Reduced order methods for parametric optimal flow control in coronary bypass grafts, towards patient-specific data assimilation

Abstract

Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease (CAD). In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step towards matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are, $\left(i\right)$. lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and $\left(ii\right)$. high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition (POD)--Galerkin.

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Cited by in corpus (11)

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• Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
• An optimal control approach to determine resistance-type boundary conditions from in-vivo data for cardiovascular simulations
• A non-intrusive data-driven ROM framework for hemodynamics problems
• Reduced order methods for parametrized non-linear and time dependent optimal flow control problems, towards applications in biomedical and environmental sciences
• Space-time POD-Galerkin approach for parametric flow control
• POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations
• POD-based reduced order methods for optimal control problems governed by parametric partial differential equation with varying boundary control
• A Certified Reduced Basis Method for Linear Parametrized Parabolic Optimal Control Problems in Space-Time Formulation