Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. 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 toward matching patient‐specific physiological data in patient‐specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) 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‐Galerkin.
We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, optimal control problems require a huge computational effort in order to be solved, most of all in a physical and/or geometrical parametrized setting. Reduced order methods are a reliably suitable approach, increasingly gaining popularity, to achieve rapid and accurate optimal solutions in several fields, such as in biomedical and environmental sciences. In this work, we exploit POD-Galerkin reduction over a parametrized optimality system, derived from Karush-Kuhn-Tucker conditions. The methodology presented is tested on two boundary control problems, governed respectively by (i) time dependent Stokes equations and (ii) steady non-linear Navier-Stokes equations.
In this work we will focus on recent advances in reduced order modelling for parametrized problems in computational fluid dynamics, with a special attention to the case of inverse problems, such as optimal flow control problems and data assimilation, and multi-physics applications. Among the former, we will discuss applications arising in environmental marine sciences and engineering, namely a pollutant control in the Gulf of Trieste, Italy and a solution tracking governed by quasi-geostrophic equations describing North Atlantic Ocean dynamic. Similar methodologies will also be employed in problems related to the modeling of the cardiovascular system. Among the latter, we will present further recent developments on reduction of fluid-structure interaction problems, based on our earlier work. Reduced order approaches for parametric optimal flow control will also be applied in combination with domain decomposition in view of further applications in multi-physics. This work is in collaboration with Y. Maday (UPMC Université Paris 06, France), L. Jiménez-Juan (Sunnybrook Health Sciences Centre, Toronto, Canada), P. Triverio (University of Toronto, Canada), R. Mosetti (National Institute of Oceanography and Applied Geophysics, Trieste, Italy).
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, (i). lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (ii). 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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