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Abstract. We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The fluid flow is modeled by the time-dependent Navier- Stokes equations in a three-dimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the two-dimensional linearly elastic Koiter shell equations coupled to a one-dimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many ap- plications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary Lagrangian-Eulerian approach, and a non-trivial extension of the Aubin-Lions-Simon compactness result to problems on moving domains.
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Geometric optimization of vascular stents modeled as networks of 1D rods
We develop a novel mathematical and computational framework for geometric optimization of mesh-like devices such as stents, based on modeling mesh-like structures as networks of one-dimensional curved rods. To simplify calculations, the curved rods are approximated by piecewise straight rods. Constrained optimization problems for different cost functionals are stated and mathematically analyzed. The cost functionals considered include: (1) stents' compliance, (2) norm of displacement, (3) norm of contact moment (which is related to fatigue), and (4) multicriteria optimization in which stents are optimized to achieve maximal radial stiffness and minimal bending rigidity. The optimization parameters are stent's vertices, namely, the location of points where the stent struts meet. Existence of solutions to the mathematically posed optimization problems is obtained, and a numerical method based on the gradient descent algorithm is proposed to find the solutions. Three representative stents' geometries are numerically analyzed to show that the optimization algorithms provide tangible solutions. The stent geometries considered are those of Palmaz type stents, single zig-zag stent rings, and Express type stents. Interesting findings are obtained, including several new stent designs. Several optimized stents are presented, including an optimized Palmaz stent with a reduction in contact moment of 30%, and optimized Express and Palmaz stents with a reduction in compliance by more than 70%.
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- PAR ID:
- 10500526
- Publisher / Repository:
- Science Direct
- Date Published:
- Journal Name:
- Journal of Computational Physics
- Volume:
- 494
- Issue:
- C
- ISSN:
- 0021-9991
- Page Range / eLocation ID:
- 112497
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jcp.2023.112497
