Tissue Modeling and Analyzing for Cranium Brain with Finite Element Method

Numerous methods for measuring intracranial pressure (ICP) have been described, and many of them are suitable for different clinical disorders [1-5]. One method for ICP monitoring is through the ventricular system [6,7], which requires stereotaxic techniques and may not be practical for surgical experiments in the brain regions. Ventricular monitoring of ICP is also associated with intracerebral hemorrhage and infection [6]. Another method to monitor ICP is through the subarachnoid space at the cisterna magna, in which catheter placement may be difficult and dangerous due to the anatomy [8,9]. Some studies monitored ICP via epidural [10,12], which has limitations in measuring acute changes in ICP and is inaccurate in some cases when compared with ventricular monitoring [8]. These methods have many disadvantages of invasion, low-accuracy, cross-infection, etc [13,14]. Although many efforts have recently been made to improve the minitraumatic or non-invasive methods [15-19], noninvasive means of measuring ICP do not exist unfortunately in clinic [20,21]. With the significance of raised ICP in the studies of intracranial pathophysiology, espacially in neurosurgical disorders, it would be valuable to have a simple and reliable method to monitor intracranial pressure (ICP) in clinic. Therefore, the minitraumatic or non-invasive, accurate and simple method to measure ICP is an important question of research in neurosurgery. In this study, we propose a new, minitraumatic, simple, and reliable measurable system that can be used to monitor ICP from the exterior surface of skull bone.


Introduction
Numerous methods for measuring intracranial pressure (ICP) have been described, and many of them are suitable for different clinical disorders [1][2][3][4][5].One method for ICP monitoring is through the ventricular system [6,7], which requires stereotaxic techniques and may not be practical for surgical experiments in the brain regions.Ventricular monitoring of ICP is also associated with intracerebral hemorrhage and infection [6].Another method to monitor ICP is through the subarachnoid space at the cisterna magna, in which catheter placement may be difficult and dangerous due to the anatomy [8,9].Some studies monitored ICP via epidural [10,12], which has limitations in measuring acute changes in ICP and is inaccurate in some cases when compared with ventricular monitoring [8].These methods have many disadvantages of invasion, low-accuracy, cross-infection, etc [13,14].Although many efforts have recently been made to improve the minitraumatic or non-invasive methods [15][16][17][18][19], noninvasive means of measuring ICP do not exist unfortunately in clinic [20,21].With the significance of raised ICP in the studies of intracranial pathophysiology, espacially in neurosurgical disorders, it would be valuable to have a simple and reliable method to monitor intracranial pressure (ICP) in clinic.Therefore, the minitraumatic or non-invasive, accurate and simple method to measure ICP is an important question of research in neurosurgery.In this study, we propose a new, minitraumatic, simple, and reliable measurable system that can be used to monitor ICP from the exterior surface of skull bone.The 'Monro [22] -Kellie [23] doctrine' states that an adult cranial compartment is incompressible, and the volume inside the cranium is a fixed volume thus creates a state of volume equilibrium, such that any increase of the volumes of one component (i.e.blood, CSF, or brain tissue) must be compensated by a decrease in the volume of another.If this cannot be achieved then pressure will rise and once the compliance of the intracranial space is exhausted then small changes in volume can lead to potentially lethal increases in ICP.The compensatory mechanism for intracranial space occupation obviously has limits.When the amount of CSF and venous blood that can be extruded from the skull has been Finite Element Analysis -From Biomedical Applications to Industrial Developments 252 exhausted, the ICP becomes unstable and waves of pressure develop.As the process of space occupation continues, the ICP can rise to very high levels and the brain can become displaced from its normal position.Dr. Sutherland firstly perceived a subtle palpable movement within the bones of cranium.Dr. Upledger [24] discovered that the inherent rhythmic motion of cranial bones was caused by the fluctuation of CSF.Accordingly, the cranium can move and be deformed as the ICP fluctuates.By pasting strain foils on the exterior surface of skull bone, the skull strains can be measured with the strain gauge.ICP variation can be obtained through the corresponding processing based on the strains.So the ICP can be monitored by measuring the strains of skull bone [25].

