Ultrasonic-Measurement-Integrated Simulation Research Articles

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

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.

Numerical Analysis of Effects of Measurement Errors on Ultrasonic-Measurement-Integrated Simulation

Ultrasonic-measurement-integrated (UMI) simulation, in which feedback signals are applied to the governing equations based on errors between ultrasonic measurement and numerical simulation, has been investigated for reproduction of the blood flow field. However, ultrasonic measurement data inherently include some errors. In this study, the effects of four major measurement errors, namely, errors due to gaussian noise, aliasing, wall filter, and lack of data, on UMI simulation were examined by a numerical experiment dealing with the blood flow field in the descending aorta with an aneurysm, the same as in our previous study. While solving the governing equations in UMI simulation, gaussian noise did not prevent the UMI simulation from effectively reproducing the blood flow field. In contrast, aliasing caused significant errors in UMI simulation. Effects of wall filter and lack of data appeared in diastole and in the whole period, respectively. By detecting significantly large feedback signals as a sign of aliasing and by not adding feedback signals where measured Doppler velocities were aliasing or zero, the computational accuracy substantially improved, alleviating the effects of measurement errors. Through these considerations, UMI simulation can provide accurate and detailed information on hemodynamics with suppression of four major measurement errors.

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

In ultrasonic-measurement-integrated (UMI) simulation of blood flows, feedback signals proportional to the difference of velocity vector optimally estimated from Doppler velocities are applied in the feedback domain to reproduce the flow field. In this paper, we investigated the transient and steady characteristics of UMI simulation by numerical experiment. A steady standard numerical solution of a three-dimensional blood flow in an aneurysmal aorta was first defined with realistic boundary conditions. The UMI simulation was performed assuming that the realistic velocity profiles in the upstream and downstream boundaries were unknown but that the Doppler velocities of the standard solution were available in the aneurysmal domain or the feedback domain by virtual color Doppler imaging. The application of feedback in UMI simulation resulted in a computational result approach to the standard solution. As feedback gain increased, the error decreased faster and the steady error became smaller, implying the traceability to the standard solution improves. The positioning of ultrasound probes influenced the result. The height less than or equal to the aneurysm seemed better choice for UMI simulation using one probe. Increasing the velocity information by using multiple probes enhanced the UMI simulation by achieving ten times faster convergence and more reduction of error.

Numerical Experiment for Ultrasonic-Measurement-Integrated Simulation of Three-Dimensional Unsteady Blood Flow

Integration of ultrasonic measurement and numerical simulation is a possible way to break through limitations of existing methods for obtaining complete information on hemodynamics. We herein propose Ultrasonic-Measurement-Integrated (UMI) simulation, in which feedback signals based on the optimal estimation of errors in the velocity vector determined by measured and computed Doppler velocities at feedback points are added to the governing equations. With an eye towards practical implementation of UMI simulation with real measurement data, its efficiency for three-dimensional unsteady blood flow analysis and a method for treating low time resolution of ultrasonic measurement were investigated by a numerical experiment dealing with complicated blood flow in an aneurysm. Even when simplified boundary conditions were applied, the UMI simulation reduced the errors of velocity and pressure to 31% and 53% in the feedback domain which covered the aneurysm, respectively. Local maximum wall shear stress was estimated, showing both the proper position and the value with 1% deviance. A properly designed intermittent feedback applied only at the time when measurement data were obtained had the same computational accuracy as feedback applied at every computational time step. Hence, this feedback method is a possible solution to overcome the insufficient time resolution of ultrasonic measurement.

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

Cardiovascular diseases are closely related to blood flow. Ultrasonic-Measurement-Integrated (UMI) simulation, in which results of ultrasonic measurement are fed back to the flow simulation, was proposed in a previous study in order to reproduce the real blood flow accurately and efficiently. The usability of the UMI simulation was confirmed by numerical experiment, but the effectiveness of this simulation was strongly affected by the accuracy of the ultrasonic measurement. In this paper, we examined the accuracy of a commercial ultrasonic measurement device by an experiment with a PVA-H straight tube phantom. By analyzing the measured color Doppler images for a developed laminar flow inside the phantom, we obtained the relationship between the color Doppler value and the Doppler velocity (C-V relationship). It was revealed that the original C-V relationship provided in the device as a color bar was not suitable for quantitative evaluation of Doppler velocity to be used in UMI simulation. Compared with the original C-V relationship, the present C-V relationship results are in far better agreement with the analytic solution. Investigation of the normalized error confirmed that the result obtained with the present C-V relationship was reliable in cases of relatively high Reynolds number in the flow domain except near the wall. The two signal conditioning factors of the device had little influence on the Doppler velocity. Finally, we investigated the effect of temporal and spatial averaging of ultrasonic measurement data to clarify the relation between the number of averagings and the level of agreement with the analytic solution.

