Reproduction of pressure field in ultrasonic‐measurement‐integrated simulation of blood flow

Funamoto, Kenichi; Hayase, Toshiyuki

doi:10.1002/cnm.2522

Cited by 15 publications

(13 citation statements)

References 32 publications

(44 reference statements)

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“…To incorporate the signal f into the system, the conventional feedback control-based approaches [16][17][18] impose it into the momentum Equation 2 as a body force. However, it is still an open question whether the body force would bring an unphysical flow acceleration and rotation.…”

Section: Basic Idea Of the Pfc-da Methodsmentioning

confidence: 99%

“…Next, we compare the present approach with 2 other approaches: one is the body-force type feedback control approach [16][17][18] ; the other is a method applying the reference velocity for the inflow velocity as the Dirichlet boundary condition, termed the "body-force approach" and "inflow-velocity approach," respectively. In the body-force approach, the reference velocity is defined at the same location of the discrete fluid velocity in the staggered arrangement, and the body force 5 is added to the momentum equation in the prediction phase 12, where the exact velocity profile following the Poiseuille flow is imposed on the inlet boundary as the Dirichlet boundary condition.…”

Section: Validation On Plane-poiseuille Flowmentioning

confidence: 99%

“…Ideally this would be remedied in a postprocedure on the obtained pressure field. 18 However, it is still unclear that the body force would bring an unphysical acceleration or rotation in the flow around the location where the body force is imposed. As compared with optimal control-based approaches, the conventional feedback control-based approach is not guaranteed to provide the optimal solution because the velocity residual between the reference and numerical data is treated as a kind of penalty.…”

Section: Introductionmentioning

confidence: 99%

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Physically consistent data assimilation method based on feedback control for patient‐specific blood flow analysis

Satoshi

Adib

Watanabe

et al. 2017

Numer Methods Biomed Eng

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This paper presents a novel data assimilation method for patient-specific blood flow analysis based on feedback control theory called the physically consistent feedback control-based data assimilation (PFC-DA) method. In the PFC-DA method, the signal, which is the residual error term of the velocity when comparing the numerical and reference measurement data, is cast as a source term in a Poisson equation for the scalar potential field that induces flow in a closed system. The pressure values at the inlet and outlet boundaries are recursively calculated by this scalar potential field. Hence, the flow field is physically consistent because it is driven by the calculated inlet and outlet pressures, without any artificial body forces. As compared with existing variational approaches, although this PFC-DA method does not guarantee the optimal solution, only one additional Poisson equation for the scalar potential field is required, providing a remarkable improvement for such a small additional computational cost at every iteration. Through numerical examples for 2D and 3D exact flow fields, with both noise-free and noisy reference data as well as a blood flow analysis on a cerebral aneurysm using actual patient data, the robustness and accuracy of this approach is shown. Moreover, the feasibility of a patient-specific practical blood flow analysis is demonstrated.

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Section: Basic Idea Of the Pfc-da Methodsmentioning

confidence: 99%

Section: Validation On Plane-poiseuille Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Physically consistent data assimilation method based on feedback control for patient‐specific blood flow analysis

Satoshi

Adib

Watanabe

et al. 2017

Numer Methods Biomed Eng

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“…We mention, for instance, the work in electrocardiology for the setup of patient-specific models in [19], and for estimating cardiac conductivities [32,37,74]. Other applications can be found, e.g., in [17,29]. In particular, in [24,26] DA methods are advocated for filling the gap between available boundary data and mathematical conditions required to solve the problem.…”

Section: Some Applications Of Data Assimilation In Hemodynamics Problemsmentioning