Mechanical analysis of cranial cavity deformation 2.1 Mechanical analysis of deformation of the skull as a whole
There are two aspects of effects on forces on the objects.One can make objects produce the acceleration, another is make objects deform.In discussing the external force effect, the objects are assumed to be a rigid body not compressed.But in fact, all objects will deform under loading, but different with the degrees.Here, we will mechanically analyze the overall deformation of cranial cavity under the external force.

(1) Two basic assumptions
To simplify the analysis of deformation of human skull, we assume:

Uniformly-continuous materials
The human skull is presumed to be everywhere uniform, and the sclerotin is no gap in bone of cranial cavity.

The isotropy
The human skull is supposed to have the same mechanical properties in all directions.The thickness and curvature of human skull vary here and there.The external and internal boards are all compact bones, in which external board is thicker than internal board but the radian of external board is smaller than that of the internal board.T he diplo e i s t he cancellous bone between the external board and the internal board, which consists of the marrow and diploe vein.The parietal bone is the transversely isotropic material [26], namely, it has the mechanical property of rotational symmetry in any axially vertical planes of skull [27].The tensile and compressive abilities of compact bone are strong.The important mechanical characteristics of cancellous bone are viscoelasticity [28], which is generally considered as the construction of semi-closed honeycomb composed of bone trabecula reticulation.The main composition of cerebral duramater, a thick and tough bilayer membrane, is collagenous fiber11, which is viscoelastic material [29].And the thickness of duramater is obviously variable with the changing ICP [30].The mechanical performance of skull is isotropic along tangential direction on the skull surface [31], in which the performance of compact bone in the external board is basically the same as that in the internal board [32], thus both cancellous bone and duramater can be regarded as isotropic materials [33].And the elastic modulus of fresh duramater is variable with delay time [34].And there are a number of sutures in the cranial cavity.But while a partial skull is studied on the local deformation, we can regard each partial skull as quasi-homogeneous and quasi-isotropic.In addition, the sutures of cranial cavity are also the continuous integration with ages.
(2) Two concepts 1. stress (  ) Stress is the internal force per unit area.The calculation unit is 2 kg/cm or 2 kg/mm .

Transverse deformation coefficient
When the objects are under tension, not only the length is drawn out from l to 1 l , but also the width is reduced from b to 1 b .This shows that there are the horizontal compressive stresses in the objects.Similarly, while the object is compressed, not only its length shortens but its width increases.It indicates that the horizontal tensile stress distributes in the objects.
The horizontal absolute deformation is noted as 1 bbb   , and the transverse strain is 0 bb   .
In mechanics of materials, the transverse strain 0  is proportional to the longitudinal strain  of the same material within the scope of the Hooke theorems' application.The ratio of its or Poisson ratio.The Poisson ratio of any objects can be detected by the experiment.
While vertically compressed, the objects simultaneously have a horizontal tension.Therefore, when the head attacked in opposite directions force, the entire human skull will take place the longitudinal compression and transverse tension with the same direction of force.Then the longitudinal compressive stress and the horizontal tensile stress will be generated in the scelrotin.Thus, the stress of arbitrary section along radial direction in shell is just equal to the tangential pulling force along direction perpendicular to the normal vertical when ICP is raised.

The finite-element analysis of strains by ignoring the viscoelasticity of cranial cavity
The geometric shape of human skull is irregular and variable with the position, age, gender and individual.So the cranial cavity system is very complex.Moreover, the cranial cavity is a kind of viscoelactic solid with large elastic modulus, and the brain tissue is also a viscoelastic fluid with great bulk modulus.It is now almost impossible to accurately analyze the brain system.Only by some simplification and assumptions, the complex issues can be made.Considering the special structure of cranial cavity composed of skull, duramater, encephalic substance, etc, here we simplify the model of cranial cavity as a regular geometry spheroid of about 200mm external diameter, which is an hollow equal-thickness thin-wall shell.
The craniospinal cavity may be considered as a balloon.For the purpose of our analysis, we adopted the model of hollow sphere.We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of human skull corresponding to the ICP change.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.Based on the established knowledge of cranial cavity importantly composed of skull and dura mater (Fig2.1), a thin-walled structure was simulated by the composite shell elements of the finite-element software [35].The thickness of skull is 6mm, that of duramater is 0.4mm, that of external compact bone is 2.0mm, that of cancellous bone is 2.8mm, and that of internal compact bone is 1.2mm.Above all, we should prove the theoretical feasibility of the strain-electrometric method to monitor ICP.We simplify the theoretical calculation by ignoring the viscoelasticity of cancellous bone and dura mater.And then we make the analysis of the actual deformation of cranial cavity by considering the viscoelasticity of human skull-dura mater system with the finite-element software.At the same time, we can determine how the viscoelasticity of human skull and dura mater influences the strains of human skull respectively by ignoring and considering the viscoelasticity of human skull and dura mater.

