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In this work, the advantages of face-based smoothing technique and extended finite element method (XFEM) are combined to develop a face-based smoothed extended finite element method (FS-XFEM). By this new method, arbitrary crack geometry can be modeled and crack advance can be simulated without remeshing. At the same time, the integration of singular term over the volume around the crack front can be eliminated induced by the transformation of volume integration into area integration. Numerical examples are presented to test the accuracy and convergence rate of the FS-XFEM. From the results, it is clear that smoothing technique can improve the performance of XFEM for three-dimensional fracture problems.

Background: Three-dimensional computed tomography (3D-CT) imaging has enabled more accurate preoperative planning. The purpose of this study was to investigate the results of a novel, computer-assisted, 3D corrective osteotomy using prefabricated bone graft substitute to treat malunited fractures of the distal radius.

Methods: We investigated 19 patients who underwent the computer-assisted 3D corrective osteotomy for a malunited fracture of the distal radius after the operation was stimulated with CT data. A prefabricated bone graft substitute corresponding to the patient’s bone defect was implanted and internal fixation was performed using a plate and screws. We compared postoperative radiographic parameters of the patient’s operated side with their sound side and analyzed clinical outcomes using Mayo wrist score.

Results: All patients achieved bone union on X-ray imaging at final follow-up. The mean differences of palmar tilt, radial inclination and ulnar variance between the operation side and the sound side were 4.3°, 2.3° and 1.2 mm, respectively. The Mayo wrist score was fair in 4 patients and poor in 15 patients before surgery. At the final follow-up after surgery, the scores improved to excellent in 3 patients, good in 11 patients and fair in 5 patients. There were two patients with correction loss at the final follow-up, but no patient complained of hand joint pain.

Conclusions: We believe that computer-assisted 3D corrective osteotomy using prefabricated bone graft substitute achieved good results because it worked as a guide to the accurate angle.