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Skull Repair Using Active Contour Models
Available online at www.sciencedirect.com
ScienceDirect Procedia Manufacturing 11 (2017) 2164 – 2169
27th International Conference on Flexible Automation and Intelligent Manufacturing, FAIM2017, 27-30 June 2017, Modena, Italy
Skull Repair Using Active Contour Models Yu-Cheng Lin, Chen-Yang Cheng,*, Yi-Wen Cheng, Cheng-Ting Shih Abstract Skull defects will result in high risk of brain infection and low brain protection. In order to avoid risks and re-injury, we need to reconstruct the defect by grafting bone onto the deficient region. With rapid customization manufacturing of additive manufacturing (AM) and 3D printing (3DP) technology, the fitted shape of a skull prosthesis can be fabricated accurately and efficiently during cranioplasty surgery. However, an unfitted skull prosthesis made of artificial polymer or a metal implant can cause repeated infection, which may need an additional surgery. This paper presents a method to create suitable geometric graphics of skull defects to be applied in skull repair by using active contour models. The active contour models can be adjusted in every tomography slice, and the curves that represent the defect in the skull bone can be modeled. The generated graphics can adequately mimic and compensate for a fitted curvature. Clinical surgeons will be able to define, process, and implant a customized prosthesis to patients very quickly in surgery with this research. Especially, patients who have urgently skull defect problem can be solved and obtained maximum surgical quality. © by Elsevier B.V. by This is an open access article under the CC BY-NC-ND license ©2017 2017Published The Authors. Published Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 27th International Conference on Flexible Automation and Peer-review under responsibility of the scientific committee of the 27th International Conference on Flexible Automation and Intelligent Manufacturing. Intelligent Manufacturing Keywords: Prosthesis, Tomography, Geometric Modeling, Active Contour Models, Snakes
1. Introduction Skull defects usually occur in patients with trauma or congenital malformations [1-5]. When patients with skull defects, the protection of brain is reduced [6, 7]. In addition, the appearance of the incomplete skull also causes the patient psychological stress and social barriers. Therefore, the reconstruction of the skull is an important issue in physiological function and psychological condition of the patient. To reconstruct skull defects that using size- and
* Corresponding author. E-mail address: [email protected]
2351-9789 © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 27th International Conference on Flexible Automation and Intelligent Manufacturing doi:10.1016/j.promfg.2017.07.362
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shape-matched bone flaps, is a common operation in clinical [8, 9]. Currently, many types of skull bone flaps have been applied in clinical, including autografts, allograft, xenograft and synthetic bone. Compare with these flaps, the autografts have a low risk of infection and immune response [10]. The bone flaps original removed or modified from tibia and rib bones [5, 11]. However, the autografts need to be preserved well before implantation. Consequently, the autografts are usually unavailable in an emergency. Bone cement is a common material used in clinical to repair patient’s bones. It can be rapid solidification, arbitrary shaping and it is cheap[12] and has been widely applied in vertebroplasty [13, 14], hip-joint replacement [15] and cranioplasty. However, in cranioplasty, bone cement needs to be manual shaping by clinical engineers during operation, which prolongs the operation time and increase the risk of anesthesia and surgical complications. In recent years, medical imaging and additive manufacturing (AM) have been widely and rapidly developed [16-18]. The anatomical structural information can be accurately acquired using high-resolution computed tomography (CT). Bone flaps can be designed based on the CT images and can be further produced using additive manufacturing techniques. The quality of cranioplasty can be improved by reducing operation time and accurate bone flaps. However, current bone flap modeling still relies on manual designs. Depending on the experience of engineers, single bone flap modeling could take several hours or even days. Eventually, the operation may be delayed. In this research, a novel algorithm was proposed to automatically model the skull defects. An active contour model was used to calculate the defect parts and to recover the skull slice by slice. Based on the results, the bone flap that accurately fit to the defect. The rest of this paper is organized as follows. Section 2 reviews the other skull repair method. Section 3 describes the proposed method and procedure. Section 4 presents the experimental studies and discussions. Finally, conclusions and future work will be given in Section 5. 2. Active Contour Models Active contour models, also called snakes. Snakes main strategy is evolving curves driven by minimizing the internal and external energies [19]. Their energy function is shown in Equation (1).
