Methods of modeling anatomical structures, along with pathology including the vasculature, spine and internal organs, for visualization and manipulation in simulation systems. A representation of on the human vascular network is built up from medical images and a geometrical model produced therefrom by extracting topological and geometrical information. The model is constructed using topological and geometrical information. The model is constructed using segments containing topology structure information, flow domain information contour domain information and skeletal domain information. A realistic surface is then applied to the geometric model, by generating a trajectory along a central axis of the geometric model, conducting moving trihedron modeling along the generated trajectory and then creating a sweeping surface along the trajectory. A novel joint reconstruction approach is also proposed whereby a part surface sweeping operation is performed across branches of the joint and then a surface created over the resultatn holes therebetween. A 3-D mesh may also be generated, based upon this model, for finite element analysis and pathology creation.