2D versus 3D cross-correlation-based radial and circumferential strain imaging in a 3D atherosclerotic carotid artery model using ultrafast plane wave ultrasound

Three-dimensional vascular strain estimation is crucial for assessment of the location of high strain regions in the carotid artery (CA) and the identification of vulnerable plaque features. This study compares 2D vs. 3D displacement estimation in terms of radial and circumferential strain using simulated ultrasound images of a 3D atherosclerotic CA model at the bifurcation embedded in surrounding tissue. The 3D finite element model (FEM) of a patient-specific, pulsating atherosclerotic CA (pulse pressure 60 mmHg) was generated with ABAQUS FEM software. Global longitudinal motion was superimposed to the model. Radiofrequency (RF) ultrasound data were simulated in Field II by moving point scatterers (vessel wall) according to the deformation patterns of the model. A linear array transducer (f
c
= 9 MHz, pitch = 198 µm, 192 elements) was used which transmitted plane waves at 3 alternating angles (+19.5°, 0°, −19.5°) at a pulse repetition rate of 10 kHz. Simulations with 20 ms (systole) and 100 ms (diastole) inter-frame (IF) time were performed for 191 equally spaced (0.1 mm) longitudinal positions of the internal CA containing fatty and calcified areas. After delay-and-sum beamforming, IF axial displacements were estimated using a coarse-to-fine normalized cross-correlation method. The axial displacement at 0° was used as the vertical displacement component. Projection of the −19.5° and +19.5° axial displacements yielded the horizontal displacement component. A polar grid and the lumen center were determined in the end-diastolic frame of each longitudinal position and used to convert the tracked vertical and horizontal displacements into radial and circumferential displacements. Least squares strain estimation was performed to determine accumulated radial and circumferential strain. The performance of the 2D and 3D method was compared by calculating the root-mean-squared error (RMSE) of the estimated strains with respect to the reference strains obtained from the model. More accurate strain images were obtained using the 3D displacement estimation for the entire cardiac cycle. The 3D technique clearly outperforms the 2D technique in phases with high IF longitudinal motion.