0
Technical Brief

Efficient Inverse Isoparametric Mapping Algorithm for Whole-Body Computed Tomography Registration Using Deformations Predicted by Nonlinear Finite Element Modeling

[+] Author and Article Information
Mao Li

Intelligent Systems for Medicine Laboratory,
School of Mechanical Engineering,
The University of Western Australia,
M050, 35 Stirling Highway,
Crawley, Perth, Western Australia 6009, Australia
e-mail: mao.li@research.uwa.edu.au

Adam Wittek

Intelligent Systems for Medicine Laboratory,
School of Mechanical Engineering,
The University of Western Australia,
M050, 35 Stirling Highway,
Crawley, Perth, Western Australia 6009, Australia
e-mail: adam.wittek@uwa.edu.au

Karol Miller

Intelligent Systems for Medicine Laboratory,
School of Mechanical Engineering,
The University of Western Australia,
M050, 35 Stirling Highway,
Crawley, Perth, Western Australia 6009, Australia
e-mail: karol.miller@uwa.edu.au

1Corresponding author.

Manuscript received December 6, 2013; final manuscript received April 22, 2014; accepted manuscript posted May 14, 2014; published online June 3, 2014. Assoc. Editor: David Corr.

J Biomech Eng 136(8), 084503 (Jun 03, 2014) (6 pages) Paper No: BIO-13-1568; doi: 10.1115/1.4027667 History: Received December 06, 2013; Revised April 22, 2014; Accepted May 14, 2014

