For the structure mechanics of human body, it is almost impossible to conduct mechanical experiments. Then the finite element model to simulate mechanical experiments has become an effective tool. By introducing several common methods for constructing a 3D model of cranial cavity, this paper carries out systematically the research on the influence law of cranial cavity deformation. By introducing the new concepts and theory to develop the 3D cranial cavity model with the finite-element method, the cranial cavity deformation process with the changing ICP can be made the proper description and reasonable explanation. It can provide reference for getting cranium biomechanical model quickly and efficiently and lay the foundation for further biomechanical experiments and clinical applications.
There have been many methods used to study the biomechanics of tissue structure today. Biological tissues are widely used in animal experiments, physical experiments, and
At present, most biomechanical methods can only detect the external mechanical changes of human specimens. Thus, it is difficult to fully reveal the mechanisms of interaction of each part, and the internal structure displacement and internal stress change can be only presumed according to the pathological process, which lacked objective experimental support. Three-dimensional image reconstruction and finite element simulation can solve these problems. Computer simulation experiments, such as finite element models, can reflect the situations after reconstructing repeatedly simulating experiments or changing some parameters according to the biomechanical characteristics, which cannot be obtained by other methods. Finite element method (FEM) has been shown to be an effective analysis of theoretical biomechanics. It uses the mathematical model of mechanics to perform numerical value mechanical analysis and reduce mathematical behavior characteristics of engineering system. Mathematical characteristics of tissue simulated in the form of mathematics include node, element, material attribute, loading, and boundary condition, which are acquired based on physical prototype. An alteration of local structure, parameters, and loading can simulate the displacement and stress in any place and explain the stress change of tissue during physiopathological process to acquire overall information.
The creation of digital copies of humans is an innovation in anatomy education. These 3D meshes create a new alternative for students and researchers. It also allows the remote access and the manipulation of the pieces without manual consuming. The 3D visualization of the human skull represents an advance in the interpretation of images, because it makes possible the volumetric analysis of the anatomical structures and it evidences more clarity in its space configurations and its relations with other organs [
The “Monro [
Clinical data shows that increased pressure within the brain matter caused by lesions or swelling within the brain matter itself resulted in raised intracranial pressure (ICP) is a serious and often fatal condition, and compression of vital brain structures and blood vessels can lead to serious, permanent neurologic deficits or even death. It is hard to perform biomechanical analysis of stress and strain of cranial cavity with the changing ICP, even through experiments. Therefore, a mechanical model was established through the use of three-dimensional finite element method to provide an effective pathway for biomechanical research of cranium brain.
Finite Element Method (FEM) is an integrated product of many disciplines, including mechanics, mathematical physics, computational methods, and computer technology. The three research methods, theoretical analysis, scientific experiments, and scientific computing, have been applied to study the nature problems. Because of the limitations of scientific theory and experiments, the scientific computing becomes one of the most important research tools. As one of ways to carry out the scientific computing, the finite element method can almost analyze any complex engineering structure so as to obtain various mechanical properties in most engineering fields.
The essence of the finite element method is that a complex continuum is divided into a limited number of simple elements transformed the infinite freedom degree to the limited one, and the differential equation to the algebraic equations of finite parameters. While analyzing the problems of engineering structure with the finite element method, after the discretization of an ideal discrete body, it is one of mainly discussed contents of the finite element theory of how to ensure the convergence and stability of numerical solution. The convergence of numerical solution is related to the element division and shape. During the solving process, as the basic variable, the displacement is usually solved through the virtual displacement or minimum potential energy principle.
The solving steps for the strains of cranial cavity with the ICP changes are shown in Figure identifying the discretized cranial cavity, selecting the displacement mode, analyzing the mechanical properties of elements and deriving the element stiffness matrix, collecting all relationship between force and displacement and establishing the relationship between force and displacement of cranial cavity, solving the nodal displacement, classifying the nodal displacement and the strain and stress in each element then calculating.
Block diagram of numerical solution steps of cranial cavity with the finite element method.
It is a great achievement for the finite element method to be applied in the quantitative research in the life science. In particular, its great superiority is demonstrated in the research on human biomechanics. After a long evolution of human labor, the human skeleton has almost formed a perfect mechanical structure. However, the mechanics experiment is almost impossible to directly develop while the mechanical structure of human body is studied. At that time, it is an effective means that the finite element numerically simulates the mechanical experiments.
In 1960s, the finite element method was initially applied in the cardiovascular system study on mechanical problems. From the 1970s, the orthopedic biomechanics research began to be initially applied to spine. After 80 years, the applicable range is gradually extended to craniofacial bone, mandible bone, femur [ Improvement and optimization design of equipment. The mechanical simulation experiment by finite element model. Nowadays, the finite element method has been widely used in the country and has made a lot of successes. Particularly, there is more certain guidance in the clinical application. In biomechanics, the finite element application, there are a large number of opportunities to research the shape and structure of finite element model.
