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Echocardiographic Particle Image Velocimetry Data Assimilation with Least-Square Finite Element Method Ìý

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Date and time:Ìý

Tuesday, March 11, 2014 - 10:30am

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Grandview Conference Room, 1320 Grandview Avenue

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Recent advancements in the field of echocardiography have introduced various methods to image blood flow in the heart [1]. Our particular interest is in the left ventricle (LV) of the heart, which pumps oxygenated blood from the lungs out through the aorta. One method for imaging blood flow is injecting FDA-approved micro-bubbles into the left ventricle, and then, using the motion of the mcro-bubbles and the frame rate of the ultrasound scan (i.e., using Particle Imagining Velocimetry or echo-PIV), the blood velocity can be calculated [2]. In addition to blood velocity, echocardiologists are also interested in calculating pressure gradients and other flow properties, but this is not currently possible because the velocity data obtained is two-dimensional and noisy. Our goal is to assimilate two-dimensional velocity data from micro-bubble ultrasound experiments into a three-dimensional computer model. In order to achieve this objective a numerical method is needed that can approximate the solution of a system of differential equation and assimilate an arbitrary number of noisy experimental data points at arbitrary locations within the domain of interests to provide a ‘most probable’ approximate solution that is properly influenced by the experimental data. Our progress in this particular area over the past few years is to develop a novel data assimilation strategy for combing two-dimensional noisy echo-PIV data in a very flexible and consistent manner for numerically approximating the solution to the Navier-Stokes equation. The approximate solution is calculated using the least-squares finite element method (LSFEM) and this method has been shown to be very flexible when assimilating noisy echo-PIV data [1]. This flexibility is due to the ability of the method to weight the more accurate echo-PIV data and use a lower weight for noisy data. This LSFEM method for assimilating echo-PIV data have been used to predict the 3-dimensional LV blood flow. Results from the current method clearly show the impact of matching the echo-PIV data weakly, and visualize the three-dimensional velocity field.

REFERENCES
1. Borazjani, I., et al., Left Ventricular Flow Analysis: Recent Advances in Numerical Methods and Applications in Cardiac Ultrasound. Computational and Mathematical Methods in Medicine, 2013.
2. Heys, J.J., et al., Weighted least-squares finite elements based on particle imaging velocimetry data. Journal of Computational Physics, 2010.229(1): p. 107-118.