Automatic detection of symmetry plane for computer-aided surgical simulation in craniomaxillofacial surgery

Abstract

Symmetry plane calculation is used in fracture reduction or reconstruction in the midface. Estimating a reliable symmetry plane without advanced anatomic knowledge is the most critical challenge. In this work, we developed a new automated method to find the mid-plane in CT images of an intact skull and a skull with a unilateral midface fracture. By use of a 3D point-cloud of a skull, we demonstrate that the proposed algorithm could find a mid-plane that meets clinical criteria. There is no need for advanced anatomical knowledge through the use of this algorithm. The algorithm used principal component analysis to find the initial plane. Then the rotation matrix, derived from an iterative closest point (ICP) registration method, is used to update the normal vector of the plane and find the optimum symmetry plane. A mathematical index, Hausdorff distance (HD), is used to evaluate the similarity of one mid-plane side in comparison to the contralateral side. HD decreased by 66% in the intact skull and 65% in a fractured skull and converged in just six iterations. High convergence speed, low computational load, and high accuracy suggest the use of the algorithm in the planning procedure. This easy-to-use algorithm with its advantages, as mentioned above, could be used as an operator in craniomaxillofacial software.

Graphic abstract

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

References

  1. 1.

    Cevidanes LHS, Alhadidi A, Paniagua B, Styner M, Ludlow J, Mol A, Turvey T, Proffit WR, Rossouw PE (2011) Three-dimensional quantification of mandibular asymmetry through cone-beam computerized tomography. Oral Surg Oral Med Oral Pathol Oral Radiol 111(6):757–770

    Article  Google Scholar 

  2. 2.

    Bockey S, Berssenbrügge P, Dirksen D, Wermker K, Klein M, Runte C (2018) Computer-aided design of facial prostheses by means of 3D-data acquisition and following symmetry analysis. J Cranio-Maxillofac Surg 46(8):1320–1328

    Article  Google Scholar 

  3. 3.

    Li J, Yuan P, Chang CM, Ho DCY, Lo YF, Shen S, Kim D, Teichgraeber JF, Alfi DM, Gateno J, Xia JJ (2017) New approach to establish an object reference frame for dental arch in computer-aided surgical simulation. Int J Oral Maxillofac Surg 46(9):1193–1200

    CAS  Article  Google Scholar 

  4. 4.

    Ho JPTF, Schreurs R, Milstein DMJ, Dubois L, Maal TJJ, de Lange J, Becking AG (2016) Measuring zygomaticomaxillary complex symmetry three-dimensionally with the use of mirroring and surface based matching techniques. J Cranio-Maxillofac Surg 44(10):1706–1712

    Article  Google Scholar 

  5. 5.

    Ho JPTF, Schreurs R, Aydi S, Rezai R, Maal TJJ, van Wijk AJ, Beenen LFM, Dubois L, Milstein DMJ, Becking AG (2017) Natural variation of the zygomaticomaxillary complex symmetry in normal individuals. J Cranio-Maxillofac Surg 45(12):1927–1933

    Article  Google Scholar 

  6. 6.

    De Momi E, Chapuis J, Pappas I, Ferrigno G, Hallermann W, Schramm A, Caversaccio M (2006) Automatic extraction of the mid-facial plane for cranio-maxillofacial surgery planning. Int J Oral Maxillofac Surg 35(7):636–642

    Article  Google Scholar 

  7. 7.

    Roumeliotis G, Willing ÃR, Neuert M, Ahluwalia R, Jenkyn T, Yazdani A (2015) Application of a novel semi-automatic technique for determining the bilateral symmetry plane of the facial skeleton of normal adult males. J Craniofac Surg 26(6):1997–2001

    Article  Google Scholar 

  8. 8.

    Willing RT, Roumeliotis G, Jenkyn TR, Yazdani A (2013) Development and evaluation of a semi-automatic technique for determining the bilateral symmetry plane of the facial skeleton. Med Eng Phys 35(12):1843–1849

    Article  Google Scholar 

  9. 9.

    Di Angelo L, Di Stefano P, Governi L, Marzola A, Volpe Y (2019) A robust and automatic method for the best symmetry plane detection of craniofacial skeletons. Symmetry (Basel) 11(2):1–13

    Google Scholar 

  10. 10.

    Martini M, Klausing A, Messing-Jünger M, Lüchters G (2017) The self-defining axis of symmetry: a new method to determine optimal symmetry and its application and limitation in craniofacial surgery. J Cranio-Maxillofac Surg 45(9):1558–1565

    Article  Google Scholar 

  11. 11.

    AlHadidi A, Cevidanes LH, Paniagua B, Cook R, Festy F, Tyndall D (2014) 3D quantification of mandibular asymmetry using the SPHARM- PDM tool box. Int J Comput Assist Radiol Surg 7(2):265–271

    Article  Google Scholar 

  12. 12.

