Generating Anatomically Accurate Finite Element Meshes for Electrical ...

Generating Anatomically Accurate Finite Element Meshes for Electrical Impedance Tomography of the Human Head Bin Yang, Canhua Xu, Meng Dai, Feng Fu, Xiuzhen Dong Department of Biomedical Engineering, Fourth Military Medical University, Xi’an 710032, People’s Republic of China ABSTRACT For electrical impedance tomography (EIT) of brain, the use of anatomically accurate and patient-specific finite element (FE) mesh has been shown to confer significant improvements in the quality of image reconstruction. But, given the lack of a rapid method to achieve the accurate anatomic geometry of the head, the generation of patient-specifc mesh is time-comsuming. In this paper, a modified fuzzy c-means algorithm based on non-local means method is performed to implement the segmentation of different layers in the head based on head CT images. This algorithm showed a better effect, especially an accurate recognition of the ventricles and a suitable performance dealing with noise. And the FE mesh established according to the segmentation results is validated in computational simulation. So a rapid practicable method can be provided for the generation of patient-specific FE mesh of the human head that is suitable for brain EIT. Keyword: Computerized tomography, image segmentation, mesh generation, electrical impedance tomography

1. INTRODUCTION Electrical impedance tomography (EIT), as a new imaging technique, can reconstruct cross-sectional images of impedance changes inside the human body related to functional or pathological changes in tissues or organs through the safety micro current injection and voltage measurements which performed by electrodes attached to the surface of the body. EIT does not use ionizing radiation and is safe and cheap would be of great value. Thereby, EIT presents significant possibilities for medical imaging and has reported to be used as research devices to investigate lung function, heart function, abdominal function and neurological function. Up to now, one of the most important factors limited clinical practical applications of EIT is that the quality of EIT images is relatively poor. Especially, low resolution and localisation accuracy disturb the representation of impedance changes within the brain in the way of EIT and make reconstructed images complicated to understand. Differences in boundary shapes between the subject and the underlying geometry of the forward model appear to be a source of image degradation in EIT. In previous research, to improve the accuracy of the forward model of the head, a FE model incorporating realistic geometry was presented, which achieved by manual or semi-automatic segmentation of magnetic resonance images (MRIs) and tetrahedral dissection using custom adaptation of industry standard commercial design software packages[1]. But this method is painstaking and generation time of the head model is too excessive for the specific patient which is considered as unfit for any time-critical clinical use. Then, this researcher proposes a more rapid method of generating more geometrically accurate finite element (FE) meshes of the specific human head by warping existing meshes such that the surface boundary beneath the electrodes closely matches that of the subject with minimal degradation to the quality of the mesh[2]. The process provides a timely and productive construction of forward models for clinical applications of the brain EIT, though the electrode positions are required to measure manually as geometric prior information for defining patient geometry and the geometry is only modeled accurately on the surface. But, bedside real-time EIT monitoring for the patient suffering from intracranial haemorrhage cannot use similar methods above mentioned establishing patient-special FE model of the head because of their high computation complexity and manual operation. Therefore, a process to allow rapid and precise construction of the patient-specific FE model of the head for brain 2D-EIT is necessary. In this work, we propose a fast method to establish the FE mesh of the head incorporated segments for scalp, skull, cerebrospinal fluid (CSF), ventricle and brain parenchyma from the segmentation of CT and discretization in Fifth International Conference on Digital Image Processing (ICDIP 2013), edited by Yulin Wang, Xie Yi, Proc. of SPIE Vol. 8878, 88783L · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2030736

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triangulation. The resulting meshes will be used for EIT simulations.