(1)
where represents the position point of a snake; is the internal energy of a spline which control bending of spline; is external energy that force of the spline moving toward the lines, edges, and terminations in the image; and gives rise to external constraint forces. consists of the three energy functions shown in Equation (2).
(2)
where , , and are an energy function that forces the snake to be attracted to lines, edge of contours, and terminations of line segments and corners, respectively; and , , and are the weights of these three energy functions. A higher weight indicates more influence of the energy function. The details are provided by [19]. Internal energy makes the contour tense and stiff. External energy derived from the image features and guides the contour toward the region of interest [20]. The objective of snakes is to minimize the internal and external energies for deriving the Euler–Lagrange equation shown in Equation (3):
(3)
where denotes the coordinate vector of the contour with entities , for = 1, 2,…, N (the number of vertices on the contour). The leading two parts of the equation is the internal energy and the coefficients , control the tension and stiffness of the curve. The last part of the equation is the external energy. The external energy forces the curve to move toward the lines, edges, and terminations in the image.
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Yu-Cheng Lin et al. / Procedia Manufacturing 11 (2017) 2164 – 2169
(4)
After a further expansion using a finite difference to approximate derivatives, the Euler–Lagrange equation becomes Equation (4), which can be rewritten into the matrix form: , where is a matrix consisting of and , and is associated with external energy. can be solved using matrix inversion. The details of the decomposition methods for active contour models are provided by [19]. 3. Proposed Method In cranioplasty, a prosthesis is required to repair defects of the skull bone. Liao, et al. [20] use Snake and registration in cranial defect reconstruction. But they mainly use Snake in image noises elimination not used in skull modelling. In addition, from their study, we observe feature of Snake that curves moving close to the skull border can used in skull modelling. Active contour models can fulfill all requirements of skull modeling. The first step is the acquirement and processing of CT images. In this study, all medical tomography images were extracted in the Digital Imaging and Communications in Medicine (DICOM) file format. In this step, the brain or other soft tissues are eliminated from the CT images. After filtering out the skull bone region, only the inner and outer borders are acquired and used for the next step. The second step is the reconstruction of the geometrical model of the missing region by using active contour models. Suitable arcs can be identified using snakes. The details are shown in Section 3.1.In the third step, all layers of processed CT images in the second step are stacked and build into a 3D visualization of the skull. The cranial prosthesis is visually validated. Its suitability is confirmed in this step. The fourth step is the final stage, in which the physical model of the cranial prosthesis is printed by using 3D printing technology. In this study, the details of the printing of the cranial prosthesis are not included in the results and discussion. Figure 1 shows the active contour model used for skull repair in this study. The main purpose of the method proposed in this study is to repair the damaged skull and obtain the prosthesis. The active contour model in this study is used to generate curves of different shapes. A laterally missing white region sample damaged skull is shown in Figure 1(a). The white region represents the remaining skull bone area; we modeled the incomplete skull bone by acquiring the borders of the white region, as illustrated in Figure 1(b). We separately performed the inner and outer border experiments. So we can automatically get the thickness of the skull. The inner and outer borders of the skull bone are shown in Figure 1(c) and Figure 1(d), respectively. Our research goal was to use the deformed curves generated by the active contour model to fill the skull defect, as shown in Figure 1(e).
(a)
(c)
(b)
(d)
(e)
Figure 1 (a) CT slice of the broken skull (b) Inner and outer borders of the skull bone (c) Inner border of the skull bone (d) Outer border of the skull bone (e) Example of filling the skull defect
3.1. Active Contour Model and Thickness Trimming From the perspective of skull anatomy, the curve of the skull in each CT images is not all the same, but most of curves are oval [21]. Therefore, the curve in each image can be modeled as being similarly oval shapes. Active contour models can fulfill all requirements of skull modeling. According to the characteristics of active contour models, the generated curve will move as close as possible to the inner and outer border. For example, a schematic diagram of a snake is shown in Figure 2. The blue dotted line represents the initial contour and the red dotted line
Yu-Cheng Lin et al. / Procedia Manufacturing 11 (2017) 2164 – 2169
represents the final suitable contour in the snake. The blue dotted line gradually moves toward the red dotted line based on the characteristics of snake. Once the initial contour stops moving, the suitable contour in this CT image is found.