The stress and strain analysis of discretized elements of cranial cavity
In order to obtain the numerical solution of the skull strain, the continuous solution region of cranial cavity divided into a finite number of elements, and a group element collection glued on the adjacent node points.Then the large number of cohesive collection can be simulated the overall cranial cavity to carry out the strain analysis in the solving region.Based on the block approximation ideas, a simple interpolation function can approximately express the distribution law of displacement in each element.The node data of the selected field function, the relationship between the nodal force and displacement is established, and the algebraic equations of regarding the nodal displacements as unknowns can be formed, thus the nodal displacement components can be solved.Then the field function in the element collection can be determined by using the interpolation function.If the elements meet the convergence requirements, with the element numbers increase in the solving region with the shrinking element size, and the approximate solution will converge to exact solutions [36].
The solving steps for the strains of cranial cavity with the ICP changes are shown in Fig2.2.The specific numerical solution process is: 1.The discretized cranial cavity The three-dimensional hollow sphere of cranial cavity is divided into a finite number of elements.By setting the nodes in the element body, an element collection can replace the structure of cranial cavity after the parameters of adjacent elements has a certain continuity.To make the nodal displacement express the displacement, strain and stress of element body, the displacement distribution in the elements are assumed to be the polynomial interpolation function of coordinates.The items of polynomial number are equal to the freedom degrees number of elements, that is, the number of independent displacement of element node.The orders of polynomial contain the constant term and linear terms.
According to the selected displacement mode, the nodal displacement is derived to express the displacement relationship of any point in the elements.Its matrix form is: Where:  

Collecting all relationship between force and displacement, and establish the relationship between force and displacement of cranial cavity
According to the displacement equal principle of the public nodes in all adjacent elements, the relationship between force and displacement of overall cranial cavity collected from the element stiffness matrix: Where:   F -Load array;   K -The overall stiffness matrix;    -The nodal displacement array of the entire cranial cavity.

Solve the nodal displacement
After the formula (2.1) ~ (2.5) eliminating the stiffness displacement of geometric boundary conditions, the nodal displacement can be solved from the gathered relationship groups between force and displacement.
6.By classifying the nodal displacement solved from the formula (2.2) and (2.3), the strain and stress in each element can be calculated.
In this paper, the studied cranial cavity is a hollow three-dimensional sphere, its external radius 100 mm R  , the curvature of hollow shell is 001 rad/mm ., the thickness of shell wall is 6mm, so the element body of hollow spherical can be treated as the regular hexahedron.The following is the stress and strain analyses in the three-dimensional elements in the cranial space.The 8-node hexahedral element (Fig2.3) is used to be the master element.The origin is set up as the local coordinate system ( ,,    ) in the element.
Trough the transformation between rectangular coordinates and local coordinates, the space 8-node isoparametric centroid element can be obtained.The relationship of coordinate transformation is: Then the displacement function of element is: Where: i The derivative of composite function to local coordinates is: The strain relationship of space elements is: The strain matrix   B of space element:  00 00 00 0 0 (2.12) The shape function was derivative to be: The matrix   J is the three-dimensional Yake ratio matrix of coordinate transformation: The stress-strain relationship of space elements is: The elasticity matrix   The element stiffness matrix from the principle of virtual work is:    ddd Where: The equivalent nodal forces acting on the space element nodes are: Because the internal pressure in the cranial cavity is surface force, the equivalent load for the pressure acting on the element nodes is: The relationship between force and displacement in the entire cranial cavity is: Then after obtaining the nodal displacement, the stress and strain in each element can be calculated by combining the formula (2.11) and (2.15).

