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Top1. Introduction
Magnetic resonance angiography (MRA) is used to image blood vessels, thus informing clinicians about the vascular anatomy and indicating regions affected by vascular disease such as atherosclerotic plaques, aneurysms, and arteriovenous malformation. With current advances in numerical modeling and rapid prototyping it became possible to generate patient-specific, three-dimensional models of these vascular regions (Cebral et al., 2005; Cebral, Mut, Weir, & Putman, 2011; Dillon-Murphy, Noorani, Nordsletten, & Figueroa, 2016; Sforza, Putman, & Cebral, 2012; Steinman, Milner, Norley, Lownie, & Holdsworth, 2003; Taylor & Figueroa, 2009; Taylor & Steinman, 2008). MRA-based numerical simulations of blood flow can compute patient-specific velocity and pressure fields and determine clinically-relevant flow descriptors, such as wall shear stress which affect vascular disease progression (Boussel et al., 2008; Cebral et al., 2017; Meng, Tutino, Xiang & Siddiqui, 2014; Baretta et al., 2011). These models can help treatment planning by providing valuable information on existing conditions and predicting post-surgical flow patterns (Chung & Cebral, 2015; Rayz et al., 2015; Taylor et al., 1999; Walcott et al., 2016; Bale-Glickman, Selby, Saloner, & Savas, 2003). Patient-specific models generated with 3D printing are used to construct flow phantoms for in vitro flow experiments (Raben, Hariharan, Robinson, Malinauskas, & Vlachos, 2016; Trager, Sadasivan, Seong, & Lieber, 2009; Zhou et al., 2010). Even without conducting flow analysis, 3D models can help neurovascular surgeons to visualize the structure and orientation of blood vessels they intend to treat.
Improved efficiency of the simulation algorithms enabled faster computational speeds (Mittal, 2015; van Tyen, Saloner, Jou, & Berger, 1994) reducing simulation times from days to hours if not minutes. However, the extraction of vascular geometries from medical imaging data still remains the most time-consuming step in patient-specific modeling process, often requiring many hours of manual labor. While there is an abundance of software capable of automatic image segmentation, the current segmentation algorithms are based on analysis of image intensity rather than on the knowledge of the vascular anatomy. Segmentation methods such as thresholding or region-growing are using the intensity values of the voxels to segment gray-scale image. For example, in the simplest thresholding approach all voxels that appear brighter than a certain intensity threshold is assigned to blood vessels, while darker voxels are considered to represent extra-vascular tissues. All these methods are therefore affected by the image signal-to-noise (SNR) ratio or limited spatial resolution, which can result in substantial segmentation errors. In example shown in Figure 1a, two adjacent arteries are blended into the same structure as the algorithm is unable to detect the sub-voxel space separating the vessels. Figure 1b shows another example where insufficient intensity of the voxels in a smaller artery resulted in erroneous termination of the segmented domain.
The quality of image-segmentation can be enhanced by machine learning methods where the algorithms are trained on large imaging datasets. While these methods are effective in elimination of most typical segmentation errors, they still fail in recognizing the structures in some complicated pathological cases where vessels are severely distorted by the disease.