Interactive decomposition and mapping of saccular cerebral aneurysms using harmonic functions: its first application...

Recent developments in medical imaging and advanced computer modeling simulations) now enable studies designed to correlate either simulated or measured "patient-specific" parameters with the natural history of intracranial aneurysm i.e., ruptured or unruptured. To achieve significance, however, these studies require rigorous comparison of large amounts of data from large numbers of aneurysms, many of which are quite dissimilar anatomically. In this study, we present a method that can likely facilitate such studies as its application could potentially simplify an objective comparison of surface-based parameters of interest such as wall shear stress and blood pressure using large multi-patient, multi-institutional data sets. Based on the concept of harmonic function/field, we present a unified and simple approach for mapping the surface of an aneurysm onto a unit disc. Requiring minimal human interactions the algorithm first decomposes the vessel geometry into 1) target aneurysm and 2) parent artery and any adjacent branches; it, then, maps the segmented aneurysm surface onto a unit disk. In particular, the decomposition of the vessel geometry quantitatively exploits the unique combination of three sets of information regarding the shape of the relevant vasculature: 1) a distance metric defining the spatially varying deviation from a tubular characteristic (i.e., cylindrical structure) of a normal parent artery, 2) local curvatures and 3) local concavities at the junction/interface between an aneurysm and its parent artery. These three sets of resultant shape/geometrical data are then combined to construct a linear system of the Laplacian equation with a novel shape-sensitive weighting scheme. The solution to such a linear system is a shape-sensitive harmonic function/field whose iso-lines will densely gather at the border between the normal parent artery and the aneurysm. Finally, a simple ranking system is utilized to select the best candidate among all possible iso-lines. Quantitative analysis using “patient-specific” aneurysm geometries taken from our internal database demonstrated that the technique is robust. Similar results were obtained from aneurysms having widely different geometries (bifurcation, terminal and lateral aneurysms). Application of our method should allow for meaningful, reliable and reproducible model-to-model comparisons of surface-based physiological and hemodynamic parameters.