A parametric method for characterization of deformation in the residuum vasculature

Objective: To demonstrate the relationship between modified Hausdorff distance (MH) and the spatial change of arterial vasculature in residuum. Methods: Data of the vascular model were obtained from CT scans of clinical cases, and a centerline model of the residuum vasculature was established by setting the appropriate parameter of distance between control points (DCP) in MIMICS 10.0. Deformation was applied on the model through compiling the program in MATLAB. The MH values before and after the deformation were calculated and analyzed. According to different locations of the rotation axis, the deformation was divided into four cases (C₁, C₂, C₃, C₄) on the basis of growth order in node numbers and total length of the vasculature. Results: MH increased with the increment of the vascular rotation angle, but due to different maximum rotation radius and total length of the vascular vessel, 4 deformed models showed different growth trends. With the rotation angle increasing, MH gradually increased from C₁ to C₄. The maximum change occurred from C₂ to C₃, and minimal change occurred from C₃ to C₄. Specifically, the maximum rotation radius and total length of the vessels from C₁ to C₂ increased by 22.2% and 91.3%, while those from C₃ to C₄ increased by 14.1% and 26.8%, respectively. Moreover, the maximum change of MH value was 60.4% from C₁ to C₂ and 4.5% from C₃ to C₄. Conclusions: MH can be an effective parameter to indicate spatial change of the residuum vasculature. MH of the residuum vasculature is proportional to deformation angle of the vessel, and the maximum rotation angle has a significant influence on MH. Moreover, when DCP is smaller than 3 mm, the influence of parameter setting can be avoided effectively. In addition, MH can also be applied in the studies of vasculature change and comparison.