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

Abstract

Abstract-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.

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

“…The subject (a 62-yearold male patient with a chronic aortic aneurysm in his descending aorta), as well as the measurement devices and method [an ultrasound device (SONOS 5500, Philips Medical Systems, Andover, MA, USA) with a trans-esophageal ultrasonic transducer (T6210, Philips Medical Systems, Andover, MA, USA)] in this study were the same as those in the former work (15) . Ultrasonic measurement was carried out with a color Doppler imaging technique from inside the esophagus.…”

“…Secondly, for feedback formula B, the effect of feedback gains (K v , K p ) on momentum and pressure equations is investigated. In the former study (15) , for the sake of simplicity, limited conditions K v = K p were investigated. In the present study, however, the optimum combination of the multiple feedback gains is investigated by changing them in two-dimensional parameter space.…”

“…The present paper deals with further investigation of the feedback law of UMI simulation using the same twodimensional model problem as that of the former study (15) . First, the effects of the arrangement of feedback points are investigated.…”

“…Detailed particulars remain to be accounted for. In a former study (15) , the authors numerically investigated the efficiency of UMI simulation using a two-dimensional model problem of blood flow in an aneurysmal aorta. The work defined two rectangular feedback domains, which covered an aneurysm or the blood vessel around the aneurysm, and applied feedback at all grid points in those domains.…”

“…For this purpose, we have proposed UltrasonicMeasurement-Integrated (UMI) simulation (15) , introducing the concept of flow observer to blood flow simulation to reproduce the real blood flow numerically with the aid of feedback from measurement (16) - (18) . In other fields, Hayase et al applied flow observer to a turbulent flow through a square duct (16) , and Nisugi et al developed a hybrid wind tunnel and investigated the flow with a Karman vortex street (17), (18) .…”