The stress and strain analysis for complex structure of cranial cavity deformation
Cranial cavity is the hollow sphere formed by the skull and the duramater.From the Fig2.2, there are obvious interfaces among the various parts of outer compact bone, middle cancellous bone, inner compact bone and duramater, which is consistent with the characteristics of composite materials [37].Four layered composite structure of cranial cavity is almost lamelleted distribution.Therefore, the lamelleted structure is adopted to establish and analyze the finite-element model of cranial cavity, and the laminated shell element is used to describe the thin cranial cavity made up of skull and duramater.Here the cranial cavity deformation of laminated structure is analyzed as follows: (1) The stress and strain analysis for the single layer of cranial deformation Each layers of cranial cavity are all thin flat film.The skulls are transversely isotropic material.The thickness of Tabula externa, diploe, Tabula interna, duramater is all very small.So compared with the components in the surface, the stress components are very small along the normal direction, and can be neglected.So the deformation analysis to single-layer cranial cavity can be simplified to be the stress problems of two-dimensional generalized plane.
The stress-strain relationship of each single-layer structure in the cranial cavity:

22)
Namely: Where, 1,2 -The main direction of elasticity in the plane;    -Poisson's ratio of transverse strain along the 2 direction that the stress acts on the 1 direction.
(2) The stress and strain analysis for the laminated deformation of cranial cavity The cranial cavity is as a whole formed by the four-layer structures.So the material, thickness and elastic main direction are all different.The overall performance of cranial cavity is anisotropic, macroscopic non-uniformity along the thickness direction and noncontinuity of mechanical properties.Thus, the assumptions need to be made before analyzing the overall deformation of cranial cavity [38]: 1.The same deformation in each layer Each single layer is strong glued.There are the same deformation, and no relative displacement;

No change of direct normal
The straight line vertical to the middle surface in each layer before the deformation remains still the same after the deformation, and the length of this line remains unchanged whether before or after deformation; The positive stress along the direction of thickness is small compared to other stress, and can be ignored; 4. The plane stress state in each single layer Each single-layer structure is similar to be assumed in plane stress state.
From the four-layer laminated structure composed of Tabula externa, diploe, Tabula interna, duramater, the force of each single-layer structure is indicated in Fig2.4.The middle surface in the laminated structure of cranial cavity is the xy coordinate plane.z axis is perpendicular to the middle surface in the plate.Along the z axis, each layer in turn will be compiled as layer 1, 2, 3, and 4. The corresponding thickness is respectively 1 t , 2 t , 3 t , 4 t .As a overall laminated structure, the thickness of cranial cavity is h , shown in Fig2.5.The displacement components at any point within the laminated structure of cranial cavity: The strain is: The mean internal force and torque acting on the laminated structure of cranial cavity in the unit width is: Taking into account the discontinuous stress caused by the discontinuity along the direction of laminated structure in the cranial cavity, the formula (2.28) can be rewritten in matrix form: After substituting the formula (2.22) and (2.27) into equation (2.29), the average internal force and internal moment of the laminated structure in the cranial cavity is: Where:   A -The stiffness matrix in the plane, Then the flexibility matrix of laminated structure in the cranial cavity is:


Thus, the stress-strain relationship of laminated structure in the cranial cavity is: With the changing ICP, to determine how the viscoelasticity of human skull and duramater influences the strains of human skull respectively by ignoring and considering the viscoelasticity of human skull and duramater, we make the analysis of the actual deformation of cranial cavity by considering the viscoelasticity of human skull-duramater system with the finite-element software MSC_PATRAN/NASTRAN and ANSYS.
Considering the complexity to calculate the viscoelasticity of human skull and duramater, we can simplify the calculation while on-line analysis only considering the elasticity but ignoring the viscoelasticity of human skull and duramater after obtaining the regularity how the viscoelasticity influences the deformation of cranial cavity.

The finite-element analysis of strains by ignoring the viscoelasticity of human skull and duramater
The craniospinal cavity may be considered as a balloon.For the purpose of our analysis, we adopted the model of hollow sphere (Fig2.6).We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of human skull corresponding to the ICP change.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.Based on the established knowledge of cranial cavity importantly composed of skull and duramater, a thin-walled structure was simulated by the composite shell elements of the finite-element software [39].