confidence: 99%

Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction

Bertagna

D’Elia

Perego

et al. 2014

Fluid-Structure Interaction and Biomedical Applications

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Numerical methods for incompressible fluid dynamics have recently received a strong impulse from the applications to the cardiovascular system. In particular, fluid-structure interaction methods have been extensively investigated in view of an accurate and possibly fast simulation of blood flow in arteries and veins. This has been strongly motivated by the progressive interest in using numerical tools not only for understanding the general physiology and pathology of the vascular system. The opportunity offered by medical images properly preprocessed and elaborated to simulate blood flow in real patients highlighted the potential impact of scientific computing on the clinical practice. Therefore, in silico experiments are currently extensively used in bioengineering for completing (and sometimes driving) more traditional in vivo and in vitro investigations. Parallel to the development of numerical models, the need for quantitative analysis for diagnostic purposes has strongly stimulated the design of new methods and instruments for measurements and imaging. Thanks to these developments, a huge amount of data is nowadays available. Data Assimilation is the accurate merging of measures (including images) and numerical simulations for a mathematically sound integration of different sources of information. The outcome of this process includes both the patient-specific measures and the general principles underlying the development of mathematical models. In this way, simulations are adapted to the availability of individual data and are therefore supposed to be more reliable; measures are correspondingly filtered by the mathematical models assumed to describe the underlying phenomena, resulting in a (hopefully) significant reduction of the noise.This chapter provides an introduction to methods for data assimilation, mostly developed in fields like meteorology, applied to computational hemodynamics. We focus mainly on two of them: methods based on stochastic arguments (Kalman filtering) and variational methods. We also address some examples that have been approached with different techniques, in particular the estimation of vascular compliance from displacement measures.

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“…The effective solution of inverse problems in cardiovascular mathematics is therefore an exciting and up-to-date challenge for the intrinsic mathematical value and for the impact it is expected to have on medicine and society. The first paper [1] by K. Funamoto and T. Hayase addresses an example of integration of numerical simulation and measurements to improve the quality of the quantitative computation of blood pressure and velocity when the knowledge of boundary conditions is defective. This is known as Ultrasonic Measurement Integrated.…”

Section: Editorialmentioning

confidence: 99%

Inverse problems in Cardiovascular Mathematics: toward patient‐specific data assimilation and optimization

Veneziani

Vergara

2013

Numer Methods Biomed Eng

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In the last 25 years, mathematical and numerical modeling of cardiovascular problems has experienced a spectacular progress. Moving progressively from the stage of idealized models supporting traditional in vitro and in vivo approaches -basically with proofs of concept -Cardiovascular Mathematics has been transforming into a unique tool for patient-specific analysis. This has been made possible by the strong integration with imaging devices. Nowadays, the work pipeline starting from a medical image in the Digital Imaging and Communications in Medicine (DICOM) format to retrieve the patient-specific geometry of an artery or the left ventricle to be used as computational domain in a numerical simulation is well established. This has initiated a paradigm shift in the interactions between mathematicians, bioengineers, and medical doctors. The latter are progressively getting used to in silico analysis as an important component of their research [3].The introduction of numerical procedures as a part of an established clinical routine and more in general of a consolidated support to the decision-making process of physicians still requires some steps both in terms of infrastructures (to bring computational tools to the operating room or the bedside) and methods. In particular, the quality of the numerical results needs to be assessed and certified. The reliability of simulations calls for an accurate quantification and possibly reduction of uncertainty. In this scenario and in view of terrific advancements of measuring techniques, an important research line -quite established in other fields -is data assimilation [4,6,9], that is, the integration of numerical simulations and measurements. We may say that numerical models provide a background knowledge (based on physical principles and constitutive laws, not patient-specific), whereas measures give a foreground (individual) information; accuracy of in silico procedures relies on the correct integration of these two levels of knowledge of the problem [9,10]. As a matter of fact, numerical models depend on parameters and boundary/initial conditions. Their knowledge is in practice usually incomplete, inaccurate, and noisy. In some cases, the sensitivity itself of the final results to these parameters is unclear and needs to be quantified. Such an uncertainty may be significantly reduced by the availability of patient-specific measures; on the other hand, the quality of measures can be strongly enhanced by comparison with mathematical models (after all, noise is in general not educated, it does not know PDEs . . . ) [4,5,7,8,9,11]. We think therefore that, in the future, a crucial step for the clinical application of Cardiovascular Mathematics will be the passage from numerical simulation to data assimilation. To be concrete, borrowing a motto by Michel Fortin supporting mesh adaptivity in finite element simulations, stating that a 'grid should not be considered a data, but an unknown of the problem', we think that many parameters currently tuned on the basis of nonpatient ...

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Reproduction of pressure field in ultrasonic‐measurement‐integrated simulation of blood flow

Cited by 15 publications

References 32 publications

Physically consistent data assimilation method based on feedback control for patient‐specific blood flow analysis

Physically consistent data assimilation method based on feedback control for patient‐specific blood flow analysis

Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction

Inverse problems in Cardiovascular Mathematics: toward patient‐specific data assimilation and optimization

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