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.

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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

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Fig. 2

The numbering system for the isoparametric hexahedral element

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Fig. 3

The whole-body finite element model

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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

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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.

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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.




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