The craniospinal cavity may be considered as a balloon. For the purpose of our analysis, we adopted the model of hollow sphere (Figure
The sketch of 3D cranial cavity and grid division.
Of course, the structure, dimension, and characteristic parameter of human skull must be given before the calculation. The thickness of calvaria [
ICP is not a static state, but one that influenced by several factors. But so far there are almost no records of the actual human being’s ICP in clinic. The geometry and structure of monkey’s skull, mandible, and cervical muscle are closer to those of human beings than other animals. So the ICP of monkeys [
In this paper, the finite element software MSC_PATRAN/NASTRAN, Ansys, and Mimics are applied to theoretically analyze the deformation of human skull with the changing ICP. The skull is a layered sphere constructed in a specially designed form with a Tabula externa, Tabula interna, and a porous Diploe sandwiched in between (Figure
Sketch of layered sphere. The thin-walled structure of cranial cavity is mainly composed of Tabula externa, Diploe, Tabula interna, and dura mater.
Considering the characteristic of compact bone, cancellous bone, and dura mater, their mean elastic modulus and Poisson ratios are 1.5 × 104 MPa, 4.5 × 103 MPa [
In addition, human skull has the viscoelastic material [
Finite element model of 1/8 cranial cavity shell.
In the finite element software Ansys, there are three kinds of models to describe the viscoelasticity of actual materials, in which the Maxwell model is the general designation for the combined Kelvin and Maxwell models. Considering the mechanical properties of human skull and dura mater, we adopt the finite element Maxwell model to simulate the viscoelasticity of human skull-dura mater system. The viscoelastic parameters of human skull and dura mater are, respectively, listed in Tables
Coefficients for the viscoelastic properties for human skull.
Elastic Modulus (GPa) | Viscosity (GPa/s) | Delay time |
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Compression |
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Tension |
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Creep coefficients for the viscoelastic properties for fresh human dura mater.
Elastic Modulus (MPa) | Delay time |
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Dura mater | 16.67 | 125.0 | 150.0 | 93.75 | 40 | 104 | 106 |
After ignoring the viscoelasticity of human skull and dura mater, the stress and strain graphs of skull bone are shown in Figure
The stress and strain distribution ignoring viscoelasticity of human skull and dura mater. (a) Stress distribution, (b) strain distribution, (c) the maximal stress vector distribution, (d) the maximal strain vector distribution, (e) stress vector distribution, and (f) strain vector distribution.
Figure
The stress and strain distribution considering viscoelasticity of human skull and dura mater. (a) Stress nephogram, (b) strain nephogram, (c)
From the relationships between total, elastic, and viscous strains of human skull and dura mater in Figure
Curves among total, elastic, and viscous strain when the ICP increment is 2.5 kPa. Here EPELX is elastic strain curve, and EPPLX is viscous strain curve. The viscous strain is about 40% of total strain.
After considering and ignoring the viscoelasticity of human skull and dura mater, the stresses and strains of cranial cavity are shown in Figure
The strain curves of finite element simulation under the conditions of ignoring and considering the viscoelasticity of human skull and dura mater with the changing ICP from 1.5 kPa to 5 kPa.
Reconstructions of the finite element model of cranial cavity are mostly through the multi-CT scanning technology at home and abroad [
This paper studied importantly the deformation of cranial cavity, including brain tissue, cerebrospinal fluid, and brain blood flow with the ICP changes. So the model of cranial cavity was properly simplified: only the cavity in which the brain lies, that is, a closed cavity, is made up of the parietal bone, occipital, frontal, and temporal bones, and a layer of dura mater. For the approximate symmetry of person’s head, the 1/2 cranial cavity model is built in this paper (Figure
Skeleton of the cranial cavity trendline.
In Figure
3D model of 1/2 cranial cavity.
Finite element meshes of 1/2 cranial cavity.
The three-dimensional finite element model of cranial cavity is considered as a composite structure composed of the skull and dura mater. The hexahedral grid was adopted to mesh the entire cranial cavity. The adjacent parts were dealt with by the Glue command, and the grid refinement with the Meshing-Modify Mesh command was used as the irregular mesh to the edge, sharp, or irregular position. Thus the 1/2 finite element model of the cranial cavity, including the parietal, prefrontal, occipital, and temporal bones and dura mater, and the cell type is block unit. Figure
The mild hypothermia is the main temperature environment for the treatment of brain injury, intracranial hypertension, and so on. Mild hypothermia treatment of severe traumatic brain injury in recent years is another important means [
The finite element method extensively solves the biomechanical problem in the medical fields. Compared to other biomechanical modellings, the finite element method can more accurately express the human body geometry and architecture. Therefore, the Ansys finite element software is in this paper used to reconstruct the three-dimensional cranial cavity of human being with the mild hypothermia treatment.
