Area-Preserving Mapping of 3D Carotid Ultrasound Images Using Density-Equalizing Reference Map
Gary P. T. Choi, Bernard Chiu, Chris H. Rycroft
Abstract
Atherosclerotic plaques are focal and tend to occur at arterial bends and bifurcations. To quantitatively monitor the local changes in the carotid vessel-wall-plus-plaque thickness (VWT) and compare the VWT distributions for different patients or for the same patients at different ultrasound scanning sessions, a mapping technique is required to adjust for the geometric variability of different carotid artery models. In this work, we propose a novel method called density-equalizing reference map (DERM) for mapping 3D carotid surfaces to a standardized 2D carotid template, with an emphasis on preserving the local geometry of the carotid surface by minimizing the local area distortion. The initial map was generated by a previously described arc-length scaling (ALS) mapping method, which projects a 3D carotid surface onto a 2D non-convex L-shaped domain. A smooth and area-preserving flattened map was subsequently constructed by deforming the ALS map using the proposed algorithm that combines the density-equalizing map and the reference map techniques. This combination allows, for the first time, one-to-one mapping from a 3D surface to a standardized non-convex planar domain in an area-preserving manner. Evaluations using 20 carotid surface models show that the proposed method reduced the area distortion of the flattening maps by over 80% as compared to the ALS mapping method. The proposed method is capable of improving the accuracy of area estimation for plaque regions without compromising inter-scan reproducibility.