Geometric modeling of thick and closed surfaces : application to pelvic organs
Résumé
Although surgery is often used to treat disorders coming from physiological changes in the spatial configuration of the pelvic organs, the process is poorly reproductible and controllable from one patient to another. The work described below consists in developping a realistic geometric modeling, integrated in a patient-specific simulator.
Geometric modeling of organs with noisy scattered datasets is still a challenging problem. In our study case, each shape has been considered closed, smooth, hollow with a thick membrane. We propose a two-step method to define a physiological realistic model: the construction of the surface and the addition of a thickness.
In order to meet the physiological constraints, to manipulate the geometry and to accurately localize a point on the surface, a 0-genus B-spline surface is fitted to the data. It minimizes a bidirectional energy, characterizing the dissimilarities between the input dataset and the associated surface sampling. Its reduction is based on an alternate scheme between re-parametrization and optimal steepest descent step.Once achieved, an offset-surface is generated inwards, helped by a mesh to overcome self-intersection problems. The process created takes into account the elongated shapes of the organs, based on a curvilinear axis describing their generalized diameter. Finally, a hexahedral mesh is created from the fitted surface and its offset.% It is the start point for the next step of the project consisting in mechanically simulating the dynamic behavior of the organs.