Figure 2 Schematic diagram of a snake sample
In the final snake process, after we find the snake curve we do the thickness trimming. The thickness of the skull bone in each CT layer is another problem that should be considered [22]. In this study, we obtained the thickness of the skull bone in each CT layer by subtracting the outer border from the inner border. The procedure of thickness trimming is shown in Figure 3. Each CT image in this study consisted of binary values (0 and 1). The red dotted line in Figure 4 is the final snake contour. After filling out the outer and inner borders with solid graphics, we subtracted the outer border from the inner border. Thus, we obtained a complete skull bone figure in each CT layer. We automatically obtained the thickness of skull and do not need to consider the thickness problem [21, 22]. We stack all complete skull bone figure in each CT layer and we can obtain a complete skull. We can also use this complete skull to obtain a model of the prosthesis.
Figure 3 Thickness trimming procedure in each CT layer
4. Analyses of Results We use one testing samples in this study. This testing sample is originally broken skull from a patient. We use an originally broken in the lateral region of the skull from a patient to verify the feasibility of this study. The resolution of the patient CT image was 512 × 512, and it could be transformed into 265 layers. The snake script was programmed in MATLAB. First, we extracted the skull bone from the CT image and identified the inner and outer borders of the skull bone in each layer. Subsequently, according to the skull bone border in Figure 1(c) and Figure 1(d), we used the snake to fill the skull defect. The vital parameter values of Snake are shown in Table 1. Parameter controls the elastic deformation of the contour. If is too high, the contour generated by the snake zooms out into a small circle. Therefore, was set at
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0.1. We set to be slightly more than zero. , , and are the weights of the image forces. Higher weights indicate that the Snake is more influenced moving toward lines, edges, and terminations. According to the observation in this study, the attraction to the edges is the most crucial because many skull border images consist of discontinuous curves. Therefore, we set . If we set the weights and to be higher, the Snake would not conform to the demand. represents the total points of the final Snake. Table 1 Vital parameter values of the snake
Parameters/Snake
value
0.1 0.3 0.04 4 0.1 200
4.1. Results and Discussion
The objective of this study was to identify suitable fitting cranial curve by using active contour models. However, the fitting curve might not be the optimal solution because of some problems at the junction between the realistic and fitting curves. In this case, both the inner and outer borders are not 100 percent aligned with the contact point. This problem should be solved in future research. A partial deficient in the lateral region of the skull was used as a testing sample in this study. The white region represents the skull bone, and the red region represents the prosthesis generated using our method, as shown in Figure 4. The experiment proves the proposed method is feasible.
Figure 4 Result of the experiment
5. Conclusion Irregularities of the skull or skull defects result in low protection of the brain, a high risk of brain infection, and poor postoperative recovery for patients. Moreover, it also affect the aesthetic appearance. Cranioplasty is a common method used to restore the integrity of the cranial cavity. This paper presents a method of prosthesis modeling by using Snake. We developed a self-adjusting bone curvature algorithm that involves using Snake. The experiments validated the proposed method could build a model of a broken skull bone. The significant contribution of this work is that Snake can be used to model an arc curve for which information missing in the image. The proposed method can also save time for the manufacture of prosthesis for surgeons. Thus, the proposed method is a promising technique for medical professionals solving prosthesis modeling problems. We believe that the proposed method is a convenient strategy that can be used by medical professionals to repair the skull bone defects for patients. References [1] B. Aarabi, D. C. Hesdorffer, E. S. Ahn, C. Aresco, T. M. Scalea, and H. M. Eisenberg, "Outcome following decompressive craniectomy for malignant swelling due to severe head injury," Journal of neurosurgery, vol. 104, pp. 469-479, 2006. [2] D. J. Cooper, J. V. Rosenfeld, L. Murray, Y. M. Arabi, A. R. Davies, P. D'urso, et al., "Decompressive craniectomy in diffuse traumatic brain
