# Towards an adaptive volume mesh derived from
Computed Tomography data

Ho Quang Nguyen, Tien Tuan Dao, Alain Rassineux, Marie-Christine Ho Ba Tho

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Ho Quang Nguyen, Tien Tuan Dao, Alain Rassineux, Marie-Christine Ho Ba Tho. Towards an adaptive volume mesh derived from Computed Tomography data. 12e Colloque national en calcul des structures, CSMA, May 2015, Giens, France. hal-01516440

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Submitted on 1 May 2017

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# Towards an adaptive volume mesh derived from Computed Tomography data.

H-Q.Nguyen<fnref n="1" />, T-T.Dao<fnref n="1" />, A.Rassineux<fnref n="2" />, M-C.Ho Ba Tho<fnref n="1" />

**Abstract** —This paper presents a single process to create an adaptive volume mesh composed of elements integrated with CT information for finite element modelling of lumbar vertebrae. From the CT images of the lumbar spine, a semi-automatic segmentation using Canny method was implemented to extract the boundaries of the bone which were then used as an input to create the surface mesh of the vertebrae by applying Matching cubes algorithm. Subsequently, the volumetric mesh was automatically generated and CT information was mapped on to the relevant elements.

**Key words** — segmentation, modelling, mesh generation, lumbar spine, CT images

## 1. Introduction

Low back pain, a common chronic musculoskeletal disorders, is adversely affected by problems in the lumbar spine. Numerical models like patient specific finite element models derived from medical imaging have been commonly developed to provide quantitative and objective indicators for the better diagnosis and treatment prescription of the spinal disease. Some commercial software are specialized in generation of 3D geometrical and meshed models derived from medical images, however, it is inflexible to control the mesh element type with triangle-based surface model. Numerous studies individually focused on developing of specific segmentation methodologies, meshing technique or material properties assignment, statistical models and morphing techniques have been developed.

Some techniques [1,2,3] for the direct automatic generation of voxel-based patient-specific FE models from the CT data based on matching cubes algorithm [4] have been studied. However, being a voxel-based method, the resultant number of finite elements is significant. Recently, a robust modeling protocol was developed to perform the meshing using bicubic Hermite patches with the contour-based geometries [5], [6]. Although these above approaches provide flexible geometrical models for meshing purpose and overcome the geometrical complexity (bifurcation) of the biological tissue, there is no consideration into material properties assignment to element. Moreover, material assignment using commercial software usually used literature-based laws leading to the requirement of a serious validation process. Many material properties assignment methods have been developed to improve the patient-specificity as well as the level of automation [7, 8, 9, 10]. However, in order to perform FEM simulation for complex bio-structure like lumbar spine, material properties assignment step created by aforementioned methods needs to be associated with the commercial software packages related to geometry modelling and mesh generation.

In the framework of finite element modeling of the lumbar spine, there is no fully integrated process for geometric modeling, adaptive meshing and material assignment of the spinal structures. In fact, the purpose of this study is to provide solutions for this modeling challenge.

<footnote n="1">¹BMBI, University of Technology of Compiègne, { ho-quang.nguyen, tien-tuan.dao, marie-christine.ho-ba-tho } @utc.fr</footnote>

<footnote n="2">² Roberval, University of Technology of Compiègne, alain.rassineux@utc.fr;</footnote>
## 2. Materials and methods

A modeling workflow was developed to take the geometric modeling, meshing and CT information assignment into a whole modeling process (Figure 1). The input of this process comprised 343 CT slices of the lumbar spine with 0.625 mm slice distance, 1.25 mm slice thickness and a resolution of 0.607/pixel.

For the first step, from these medical images, the semi-automatic segmentation using Canny method [11] was implemented to extract boundaries of the vertebrae. In this step, the Canny method finds edges by looking for local maxima of the gradient of image associated with a Gaussian filter. The method uses two thresholds: a high threshold related to the highest value of the gradient magnitude of the image for selecting strong edges, and a 0.4*high threshold, named low threshold, for selecting weak edges which are connected to strong edges. It is important to note that the threshold is based on strong material properties knowledge of our team [7]. Then, the post-processing has been automatically performed to remove from binary image small objects with minimal number of pixels criteria.

<figure><img src="image_1.png" /><figcaption>Figure 1 - Modelling workflow</figcaption></figure>

In the second step, based on the masks created by the labeled contours, the triangulated surface mesh of each vertebra was constructed by applying Matching cubes algorithm [4]. At the beginning of the last step, the surface mesh was cleaned up to get the high quality surface mesh by eliminating duplicate and overlapping or redundant faces, edges. After that, from this cleaned surface mesh, the tetrahedral mesh was automatically generated [12]. Finally, intensity values in grey level which were mapped could be integrated into relevant elements of this volume mesh.

