Skull Mechanics Study of PI Procedure Plan for Craniosynostosis Correction Based on Finite Element

Method

Xianfeng Jiang1,a, Jia You1,b, Ning Wang2,c, Zhipeng Shen2, Junyuan Li1,d 1 Mechanics Engineer Institute, Zhejiang University of Technology, Hangzhou, Zhejiang Prov., China

2 Neurosurgery Department, Children's Hospital of Zhejiang University School of Medicine, Hangzhou, Zhejiang Prov., China Email: a xfjiang@zjut.edu.cn, b yjmp8745@126.com, c wealy001@163.com, d lijunyuan@zjut.edu.cn

Abstract—Objective: The main purpose of correction craniosynostosis is to reopen cranial sutures with some bone slots in order to free the skull transformation with the brain development from the closed craniums. The intent of this paper is to analysis the relationship between the shapes of bone slots and the skull rigidity. Finite element method is utilized to obtain the stress distribution and deformation clouds of the different surgery schemes. And then a best cranial suture bone slot’s shape is brought up according to the stress distribution simulation results. Methods: A Congenital craniosynostosis case is selected to design the surgery treatment plan. PI-shape craniosynostosis correction scheme is used, and bone slots used for reconstruction the cranial suture are in variance to simulate the stress distribution change after the slots shape change. The cranial bone and endocranium models are meshed as tetrahedron element for finite element analysis. For the instantaneous stress take into account when the slots shape change, the viscoelastic material properties of the crianial bone and endocranium are ignored here. Abaqus is used to calculate the stress result. Results: Different bone slot shapes induce different cranium stress distribution and skull rigidity. Appropriate bone slots as the new cranial suture can make the cranium to win the maximum stress value about 46.12Mpa and the maximum displacement about 10.25mm. Conclusion: The results of stress distribution and deformation of cranial bone under the intracranial pressure after the correction craniosynostosis operation can be obtained by the finite element method. These results reflect the ability of the cranial bone expanding with the brain tissues growth. With finite element method, surgical prediction can be made to guide surgeons to make the decision of improving surgical treatment.

Keywords- finite element method; preoperation evaluation; PI procedure; craniosynostosis; skull mechanics; bone slot design

I. INTRODUCTION Congenital craniosynostosis syndrome, is known as

premature ossification of the skull and cranial suture narrow disease, means a variety of skull malformations which are caused by premature ossification of cranial suture closure before or after the babies are born, a congenital disease hinders brain development [1]. The general way to treat craniosynostosis is to open the premature closure of the cranial

suture to offer the free for the development of the brain, and to make the skull expanding to the normal shape as the brain developed. The craniofacial surgery was established by Tessier in the 1960's [2]. In 1978, Jane J. A. et al. developed the PI procedure for correction craniosynostosis [3]. Many surgical methods for correction congenital craniosynostosis have been developed at that time and after. For Boat-shaped head skull deformity correction surgery, there are a number of surgical methods, such as PI procedure, sagittal suturectomy, linear craniectomy, extended sagittal craniectomy, complete calvarial remodeling and so on [4].

The main purpose of correction craniosynostosis is to reopen the cranial suture in order to free the skull transformation with the brain development from the closed cranial. This means that as the brain growth the skull can make sufficient expanding under the sustained stress generated by brain and served on the inner surface of the skull through the endocranium. After the cranial suture is reopened with some slots in the skull in craniosynostosis surgery, the bone rigidity of the skull will be changed and the stress will be redistributed. A well stress distribution in skull is the basis of fine cure results of craniosynostosis operation, however doctors can not acquire the right stress distribution in skull after the surgery is carried out when they design and implement the craniosynostosis surgery.

In recent years, as the development and application of CT/MRI technologies, the three-dimensional medical image reconstruction technologies and finite element technologies are widely used in surgical operation design assistant and evaluation. Hemmy firstly introduced the application with the three-dimensional medical image reconstruction technique to cranio-maxillofacial surgery in 1983 [5]. And then the technique is applied gradually to the fields of cranio-maxillofacial surgery such as craniosynostosis treatments to improve the preoperative scheme and operation assistance [6-7]. The finite element technologies have been widely utilized to analyze the stress distribution after surgery and predict the bone remodeling around the implant systems for the knee replacement and dental implantation [8], but the use for the treatment of correction craniosynostosis is lack.

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By the using of the three-dimensional finite element technique, this thesis presents a method to simulate the stress distribution and change of the skull for the craniosynostosis correction treatment with PI-shape craniosynostosis surgery procedure [9]. Variant slots for the treatment are calculated to contrast the stress distribution changing. And the calculation results can help the surgeons to make the adjustment to the surgical treatment in order to achieve the best surgical expected results.

