Physically consistent data assimilation method based on feedback control for patient‐specific blood flow analysis

Abstract

This paper presents a novel data assimilation method for patient-specific blood flow analysis based on feedback control theory called the physically consistent feedback control-based data assimilation (PFC-DA) method. In the PFC-DA method, the signal, which is the residual error term of the velocity when comparing the numerical and reference measurement data, is cast as a source term in a Poisson equation for the scalar potential field that induces flow in a closed system. The pressure values at the inlet and outlet boundaries are recursively calculated by this scalar potential field. Hence, the flow field is physically consistent because it is driven by the calculated inlet and outlet pressures, without any artificial body forces. As compared with existing variational approaches, although this PFC-DA method does not guarantee the optimal solution, only one additional Poisson equation for the scalar potential field is required, providing a remarkable improvement for such a small additional computational cost at every iteration. Through numerical examples for 2D and 3D exact flow fields, with both noise-free and noisy reference data as well as a blood flow analysis on a cerebral aneurysm using actual patient data, the robustness and accuracy of this approach is shown. Moreover, the feasibility of a patient-specific practical blood flow analysis is demonstrated.

A perspective review: Technical study of combining phase contrast magnetic resonance imaging and computational fluid dynamics for blood flow on carotid bifurcation artery

“…Moreover, the configuration and position of shearing velocity in PC-MRI integrated with CFD were similar in term of flow direction as reported by Isoda et al [95]. Furthermore, Mohd Adib et al, [96] claimed that lowvelocity difference was achieved with velocity-field-optimized (V-optimized) approach and they also introduced a physically consistent feedback control-based data assimilation (PFC-DA) method [97] to improve blood flow analysis by coupling the body force with the pressure boundary condition, but there was still 20% of deviation on the velocity difference.…”

Inverse problems in blood flow modeling: A review

“…In order words, this is equivalent to taking only the divergence‐free part of the feedback term in order to avoid pressure perturbations. Results showed to be more accurate than the approach without any correction from Funamoto et al 156 In Ii et al, 159 the approach was further refined to applying then divergence‐free feedback term only at inlet and outlet boundaries, showing that the observer presents reduced perturbations from to the measurement noise with respect to the feedback applied on the whole domain. As the authors claimed, theoretical analysis that supports the theoretical results remains an open task.…”

Data Assimilation for Full 4D PC‐MRI Measurements: Physics‐Based Denoising and Interpolation

“…PC‐MRI and ultrasound) use data assimilation to match simulation data with measured data. Many of these approaches focus on finding the optimal boundary conditions to match a target velocity field, for example, a measured velocity field [DPV12, FNE*18, IAWW18, GCM*18]. They often consider the whole measurement to find the 2D in/out‐flow conditions that best match the measured data.…”