We present a novel method for the automated extraction of blood vessel centerlines. There are two major contributions. First, in order to avoid the shortcuts to which minimal path methods are prone, we find optimal paths in a computed flow field. We solve for a steady state porous media flow inside a region of interest and trace centerlines as maximum flow paths. We explain how to estimate anisotropic orientation tensors which are used as permeability tensors in our flow field computation. Second, we introduce a convolutional neural network (CNN) classifier for removing extraneous paths in the detected centerlines. We apply our method to the extraction of coronary artery centerlines found in Computed Tomography Angiography (CTA). The robustness and stability of our method are enhanced by using a model-based detection of coronary specific territories and main branches to constrain the search space [ 15 ]. Validation against 20 comprehensively annotated datasets had a sensitivity and specificity at or above 90 %. Validation against 106 clinically annotated coronary arteries showed a sensitivity above 97 %. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Many flow visualization techniques, especially integration-based methods, are problematic when the measured data exhibit noise and discretization issues. Particularly, this is the case for flow-sensitive phase-contrast magnetic resonance imaging (PC-MRI) data sets which not only record anatomic information, but also time-varying flow information. We propose a novel approach for the visualization of such data sets using integration-based methods. Our ideas are based upon finite-time Lyapunov exponents (FTLE) and enable identification of vessel boundaries in the data as high regions of separation. This allows us to correctly restrict integration-based visualization to blood vessels. We validate our technique by comparing our approach to existing anatomy-based methods as well as addressing the benefits and limitations of using FTLE to restrict flow. We also discuss the importance of parameters, i.e., advection length and data resolution, in establishing a well-defined vessel boundary. We extract appropriate flow lines and surfaces that enable the visualization of blood flow within the vessels. We further enhance the visualization by analyzing flow behavior in the seeded region and generating simplified depictions.