Semi-3D strain imaging of an atherosclerotic carotid artery by multi-cross-sectional radial strain estimations using simulated multi-angle plane wave ultrasound

Three-dimensional vascular strain estimation is crucial for assessment of the location of high strain regions in the carotid artery. This study introduces a semi-3D radial strain imaging method which is tested in a 3D model of an atherosclerotic carotid artery. A 3D finite element model (FEM) of a patient-specific, pulsating atherosclerotic carotid artery (pulse pressure 60 mmHg) was generated with ABAQUS FEM software. Radiofrequency (RF) ultrasound data were simulated in Field II by point scatterers (≈vessel wall) moving according to the deformation patterns of the model. RF element data were simulated for a linear array transducer (f
_c
= 9 MHz, pitch = 198 μm, 192 elements) which transmitted plane waves at 3 alternating angles (+20°, 0°, -20°) at a pulse repetition rate of 12 kHz. Simulations with 25 ms inter-frame time were performed for 25 equally spaced (0.5 mm) elevational positions of the internal carotid artery containing fatty and calcified areas. After delay-and-sum beamforming, inter-frame 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 -20° and +20° axial displacements yielded the horizontal displacement component. Tracking was performed to accumulate displacements for each transversal position. A polar grid and the lumen center were determined in the end-diastolic frame of each elevational position and used to convert the tracked axial and lateral displacements into radial displacements. Least squares strain estimation was performed to determine accumulated radial strain. The root-mean-squared error (RMSE) of the estimated strains was calculated with respect to the ground truth strains obtained from the model. Fair agreement between the ground truth and the estimated radial strain was observed for all volumes over the entire pressure cycle. The RMSE between the ground truth and estimated strain was 1.4% at the maximum systolic pressure and revealed a ≈-7% strain region corresponding to a fatty region and a ≈-2% strain region corresponding to a calcified region. These preliminary results show the feasibility of 3D carotid strain imaging using plane wave imaging.