Background
Anatomical and clinical descriptions of variations in arteries are based solely on anatomical terminology. New diagnostic techniques depend on terms such as the anterior, posterior, superior, inferior, medial, and lateral location of arteries and their branches or bifurcations, trifurcations, and fenestrations. However, these methods may be obsolete and such a simplistic approach is inadequate, especially for procedures that require precise morphological and morphometrical descriptions in 3D space. This is critical for neruonavigational surgery and interventional vascular radiology.
Material and Method
This paper presents a new system for the accurate location and description of structural variations in vessels which is based on the alpha, beta, and gamma direction cosines. The algorithm can be summarized in the following steps: acquisition of the point coordinates in 3D space, interpolation, recovery of the 3D point coordinates, and calculation of the interpolated trajectory.
Results
New parameters (cos alpha, beta, and gamma, the tortuous index TI, and the deviation index DI) were calculated for the spatial description of vessels.
Conclusions
By using this new method, new vascular descriptive methods have been proposed. It is possible that new categories as well as vessel variations may be found. The curvature and tortuosity of the vascular segments can also be considered more effective when incorporated into the description of vessels, especially in cases where pathologies such as tumors have altered the vessel in some way.

Keywords: Mathematics, Software, Imaging, Three-Dimensional - methods, Magnetic Resonance Angiography - methods, Image Processing, Computer-Assisted - methods, Image Enhancement - methods, Image Interpretation, Computer-Assisted - methods, Tomography, X-Ray Computed - methods, Cerebral Arteries - pathology, Algorithms