## 3. Results and discussion

The segmentation process was done on a sequence of CT slices of lumbar vertebrae (provided by European project MySpine).

(A)

<figure><img src="image_2.png" /></figure>

Figure 2 shows an example of a CT mapping input in gray level and Hounsfield unit (2A), extracted boundaries with a manual correction (2B) and the output labeled masks in binary or Hounsfield unit (2C).

(B)

<figure><img src="image_3.png" /></figure>

A time required to perform segmentation for each vertebra was several seconds and less than 2 minutes in case of manual intervention. This is a reasonable time compared to that of manual segmentation.

(C)

<figure><img src="image_4.png" /></figure>

Based on the Matching cubes method, the surface meshes of lumbar vertebrae from L1 to L5 were generated (Figure 3).

<caption>Figure 2 - Semi-automatic segmentation process</caption>
<figure><img src="image_5.png" /><figcaption>Figure 3 – Surface mesh of lumbar vertebrae from L1 to L5</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4 – Tetrahedral mesh of lumbar vertebrae from L1 to L5</figcaption></figure>

The final process was tested on vertebra L2. By eliminating duplicate and overlapping or redundant faces, edges, the number of triangular faces is reduced from of 91560 faces. And from this finer surface mesh, the tetrahedral mesh was automatically generated (Figure 4).

# 4. Conclusions and Perspectives

A preliminary fully integrated process of geometric modeling, meshing and CT information assignment for lumbar vertebrae has been presented. As perspectives, the strategies improving the automatic segmentation and adaptive meshing and material assignment will be implemented and studied for both vertebrae and intervertebral discs.

# References

[1] Z.L. Wang, J.C.M. Teo, C.K. Chui, S.H. Ong, C.H. Yan, S.C. Wang, H.K. Wong, S.H. Teoh. Computational biomechanical modelling of the lumbar spine using marching-cubes surface smoothened finite element voxel meshing, Computer Methods and Programs in Biomedicine 80, 25–35, 2005

[2] Q. Fang, D-A. Boas. Tetrahedral mesh generation from volumetric binary and gray scale image, IEEE. International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2009

[3] M. Viceconti, C. Zannoni, D. Testi, A. Cappello. A new method for the automatic mesh generation of bone segments from CT, Journal of Medical Engineering & Technology, Volume 23, Number 2, 77-81, 1999

[4] WE. Lorensen, HE. Cline. Marching cubes: A high resolution 3D surface construction algorithm, Computer Graphics 21 (4): 163-169, 1987

[5] T.T. Dao, A. Rassineux, F. Charleux, MC Ho Ba Tho. A Robust Protocol for the Creation of Patient Specific Finite Element Models of the Musculoskeletal System from Medical Imaging Data. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, In Press, 2014
[6] A. Rassineux, P. Villon, J-M. Savignat, O. Stab. Surface remeshing by local Hermite diffuse interpolation. International Journal for Numerical Methods in Engineering 49(1-2): 31-49, 2000

[7] MC Ho BaTho. Bone and joints modelling with individualised geometric and mechanical properties derived from medical images, Computer Mechanics and Engineering Sciences 4: 3&4. 489-496, 2003

[8] C. Zannoni, R. Mantovani, M. Viceconti. Material properties assignment to finite element models of bone structures: a new method, Medical Engineering & Physics 20, 735-740, 1998

[9] B. Helgason, F.Taddei, H. Palsson, E. Schileo, L. Cristofolini, M. Viceconti, S. Brynjolfsson. A modified method for assigning material properties to FE models of bones, Medical Engineering & Physics 30, 444-453, 2008

[10] G- U. Unnikrishnan, E- F. Morgan. A New Material Mapping Procedure for Quantitative Computed Tomography-Based, Continuum Finite Element Analyses of the Vertebra, J Biomech Eng. 133(7): 071001, 2011

[11] J. Canny. A Computational Approach to Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-8 (6): 679-698, 1986

[12] A. Rassineux. Generation and optimization of tetrahedral meshes by advancing front technique, Int. J. Num. Meth in Eng., 41, 651-674, 1998.

## Acknowledgements

This project is co-financed by the Region Picardy and CNRS (grant Collegium UTC CNRS INSIS).
The CT data are provided by the European Consortium of MySpine project – GA-269909.