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injury," New England Journal of Medicine, vol. 364, pp. 1493-1502, 2011. [3] V. Josan, S. Sgouros, A. Walsh, M. Dover, H. Nishikawa, and A. Hockley, "Cranioplasty in children," Child's Nervous System, vol. 21, pp. 200-204, 2005. [4] B. L. Rish, D. J. Dillon, A. M. Meirowsky, W. F. Caveness, J. P. Mohr, P. J. Kistler, et al., "Cranioplasty: a review of 1030 cases of penetrating head injury," Neurosurgery, vol. 4, pp. 381-385, 1979. [5] D. A. Taggard and A. H. Menezes, "Successful use of rib grafts for cranioplasty in children," Pediatric neurosurgery, vol. 34, pp. 149-155, 2001. [6] J.-R. Kuo, C.-C. Wang, C.-C. Chio, and T.-J. Cheng, "Neurological improvement after cranioplasty–analysis by transcranial Doppler ultrasonography," Journal of Clinical Neuroscience, vol. 11, pp. 486-489, 2004. [7] P. A. Winkler, W. Stummer, R. Linke, K. G. Krishnan, and K. Tatsch, "Influence of cranioplasty on postural blood flow regulation, cerebrovascular reserve capacity, and cerebral glucose metabolism," Journal of neurosurgery, vol. 93, pp. 53-61, 2000. [8] M. R. Gooch, G. E. Gin, T. J. Kenning, and J. W. German, "Complications of cranioplasty following decompressive craniectomy: analysis of 62 cases," Neurosurgical focus, vol. 26, p. E9, 2009. [9] A. Sanan and S. J. Haines, "Repairing holes in the head: a history of cranioplasty," Neurosurgery, vol. 40, pp. 588-603, 1997. [10] S. Black, "Reconstruction of the supraorbital ridge using aluminum," Surgical neurology, vol. 9, pp. 121-128, 1978. [11] F. Viterbo, A. Palhares, and E. Modenese, "Cranioplasty: the autograft option," Journal of Craniofacial Surgery, vol. 6, pp. 80-82, 1995. [12] M. A. Liebschner, W. S. Rosenberg, and T. M. Keaveny, "Effects of bone cement volume and distribution on vertebral stiffness after vertebroplasty," Spine, vol. 26, pp. 1547-1554, 2001. [13] H. Deramond, N. Wright, and S. M. Belkoff, "Temperature elevation caused by bone cement polymerization during vertebroplasty," Bone, vol. 25, pp. 17S-21S, 1999. [14] G. Lewis, "Properties of acrylic bone cement: state of the art review," Journal of biomedical materials research, vol. 38, pp. 155-182, 1997. [15] W. A. Jiranek, A. D. Hanssen, and A. S. Greenwald, "Antibiotic-loaded bone cement for infection prophylaxis in total joint replacement," J Bone Joint Surg Am, vol. 88, pp. 2487-2500, 2006. [16] G. A. D. Giacomo, P. R. Cury, N. S. d. Araujo, W. R. Sendyk, and C. L. Sendyk, "Clinical application of stereolithographic surgical guides for implant placement: preliminary results," Journal of periodontology, vol. 76, pp. 503-507, 2005. [17] P. Liacouras, J. Garnes, N. Roman, A. Petrich, and G. T. Grant, "Designing and manufacturing an auricular prosthesis using computed tomography, 3-dimensional photographic imaging, and additive manufacturing: a clinical report," The Journal of prosthetic dentistry, vol. 105, pp. 78-82, 2011. [18] F. Rengier, A. Mehndiratta, H. von Tengg-Kobligk, C. M. Zechmann, R. Unterhinninghofen, H.-U. Kauczor, et al., "3D printing based on imaging data: review of medical applications," International journal of computer assisted radiology and surgery, vol. 5, pp. 335-341, 2010. [19] M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models," International journal of computer vision, vol. 1, pp. 321-331, 1988. [20] Y.-L. Liao, C.-F. Lu, C.-T. Wu, J.-D. Lee, S.-T. Lee, Y.-N. Sun, et al., "Using three-dimensional multigrid-based snake and multiresolution image registration for reconstruction of cranial defect," Medical & biological engineering & computing, vol. 51, pp. 89-101, 2013. [21] M. Rudek, O. Canciglieri Jr, and T. Greboge, "A PSO Application in Skull Prosthesis Modelling by Superellipse," ELCVIA Electronic Letters on Computer Vision and Image Analysis, vol. 12, 2013. [22] M. Rudek, T. Greboge, L. d. S. Coelho, and O. Canciglieri Jr, "Using Genetic Algorithms to Support the Prosthesis Design in the CAD System," in Proceedings of the 21st Brazilian Congress of Mechanical Engineering COBEM 2011, 2011, pp. 24-28.
