  Carotid atherosclerosis is a focal disease at the bifurcations of the carotid
artery. To quantitatively monitor the local changes in the
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.
