Abstract
In cranioplasty, neurosurgeons use bone grafts to repair skull defects. To ensure the protection of intracranial tissues and recover the original head shape for aesthetic purposes, a custom-made pre-fabricated prosthesis must match the cranial incision as closely as possible. In our previous study (Liao et al. in Med Biol Eng Comput 49:203–211, 2011), we proposed an algorithm consisting of the 2D snake and image registration using the patient’s own diagnostic low-resolution and defective high-resolution computed tomography (CT) images to repair the impaired skull. In this study, we developed a 3D multigrid snake and employed multiresolution image registration to improve the computational efficiency. After extracting the defect portion images, we designed an image-trimming process to remove the bumped inner margin that can facilitate the placement of skull implants without manual trimming during surgery. To evaluate the performance of the proposed algorithm, a set of skull phantoms were manufactured to simulate six different conditions of cranial defects, namely, unilateral, bilateral, and cross-midline defects with 20 or 40 % skull defects. The overall image processing time in reconstructing the defect portion images can be reduced from 3 h to 20 min, as compared with our previous method. Furthermore, the reconstruction accuracies using the 3D multigrid snake were superior to those using the 2D snake.
Similar content being viewed by others
References
Agner C, Dujovny M, Evenhouse R, Charbel FT, Sadler L (1998) Stereolithography for posterior fossa cranioplasty. Skull Base Surg 8:81–86
Barrett R (1994) Templates for the solution of linear systems: building blocks for iterative methods. Society for Industrial and Applied Mathematics, Philadelphia
Briggs WL, Henson VE, McCormick SF (2000) A multigrid tutorial, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia
Bronstein MM, Bronstein AM, Kimmel R, Yavneh I (2006) Multigrid multidimensional scaling. Numer Linear Algebr Appl 13:149–171
Carr JC, Fright WR, Beatson RK (1997) Surface interpolation with radial basis functions for medical imaging. IEEE Trans Med Imaging 16:96–107
Chong CS, Lee HP, Kumar AS (2006) Automatic hole repairing for cranioplasty using Bezier surface approximation. J Craniofac Surg 17:344–352
Cremers D, Tischhäuser F, Weickert J, Schnörr C (2002) Diffusion snakes: introducing statistical shape knowledge into the Mumford–Shah functional. Int J Comput Vis 50:295–313
Dean D, Min K-J (2003) Deformable templates for preoperative computer-aided design and fabrication of large cranial implants. Int Congr Ser 1256:710–715
D’Urso PS, Effeney DJ, Earwaker WJ, Barker TM, Redmond MJ, Thompson RG, Tomlinson FH (2000) Custom cranioplasty using stereolithography and acrylic. Br J Plast Surg 53:200–204
Frohn-Schauf C, Henn S, Witsch K (2004) Nonlinear multigrid methods for total variation image denoising. Comput Vis Sci 7:199–206
Garland M, Heckbert PS (1997) Surface simplification using quadric error metrics. In: Owen GS, Whitted T, Mones-Hattal B (eds) Proceedings of the 24th annual conference on computer graphics and interactive techniques, Los Angeles. ACM Press/Addison-Wesley Publishing Co., New York, pp 209–216
Gonzalez RC, Woods RE (2008) Digital image processing. Pearson/Prentice Hall, Upper Saddle River
Gopakumar S (2004) RP in medicine: a case study in cranial reconstructive surgery. Rapid Prototyp J 10:207–221
Haber E, Modersitzki J (2006) A multilevel method for image registration. SIAM J Sci Comput 27:1594–1607
Han X, Xu C, Prince JL (2007) Fast numerical scheme for gradient vector flow computation using a multigrid method. IET Image Process 1:48–55
Kass M, Witkin A, Terzopoulos D (1987) Snakes: active contour models. Int J Comput Vis 1:321–331
Kucukyuruk B, Abuzayed B, Sanus G, Aydin S, Aydin S (2011) Cranioplasty: review of materials and techniques. J Neurosci Rural Pract 2:162–167
Lee S-C, Wu C-T, Lee S-T, Chen P-J (2009) Cranioplasty using polymethyl methacrylate prostheses. J Clin Neurosci 16:56–63
Liao Y-L, Sun Y-N, Lu C-F, Wu Y-T, Wu C-T, Lee S-T, Lee J-D (2010) Skull-based registration of intra-subject CT images: the effects of different resolutions and partial contents. In: Mahadevan V, Zhou J (eds) Proceeding of the 2nd international con-ference on bioinformatics and biomedical technology (ICBBT). Research Publishing Services, Singapore, pp 269–272