Fig. 2.6. 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 [40] varies with the position, age, gender and individual, so does dura mater [41].Tabula externa and interna are all compact bones and the thickness of Tabula externa is more than that of Tabula interna.Diploe is the cancellous bone between Tabula externa and Tabula interna [42].The parietal bone is the transversely isotropic material, namely it has the mechanical property of rotational symmetry in the axially vertical planes of skull [43].The important mechanical characteristic of cancellous bone is viscoelasticity, which is generally considered as the semi-closed honeycomb structure composed of bone trabecula reticulation.The main composition of cerebral dura mater, a thick and tough bilayer membrane, is the collagenous fiber which has the characteristic of linear viscoelasticity [44].And the thickness of dura mater obviously varies with the changing ICP [45].The mechanical performance of skull is isotropic along the tangential direction on the surface of skull bone [46], in which the performance of compact bone in the Tabula externa is basically the same as that in the Tabula interna [47].Thus both cancellous bone and dura mater can be regarded as isotropic materials.And the elastic modulus of fresh dura mater varies with the delay time [48].

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Finite Element Analysis -From Biomedical Applications to Industrial Developments 266 Next we need determine the fluctuant scope of human ICP.ICP is not a static state, but one that influenced by several factors.It can rise sharply with coughing and sneezing, up to 50 or 60mmHg to settle down to normal values in a short time.It also varies according to the activity the person is involved with.For these reasons single measurement of ICP is not a true representation.ICP needs to be measured over a period.Measured by means of a lumbar puncture, the normal ICP in adults is 8 mmHg to 18 mmHg.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 [49] can be taken as the reference to that of human beings'.The brain appears to be mild injury when ICP variation is about 2.5 kPa, moderate injury when ICP variation is about 3.5 kPa and severe injury when ICP variation is about or more than 5 kPa.Therefore, we carried out the following theoretical analysis with the ICP scope from 1.5 kPa to 5 kPa.
In this paper, the finite-element software MSC_PATRAN/NASTRAN and ANSYS are applied to theoretically analyze the deformation of human skull with the changing ICP.The external diameter of cranial cavity is about 200 mm.The thickness of shell is the mean thickness of calvarias.The average thickness of adult's calvaria is 6.0 mm, that of Tabula externa is 2.0 mm, diploe is 2.8 mm, Tabula interna is 1.2 mm and, dura mater in the parietal position is 0.4 mm.
Considering the characteristic of compact bone, cancellous bone and dura mater, we adopt their elastic modulus and Poisson ratios as 1.5×10After ignoring the viscoelasticity of human skull and dura mater, the strains of cranial cavity are shown in Table 1 with the finite-element software MSC_PATRAN/NASTRAN as ICP changing from 1.5 kPa to 5.0 kPa (Fig2.7).There is the measurable correspondence between skull strains and ICP variation.The strains of human skull can reflect the ICP change.When ICP variation is raised up to 2.5 kPa, the stress and strain graphs of skull bone are shown in Fig2.8～Fig2.13.

Fig. 2.8. Stress distribution
The scope of stress change on the outside surface is from 22.1 kPa to 25.3 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.9. Strain distribution
The scope of strain change on the outside surface is from 1.52 μ to 1.57 μ when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.10. The maximal stress vector distribution
The maximal main stress is about 22.4 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.11. The maximal strain vector distribution
The maximal main strain is about 2.2 μ when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.12. Stress vector distribution
The main stress vector is about 21.8 kPa when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

Fig. 2.13. Strain vector distribution
The main strain vector is about 2.14 μ when ICP variation is raised up to 2.5 kPa by ignoring the viscoelasticity of human skull and dura mater.

The finite-element analysis of strains by considering the viscoelasticity of human skull and dura mater
Human skull has the viscoelastic material [52].Considering the viscoelasticity of human skull and dura mater, we use the viscoelastic option of the ANSYS finite-element program to analysis the strains on the exterior surface of human skull as ICP changing.According to the symmetry of 3D model of human skull, the preprocessor of the ANSYS finite-element program is used to construct a 1/8 finite-element model of human skull and dura mater consisting of 25224 nodes and 24150 three-dimensional 8-node isoparametric solid elements, shown in Fig2.14.