    Berlin NF, Berssenbrügge P, Runte C, Wermker K, Jung S, Kleinheinz J, Dirksen D (2014) Quantification of facial asymmetry by 2D analysis—a comparison of recent approaches. J Cranio-Maxillofac Surg 42(3):265–271

    Article  Google Scholar 

  13. 13.

    Kikinis R, Pieper SD, Vosburgh KG (2014) 3D Slicer: a platform for subject-specific image analysis, visualization, and clinical support. Intraoperative imaging and image-guided therapy. Springer, New York, pp 277–289

    Google Scholar 

  14. 14.

    Dimitrov D (2008) Geometric applications of principal component analysis. Dissertation, University of Berlin

  15. 15.

    Serej ND, Ahmadian A, Kasaei S, Sadrehosseini SM, Farnia P (2016) A robust keypoint extraction and matching algorithm based on wavelet transform and information theory for point-based registration in endoscopic sinus cavity data. Signal Image Video Process 10(5):983–991

    Article  Google Scholar 

  16. 16.

    Farnia P, Ahmadian A, Khoshnevisan A, Jaberzadeh A, Serej ND, Kazerooni AF (2011) An efficient point based registration of intra-operative ultrasound images with MR images for computation of brain shift; A phantom study. Annu Int Conf IEEE Eng Med Biol Soc 2011:8074–8077

    Google Scholar 

  17. 17.

    Noori SMR, Mobaraki M, Ahmadian A, Bayat M, Bahrami N (2020) Zygomatic bone registration based on a modified student’s mixture model method. Piscataway, IEEE, pp 1–5

    Google Scholar 

  18. 18.

    Farnia P, Ahmadian A, Sedighpoor M, Khoshnevisan A, Mansoory MS (2012) On the performance of improved ICP algorithms for registration of intra-ultrasound with pre-MR images; a phantom study. Annu Int Conf IEEE Eng Med Biol Soc 2012:4390–4393

    Google Scholar 

  19. 19.

    Besl PJ, McKay ND (1992) Method for registration of 3-d shapes. Sensor fusion IV control paradigms and data structures, vol 1611. International Society for Optics and Photonics, Bellingham, pp 586–607

    Google Scholar 

  20. 20.

    Chen Y, Medioni G (1992) Object modelling by registration of multiple range images. Image Vis Comput 10(3):145–155

    Article  Google Scholar 

  21. 21.

    Rusinkiewicz S, Levoy M (2001) Efficient variants of the ICP algorithm. Proceedings third international conference on 3-D digital imaging and modeling. Piscataway, IEEE, pp 145–152

    Google Scholar 

  22. 22.

    Mathworks (2019) Parallel computing toolbox. https://www.mathworks.com/help/matlab/ref/reducepatch.html. Accessed 2019

  23. 23.

    Bentley JL (1975) Multidimensional binary search trees used for associative searching. Commun ACM 18(9):509

    Article  Google Scholar 

  24. 24.

    Sun Z, Li Z, Liu Y (2020) An improved lidar data segmentation algorithm based on euclidean clustering. In: Proceedings of the 11th international conference on modelling, identification and control, pp 1119–1130

  25. 25.

    Shahabi C, Kolahdouzan MR, Sharifzadeh M (2003) A road network embedding technique for K-nearest neighbor search in moving object databases. Geoinformatica 7(3):255–273

    Article  Google Scholar 

  26. 26.

    Alt H, Guibas LJ (1999) Discrete geometric shapes: matching, interpolation, and approximation. Handb Comput Geom 1:121–153

    Google Scholar 

  27. 27.

    Ghadimi S, Abrishami Moghaddam H, Grebe R, Wallois F (2016) Skull segmentation and reconstruction from newborn CT images using coupled level sets. IEEE J Biomed Heal Inform 20(2):563–573

    Article  Google Scholar 

  28. 28.

    Li S, Wang J, Liang Z, Su L (2016) Tree point clouds registration using an improved icp algorithm based on kd-tree. In: 2016 IEEE International Geoscience and Remote Sensing Symposium, pp 4545–4548

Download references

Funding

This study was funded by the Faculty of Medicine, Tehran University of Medical Sciences, under Grant Number 36938-30-04-96.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Alireza Ahmadian.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All procedures performed in this study were in accordance with the ethical standards of the Tehran University of Medical Science (ethical code: IR.TUMS.MEDICINE.REC.1396.4592).

Informed consent

We used archived unnamed data from Sina Hospital and Parsiss Co.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Noori, S.M.R., Farnia, P., Bayat, M. et al. Automatic detection of symmetry plane for computer-aided surgical simulation in craniomaxillofacial surgery. Phys Eng Sci Med 43, 1087–1099 (2020). https://doi.org/10.1007/s13246-020-00909-9

Download citation

Keywords

  • Sagittal plane
  • Mid-plane
  • Symmetry plane
  • Computer-aided surgery
  • Maxillofacial fracture
  • Cranio-maxillofacial surgery