Liao Y-L, Lu C-F, Sun Y-N, Wu C-T, Lee J-D, Lee S-T, Wu Y-T (2011) Three-dimensional reconstruction of cranial defect using active contour model and image registration. Med Biol Eng Comput 49:203–211
Liao Y-L, Sun Y-N, Guo W-Y, Chou Y-H, Hsieh J-C, Wu Y-T (2011) A hybrid strategy to integrate surface-based and mutual-information-based methods for co-registering brain SPECT and MR images. Med Biol Eng Comput 49:671–685
Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. ACM SIGGRAPH Comput Graph 21:163–169
Luebke DP (2001) A developer’s survey of polygonal simplification algorithms. IEEE Comput Graph Appl 21:24–35
Maes F, Vandermeulen D, Suetens P (1999) Comparative evaluation of multiresolution optimization strategies for multimodality image registration by maximization of mutual information. Med Image Anal 3:373–386
Maravelakis E, David K, Antoniadis A, Manios A, Bilalis N, Papaharilaou Y (2008) Reverse engineering techniques for cranioplasty: a case study. J Med Eng Technol 32:115–121
Melax S (1998) A simple, fast, and effective polygon reduction algorithm. Game Dev 5:44–49
Movassaghi K, Ver Halen J, Ganchi P, Amin-Hanjani S, Mesa J, Yaremchuk MJ (2006) Cranioplasty with subcutaneously preserved autologous bone grafts. Plast Reconstr Surg 117:202–206
Papandreou G, Maragos P (2007) Multigrid geometric active contour models. IEEE Trans Image Process 16:229–240
Pham DL, Prince JL (1999) Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans Med Imaging 18:737–752
Pluim JPW, Maintz JBA, Viergever MA (2001) Mutual information matching in multiresolution contexts. Image Vis Comput 19:45–52
Press WH (1992) Numerical recipes in C: the art of scientific computing. Cambridge University Press, Cambridge
Shi L, Yu Y, Bell N, Feng W-W (2006) A fast multigrid algorithm for mesh deformation. ACM Trans Graph 25:1108–1117
Taub PJ, Rudkin GH, Clearihue WJ, Miller TA (2003) Prefabricated alloplastic implants for cranial defects. Plast Reconstr Surg 111:1233–1240
Terzopoulos D (1986) Image analysis using multigrid relaxation methods. IEEE Trans Pattern Anal Mach Intell 8:129–139
Wesseling P (2004) An Introduction to Multigrid Methods. R.T. Edwards, Philadelphia
Wu T, Engelhardt M, Fieten L, Popovic A, Radermacher K (2006) Anatomically constrained deformation for design of cranial implant: methodology and validation. In: Larsen R, Nielsen M, Sporring J (eds) 9th international conference on medical image computing and computer assisted intervention (MICCAI), LNCS 4190. Springer, Berlin, pp 9–16
Wu WZ, Zhang Y, Li H, Wang WS (2009) Fabrication of repairing skull bone defects based on the rapid prototyping. J Bioact Compat Polym 24:125–136
Yamashima T (1989) Cranioplasty with hydroxylapatite ceramic plates that can easily be trimmed during surgery. Acta Neurochir 96:149–453
Acknowledgments
The authors express appreciation to Fu-Jung Chen in Medical Augmented Reality Research Center, Chang Gung Memorial Hospital for help acquiring the phantom data. Our gratitude also goes to E. William Thornton and Bill Thornton of Wallace Academic Editing for his assistance in English language editing. This work is funded by the Technology Development Program for Academia of Department of Industrial Technology, Ministry of Economic Affairs (97-EC-17-A-19-S1-035, 98-EC-17-A-19-S1-035, and 99-EC-17-A-19-S1-035), National Science Council (NSC100-2221-E-010-009, NSC98-2221-E-182-040-MY3, NSC100-2321-B-010-003, and NSC101-2221-E-010-004-MY2), NSC support for the Center for Dynamical Biomarkers and Translational Medicine, National Central University (NSC100-2911-I-008-001), and Brain Research Center, National Yang-Ming University and a grant from Ministry of Education, Aim for the Top University Plan (101AC-B902).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Liao, YL., Lu, CF., Wu, CT. et al. Using three-dimensional multigrid-based snake and multiresolution image registration for reconstruction of cranial defect. Med Biol Eng Comput 51, 89–101 (2013). https://doi.org/10.1007/s11517-012-0972-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11517-012-0972-y