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

Zainib, Zakia; Ballarin, Francesco; Fremes, Stephen E.; Triverio, Piero; Jiménez-Juan, Laura; Rozza, Gianluigi

doi:10.1002/cnm.3367

Cited by 28 publications

(40 citation statements)

References 64 publications

(103 reference statements)

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“…[11,15,30], to fluid dynamics, see e.g. [9,33,35,8], from heamodynamics [5,27,48,53] to environmental applications [37,38,45,47,48], classical discretization techniques may result in unbearable simulations, which can limit their applicability in many query contexts, where several parametric instances must be studied, possibly in a small amount of time. Furthermore, the computational complexity drastically grows when the governing equation involves time evolution.…”

Section: Introductionmentioning

confidence: 99%

A Certified Reduced Basis Method for Linear Parametrized Parabolic Optimal Control Problems in Space-Time Formulation

Strazzullo¹,

Ballarin²,

Rozza³

2021

Preprint

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In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error estimator procedure, based on easy-to-compute quantities which guarantee a rigorous and efficient bound for the error of the involved variables. First of all, we propose the analysis of the problem at hand, proving its well-posedness thanks to Nečas -Babuška theory for distributed and boundary controls in a space-time formulation. Then, we derive error estimators to apply a Greedy method during the offline stage, in order to perform, during the online stage, a Galerkin projection onto a low-dimensional space spanned by properly chosen high-fidelity solutions. We tested the error estimators on two model problems governed by a Graetz flow: a physical parametrized distributed optimal control problem and a boundary optimal control problem with physical and geometrical parameters. The results have been compared to a previously proposed bound, based on the exact computation of the Babuška inf-sup constant, in terms of reliability and computational costs. We remark that our findings still hold in the steady setting and we propose a brief insight also for this simpler formulation.

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Section: Introductionmentioning

confidence: 99%

A Certified Reduced Basis Method for Linear Parametrized Parabolic Optimal Control Problems in Space-Time Formulation

Strazzullo¹,

Ballarin²,

Rozza³

2021

Preprint

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“…The aim of this work is the development of an efficient non-intrusive data-driven reduced order model to be used within hemodynamics framework. The reader can find examples of the ROM application in the hemodynamics field in [4][5][6][7][8]. We highlight that the online evaluation of the datadriven approach used here is based only on data and does not require knowledge about the governing equations that describe the system.…”

Section: Introductionmentioning

confidence: 99%

Non-intrusive data-driven ROM framework for hemodynamics problems

et al. 2021

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Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PED) by properly combining the high-fidelity solutions of the problem obtained for several configurations, i.e. for several properly chosen values of the physical/geometrical parameters characterizing the problem. By starting from a database of high-fidelity solutions related to a certain values of the parameters, we apply the proper orthogonal decomposition with interpolation (PODI) and then reconstruct the variables of interest for new values of the parameters, i.e. different values from the ones included in the database. Furthermore, we present a preliminary web application through which one can run the ROM with a very user-friendly approach, without the need of having expertise in the numerical analysis and scientific computing field. The case study we have chosen to test the efficiency of our algorithm is represented by the aortic blood flow pattern in presence of a left ventricular (LVAD) assist device when varying the pump flow rate.

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“…Alternatively, variational approaches, such as optimal control, perform the parameter estimation by treating the governing equations as state system and the mismatch between the state solution and the patient‐specific measurements as cost functional to be minimized 26–29 . In practice, the unknown boundary conditions are chosen as control variables to minimize the cost functional.…”

Section: Introductionmentioning

confidence: 99%

An optimal control approach to determine resistance‐type boundary conditions from in‐vivo data for cardiovascular simulations

Fevola

Ballarin

Jiménez-Juan

et al. 2021

Numer Methods Biomed Eng

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The choice of appropriate boundary conditions is a fundamental step in computational fluid dynamics (CFD) simulations of the cardiovascular system. Boundary conditions, in fact, highly affect the computed pressure and flow rates, and consequently haemodynamic indicators such as wall shear stress (WSS), which are of clinical interest. Devising automated procedures for the selection of boundary conditions is vital to achieve repeatable simulations. However, the most common techniques do not automatically assimilate patient‐specific data, relying instead on expensive and time‐consuming manual tuning procedures. In this work, we propose a technique for the automated estimation of outlet boundary conditions based on optimal control. The values of resistive boundary conditions are set as control variables and optimized to match available patient‐specific data. Experimental results on four aortic arches demonstrate that the proposed framework can assimilate 4D‐Flow MRI data more accurately than two other common techniques based on Murray's law and Ohm's law.

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

Cited by 28 publications

References 64 publications

A Certified Reduced Basis Method for Linear Parametrized Parabolic Optimal Control Problems in Space-Time Formulation

A Certified Reduced Basis Method for Linear Parametrized Parabolic Optimal Control Problems in Space-Time Formulation

Non-intrusive data-driven ROM framework for hemodynamics problems

An optimal control approach to determine resistance‐type boundary conditions from in‐vivo data for cardiovascular simulations

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