Figure
Strain graph. (a) Without hypothermia treatment when ICP is 3.0 kPa, (b) with hypothermia treatment when the ICP is 3.0 kPa, (c) without hypothermia treatment when the ICP is 5.0 kPa, and (d) with hypothermia treatment when the ICP is 5.0 kPa.
A healthy male volunteer, aged 40 years old, with body height 176 cm, weighing 75 kg, was included in this study. The volunteer explained no history of cranium brain. Common projections (posterior-anterior, lateral, dual oblique, hyperextension, and hyperflexion) were made to exclude cranium brain degenerative disorders, cranial instability, and brain destruction.
Spiral CT scans (1 mm thickness) were output in the JPG image file format and saved in the computer. Prior to experiment, informed consent was obtained from this volunteer, shown in Figure
CT scan image of cranial cavity.
High-performance computer (Lenovo, X200) and mobile storage equipment were used. Solid modeling software Mimics 13.0 (Materiaise’s interactive medical image control system) was used in this study. As a top software in computer-aided design, Mimics 13.0 provides many methods of precise modeling and has been widely used for precise processing. Its equipped Ansys and Partron finite element analysis module sequence were used for finite element analysis, and then the strain and deformation regularity of the real human cranial cavity were simulated with the changing ICP.
By the insert function of AutoCAD, the spline curves of CT pictures will be simulated, shown in Figure
AUTO CAD simulative spline curve.
3D space model of cranial cavity with AutoCAD.
It can be seen that the 3D model of cranial cavity with AutoCAD software failed and cannot meet the requirements of analysis because the “poor set” or “smoke shell” commands cannot be executed.
3D model of cranial cavity.
Since the cranial cavity model is for smooth processing and mesh division in the Mimics and Ansys software, the figures are shown in Figure
The cranial cavity model after smooth processing and mesh division.
The property of viscoelastic materials is adopted in the Prony Model. The shear modulus and volume modulus are, separately,
The fitted curves were assigned into different layers to construct the solid structure of bone (Tabula externa, Tabula interna, Diploe sandwiched in between, dura mater), and spongy. During reconstructing the structure of Tabula externa, Tabula interna, Diploe sandwiched in between, and dura mater, each part was established independently, and then the whole part was set up. The three-dimensional finite element models in each direction of cranial cavity are shown in Figure
Each view drawing on the 3D finite element model in of cranial cavity.
Following type selection, finite element mesh generation was performed in the above-mentioned models which were given material characteristics. Then, through simulating practical situation, boundary condition was exerted as well as the proper numerical process. And the three-dimensional analysis was performed. 3D finite element model of cranial cavity is meshed in Figure
3D finite element model of cranial cavity is meshed.
Finite element model of 1/2 cranial cavity.
Loads on the finite element model of 1/2 cranial cavity.
Strain graph when the ICP is 3.0 kPa.
Strain graph when the ICP is 5.0 kPa.
Strains curve of cranial cavity with the ICP variation.
Analysis of cranial cavity with Prony model.
The analysis results of cranial cavity with material properties of Prony model in the Mimics and Ansys software are shown in Figure
After fitting the relationship of skull strain and intracranial pressure, the curve is shown in Figure
The relationship of skull strain and intracranial pressure.
It can be seen that the strains of cranial cavity are close to the index growth with the increasing intracranial pressure. The relationship of skull strain and intracranial pressure is
Biomechanical model has been shown to play a key role in study of cranium brain, because it can be used to investigate the pathogenesis through model observation, thereby to propose the strategy of diagnosis and treatment.
Owing to irregular geometry and nonuniform composition of cervical spine cranium bone as well as impossible human mechanical tests, increasing attention has been recently paid to finite element method included in the biological study of cranium brain injury because this method exhibits unique advantages in analysis of complex structure.
Experimental results are the best method to verify model accuracy. When exerting persistent pressure to vertebral spine, nonlinear computation is supplemented to the two-dimensional unit calculation of ligament structure, which corresponds more to human mechanical structure. Statics solver exhibits the self-testing function and can automatically analyze computation process, report errors, and control error range. The displacement graph, stress graph, and isogram drawn by postprocessor visualize the distribution ranges of stress or strain loaded on each part of cranium brain with the changing ICP. When loads are vertically added, the stress on the posterior wall of cranium brain, as well as on the end plate and the posterior part of intervertebral discs, relatively centralizes.
Finite element analysis is an important mean to simulate human structural mechanical function in the field of biomechanics. A human finite element model with physical material characteristics under proper simulated