ScienceDirect Procedia Manufacturing 11 (2017) 2164 – 2169
27th International Conference on Flexible Automation and Intelligent Manufacturing, FAIM2017, 27-30 June 2017, Modena, Italy
Skull Repair Using Active Contour Models Yu-Cheng Lin, Chen-Yang Cheng,*, Yi-Wen Cheng, Cheng-Ting Shih Abstract Skull defects will result in high risk of brain infection and low brain protection. In order to avoid risks and re-injury, we need to reconstruct the defect by grafting bone onto the deficient region. With rapid customization manufacturing of additive manufacturing (AM) and 3D printing (3DP) technology, the fitted shape of a skull prosthesis can be fabricated accurately and efficiently during cranioplasty surgery. However, an unfitted skull prosthesis made of artificial polymer or a metal implant can cause repeated infection, which may need an additional surgery. This paper presents a method to create suitable geometric graphics of skull defects to be applied in skull repair by using active contour models. The active contour models can be adjusted in every tomography slice, and the curves that represent the defect in the skull bone can be modeled. The generated graphics can adequately mimic and compensate for a fitted curvature. Clinical surgeons will be able to define, process, and implant a customized prosthesis to patients very quickly in surgery with this research. Especially, patients who have urgently skull defect problem can be solved and obtained maximum surgical quality. © by Elsevier B.V. by This is an open access article under the CC BY-NC-ND license ©2017 2017Published The Authors. Published Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 27th International Conference on Flexible Automation and Peer-review under responsibility of the scientific committee of the 27th International Conference on Flexible Automation and Intelligent Manufacturing. Intelligent Manufacturing Keywords: Prosthesis, Tomography, Geometric Modeling, Active Contour Models, Snakes
1. Introduction Skull defects usually occur in patients with trauma or congenital malformations [1-5]. When patients with skull defects, the protection of brain is reduced [6, 7]. In addition, the appearance of the incomplete skull also causes the patient psychological stress and social barriers. Therefore, the reconstruction of the skull is an important issue in physiological function and psychological condition of the patient. To reconstruct skull defects that using size- and
* Corresponding author. E-mail address: [email protected]
2351-9789 © 2017 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 27th International Conference on Flexible Automation and Intelligent Manufacturing doi:10.1016/j.promfg.2017.07.362
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Yu-Cheng Lin et al. / Procedia Manufacturing 11 (2017) 2164 – 2169
shape-matched bone flaps, is a common operation in clinical [8, 9]. Currently, many types of skull bone flaps have been applied in clinical, including autografts, allograft, xenograft and synthetic bone. Compare with these flaps, the autografts have a low risk of infection and immune response [10]. The bone flaps original removed or modified from tibia and rib bones [5, 11]. However, the autografts need to be preserved well before implantation. Consequently, the autografts are usually unavailable in an emergency. Bone cement is a common material used in clinical to repair patient’s bones. It can be rapid solidification, arbitrary shaping and it is cheap[12] and has been widely applied in vertebroplasty [13, 14], hip-joint replacement [15] and cranioplasty. However, in cranioplasty, bone cement needs to be manual shaping by clinical engineers during operation, which prolongs the operation time and increase the risk of anesthesia and surgical complications. In recent years, medical imaging and additive manufacturing (AM) have been widely and rapidly developed [16-18]. The anatomical structural information can be accurately acquired using high-resolution computed tomography (CT). Bone flaps can be designed based on the CT images and can be further produced using additive manufacturing techniques. The quality of cranioplasty can be improved by reducing operation time and accurate bone flaps. However, current bone flap modeling still relies on manual designs. Depending on the experience of engineers, single bone flap modeling could take several hours or even days. Eventually, the operation may be delayed. In this research, a novel algorithm was proposed to automatically model the skull defects. An active contour model was used to calculate the defect parts and to recover the skull slice by slice. Based on the results, the bone flap that accurately fit to the defect. The rest of this paper is organized as follows. Section 2 reviews the other skull repair method. Section 3 describes the proposed method and procedure. Section 4 presents the experimental studies and discussions. Finally, conclusions and future work will be given in Section 5. 2. Active Contour Models Active contour models, also called snakes. Snakes main strategy is evolving curves driven by minimizing the internal and external energies [19]. Their energy function is shown in Equation (1).
