Modeling and Numerical Analysis of a Cervical Spine Unit - Biologically Responsive Biomaterials for Tissue Engineering - page 160

Fig. 7.19 Loading and fi xing conditions applied on the ICU structure

7.4.2 Mechanical Effects at the Bone-Screw Interfaces

The bone-screw interface is the boundary of two materials: the vertebral bone and
titanium alloy. The crucial differences between these materials are the Young's
modulus, the anisotropy of the bone comparing with the titanium screws, and the
bone's inhomogeneity.
In the performed simulation, simplifications like isotropy and homogeneity of
the bone¢ material have been assumed. Since the titanium has a higher Young's
modulus than the bone (see Table 7.2 ), from the theoretical point of view, higher
stress concentration in the bone screws and higher strains in the bone were expected.
This theoretical principle was sustained by the results of simulation.
The stress and strain records that are presented were sampled from screw and
bone sections and they refer to equivalent elastic stress and strain according to the
von Misses yield criterion. These were computed by the simulation software using
( 7.1 ) and ( 7.2 ) formulas [ 19, 33 ] , where n ¢ represents the effective Poisson's ratio:

1/2

⎛ 1 ( ⎞

2 2 2

σ

−= σ − + − +− σ )( σ σ )( σ σ )]

(7.1)

⎜ ⎟

Von Mises

⎝

1 2 2 3 3 1

⎠

2

1/2

1 ⎛ ⎞

2 2 2

σ

−= ( ε − +− +− ε )( ε ε )( ε ε )] (7.2)

⎜ ⎟

Von Mises

⎝

1 2 2 3 3 1

⎠

1 +′ v 2

The first aspect of this simulation is focused on the strains acting at the bone-
screw interface. In bone-strain evaluation the challenge was to establish whether
the bone can support or not the strain action, and which is the strain distribution
along the bone threads. Due to the symmetry in lateral plane of both screws' posi-
tioning and loading conditions, the results were evaluated and presented for one side
only. The behavior of the superior screw Ss (tapped into the C2 vertebra) and the
inferior screw Si (tapped into the C3 vertebra) is highlighted.