II. METHODS

A. Three-Dimensional Cranium Model for the Patient A three-dimensional cranium model is created by MIMICS

software with patient’s skull CT data. The PI-shape craniosynostosis surgery procedure in this paper is shown in Figure 1, in which region A (PI-shape skull) is required to be removed in the process of surgery to form new cranial suture. The slots as the region B show in Figure 1 are formed in the surgery procedure to reduce the parietal’s rigidity. In order to get a good postoperative effect the parietal bone must be fully developed as brain expansion, so the region D should gain biggish stress after surgery. Considering the healing speed control of the new cranial suture, the width on the top of the PI-shape is 10mm and the other is made the range from 10mm to 20mm according to G. J. Murad et al. [10]. In order to

protect superior sagittal sinus, some parts of cranial bone should be preserved which index in Figure 1 with the length of L1 to L3. For the changes of the length and width of the slots of the region B will make the change of the stress on the region D, five schemes are designed by variation the width and length and two big rounded holes open at the root of slot 1 (refer as Table Ⅰand Figure 2). Scheme 0 to scheme 5 will be contrasted according to its stress distribution mainly at the region D. As the intracranial pressure is loaded through endocranium to cranial bone, the endocranium model is also need to be reconstructed but the shape region is almost the same as the cranium model (refer as Figure 3).

TABLE I. PARAMETER OF SCHEMES

Scheme name Items Bone slot 1 width Length L1 Circle diameter Bone slot 2, 3 width Length L2, L3

Scheme 0（Figure 2A） nought nought nought nought nought Scheme 1（Figure 2B） 7mm 40mm nought 7mm 40mm Scheme 2（Figure 2C） 7mm 40mm nought 7mm 40mm Scheme 3（Figure 2D） 12mm 40mm nought 7mm 40mm Scheme 4（Figure 2E） 12mm 20mm nought 7mm 40mm Scheme 5（Figure 2F） 7mm 20mm 12mm 7mm 40mm

B. Cranium Finite Element Model

The cranium and the endocranium model are established by the Mimics software with congenital craniosynostosis patient’s skull CT data. The separated cranial bone models of scheme 1 to scheme 5 are made with the PI-shape bone and slots cutting off. The finite element mesh models are generated by MIMICS and exported as the data format for Abaqus. The finite element analysis is made under the Abaqus. After the cranial bone and endocranium mesh models are imported in Abaqus, some tasks should be made such as to assemble the cranial bone and the endocranium meshes with contact relationship, to set the boundary conditions and loads,

to define material activities and to assign the material properties.

To facilitate the calculation, the restriction of the scalp on

the skull is ignored. A fully constraint is imposed at the

Figure 3. Finite element model for cranium

Intracranial pressure load on the inside of

endocranium

The boundary condition of fully constraint at the

bottom edge of the cranium

The cranium model after surgical cutting

Endocranium

Chart A is the original meshed model of the cranial bone; Chart B, C, D, E, F are the mesh models with different surgical treatment. Figure 2. Models of the cranial bone

A B C D E F

Figure 1. The PI procedure for craniosynostosis

L1

L2

L3

Region B: Parietal bone slots

Region A: PI bone slots

Region C: forehead bone slots Bone slot 3 Bone slot 1 Bone slot 2

Region D: Stress region

Point 1

Point 4

Point 3

Point 2

bottom edge of the parietal bone flap model. The outside surface of the endocranium model is contacted with the inside surface of the cranium model. A constant intracranial pressure with the value of 2kpa is loaded to the inside surface of the endocranium model [11]. The cranium and the endocranium are defined as the isotropic elastic material, and the viscoelastic material effects can be ignored [12]. The material properties such as Young's modulus, Poisson's ratio and density of those models are listed in Table II.

TABLE II. MATERIAL PROPERTIES [13]

Models Material properties

Young's modulus（MPa）

Poisson’s ratio

Density（kg/cm3）

skull 2500 0.22 2.15 dura 34.5 0.45 1.14

III. RESULTS Figure 4 shows the finite element analysis results of the

schemes with different bone slot models as in Figure 2 and Table I. The results of stress clouds show that the stresses in these surgical treatments except scheme 0 are concentrated in the region D, which is between the last pair of slots on the cranium. The rapid stress decline is appeared near the front top of cranial bone, and in the vicinity of first bone slot there is no stress concentration occurred. The results of

