Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

Lassila, Toni; Manzoni, Andrea; Quarteroni, Alfio; Rozza, Gianluigi

doi:10.1051/m2an/2012059

Cited by 30 publications

(30 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The shape of the graft is optimized by changing the values of the design variables. In addition, some researchers have investigated the two-dimensional or threedimensional designs of the arterial graft geometries by the gradient-free methods (Marsden et al 2008;Dur et al 2011;Probst et al 2010a;Lassila et al 2013 ;Manzoni et al 2012a, b).…”

Section: Introductionmentioning

confidence: 99%

Topology optimization study of arterial bypass configurations using the level set method

Zhang

Liu

2014

Struct Multidisc Optim

View full text Add to dashboard Cite

We studied the arterial bypass design problem using a level set based topology optimization method. The blood flow in the artery was considered as the non-Newtonian flow governed by the Navier-Stokes equations coupled with the modified Cross model for the shear dependent viscosity. The fluid-solid interface is immersed in the design domain by the level set method and the fictitious porous material method. The sensitivity velocity derived by the level set based continuous adjoint method was utilized to control the evolution of the level set function. In order to accommodate the irregular analysis domains, the flow equations and the level set equations were computed on two different unstructured grids respectively. Three idealized arterial bypass configurations problems with the minimum flow shear stress objective were studied in the numerical examples. The results indicated that the optimal arterial bypass designs can effectively reduce integral of the squared shear rate in the artery and have a superior performance for the arterial grafting.

show abstract

Section: Introductionmentioning

confidence: 99%

Topology optimization study of arterial bypass configurations using the level set method

Zhang

Liu

2014

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…The integration of the RBF parametrization technique within the reduced basis framework, as well as its application to blood flow simulation on geometries reconstructed from patient data, looks promising in its flexibility and ability to express a variety of shape deformations. Further elements that may be explored deal with the uncertainty quantification [5] and/or robust optimization and control problems [6] for patient-specific scenarios. …”

Section: Discussionmentioning

confidence: 99%

“…In the end, at the outer level a suitable iterative procedure for the optimization is performed. A brief presentation of the whole framework can be found in [8], while a more detailed analysis has been recently addressed in [5,6].…”

Section: A General Strategy For Reduction In Shape Dependent Flowsmentioning

confidence: 99%

Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics

Lassila

Manzoni

Rozza

2013

IFIP Advances in Information and Communication Technology

Self Cite

View full text Add to dashboard Cite

Abstract. This work deals with the development and application of reduction strategies for real-time and many query problems arising in fluid dynamics, such as shape optimization, shape registration (reconstruction), and shape parametrization. The proposed strategy is based on the coupling between reduced basis methods for the reduction of computational complexity and suitable shape parametrizations -such as free-form deformations or radial basis functions -for low-dimensional geometrical description. Our focus is on problems arising in haemodynamics: efficient shape parametrization of cardiovascular geometries (e.g. bypass grafts, carotid artery bifurcation, stenosed artery sections) for the rapid blood flow simulation -and related output evaluation -in domains of variable shape (e.g. vessels in presence of growing stenosis) provide an example of a class of problems which can be recast in the real-time or in the manyquery context.

show abstract

“…Moreover, velocity profiles and separation of flows have been investigated when studying the bypass end-to-side anastomosis [35,36]. Studies with idealized geometrical models have been proposed in order to define an optimal design for the anastomosis [37]. Nevertheless, the geometry of the vessel is one of the most important factors that affect the pattern of the wall shear stress.…”

Section: Application and Motivationmentioning

confidence: 99%

Reduced Numerical Approximation of Reduced Fluid-Structure Interaction Problems With Applications in Hemodynamics

Colciago

Deparis

2018

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

This paper deals with fast simulations of the hemodynamics in large arteries by considering a reduced model of the associated fluid-structure interaction problem, which in turn allows an additional reduction in terms of the numerical discretisation. The resulting method is both accurate and computationally cheap. This goal is achieved by means of two levels of reduction: first, we describe the model equations with a reduced mathematical formulation which allows to write the fluid-structure interaction problem as a Navier-Stokes system with non-standard boundary conditions; second, we employ numerical reduction techniques to further and drastically lower the computational costs. The non standard boundary condition is of a generalized Robin type, with a boundary mass and boundary stiffness terms accounting for the arterial wall compliance. The numerical reduction is obtained coupling two well-known techniques: the proper orthogonal decomposition and the reduced basis method, in particular the greedy algorithm. We start by reducing the numerical dimension of the problem at hand with a proper orthogonal decomposition and we measure the system energy with specific norms; this allows to take into account the different orders of magnitude of the state variables, the velocity and the pressure. Then, we introduce a strategy based on a greedy procedure which aims at enriching the reduced discretization space with low offline computational costs. As application, we consider a realistic hemodynamics problem with a perturbation in the boundary conditions and we show the good performances of the reduction techniques presented in the paper. The results obtained with the numerical reduction algorithm are compared with the one obtained by a standard finite element method.The gains obtained in term of CPU time are of three orders of magnitude.

show abstract

Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

Cited by 30 publications

References 61 publications

Topology optimization study of arterial bypass configurations using the level set method

Topology optimization study of arterial bypass configurations using the level set method

Reduction Strategies for Shape Dependent Inverse Problems in Haemodynamics

Reduced Numerical Approximation of Reduced Fluid-Structure Interaction Problems With Applications in Hemodynamics

Contact Info

Product

Resources

About