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Automated vortex identification based on Lagrangian averaged vorticity deviation in analysis of blood flow in the
Ke Yang1, Shiqian Wu2, Dhanjoo N Ghista3
1Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan, China; Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan, China.
Objective:
To present and validate a method for automated identification of the Lagrangian vortices and Eulerian vortices for analyzing flow within the right atrium (RA), from phase contrast magnetic resonance imaging (PC-MRI) data.
Methodology:
Our proposed algorithm characterizes the trajectory integral associated with vorticity deviation and the spatial mean of vortex rings, for the Lagrangian averaged vorticity deviation (LAVD) based identification and tracking of vortex rings within the heart chamber. For this purpose, the optical flow concept was adopted to interpolate the time frames between larger discrete frames, to minimize the error caused by constructing a continuous velocity field for the integral process of LAVD. Then the Hough transform was used to automatically extract the vortex regions of interest. The computed flow data within the RA of the participants' hearts was then used to validate the performance of our proposed method.
Results:
In the paper, illustrations are provided for derived evolution of Euler vortices and Lagrangian vortices of a healthy subject. The visualization results have shown that our proposed method can accurately identify the Euler vortices and Lagrangian vortices, in the context of measuring the vorticity and vortex volume of the vortices within the RA chamber. Then the employment of Hough transform-based automated vortex extraction has improved the robustness and scalability of the LAVD in identifying cardiac vortices. The analytical results have demonstrated that the introduction of the Horn-Schunck optical flow can more accurately synthesize the intermediate PC-MRI to construct a continuous velocity field, compared with other interpolation methods.
Conclusion:
A novel analytical framework has been developed to accurately identify the flow vortices in the RA chamber based on Horn-Schunck optical flow and Hough transform. From the obtained analytical study results, the development and changes of dominant vortices within this cardiac chamber during the cardiac cycle can be acquired. This can provide to cardiologists a deeper understanding of the hemodynamics within the heart chambers.