(1)
where represents the position point of a snake; is the internal energy of a spline which control bending of spline; is external energy that force of the spline moving toward the lines, edges, and terminations in the image; and gives rise to external constraint forces. consists of the three energy functions shown in Equation (2).
(2)
where , , and are an energy function that forces the snake to be attracted to lines, edge of contours, and terminations of line segments and corners, respectively; and , , and are the weights of these three energy functions. A higher weight indicates more influence of the energy function. The details are provided by [19]. Internal energy makes the contour tense and stiff. External energy derived from the image features and guides the contour toward the region of interest [20]. The objective of snakes is to minimize the internal and external energies for deriving the Euler–Lagrange equation shown in Equation (3):
(3)
where denotes the coordinate vector of the contour with entities , for = 1, 2,…, N (the number of vertices on the contour). The leading two parts of the equation is the internal energy and the coefficients , control the tension and stiffness of the curve. The last part of the equation is the external energy. The external energy forces the curve to move toward the lines, edges, and terminations in the image.
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(4)
After a further expansion using a finite difference to approximate derivatives, the Euler–Lagrange equation becomes Equation (4), which can be rewritten into the matrix form: , where is a matrix consisting of and , and is associated with external energy. can be solved using matrix inversion. The details of the decomposition methods for active contour models are provided by [19]. 3. Proposed Method In cranioplasty, a prosthesis is required to repair defects of the skull bone. Liao, et al. [20] use Snake and registration in cranial defect reconstruction. But they mainly use Snake in image noises elimination not used in skull modelling. In addition, from their study, we observe feature of Snake that curves moving close to the skull border can used in skull modelling. Active contour models can fulfill all requirements of skull modeling. The first step is the acquirement and processing of CT images. In this study, all medical tomography images were extracted in the Digital Imaging and Communications in Medicine (DICOM) file format. In this step, the brain or other soft tissues are eliminated from the CT images. After filtering out the skull bone region, only the inner and outer borders are acquired and used for the next step. The second step is the reconstruction of the geometrical model of the missing region by using active contour models. Suitable arcs can be identified using snakes. The details are shown in Section 3.1.In the third step, all layers of processed CT images in the second step are stacked and build into a 3D visualization of the skull. The cranial prosthesis is visually validated. Its suitability is confirmed in this step. The fourth step is the final stage, in which the physical model of the cranial prosthesis is printed by using 3D printing technology. In this study, the details of the printing of the cranial prosthesis are not included in the results and discussion. Figure 1 shows the active contour model used for skull repair in this study. The main purpose of the method proposed in this study is to repair the damaged skull and obtain the prosthesis. The active contour model in this study is used to generate curves of different shapes. A laterally missing white region sample damaged skull is shown in Figure 1(a). The white region represents the remaining skull bone area; we modeled the incomplete skull bone by acquiring the borders of the white region, as illustrated in Figure 1(b). We separately performed the inner and outer border experiments. So we can automatically get the thickness of the skull. The inner and outer borders of the skull bone are shown in Figure 1(c) and Figure 1(d), respectively. Our research goal was to use the deformed curves generated by the active contour model to fill the skull defect, as shown in Figure 1(e).
(a)
(c)
(b)
(d)
(e)
Figure 1 (a) CT slice of the broken skull (b) Inner and outer borders of the skull bone (c) Inner border of the skull bone (d) Outer border of the skull bone (e) Example of filling the skull defect
3.1. Active Contour Model and Thickness Trimming From the perspective of skull anatomy, the curve of the skull in each CT images is not all the same, but most of curves are oval [21]. Therefore, the curve in each image can be modeled as being similarly oval shapes. Active contour models can fulfill all requirements of skull modeling. According to the characteristics of active contour models, the generated curve will move as close as possible to the inner and outer border. For example, a schematic diagram of a snake is shown in Figure 2. The blue dotted line represents the initial contour and the red dotted line
Yu-Cheng Lin et al. / Procedia Manufacturing 11 (2017) 2164 – 2169
represents the final suitable contour in the snake. The blue dotted line gradually moves toward the red dotted line based on the characteristics of snake. Once the initial contour stops moving, the suitable contour in this CT image is found.