Fig. 2.14. Finite element model of 1/8 cranial cavity shell
The three-dimensional stress-strain relationships for a linear isotropic viscoelastic material are given by:  -the volumetric strain; t -the present time;  -the past time.
Before the theoretical analysis of the minitraumatic strain-electrometric method, we need to set up the viscoelastic models to describe the relevant mechanical properties of human skull and dura mater. (

1) Viscoelastic Model of human skull
Under the constant action of stress, the strain of ideal elastic solid is invariable and that of ideal viscous fluid keeps on growing at the equal ratio with time.However, the strain of actual material increases with time, namely so-called creep.Generally, Maxwell and Kelvin models are the basic models to describe the performance of viscoelastic materials.Maxwell model represents in essence the liquid.Despite the representative of solid, Kelvin model can't describe stress relaxation but only stress creep (Fig2.15).So the combined models made up of the primary elements are usually adopted to describe the viscoelastic performance of actual materials.The creep of linear viscoelastic solid can be simulated by the Kelvin model of three parameters or the generalized Kelvin model.00 After the calculation based on the equation ( 1), the elastic modulus of human skull is the Fig2. (

2) Viscoelastic Model of human duramater
The generalized Kelvin model is shown in Fig2.17 (c).Fig2.17(a) is the creep experimental curves of human duramater.Fig2.17(b) is the curves of creep compliance for the generalized Kelvin model.It shows that the tendency of creep curve in the experiment is coincident with that of creep compliance for the generalized Kelvin model.Creep is the change law of material deformation with time under the invariable stress, so here  is constant.For the generalized Kelvin model, the stress-strain relationship is (t) J(t)    .Thus the tendency of theoretical creep curve is totally the same as that of experimental one for human duramater.So in this paper, the generalized Kelvin model composed of three Kelvin-unit chains and a spring is adopted to simulate the viscoelasticity of human dura mater in this paper.
After the calculation based on the equation (2.36), the creep compliance of human dura mater is equation (2.37), Then the elastic modulus of human dura mater is equation (2.38), 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

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(3) The stress and strain distribution by the finite-element analysis Fig2.18(a) ~ (e) are the analytic graphs of stress and strain with finite-element software ANASYS when ICP variation is raised up to 2.5 kPa.After considering the viscoelasticity of human skull and duramater, the stresses and strains of cranial cavity are shown in Fig2.18 as the ICP changing from 1.5 kPa to 5kPa with the finite-element software ANSYS.It shows that the stress and strain distributions on the exterior surface of human skull are wellproportioned and that the stress and strain variation on the exterior surface of cranial cavity is relatively small corresponding to the ICP change.The strains of cranial cavity are coincident with ICP variation.The deformation scope of human skull is theoretically from 0.9 με to 3.4 με as the ICP changing from 1.5 kPa to 5.0 kPa.Corresponding to ICP of 2.5 kPa, 3.5 kPa and 5.0 kPa, the strain of skull deformation separately for mild, moderate and severe head injury is 1.5 με , 2.4 με , and 3.4 με or so.From the relationships about total, elastic and viscous strains of human skull and dura mater in Fig2.19, the viscous strains account for about 40% and the elastic strains are about 60% of total strains with the increasing ICP.Fig. 2.19.Curves among total, elastic and viscous strain when the ICP increment is 2.5 kPa.
Here EPELX is elastic strain curve, EPPLX is viscous strain curve.The viscous strain is about 40% of total strain.

Finite-element model of human cranial cavity
3.1 Materials and methods

CT scan
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 Fig3.1.

Experimental equipment
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, 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.

Image boundary tracking
A self-programmed image boundary automatic recorder was used to acquire cranial information along the superior border to inferior border of cranium brain.The spatial boundary was recorded layer by layer.Following point selection from interior and exterior border of images, two-dimensional space coordinates were automatically recorded and saved in the .CDB form.After conversion, this file can be directly input into Mimics or CAD software.

