Model-based 3D Tracking of Cardiac Motion in HARP Images

We present an automated method for tracking 3D motion in planar tagged MRI. First, displacement between successive 2D image frames is estimated from their local phase, also known as HARP. The displacement estimates then drive a 3D finite element model which tracks systolic motion. The 3D model allows for 1) estimating 3D motion from niultiple 2D tagged images and 2) for regularizing the phase estimates, which are susceptible to image artifacts and noise. This technique allows for calculation of both global displacements and regional strain. Local Phase Estimation Given a repeating pattern, such as MRI tissue tags, the local phase can be used as a material marker of a point on this pattern. We use quadrature filters to estimate the local phase. This method is different for that in HAW [ 11, where a elliptical bandpass filter must set by the user. In general, phase is measured in 2D images using a set of four quadrature filters. For each coordinate direction u in the frequency domain, a spherically separable quadrature filter is defined as [2] F ( u ) = R(p)D(h), where p is the magnitude and h is the unit direction u. The directional function D(C) is oriented along the initial direction of the 2D tags. The radial frequency function R(p) is a Gaussian function on a logarithmic scale, and p is set to the tagging frequency. This function defines the frequency characteristics of the quadrature filter. After convolving the each image with these filters, the phase difference Aq5 is calculated as A$ = arg(ql * q2) . The quantity provides a measure for the certainty of the estimate. Finally, the displacement is proportional to the phase disparity: z = y .