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May  2010, 4(2): 241-255. doi: 10.3934/ipi.2010.4.241

Level set based brain aneurysm capturing in 3D

Bin Dong 1, , Aichi Chien 2, , Yu Mao 1, , Jian Ye 1, , Fernando Vinuela 2, and  Stanley Osher 3,

1. 

Department of Mathematics, University of California Los Angeles, CA 90095, United States, United States, United States
2. 

Division of Interventional Neuroradiology, David Geffen School of Medicine, University of California Los Angeles, 10833 LeConte Ave, Los Angeles, CA, United States, United States
3. 

Department of Mathematics, University of California, Los Angeles, CA 90095, United States

Received  February 2009 Revised  September 2009 Published  May 2010

Brain aneurysm rupture has been reported to be closely related to aneurysm size. The current method used to determine aneurysm size is to measure the dimension of the aneurysm dome and the width of the aneurysm neck. Since aneurysms usually have complicated shapes, using just the size of the aneurysm dome and neck may not be accurate and may overlook important geometrical information. In this paper we present a level set based surface capturing algorithm to first capture the aneurysms from the vascular tree. Since aneurysms are described by level set functions, volumes, curvatures and other geometric quantities of the aneurysm surface can easily be computed for medical studies. Experiments and comparisons with models used for capturing illusory contours in 2D images are performed. Applications to medical images are also presented to show the accuracy, consistency and robustness of our method in capturing brain aneurysms and volume quantification.
Keywords: mean curvature, partial differential equations, volumetric image analysis., brain aneurysm, level set method, Gaussian curvature, Aneurysm geometry.
Mathematics Subject Classification: Primary: 92C55, 68U10; Secondary: 65D18, 53C4.
Citation: Bin Dong, Aichi Chien, Yu Mao, Jian Ye, Fernando Vinuela, Stanley Osher. Level set based brain aneurysm capturing in 3D. Inverse Problems and Imaging, 2010, 4 (2) : 241-255. doi: 10.3934/ipi.2010.4.241
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