Biomedical Engineering Reference
In-Depth Information
table 21.1
mechanical Properties and element types in the eye model
Structures
density (kg m
-3
)
material model
material Parameters
Source
Cornea
1076
Elastic
Nonlinear stress-strain
Union et al. (1999)
Sclera
1243
Elastic
Nonlinear stress-strain
Union et al. (1999)
Lens
1078
Elastic
E = 6.88 MPa
Czyan et al. (1996)
Zonules
1000
Elastic
E = 357.78 MPa
Power et al. (2002)
Ciliary
1600
Elastic
E = 11 MPa
Power et al. (2002)
Retina
1100
Elastic
E = 20 kPa
Jones et al. (1992)
Aqueous
1000
Liquid
Shock EOS linear
C
1
= 1530 m/s, s
1
= 2.1057
Duck (1990)
Vitreous
950
Viscoelastic
G
0
= 10 Pa,
G
∞
= 0.3 Pa, B = 14.26 1/s,
K = 2.0 GPa
Lee et al. (1992)
Fat
970
Viscoelastic
G
0
= 0.9 kPa,
G
∞
= 0.5 kPa, B = 0.2,
K = 2.2 GPa
Schoemaker et al. (2006)
Orbit
1610
Elastic
E = 14.5 GPa
Robbins and Wood (1969)
Notes:
E, elastic modulus; K, bulk modulus; G
0
, initial shear modulus; G
∞
, infinite shear modulus; β, viscoelastic decay
constant; C
1
, speed of sound through the material; s
1
, coefficient related to the speed of the shocked material.
The compliance function ()
0
Jt
for a standard linear solid viscoelastic model can be expressed as
1
G
GG
M
t
Jt
m
()
=−
)
exp(
−
)
0
G
M
m
(
M
+
G
M
τ
e
e
e
m
s
The parameters of the current model were obtained by curve fitting the experimental data for
Burgers model. Parameters from the fitting were obtained and applied to our eye model. The mate-
rial parameters of ocular tissues are listed in Table 21.1.
21.2.3 m
eSH
c
reation
and
B
oundary
c
ondition
The mesh was created using special meshing software, ANSYS ICEM CFD. This software can gen-
erate high-quality volume or surface meshes for finite element solutions. During simulation, tetra-
hedron elements are known to exhibit mesh locking for incompressible materials. In the eye model,
the vitreous, aqueous, and fat have the properties of incompressibility (Poisson's ratio close to 0.49).
A hexahedron mesh was applied to these tissues. A hexahedron mesh also has greater calculation
accuracy and efficiency compared to a tetrahedron mesh. Figure 21.5 illustrates the process of mesh
creation in ANSYS ICEM CFD (taking the vitreous as an example). ICEM can mesh geometry
created using other dedicated CAD packages, such as SolidWorks. According to the geometrical
features of the vitreous, the model was separated into several independent surfaces (Figure 21.5a).
Once the geometry was created, the next step was to generate a suitable block. Using the blocking
tab, a block can be created around the entire geometry and then split up into several subsections
(Figure 21.5b). Once the blocks have been created and a meshing density set, the premesh tool can
then be used to view the meshing (Figure 21.5c). Finally, after confirming the quality of the mesh,
a satisfactory model can be obtained (Figure 21.5d).
All the structures, except the orbit, were meshed using hexahedron elements. The orbit model
used a tetrahedron mesh because of its irregular geometry and because a tetrahedral mesh is more
suitable for complicated volumes (Figure 21.6). The cornea, sclera, lens, zonules, and ciliary were
grouped into a “multibody part” to permit node-sharing. The boundary relationships between orbit
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