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.