be provided by an interventional cardiologist. 2. A fluid-stent-poroelastic structure interaction module simulating the interaction between the blood flow and artery wall with implanted stent, where the arterial walls are modeled as poroelastic solids consisting of two layers: a thin reticular shell layer modeling the intimal layer of arterial walls, and a thick hyperelastic layer modeling the media-adventitia complex. This is the first fluid-structure interaction model that accounts for the multi-layered poroelastic structure of arterial walls, and it includes an implanted stent. A novel partitioned scheme to solve this problem will be developed. 3. A nonlinear advection-reaction-diffusion module simulating drug transport within the vascular wall and in the vascular lumen capturing the pharmacokinetics and advection, reaction, and diffusion processes of anti-inflammatory agents used to coat DES. The models are defined on moving domains. They utilize the advection velocity and the moving domain location calculated in Step 2 above. A monolithic computational scheme will be developed to solve the problem. This module is particularly relevant for the analysis of the performance of drug eluting stents. An integral part of the project will be interdisciplinary student mentoring and research dissemination. This will be achieved by running a Hot Topics Workshop at the SLMath Institute, publishing in first-rate journals, and presenting research at mathematical, engineering, and medical conferences and workshops. 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.