displacement clouds show that a larger distortion appears at the top portion of cranium, and bone in the position of third slot is remain unchanged. In table Ⅲ the result items such as max stress value, average stress value, max displacement value and average displacement value of various schemes are listed. From the table we can find that the scheme 0, the primal cranial bone without any slots at it, has the maximum stress value of 14.7Mpa and the maximum deformation value is only 0.133mm, and the stress distribution of cranial bone is in a uniformity state, so it’s the worst operation in all plans. In contrast, scheme 4 and scheme 5 are the best two schemes, the maximum stress value respectively reaches 41.34Mpa and 46.12Mpa, and the maximum displacement is 9.418mm in scheme 4 and 10.25mm in scheme 5. From the analysis results we can see that cranial bone rigidity is an important factor which has a great influence on postoperative results of correction congenital craniosynostosis. The lower bone rigidity, the better surgery results will achieve. Figure 5 shows the stress value curves of 4 observation points in 6 schemes. From the figure we find that the last three schemes have high stress levels and the greater stress values at 4 points the weaker cranial bone rigidity will happen. So in the steps of making preoperative craniosynostosis treatment, effective measures should be taken such as the methods in scheme 3, 4 and 5, for reasonable layout the rigidity of cranial bone.

TABLE III. THE ANALYSIS RESULTS OF VARIOUS SCHEMES

Analysis items

Scheme name Scheme

0 Scheme

1 Scheme

2 Scheme

3 Scheme

4 Scheme

5 Max stress （MPa） 14.7 25.31 20.38 36.26 41.34 46.12

Average stress

（MPa） 8.0517 13.71 11.039 19.644 22.393 24.984

Max deformation （mm）

0.133 3.348 3.026 7.73 9.418 10.25

Average deformation （mm）

0.0718 1.813 1.639 4.187 5.101 5.552

Figure 5. The stress curves of four evaluation points in 6 schemes

Scheme 0 Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5

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Point 1 Point 2 Point 3 Point 4

Stress value (Mpa)

Displacement clouds from scheme 0 to scheme 5 Figure 4. The FEM results of each scheme

Stress clouds from scheme 0 to scheme 5

IV. DISCUSSION Finite element method has been widely used in the

biomedical fields. Applications have been made in Maxillary biomechanics analysis with finite element analysis to learn the stress situation when some force loaded [14], but the analysis used for craniosynostosis surgery treatment is less. The analysis with finite element method is made in this paper for the slots shapes and parameters used in the PI-shape craniosynostosis surgery. The cranium mechanics simulation results under the intracranial pressure forcing are carried out according to the PI-shape surgery plan together with skull model and load condition simplification. Results show that stress concentration appeared in the third pair bone slot roots, and main stress is distributed between the last pair bone slots and the second pair bone slots. Sufficient stress over long period of time may cause microcracks in bones, it has been suggested that biological process can repair microdamage at the physiological activity of the bone resorption by osteoclas and the bone accumulation by osteoblast. However, high physiological stress in excess of 50Mpa, the rate of biological repair may lag behind the rate of damage accumulation and stress fractures can occur [15]. Simulation results show that the maximum stress in these surgical treatment plans has suitable stress about 46.12Mpa. This could make bone rebuild easily and the bone microcracks induced by stresses may not lead to bone fractures. These microcracks have been shown to act as a kind of stimulus for bone remodeling. It is not well known how the microcracks formed and repaired, but a hypothesis has been made that our bodies can detect the presence of damage in the form of cracks and take appropriate action to reduce stress levels [16]. By choosing a reasonable surgical plan to produce a certain stress will contribute to the skull expansion with increased brain volume.

Person's head is a complex system. Intracranial pressure is constantly changing, and the pressure forces through endocranium to cranium. The skull surface is restrained by scalp. These factors will impact on the craniosynostosis surgery’s effect. The use of finite element method to analyze craniosynostosis preoperative design plan has great significance. The analysis results of finite element method can help doctors to make decisions more scientifically together with the clinical experiences. Optimized operation scheme will give more successful rate of surgery and increase the satisfaction of the results.

V. CONCLUSIONS In this paper the technique of finite element is used to

analyze stress distribution and deformation of the cranium under intracranial pressure after craniosynostosis PI-shape surgery operated. With finite element method, an intuitionistic view of surgical result prediction can give surgeons to make the decision of improving surgical treatment. According to the stress analysis results, scheme 5 (refer to Figure 2 F) is the best PI-shape craniosynostosis surgery plan.

The craniosynostosis surgery case presented in this paper has been operated with very good result. Our studies have also

applied in several other pre-surgery plan designs of correction craniosynostosis.

ACKNOWLEDGMENT This work is support from Key Laboratory of Special

Purpose Equipment and Advanced Processing Technology (Zhejiang University of Technology) of Ministry of Education, Digital Medical Engineering Research Center of Zhejiang University of Technology, and the Children’s Hospital of Zhejiang University School of Medicine.

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