Lagrangian displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging

Abstract

Purpose: Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires Lagrangian description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. Methods: Lagrangian based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polargrid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure Lagrangian description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. Results: A finite element based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the finite element model and our Lagrangian approach to strain estimation. Traditional Eulerian based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. Conclusions: Lagrangian displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both finite element and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.

Ultrasound elastography using multiple images

“…the Lagrangian particle tracking (e.g. for cardiac strain imaging over the cardiac cycle (Shi et al, 2008;Ma and Varghese, 2012)), and (2) strain images are averaged to reduce noise. In Lagrangian particle tracking, one should note that the location of a particle keeps changing in the image sequence, and therefore appropriate displacements must be accumulated.…”

Analysis of 2-D Ultrasound Cardiac Strain Imaging Using Joint Probability Density Functions

“…The incremental strain values directly derived from the 3D FEA cardiac model (denoted as “ideal strain”) can be utilized to evaluate the accuracy of strain estimation based on the corresponding estimated incremental strain along with the variations in the strain over several cardiac cycles (Chen and Varghese 2009; Chen and Varghese 2010; Ma and Varghese 2012b; Ma and Varghese 2012a). Plots of the strain probability distribution at different frame rates are shown in Fig.…”

“…Note that while the mean strain estimated using RF signals follow the ideal FEA curve closely for frame rates as low as 42 Hz, strain estimated using envelope signals fail to track the ideal curve even at an 83 Hz frame rate. Detailed analysis on strain estimated using RF and envelope strains at 250 Hz was described in our previous papers (Ma and Varghese 2012b; Ma and Varghese 2012a). Note that in Fig.…”

Segmental Analysis of Cardiac Short-Axis Views Using Lagrangian Radial and Circumferential Strain

“…A polar grid generation algorithm previously developed in our lab 24 was utilized. This algorithm incorporates semi-automatically tracked epi- and endocardial contours to generate a polar grid over several cardiac cycles.…”

“…In our previous work, we used a Lagrangian approach to generate axial and lateral strains over several cardiac cycles. 24 In this paper, we extend this Lagrangian approach to perform radial and circumferential strain estimation along the natural axes of deformation of the heart. Our polar grid–based approach is not limited by poor quality lateral displacement/strain estimation.…”