Location
A coordinate system was determined.The CT scanning image starting from the lowest layer of cranium brain was set as the working background.CT scan was performed based on a fixed coordinate axis, with a know layer interval and magnification proportion.The spatial threedimensional coordinate of each point in the image could be determined through drawing the horizontal coordinate of each point and referencing scanning interval.When CT machines recorded each layer of images, all images were in the same scanning range, which equaled to cranial location of two-dimensional CT images from each layer in the scanning direction.Calibration of two-dimensional images could be performed if the scar bar of CT scan images www.intechopen.comFinite Element Analysis -From Biomedical Applications to Industrial Developments 276 w e r e g i v e n .I n a d d i t i o n , e a c h l a y e r o f i m a g e w a s s c a n n e d w i t h s o m e i n t e r v a l i n t h e longitudinal direction, which was equivalent to calibration in the third dimensional direction.

Image reconstruction
In accordance with the sequence of CT scans and according to the scale bar and scan interval of CT faulted image, geometry data of each layer were input into the pre-processing module of finite element software to establish a geometry model in the rectangular coordinate in the sequence of point, line, area, and solid.The transverse plane of CT scan was parallel to xy plane, and the longitudinal plane was along the z axis.Three-dimensional reconstruction process is shown in Fig3.2.

Reconstruction results
The fitted curves were assigned into different layers to construct the solid structure of bone (Tabula externa, Tabula interna, Diploe sandwiched in between), spongy durameter.During reconstruction of structure of Tabula externa, Tabula interna, Diploe sandwiched in between, dura mater, solid of each part was generated independently, and the union of all parts was collected.The 3d finite-element models in each direction of cranial cavity are shown in Fig3.3.Owing to irregular geometry and non-uniform 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.

Strains on the external surface of cranial cavity
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 in vivo condition can be used to effectively analyze the physical characteristics of human structure, for example, stress/strain of structure, modal analysis, exterior impact response, and fatigue test.With further understanding of cranium brain diseases, some complex models have not been developed, for example, finite element models of head and cranial cavity used to study the physio-pathological influences cervical spine loading in some complex exercises on cranium brain and soft tissue.Finite element analysis exhibits unexampled advantages in the biomechanical study of a severe medical brain problem.Theoretically, finite element method can simulate nearly all biomechanical experiments.Moreover, this method can better describe the interior changes of living body than practical study.Finite element method, as an emerging technique, has a broad developing space.However, it is a theoretical simulation analyses, only in conjunction with clinical detection and observation can it truly reflect the occurrence and progression of cranium brain disease and provide evidence for predicting curative effects, thereby exhibiting a synergic effect with clinical outcomes.The present model is only a represent.It can not reflect the changes between individual interior parts and between individuals in terms of bone contour and material characteristics.The present model is only a cranium brain motion segment.Its simulation analysis results might differ from the results from multiple motion segments.Actually, when much difference and many uncertainties exist between individuals, model simplification and idealization is to strengthen some research aspect, which removes experimental inherent difference.Of course, establishment of a finite element mechanical model is to provide mechanical methods for clinical and experimental studies.The present model needs further improvements due to some limitations, i.e., unable to reflect some complex condition, but it ensures the geometry data and material characteristic approximation for application of multiple toolsequipped by various softwares during the process of model establishment.In addition, finite element method, as one of tools used in the biomechanical field, can qualitatively analyze the stress change of cranium brain interior parts when bearing forces.Only by changing local structure or materials can the present model established by finite element method simulate the common clinical situation and the effects of intervention on ICP force.The present model should be further improved in the clinical and experimental processes.