Biomechanical modeling methods can be used to predict deformations for medical image registration and particularly, they are very effective for whole-body computed tomography (CT) image registration because differences between the source and target images caused by complex articulated motions and soft tissues deformations are very large. The biomechanics-based image registration method needs to deform the source images using the deformation field predicted by finite element models (FEMs). In practice, the global and local coordinate systems are used in finite element analysis. This involves the transformation of coordinates from the global coordinate system to the local coordinate system when calculating the global coordinates of image voxels for warping images. In this paper, we present an efficient numerical inverse isoparametric mapping algorithm to calculate the local coordinates of arbitrary points within the eight-noded hexahedral finite element. Verification of the algorithm for a nonparallelepiped hexahedral element confirms its accuracy, fast convergence, and efficiency. The algorithm's application in warping of the whole-body CT using the deformation field predicted by means of a biomechanical FEM confirms its reliability in the context of whole-body CT registration.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Sint Jan, S. V., Sobzack, S., Dugailly, P.-M., Feipel, V., Lefevre, P., Lufimpadio, J.-L., Salvia, P., Viceconti, M., and Rooze, M., 2006, “Low-Dose Computed Tomography: A Solution for in Vivo Medical Imaging and Accurate Patient-Specific 3D Bone Modeling?,” Clin. Biomech., 21(9), pp. 992–998. [CrossRef]
Lee, Y. S., Kim, K. J., Do Ahn, S., Choi, E. K., Kim, J. H., Lee, S. W., Song, S. Y., Yoon, S. M., Kim, Y. S., Park, J. H., Cho, B. C., and Kim, S. S., 2013, “The Application of PET-CT to Post-Mastectomy Regional Radiation Therapy Using a Deformable Image Registration,” Radiat. Oncol., 8, p. 104–113. [CrossRef]
Zaidi, H., 2007, “Optimisation of Whole-Body PET/CT Scanning Protocols,” Biomed. Imaging Intervention J., 3(2), p. e36–44. [CrossRef]
Li, X., Yankeelov, T. E., Peterson, T. E., Gore, J. C., and Dawant, B. M., 2008, “Automatic Nonrigid Registration of Whole Body CT Mice Images,” Med. Phys., 35(4), pp. 1507–1520. [CrossRef]
Mostayed, A., Garlapati, R. R., Joldes, G. R., Wittek, A., Roy, A., Kikinis, R., Warfield, S. K., and Miller, K., 2013, “Biomechanical Model as a Registration Tool for Image-Guided Neurosurgery: Evaluation Against BSpline Registration,” Ann. Biomed. Eng., 41(11), pp. 2409–2425. [CrossRef]
Wittek, A., Miller, K., Kikinis, R., and Warfield, S. K., 2007, “Patient-Specific Model of Brain Deformation: Application to Medical Image Registration,” J. Biomech., 40(4), pp. 919–929. [CrossRef]
Hagemann, A., Rohr, K., Stiehl, H. S., Spetzger, U., and Gilsbach, J. M., 1999, “Biomechanical Modeling of the Human Head for Physically Based, Nonrigid Image Registration,” IEEE Trans. Med. Imaging, 18(10), pp. 875–884. [CrossRef]
Otoole, R. V., Jaramaz, B., Digioia, A. M., Visnic, C. D., and Reid, R. H., 1995, “Biomechanics for Preoperative Planning and Surgical Simulations in Orthopedics,” Comput. Biol. Med., 25(2), pp. 183–191. [CrossRef]
Rohlfing, T., Maurer, C. R., O'Dell, W. G., and Zhong, J. H., 2004, “Modeling Liver Motion and Deformation During the Respiratory Cycle Using Intensity-Based Nonrigid Registration of Gated MR Images,” Med. Phys., 31(3), pp. 427–432. [CrossRef]
Snedeker, J. G., Wirth, S. H., and Espinosa, N., 2012, “Biomechanics of the Normal and Arthritic Ankle Joint,” Foot Ankle Clin., 17(4), pp. 517–528. [CrossRef]
Garlapati, R. R., Roy, A., Joldes, G. R., Wittek, A., Mostaryed, A., Doyle, B., Warfield, S. K., Kikinis, R., Knuckey, N., Bunt, S., and Miller, K., 2013, “Biomechanical Modeling Provides More Accurate Data for Neuronavigation Than Rigid Registration,” J. Neurosurg. (in press). [CrossRef]
Bathe, K.-J., 1996, Finite Element Procedures, Prentice Hall, Englewood Cliffs, NJ.
Joldes, G. R., Wittek, A., and Miller, K., 2009, “Suite of Finite Element Algorithms for Accurate Computation of Soft Tissue Deformation for Surgical Simulation,” Med. Image Anal., 13(6), pp. 912–919. [CrossRef]
Lerotic, M., Lee, S. L., Keegan, J., and Yang, G. Z., 2009, “Image Constrained Finite Element Modelling for Real-Time Surgical Simulation and Guidance,” IEEE International Symposium on Biomedical Imaging From Nano to Macro, Boston, MA, pp. 1063–1066.
Wittek, A., Joldes, G., and Miller, K., 2011, “Algorithms for Computational Biomechanics of the Brain,” Biomechanics of the Brain, K.Miller, ed., Springer, New York, pp. 189–219.
Joldes, G., Wittek, A., Warfield, S. K., and Miller, K., 2012, “Performing Brain Image Warping Using the Deformation Field Predicted by a Biomechanical Model,” Computational Biomechanics for Medicine, P. M. F.Nielsen, A.Wittek, and K.Miller, eds., Springer, New York, pp. 89–96.
Murti, V., and Valliappan, S., 1986, “Numerical Inverse Isoparametric Mapping in Remeshing and Nodal Quantity Contouring,” Comput. Struct., 22(6), pp. 1011–1021. [CrossRef]
Murti, V., Wang, Y., and Valliappan, S., 1988, “Numerical Inverse Isoparametric Mapping in 3D FEM,” Comput. Struct., 29(4), pp. 611–622. [CrossRef]
Hua, C., 1990, “An Inverse Transformation for Quadrilateral Isoparametric Elements: Analysis and Application,” Finite Elem. Anal. Des., 7(2), pp. 159–166. [CrossRef]
Yuan, K. Y., Huang, Y. S., Yang, H. T., and Pian, T. H. H., 1994, “The Inverse Mapping and Distortion Measures for 8-Node Hexahedral Isoparametric Elements,” Comput. Mech., 14(2), pp. 189–199. [CrossRef]
Qian, X. D., Ren, Q. W., and Zhao, Y., 1998, “An Algorithm for Inverse Isoparametric Mapping in FEM,” Chin. J. Comput. Mech., 15, pp. 437–440. [CrossRef]
Areias, P. M. A., de Sa, J. M. A. C., Antonio, C. A. C., and Fernandes, A. A., 2003, “Analysis of 3D Problems Using a New Enhanced Strain Hexahedral Element,” Int. J. Numer. Methods Eng., 58(11), pp. 1637–1682. [CrossRef]
Irving, G., Teran, J., and Fedkiw, R., 2006, “Tetrahedral and Hexahedral Invertible Finite Elements,” Graph Models, 68(2), pp. 66–89. [CrossRef]
Nagrath, S., Jansen, K. E., and Lahey, R. T., 2005, “Computation of Incompressible Bubble Dynamics With a Stabilized Finite Element Level Set Method,” Comput. Method Appl. Mech. Eng., 194(42–44), pp. 4565–4587. [CrossRef]
Li, M., Wittek, A., Joldes, G., Zhang, G., Dong, F., Kikinis, R., and Miller, K., 2013, “Whole-Body Image Registration Using Patient-Specific Non-Linear Finite Element Model,” Computational Biomechanics for Medicine: Fundamental Science and Patient-Specific Application, B. J.Doyle, K.Miller, A.Wittek, and P. M. F.Nielsen, eds., Springer, New York, pp. 87–99.
Miller, K., 2011, Biomechanics of the Brain, Springer, New York.
Miller, K., Joldes, G., Lance, D., and Wittek, A., 2007, “Total Lagrangian Explicit Dynamics Finite Element Algorithm for Computing Soft Tissue Deformation,” Commun. Numer. Methods Eng., 23(2), pp. 121–134. [CrossRef]
Wittek, A., Joldes, G., Couton, M., Warfield, S. K., and Miller, K., 2010, “Patient-Specific Non-Linear Finite Element Modelling for Predicting Soft Organ Deformation in Real-Time: Application to Non-Rigid Neuroimage Registration,” Prog. Biophys. Mol. Biol., 103(2–3), pp. 292–303. [CrossRef]
Joldes, G. R., Wittek, A., and Miller, K., 2010, “Real-Time Nonlinear Finite Element Computations on GPU—Application to Neurosurgical Simulation,” Comput. Methods Appl. Mech. Eng., 199(49–52), pp. 3305–3314. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