2. METHOD 2.1 Segmentation algorithm of CT scan data CT data segmentation is a preliminary and indispensable stage of the rapid and automated construction of patient-specific FE model of head. A slice of cross-sectional CT data from the head CT scans dataset of a volunteer near the position of the ring of 16 scalp electrode is chosen for the partition of an image into three non-overlapping regions, brain, skull and scalp, using a modified fuzzy c-means (FCM) algorithm[3] based on non-local means (NL)[4] method. The NL-means algorithm can deal with the noise of images successfully and geometrical edges in the image can be retained perfectly. Here, the modified FCM objective function of partitioning an image into c clusters is J ( , )= where

= χ ,χ ,⋯,χ ,⋯,χ

μ D

χ , υ subject to

μ = 1 (1)

is the data set of pixel intensity of CT image, χ is the gray value of the jth pixel, μ

is the membership of the jth data in the ith cluster c , m presents the index of juzziness, and υ is the fuzzy cluster centroid of the ith cluser. The distance D, in equation (2), measure the similarity between a feature χ and a cluster centroid υ inflenced by local and non-local information. = (1 − λ )d

χ ,υ

D

χ ,υ + λ d

χ , υ (2)

where d stands for the distance measurement influenced by non-local information, d stand for the distance measurement influenced by local information which is used to prevent the NL-means algorithm from removing some fine tissue structures in CT image, and λ d with the range from zero to one, is the weighting factor controlling the tradeoff between them. The distance measurement influenced by local information d is given by d

χ ,υ

=

∑χ

ω χ ,x d χ ,υ

∈

∑χ

∈

ω χ ,χ

(3)

where N denote a chosen local square neighborhood of 7 × 7 size which centered at pixel χ , χ is close to χ in N and d (χ , υ ) is the Euclidean distance measurement, ω χ , χ

is the weight of each pixel in N and deifned as χ

χ

ω χ ,χ

=e

σ

(4)

where σ is the variance of N . The distance measurement influenced by nono-local information is computed as a weighted average of all the pixels in the given square research window S of 21 × 21 size with respect to a center pixelx : χ ,χ

0≤ω d

χ ,υ =

χ ∈

ω

χ ,χ d χ ,υ , ∈

ω

χ ,χ

≤1 =1

(5)

where the weight ω χ , χ depends on the similarity between the pixel χ and χ which is expressed as the N = x , x ∈ N . So the weight defined as N , here similarity of the intensity gray level vector (N ) and 1 ω χ ,χ = U χ , χ (6) Z χ where


)

(

U χ ,χ

,

=e (

Z χ In here

v(Nk )-v Nj

2 2,a

=

χ ∈

(7)

)

,

e

(8)

is a Gaussion weihted Euclidean distance[5],

(N ) −

N

,

=G ∗

(N ) −

=

N

χ∈

G χ

χ

−χ

(9)

where Q denote a square of fixed size centered in (0,0) and G a two dimensional Gaussian kernel of standard deviation a. The objective function is minimized when data points close to the centroid of their clusters are assigned high membership values, and low membership values are assigned to data points for from the centroid. Letting the first derivatives of J with respect to μ and υ equal to zero yields the two necessary conditions for minimizing jm as follows: ⁄(

D χ ,υ

μ =

(10)

D χ ,υ

and υ =

∑ ∑

μ χ μ

)

(11)

The modified FCM algorithm proceeds by iterating the two necessary conditions until a solution is reached and each data point will be associated with a membership value for each class. By assigning the data point to the class with the highest membership value, a segmentation of the data could be obtained. 2.2 The process for head CT segmented in layers The steps can be described as below: · Set the number of clusters C as 4 representing scalp, skull, brain and ventricle and index of fuzziness m as 2 in equation (1). Initialize the fuzzy cluster centroid vector according to the characteristic gray values achieved by histogram analysis and set ε > 0 to a very small value. · Set the neighborhood size as 7 × 7 and search window size as21 × 21. · Calculate the distance measurement D using equation (2) and update μ usingD , then updating υ usingμ . − υ | < ε. · Repeat upper step until satisfy the following termination criterion:|υ · The binary and morphological operations are used to forge a CSF layer with approximate 4mm thickness. 2.3 Meshing The segmentation results are processed for boundary extraction and the vertices presented the protrusion feature on the internal boundary of the skull region are identified, whose curvature is discontinuous. The vertices are disposed equally on the boundaries or between the protrusion vertices. All vertices above described are referred to as constrained vertices which compose a planar straight line graph (PSLG) that defined to be a collection of constrained vertices and segments whose endpoints are vertices in the PSLG. Then, the discretization of the head region is converted into triangulating a PSLG. The triangulation process is performed by a faster divide-and-conquer algorithm for constructing Delaunay triangulation and refined by inserting additional vertices called Steiner points into mesh using Delaunay refinement algorithm[6]. 2.4 Simulation A perturbation object is positioned at a known positon in the computational domain. A forward simulation was run to obtain the boundary voltages associated with the conductivity field. These simulated voltages are used to A perturbation


object is positioned at a known positon in the computational domain. A forward simulation was run to obtain the boundary voltages associated with the conductivity field. These simulated voltages are used to reconstruct the conductivity field using the FE mesh described and a damped least square (DLS) algorithm[7].

