## Weighted Least-Square Finite Element Methods for PIV Data Assimilation

## Jeff Heys

## Dept. of Chemical and Biological Engineering, Univ of Montana

## Date and time:

Monday, November 14, 2011 - 3:45pm

## Abstract:

The ability to determine and diagnose irregular flow patterns clinically in the left ventricle (LV) is currently very challenging. One potential approach for non-invasively measuring blood flow dynamics in the LV is particle image velocimetry (PIV) using microbubbles. Originally described by Shanda’s group, echo-PIV is well suited for tracking complex flow patterns of intracavitary blood flow using contrast microbubbles that can be captured in sequences of high-frame-rate, two-dimensional (2D) ultrasonographic images. To obtain local flow velocity vectors and velocity maps, PIV software calculates displacements of microbubbles over a given time interval, which is typically determined by the actual frame rate. In addition to the fluid velocity, ultrasound images of the left ventricle can be used to determine the wall position as a function of time, and the inflow and outflow fluid velocity during the cardiac cycle. Despite the abundance of data, ultrasound and PIV alone are insufficient for calculating the flow properties of interest to clinicians. Specifically, the pressure gradient and total energy loss are of primary importance, but their calculation requires a full three-dimensional velocity field. Echo-PIV only provides 2D velocity data along a single plane within the LV. Our goal is to develop methods for coupling PIV data with computational fluid dynamics (CFD) so that CFD can be used to physical interpolate and extend the 2D PIV data into a full 3D field of velocity data – either in the LV or other domains.

This talk will describe a novel weighted least-squares finite element methodology to assimilate PIV data into a CFD simulation. To illustrate and validate our approach, we simulate both a deflected cellulose acetate flap and a beating left ventricle. To account for the changing shape of the cellulose acetate film and the moving heart walls, the CFD mesh is deformed using a pseudo-solid domain mapping technique at each time step.