Automatic branch detection of the arterial system from abdominal aortic segmentation.

We present a new method to automatically identify the different arteries present in an abdominal aortic segmentation. In this approach, the arterial system is first represented by a vascular tree, extracted from the segmentation and containing the topologic and geometric features (branch position, branch direction, branch length, branch diameter) of the arterial system. Then, the branches of the vascular tree are matched with the main arteries originating from the aorta: celiac artery, superior mesenteric artery, renal arteries and common iliac arteries. This match is determined by maximizing a similarity measure between the different branches and corresponding arteries. We evaluate this method on 239 segmentations obtained from 102 different patients. The results demonstrate the accuracy of the proposed method, capable of delivering an error of less than 2.5% for the identification of the celiac and superior mesenteric arteries, 8.4% for the renal arteries, and 2.1% for the common iliac arteries.

Advection modes by optimal mass transfer.

Classical model reduction techniques approximate the solution of a physical model by a limited number of global modes. These modes are usually determined by variants of principal component analysis. Global modes can lead to reduced models that perform well in terms of stability and accuracy. However, when the physics of the model is mainly characterized by advection, the nonlocal representation of the solution by global modes essentially reduces to a Fourier expansion. In this paper we describe a method to determine a low-order representation of advection. This method is based on the solution of Monge-Kantorovich mass transfer problems. Examples of application to point vortex scattering, Korteweg-de Vries equation, and hurricane Dean advection are discussed.