3. RESULT 3.1 Segmentation results

Figure 1. Segmentation results of five examples.

The proposed segmentation algorithm was implemented under Visual C++ 2010 programming environment, which yielded the precise segmentation as Fig. 1 shown. 3.2 Mesh (b)

(0

Figure 2. An example five layers mesh containing scalp, skull, CSF, ventricle and brain.

Fig. 2(a) was an original CT image and the clear boundary of five tissues in the head was illustrated in Fig. 2(b). Using a general desktop computer (Intel E2160, 1G RAM), the anatomically accurate FE mesh was generated in 8 min as shown in Fig. 2(c), which included 3114 elements and the minimum angle of 95 percentage of triangular elements was great than . °. 3.3 Simulation EIT image was reconstructed from simulated data using another anatomically accurate mesh of the head in Fig. 3(a) containing a circular perturbation target for imitating the intracranial hemorrhage, which was distinct from the FE mesh shown in Fig 2(c) and the number of triangle was more than above one for avoiding the inverse crime problem. Gaussian white noise was added up to 0.5% in boundary voltages. The resulting image in Fig. 3(b).

Figure 3. Simulation results using up to 0.5% noise.


4. DISCUSSION Though CT segmentation has been studied previously, much of the works has focused on cerebral anatomy, but there are rare efficient method reported for the segmentation of ventricle system from CT scan because the ventricle system and CSF is hardly visible in CT scans due to the low soft-tissue contrast of this imaging modality[1]. So the FCM algorithm based on NL means method is implemented to segment the ventricle system and obtain better results, which can provide adequate anatomic information for generating accurate patient-specific FE mesh of brain EIT. However, this segmentation algorithm is also computationally expensive for the time-critical clinical application and this should be improved in future work. Furthermore, the resulting mesh is validated in computational simulation and this work provides a rapid practicable method for generation of patient-specific FE mesh of the human head that is suitable for brain EIT.

ACKNOWLEDGMENT This work was partially supported by Scientific and Technologic Development Projeots Fund of Shannxi provine under grant number S2011SF1363.

REFERENCES [1] Vonach, M., Marson, B., Yun, M. et al., “A method for rapid production of subject specific finite element meshes for electrical impedance tomography of the human head,” Physiol Meas, 33(5), 801-16 (2012). [2] Tizzard, A., and Bayford, R. H., “Improving the finite element forward model of the human head by warping using elastic deformation,” Physiol Meas, 28(7), S163-82 (2007). [3] Wang, J. Z., Kong, J., Lu, Y. H. et al., “A Modified FCM algorithm for MRI brain image segmentation using both local and non-local spatial xonstraints,” Computerized Medical Imaging and Graphics, 32, 685-698 (2008). [4] Buades, A., Coll, B., and Morel, J. M., "A non-local algorithm for image denoising." Proc CVPR, 60-65 (2005). [5] Buades, A., Coll, B., and Morel, J. M., "Denoising image sequences does not require motion estimation." Proc AVSS, 70-74 (2005). [6] Jonathan Richard, S., “Delaunay refinement algorithms for triangular mesh generation,” Computational Geometry, 22(1-3), 21-74 (2002). [7] Xu, C., Dai, M., You, F. et al., “An optimized strategy for real-time hemorrhage monitoring with electrical impedance tomography,” Physiol Meas, 32(5), 585-98 (2011).

Address of the corresponding author: Author: Xiuzhen Dong Institute: Department of Biomedical Engineering, Fourth Military Medical University Street: Changle Western Road 169 City: Xi’an Country: China Email: [email protected]