Conclusion
We develop a new minitraumatic method for measuring ICP with strain-electrometric technology.The strains of skull bone can reflect the ICP change.The surgical procedures for this new method are easy, simple, safe and reliable.
This paper carries respectively on the stress and strain analysis on both conditions of ignoring and considering the viscoelasticity of human skull and duramater by finite-element software MSC_PPATRAN/NASTRAN and ANSYS as ICP changing from 1.5 kPa to 5 kPa.The three-dimensional finite element model of cranial cavity and the viscoelastic models of human skull and duramater are constructed in this paper.At the same time, 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.The conclusion is as follows: 1.The human skull and duramater are deformed as ICP changing, which is corresponding with mechanical deformation mechanism.2. When analyzing the strain of human skull and duramater as ICP changing by the finiteelement software ANSYS, the strain by considering the viscoelasticity is about 14% less than that by ignoring the viscoelasticity of human skull and duramater.Because the viscoelasticity analysis by finite-element software ANSYS is relatively complex and the operation needs the huge memory and floppy disk space of computer, it is totally feasible to ignore the viscoelasticity while calculating the FEA strain of human skull and duramater as ICP changing.3. The viscosity plays an important role in the total deformation strain of human skull and duramater as ICP changing.In the strains analysis of human skull and duramater with the changing ICP by the finite-element software ANASYS, the viscous strain accounts for about 40% of total strain, and the elastic strain is about 60% of total strain.4. Because the strains of human skull are proportional to ICP variation and the caniocerebra characteristic symptoms completely correspond to different deformation strains of human skull, ICP can be completely obtained by measuring the deformation strains of human skull.That is to say, the minitraumatic method of ICP by strain electrometric technique is feasible.Furthermore, ICP variation is respectively about 2.5 kPa when the strain value of human skull is about 1.4 µε, about 3.5 kPa when the strain value of human skull is about 2.1 µε, and about 5 kPa when the strain value of human skull is about 3.9 µε. 5.The strains decreased under the mild hypothermia environment about 0.56% than those under the normal temperature conditions during the same circumstance of ICP changes.
6.The deformation scope of human skull is theoretically from 1.50 μ to 4.52 μ as the ICP changing from 2.0 kPa to 6.0 kPa under the normal situation, and from 1.50 μ to 4.49 μ under the mild hypothermia environment.Accordingly, the strains of skull deformation for mild, moderate and severe head injuries are separately 1.87 μ , 2.62 μ and 3.74 μ or so corresponding to ICP of 2.5 kPa, 3.5 kPa and 5.0 kPa.

Discussion
In neurosurgery, one of the principle axes of treatment for neurosurgical disease is to control ICP.Because the skull bone is outside of and close to the brain, the surgical procedure in the strain-ICP monitoring system is relatively invasive and may affect experimental results from brain tissue.The strain-ICP monitoring has several advantages.First, the strain foil is far from the brain, and will not affect the surgery or experiments in the brain.Second, the wound surface on the parietal bone is very small and just about 11 mm 2 .Third, the surgical procedure is not extremely invasive for patients compared to the conventional monitoring.Fourth, it is possible to keep the strain foil for a longer time, the fixation of strain foil to the periosteum is much easier than other methods.Fifth, the operation is performed in the cephalic skin, the risk, difficulty, infection and trauma to patients are relatively small.Sixth, no special posture of patients is demanded, skull bone can be hardly influenced by any diseases and will be deformed as long as ICP is fluctuant in brain.ICP can be synchronously and continuously monitored based on the dynamic measurement of skull strains.Thus, this system is relatively safe, and it is easier to keep the strain foils in the cranial cavity for a longer period of time.
In this paper, the finite-element simulation was carried out to analyze the deformation of cranial cavity.Many complex relationships and influencing factors lie in the actual deformation of cranial cavity with the changing ICP.Therefore, in order to obtain the accurate deformation tendency of cranial cavity, the precise simulation to the finite-element model and further experimental studies in vivo and clinic need to be carried on.

Fig. 2 . 2 .
Fig. 2.2.Block diagram of numerical solution steps of cranial cavity with the finite-element method 2. The selection of displacement mode

Fig. 2 . 7 .
Fig. 2.7.The strain curves of finite-element simulation under the conditions of ignoring and considering the viscoelasticity of human skull and duramater with the changing ICP from 1.5 kPa to 5 kPa

Fig. 2 . 16 .
Fig. 2.16.The relaxation and creep train-time curves between experiment and three parameters Kelvin theoretical model of human skull.Kelvin model of three parameters is shown in Fig2.15.Fig2.16(a) is the relaxation curves of human skull and Kelvin model of three parameters in the compressive experiment.Fig2.16(b) is the creep curves of human skull and Kelvin model of three parameters.It shows that the theoretical Kelvin model of three parameters can well simulate the

Table 2 .
1. Coefficients for the viscoelastic properties for human skull

Table 2 .
2. Creep coefficients for the viscoelastic properties for fresh human duramater www.intechopen.comTissue Modeling and Analyzing for Cranium Brain with Finite Element Method