A schematic diagram of warping the source whole-body CT images using the deformation field predicted by the patient-specific nonlinear finite element model

Grahic Jump Location
Fig. 2

The numbering system for the isoparametric hexahedral element

Grahic Jump Location
Fig. 3

The whole-body finite element model

Grahic Jump Location
Fig. 4

A wedge-shaped continuum discretized by hexahedral elements: (a) the undeformed wedge-shaped geometry and (b) the wedge-shaped geometry is deformed by an imposed displacement on the top surface

Grahic Jump Location
Fig. 5

Inverse isoparametric mapping transformation for a hexahedral element. (a) Three arbitrary points are placed in an undeformed hexahedral element and (b) the corresponding positions of these three points within a deformed element are calculated using the proposed inverse isoparametric mapping algorithm.

Grahic Jump Location
Fig. 6

Results of application of the proposed inverse mapping algorithm in registration/warping of a whole-body CT image set. A typical section through the registered image showing the lungs. Deformations between the source and target images for the registration were previously obtained in our previous study using nonlinear finite element procedures [23]. From the computed deformations, the registered/warped image was created by applying the proposed inverse isoparametric mapping algorithm to every voxel of the source images. The dotted line and the solid line are the lung contours in source and target images, respectively. The dashed line is the lung contour in the registered/warped image. It can be clearly seen that the contour obtained through registration of the source image agrees very well with the actual/“true” contour in the target image.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In