Numerical Study on Variation of Feedback Methods in Ultrasonic-Measurement-Integrated Simulation of Blood Flow in the Aneurysmal Aorta

Abstract

The complicated relationships between hemodynamics and aneurysms have been investigated intensively. However, existing methodologies have inherent limitations in providing real blood flow fields. The authors have proposed Ultrasonic-Measurement-Integrated (UMI) simulation, in which the feedback signals lead to convergence of the calculated blood flow structure to the real one even with incorrect boundary/initial conditions. In UMI simulation, determination of the feedback law is substantially important, but detailed particulars remain to be accounted for. In this paper, first, the effects of density of feedback points and feedback domains are systematically investigated. Improvement of computational accuracy in the feedback domain is achieved even in low density of feedback points of 25%, and such improvement persists in the downstream region. Secondly, the most effective combination of feedback gains for momentum and pressure equations is investigated, confirming the validity of the simple condition to use the same value for the velocity and pressure gains.

Numerical Experiment of Transient and Steady Characteristics of Ultrasonic-Measurement-Integrated Simulation in Three-Dimensional Blood Flow Analysis

“…The feedback points were defined at all grid points (6002 points in total) in the feedback domain M referring to the former study. 6 This is the ideal situation, but it has been revealed that the computational accuracy of UMI simulation is little sensitive to the reduction of feedback point density in large feedback point density (larger than 0.25 in the former two-dimensional study). 6 Especially, the acquisition of Doppler velocity data on multiple transverse cross sections of blood vessel leads better reproduction of flow field than that on longitudinal cross sections due to the effect of flow convection.…”

“…To solve this problem, we have been developing ultrasonic-measurement-integrated (UMI) simulation on the basis of the concept of flow observer. 6,7 The flow observer was proposed by Hayase and Hayashi 10 for general flow problems integrating measurement and numerical simulation to reproduce the real flow field based on the concept of observers in control theory. In a numerical experiment, Hayase and Hayashi 10 successfully reproduced a turbulent flow including fluctuation in a square duct using a flow observer with a simple feedback law to modify the pressure boundary condition based on errors in the axial velocity components in a cross section of the duct.…”

“…The effect of the arrangement of the feedback points and the feedback domain was systematically investigated to reveal detailed particulars of the UMI simulation by the same two-dimensional numerical experiment. 6 For practical use of the UMI simulation in medical procedures, extended investigation of the efficiency of the UMI simulation for the blood flow field in realistic three-dimensional geometry is essential. In addition, as the transient characteristics of the UMI simulation determine the convergence to the target flow as well as the frequency response to the oscillatory blood flow, it is critically important that they be clarified.…”

Experimental Validation of Color Doppler Velocity Measurement for Ultrasonic-Measurement-Integrated Simulation of Blood Flow

“…By performing successive computation to reduce the difference to zero, the actual flow is reproduced asymptotically. In previous studies, Funamoto et al confirmed the usability of UMI simulation by 2-D and 3-D numerical experiments with realistic geometry of a thoracic aneurysm [16][17][18] . Although these numerical experiments were performed based on the assumption that there is no measurement error in ultrasonic measurement, the result of actual ultrasonic measurement inevitably contains some measurement error.…”

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

“…Those studies revealed that the UMI simulation improved computational accuracy in comparison with the ordinary simulation, making the computational velocity vector field approach that of a model solution of real blood flow. However, the reproducibility of the pressure field was not necessarily satisfactory [21,24].…”