Conformal mapping of carotid vessel wall and plaque thickness measured from 3D ultrasound images

Adaptive area-preserving parameterization of open and closed anatomical surfaces

The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape description. However, establishing a one-to-one correspondence between the object surface and the entire unit sphere may induce a large geometric distortion in case the shape of the surface is too different from a perfect sphere. In this work, we propose adaptive area-preserving parameterization methods for simply-connected open and closed surfaces with the target of the parameterization being a spherical cap. Our methods optimize the shape of the parameter domain along with the mapping from the object surface to the parameter domain. The object surface will be globally mapped to an optimal spherical cap region of the unit sphere in an area-preserving manner while also exhibiting low conformal distortion. We further develop a set of spherical harmonics-like basis functions defined over the adaptive spherical cap domain, which we call the adaptive harmonics. Experimental results show that the proposed parameterization methods outperform the existing methods for both open and closed anatomical surfaces in terms of area and angle distortion. Surface description of the object surfaces can be effectively achieved using a novel combination of the adaptive parameterization and the adaptive harmonics. Our work provides a novel way of mapping anatomical surfaces with improved accuracy and greater flexibility. More broadly, the idea of using an adaptive parameter domain allows easy handling of a wide range of biomedical shapes.

Shape analysis via inconsistent surface registration

In this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmark-based geometric morphometr- ics methods suffer from the limited degrees of freedom, while most of the more advanced non-rigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with prominent feature landmarks, it is more desirable to have a method that automatically detects the most relevant parts of the two surfaces and finds the optimal landmark-matching alignment between these parts, without assuming any global 1-1 correspondence between the two surfaces. Our method is capable of solving this problem using inconsistent surface registration based on quasi-conformal theory. It further enables us to quantify the dissimilarity of two shapes using quasi-conformal distortion and differences in mean and Gaussian curvatures, thereby providing a natural way for shape classification. Experiments on Platyrrhine molars demonstrate the effectiveness of our method and shed light on the interplay between function and shape in nature.

Ultrasonography of vulnerable atherosclerotic plaque in the carotid arteries: B-mode imaging

The most common type of stroke, i.e. ischemic stroke, is a great challenge for contemporary medicine as it poses both diagnostic and therapeutic difficulties. Atherosclerosis, which is rapidly beginning to affect more and more social groups, is the main cause of cerebrovascular accidents. Atherosclerosis is currently defined as a generalized, dynamic and heterogeneous inflammatory and immune process affecting arterial walls. Atherosclerotic plaque is the emanation of this disease. As the paradigm of the diagnosis of atherosclerosis has changed, it has become crucial to properly identify plaque instability within the carotid arteries by evaluating parameters and phenomena that signify a developing cascade of complications, eventually leading to stroke. Irrespective of the ultrasound technique employed, proper morphological evaluation of atherosclerotic plaque, involving observation of its echogenicity, i.e. subjective analysis of its structure, with the classification to Gray-Weale–Nicolaides types as well as assessment of the integrity of its surface, makes it possible to roughly evaluate plaque morphology and thereby its stability. This enables treatment planning and therapy monitoring. This evaluation should be a prelude to further diagnostic work-up, which involves non-invasive examinations that enable unambiguous assessment of plaque stability. These examinations include contrast-enhanced ultrasound to assess progression or recession of inflammation, which presents as plaque neovascularization, or shear wave elastography to objectively define tissue stiffness, and thereby its mineralization.

Area-Preserving Mapping of 3D Carotid Ultrasound Images Using Density-Equalizing Reference Map

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.