Figure 2 Schematic diagram of a snake sample
In the final snake process, after we find the snake curve we do the thickness trimming. The thickness of the skull bone in each CT layer is another problem that should be considered [22]. In this study, we obtained the thickness of the skull bone in each CT layer by subtracting the outer border from the inner border. The procedure of thickness trimming is shown in Figure 3. Each CT image in this study consisted of binary values (0 and 1). The red dotted line in Figure 4 is the final snake contour. After filling out the outer and inner borders with solid graphics, we subtracted the outer border from the inner border. Thus, we obtained a complete skull bone figure in each CT layer. We automatically obtained the thickness of skull and do not need to consider the thickness problem [21, 22]. We stack all complete skull bone figure in each CT layer and we can obtain a complete skull. We can also use this complete skull to obtain a model of the prosthesis.
Figure 3 Thickness trimming procedure in each CT layer
4. Analyses of Results We use one testing samples in this study. This testing sample is originally broken skull from a patient. We use an originally broken in the lateral region of the skull from a patient to verify the feasibility of this study. The resolution of the patient CT image was 512 × 512, and it could be transformed into 265 layers. The snake script was programmed in MATLAB. First, we extracted the skull bone from the CT image and identified the inner and outer borders of the skull bone in each layer. Subsequently, according to the skull bone border in Figure 1(c) and Figure 1(d), we used the snake to fill the skull defect. The vital parameter values of Snake are shown in Table 1. Parameter controls the elastic deformation of the contour. If is too high, the contour generated by the snake zooms out into a small circle. Therefore, was set at
2167
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Yu-Cheng Lin et al. / Procedia Manufacturing 11 (2017) 2164 – 2169
0.1. We set to be slightly more than zero. , , and are the weights of the image forces. Higher weights indicate that the Snake is more influenced moving toward lines, edges, and terminations. According to the observation in this study, the attraction to the edges is the most crucial because many skull border images consist of discontinuous curves. Therefore, we set . If we set the weights and to be higher, the Snake would not conform to the demand. represents the total points of the final Snake. Table 1 Vital parameter values of the snake
Parameters/Snake
value
0.1 0.3 0.04 4 0.1 200
4.1. Results and Discussion
The objective of this study was to identify suitable fitting cranial curve by using active contour models. However, the fitting curve might not be the optimal solution because of some problems at the junction between the realistic and fitting curves. In this case, both the inner and outer borders are not 100 percent aligned with the contact point. This problem should be solved in future research. A partial deficient in the lateral region of the skull was used as a testing sample in this study. The white region represents the skull bone, and the red region represents the prosthesis generated using our method, as shown in Figure 4. The experiment proves the proposed method is feasible.
Figure 4 Result of the experiment
5. Conclusion Irregularities of the skull or skull defects result in low protection of the brain, a high risk of brain infection, and poor postoperative recovery for patients. Moreover, it also affect the aesthetic appearance. Cranioplasty is a common method used to restore the integrity of the cranial cavity. This paper presents a method of prosthesis modeling by using Snake. We developed a self-adjusting bone curvature algorithm that involves using Snake. The experiments validated the proposed method could build a model of a broken skull bone. The significant contribution of this work is that Snake can be used to model an arc curve for which information missing in the image. The proposed method can also save time for the manufacture of prosthesis for surgeons. Thus, the proposed method is a promising technique for medical professionals solving prosthesis modeling problems. We believe that the proposed method is a convenient strategy that can be used by medical professionals to repair the skull bone defects for patients. References [1] B. Aarabi, D. C. Hesdorffer, E. S. Ahn, C. Aresco, T. M. Scalea, and H. M. Eisenberg, "Outcome following decompressive craniectomy for malignant swelling due to severe head injury," Journal of neurosurgery, vol. 104, pp. 469-479, 2006. [2] D. J. Cooper, J. V. Rosenfeld, L. Murray, Y. M. Arabi, A. R. Davies, P. D'urso, et al., "Decompressive craniectomy in diffuse traumatic brain
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