Numerical Experiment for Ultrasonic-Measurement-Integrated Simulation of Developed Laminar Pipe Flow Using Axisymmetric Model

Many studies have been carried out on the relationship between the occurrence and progression of circulatory diseases and hemodynamics. However, it is difficult to obtain accurate and detailed information on blood flow in the living body with existing experimental and numerical methods. The authors have previously proposed the Ultrasonic-Measurement-Integrated (UMI) simulation and shown that the blood flow in an aortic aneurysm can be accurately reproduced when feedback signals derived from the difference between measured and computed Doppler velocities are fed back to the numerical simulation. In the present study, we performed a fundamental numerical experiment in which UMI simulation was applied to a developed laminar pipe flow using an axisymmetric model in order to understand the effect of the feedback law on the accuracy of UMI simulation systematically. The effect of two types of ultrasonic probes, the linear scanning type and the sector scanning type, and the effect of 70° and 110° irradiating angles of the ultrasonic beam in the linear probe were investigated. It was confirmed that the result of UMI simulation asymptotically approached the standard solution of developed laminar flow downstream of the feedback domain in all cases using the linear probe and the sector probe with axisymmetric feedback. Under the present conditions, a linear probe with a radiation angle of 70° was most effective, whereas there was not so much improvement in the accuracy in the case using the sector probe. The effect of the singularity of the axisymmetric coordinate on the pipe axis was observed in the axial velocity profile near the entrance of the feedback domain, but disappeared some distance downstream in that domain.

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

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.

637 血流の超音波計測融合シミュレーションに関する研究 : 第6報:3次元非定常血流解析(G02-6 シミュレーション(1),G02 バイオエンジニアリング)

Development and progress of circulatory diseases are closely related to the hemodynamics in the blood vessel. However, detailed and accurate information of blood flow field has yet to be obtained due to the limitations both in measurement and numerical simulation. Hence, we have proposed the Ultrasonic-Measurement-Integrated (UMI) simulation. In this method, feedback signals derived from the difference between measured and computed Doppler velocities are fed back to the numerical simulation. The transient and steady characteristics of the UMI simulation have been revealed. In this paper, we performed the numerical experiment aiming at the reproduction of the three-dimensional unsteady flow field. As the result, the application of the feedback in the UMI simulation made the computational results converge and trace to the model of real blood flow.

Detection and correction of aliasing in ultrasonic measurement of blood flows with Ultrasonic-Measurement-Integrated simulation

Detailed information of real blood flows is essential to develop an accurate diagnosis or treatment for serious circulatory diseases such as aortic aneurysms. Ultrasonic-Measurement-Integrated (UMI) simulation, in which feedback signals from the ultrasonic measurement make the simulation converge to the real blood flow, is a key to solving this problem. However, aliasing in the ultrasonic blood velocity measurement causes UMI simulation to converge to an erroneous result. In this paper, we have investigated the detection and the correction of aliasing in UMI simulation. The artificial force in the feedback of UMI simulation can be used as an index to detect the aliasing. We have proposed two ways for the correction of the aliasing. Correction A, in which measurement velocity is replaced with the computational one at the monitoring point where the aliasing is detected, substantially improves the accuracy of UMI simulation. Correction B, in which measurement velocity is replaced with an estimated Doppler velocity, can provide exactly the same result as that of UMI simulation using the nonaliased standard solution. Although correction B gives the most accurate result, correction A seems more robust and, therefore, a beneficial choice considering the other artifacts in the measurement.

Fundamental Study of Ultrasonic-Measurement-Integrated Simulation of Real Blood Flow in the Aorta

Acquisition of detailed information on the velocity and pressure fields of the blood flow is essential to achieve accurate diagnosis or treatment for serious circulatory diseases such as aortic aneurysms. A possible way to obtain such information is integration of numerical simulation and color Doppler ultrasonography in the framework of a flow observer. This methodology, namely, Ultrasonic-Measurement-Integrated (UMI) Simulation, consists of the following processes. At each time step of numerical simulation, the difference between the measurable output signal and the signal indicated by numerical simulation is evaluated. Feedback signals are generated from the difference, and numerical simulation is updated applying the feedback signal to compensate for the difference. This paper deals with a numerical study on the fundamental characteristics of UMI simulation using a simple two-dimensional model problem for the blood flow in an aorta with an aneurysm. The effect of the number of feedback points and the feedback formula are investigated systematically. It is revealed that the result of UMI simulation in the feedback domain rapidly converges to the standard solution, even with usually inevitable incorrect upstream boundary conditions. Finally, an example of UMI simulation with feedback from real color Doppler measurement also shows a good agreement with measurement.

1108 血流の超音波計測融合シミュレーションに関する研究 : 第4報:血行力学解析の高精度化(S14-2 制御と情報・生体への応用(2),S14 制御と情報・生体への応用)

Hemodynamics plays an important role in the development, progress and rupture of aneurysms, and therefore, is essential for advanced diagnosis. However, existing methodologies have yet to provide detailed and accurate information of blood flow field due to their individual limitations. As a solution to the problem, we have proposed Ultrasonic-Measurement-Integrated (UMI) simulation. In this method, feedback signals derived from the difference between measured Doppler velocity and the calculated one by numerical simulation are fed back to the numerical simulation. In this paper, we validate the efficacy of three-dimensional UMI simulation by the numerical analysis with various irradiation methods of ultrasonic beam. As the result, UMI simulation improves computational accuracy and enables us to obtain more accurate information of blood flow field including wall shear stress.