Numerical Validation of MR-Measurement-Integrated Simulation of Blood Flow in a Cerebral Aneurysm

Funamoto, Kenichi; Suzuki, Y.; Hayase, Toshiyuki; Kosugi, Takashi; Isoda, Haruo

doi:10.1007/s10439-009-9689-y

Cited by 25 publications

(25 citation statements)

References 22 publications

(26 reference statements)

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“…In [37] Least Squares Finite Elements are used because of their versatility in managing different boundary conditions. In [26], merging of velocity data is carried out by using a "virtual" forcing term as CV. Here, we resorted to a control approach that in preliminary test cases provides promising results.…”

Section: Perspectivesmentioning

confidence: 99%

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Applications of variational data assimilation in computational hemodynamics

D’Elia

Mirabella

Passerini

et al. 2012

MS&A

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The development of new technologies for acquiring measures and images in order to investigate cardiovascular diseases raises new challenges in scientific computing. These data can be in fact merged with the numerical simulations for improving the accuracy and reliability of the computational tools. Assimilation of measured data and numerical models is well established in meteorology, whilst it is relatively new in computational hemodynamics. Different approaches are possible for the mathematical setting of this problem. Among them, we follow here a variational formulation, based on the minimization of the mismatch between data and numerical results by acting on a suitable set of control variables. Several modeling and methodological problems related to this strategy are open, such as the analysis of the impact of the noise affecting the data, and the design of effective numerical solvers. In this chapter we present three examples where a mathematically sound (variational) assimilation of data can significantly improve the reliability of the numerical models. Accuracy and reliability of computational models are increasingly important features in view of the progressive adoption of numerical tools in the design of new therapies and, more in general, in the decision making process of medical doctors.

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Section: Perspectivesmentioning

confidence: 99%

“…In particular, we mention [11,51,52,53,70], essentially based on Kalman filtering techniques, and [26] for the variational approach.…”

Section: Introductionmentioning

confidence: 99%

Applications of variational data assimilation in computational hemodynamics

D’Elia

Mirabella

Passerini

et al. 2012

MS&A

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“…Compared with the Kalman filter, which usually employs a low-dimensional linear model, the MI simulation, which uses computational fluid dynamics as a mathematical model, can provide a solution with high accuracy once a convergent result is obtained although there is no systematic design method of the feedback signal. The authors have applied MI simulation to blood flow analysis by integrating medical measurement (ultrasonic measurement or phase-contrast MRI) and numerical simulation [19,20]. With ultrasonic-measurement-integrated (UMI) simulation, the blood flow field is analyzed by applying artificial body forces proportional to the differences between the measured and computed Doppler velocities of the blood flow.…”

Section: Introductionmentioning

confidence: 99%

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

Funamoto

Hayase

2012

Numer Methods Biomed Eng

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Ultrasonic-measurement-integrated (UMI) simulation of blood flow is used to analyze the velocity and pressure fields by applying feedback signals of artificial body forces based on differences of Doppler velocities between ultrasonic measurement and numerical simulation. Previous studies have revealed that UMI simulation accurately reproduces the velocity field of a target blood flow, but that the reproducibility of the pressure field is not necessarily satisfactory. In the present study, the reproduction of the pressure field by UMI simulation was investigated. The effect of feedback on the pressure field was first examined by theoretical analysis, and a pressure compensation method was devised. When the divergence of the feedback force vector was not zero, it influenced the pressure field in the UMI simulation while improving the computational accuracy of the velocity field. Hence, the correct pressure was estimated by adding pressure compensation to remove the deteriorating effect of the feedback. A numerical experiment was conducted dealing with the reproduction of a synthetic three-dimensional steady flow in a thoracic aneurysm to validate results of the theoretical analysis and the proposed pressure compensation method. The ability of the UMI simulation to reproduce the pressure field deteriorated with a large feedback gain. However, by properly compensating the effects of the feedback signals on the pressure, the error in the pressure field was reduced, exhibiting improvement of the computational accuracy. It is thus concluded that the UMI simulation with pressure compensation allows for the reproduction of both velocity and pressure fields of blood flow.

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“…has been also investigated [26]. The computational accuracy and the fundamental characteristics, such as steady and transient characteristics, of the MR-MI simulation were investigated by a numerical experiment for the three-dimensional steady and unsteady blood flow fields in a cerebral aneurysm developed at a bifurcation ( Figure 18).…”

Section: Blood Flowsmentioning

confidence: 99%

“…Figure 3 shows the critical feedback gains with the computational time step plotted for the results of UMI simulation for blood flow in an aneurismal aorta (Case 1) [25] [30], magnetic-resonance measurement-integrated (MR-MI) blood flow simulation in a cerebral aneurism (Case 2) [26], and MI simulation for the turbulent flow in a square duct (Case 4). Theoretical values for the critical feedback gain were obtained from Equation (17).…”

Section: Stabilizationmentioning

confidence: 99%

A Review of Measurement-Integrated Simulation of Complex Real Flows

Hayase¹

2015

JFCMV

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In spite of the inherent difficulty, reproducing the exact structure of real flows is a critically important issue in many fields, such as weather forecasting or feedback flow control. In order to obtain information on real flows, extensive studies have been carried out on methodology to integrate measurement and simulation, for example, the four-dimensional variational data assimilation method (4D-Var) or the state estimator such as the Kalman filter or the state observer. Measurement-integrated (MI) simulation is a state observer in which a computational fluid dynamics (CFD) scheme is used as a mathematical model of the physical system instead of a small dimensional linear dynamical system usually used in state observers. A large dimensional nonlinear CFD model makes it possible to accurately reproduce real flows for properly designed feedback signals. This review article surveys the theoretical formulations and applications of MI simulation. Formulations of MI simulation are presented, including governing equations of a flow field observer, those of a linearized error dynamics describing the convergence of the observer, and stabilization of the numerical scheme, which is important in implementation of MI simulation. Applications of MI simulation are presented ranging from fundamental turbulent flows in pipes and Karman vortices in a wind tunnel to clinical application in diagnosis of blood flows in a human body.

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Numerical Validation of MR-Measurement-Integrated Simulation of Blood Flow in a Cerebral Aneurysm

Cited by 25 publications

References 22 publications

Applications of variational data assimilation in computational hemodynamics

Applications of variational data assimilation in computational hemodynamics

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

A Review of Measurement-Integrated Simulation of Complex Real Flows

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