Correspondence optimization in 2D standardized carotid wall thickness map by description length minimization: A tool for increasing reproducibility of 3D ultrasound-based measurements

Purpose: The previously described 2D standardized vessel-wall-plus-plaque thickness (VWT) maps constructed from 3D ultrasound vessel wall measurements using an arc-length (AL) scaling approach adjusted the geometric variability of carotid arteries and has allowed for the comparisons of VWT distributions in longitudinal and cross-sectional studies. However, this mapping technique did not optimize point correspondence of the carotid arteries investigated. The potential misalignment may lead to errors in point-wise VWT comparisons. In this paper, we developed and validated an algorithm based on steepest description length (DL) descent to optimize the point correspondence implied by the 2D VWT maps. Methods: The previously described AL approach was applied to obtain initial 2D maps for a group of carotid arteries. The 2D maps were reparameterized based on an iterative steepest DL descent approach, which consists of the following two steps. First, landmarks established by resampling the 2D maps were aligned using the Procrustes algorithm. Then, the gradient of the DL with respect to horizontal and vertical reparameterizations of each landmark on the 2D maps was computed, and the 2D maps were subsequently deformed in the direction of the steepest descent of DL. These two steps were repeated until convergence. The quality of the correspondence was evaluated in a phantom study and an in vivo study involving ten carotid arteries enrolled in a 3D ultrasound interscan variability study. The correspondence quality was evaluated in terms of the compactness and generalization ability of the statistical shape model built based on the established point correspondence in both studies. In the in vivo study, the effect of the proposed algorithm on interscan variability of VWT measurements was evaluated by comparing the percentage of landmarks with statistically significant VWT-change before and after point correspondence optimization. Results: The statistical shape model constructed with optimized correspondence was more compact and had a better generalization ability than that constructed using the AL approach in both the phantom and in vivo studies. A statistical test on the group-average VWT-Change at each point of the 2D carotid template showed that the group-average VWT-change was significantly different from 0 in 18% of landmarks when the AL approach was used, and this percentage was reduced to 11% after correspondence optimization. Conclusions: The optimized correspon