Modeling and Numerical Analysis of a Cervical Spine Unit - Biologically Responsive Biomaterials for Tissue Engineering - page 158

Table 7.2 Properties of the materials of ICU components
Material Young's modulus (MPa) Poisson ratio (-)

Titanium alloy 110,000 0.280

Stainless steel 193,000 0.300

Cortical bone 12,000 0.300

Spongy bone 100 0.200

Ligament 18 0.350

Annulus fi brosus 450 0.300

Nucleus pulposus 0.13 0.499

• Ligament properties for the facet joints and interspinous ligament

• Their own characteristics for the nucleus pulposus and annulus fibrosus

In static structural analysis, material properties like Young's modulus and Poisson
ratio are essentials. Their values are presented in Table 7.2 for each material involved
in the study, as a result of a bibliographic selection [ 13, 20, 68 ] . The properties pre-
sented in Table 7.2 are essentials and sufficient for this type of evaluation [ 34 ] .
The mesh structure generation using tetrahedron elements can be created in
two ways: in automatic mode and by setting up the element size separately for
each component [ 39 ]. In the automatic mode, the element size is modified in
order to adjust the geometrical requirements of the components. In order to
have a constant fine mesh accordingly to the part's sizes, a manual mesh
re fi nement was used.
In our study, the mesh characteristics are a constant element size of 1 mm for
the mechanical parts and another mesh structure of 2 mm element size for the
anatomical parts (see Fig. 7.18 ). The reason of choosing a smaller element size for
the mechanical elements results from their reduced dimensions, comparing with
the anatomical structure.
Defining the same small size elements for the whole assembly will dramatically
increase the computing requirements due to the complex geometry of the vertebrae.
The loading conditions applied to the structure were assigned taking into account
the gravity force generated by the head and neck's masses, and the bending forces
and moment which act in a normal flexion movement.
The gravity effect acts as distributed forces on three surfaces: the vertebral body
plateau and symmetrical facet joints. The quantum of these forces usually repre-
sents 5-7 % of the whole body weight [ 30 ], so for a subject having 70 kg weight,
the gravitational force at C2 vertebral level is around 50 N. This value is distributed
( F 1 , F 4 , and F 5 ) on the three surfaces: vertebral body (vertical force F 1 = 30 N) and
the symmetrical facet joints. The forces on the facet joints have values of 10 N each,
resulting in a value of perpendicular component force of 6.8 N. In simulation, only
the perpendicular component on the facet joint was considered. This has a value
diminished by the facet's angle (see Table 7.3 ).
The bending movement of the head was simulated by a bending moment M f
applied perpendicular to the spinal axis and two additional shear forces F 2 and F 3
simulating the pullout effect on the bone screws. The bending moment M f of 2.5 Nm