ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Typical dimensions of lumbar vertebral bodies have been taken from literature (e.g. [3])
and suitable parameters have been chosen to achieve a representative shape. The final
geometric model is depicted in Fig. 1 and the corresponding parameters are listed in
Tab. 1.
Ellipsoid Concavity:
= 12 = 0.07
= 21
= 18
Anterior Part: Vertebral Foramen:
= 0.35 = −0.45
= 90° = 270°
= 40 ° = 30 °
Fig. 1: Geometric model Tab. 1: Parameters of the geometric model
5. THERMO-MECHANICALLY COUPLED FE-SIMULATION
The geometric model has been automatically meshed using an unstructured hexahedral
FE-mesh approach and material regions have been defined by assigning different
material laws. Thereby, the outer elements layer represents the cortical shell of the
vertebral body with isotropic elastic material behaviour. The remaining elements
initially represent the cancellous bone of the vertebral body and are described by
transversely isotropic linear elastic material behaviour. Furthermore, isotropic thermal
behaviour is assumed for both material regions. The chosen mechanical and thermal
material parameters for cortical and cancellous bone are summarized in Tab. 2.
Cortical bone Cancellous bone
Linear elasticity [4] Isotropic Transversal isotropic
= 10 000 MPa = 200 / 140 MPa
= 0.3 = 0.45 / 0.315
Density [5] = 2000 kg/m = 1000 kg/m
Thermal conductivity [5] = 0.4 W / m K = 0.6 W / m K
Spec. heat capacity [5] = 1300 J/kg K = 4190 J/kg K
Tab. 2: Material parameters of cortical and cancellous bone based on literature data
Subsequently, a region representing the injected acrylic bone cement has been defined
by manual picking of corresponding elements of the cancellous bone region. The
material behaviour of the chosen elements has been reassigned by the developed
material model described in section 2. In our example depicted in Fig. 2 (left), the
defined bone cement region corresponds to an ideal symmetrical, bipedicular injection
procedure with two fillings each consisting of around 4.5 ml (~ 15 % of the total
vertebral body volume for each plug).
In order to save computational time, symmetries of the model have been utilized.
Therefore, thermal and mechanical symmetry conditions have been applied (cf. Fig. 2
right). Moreover, zero displacement conditions in all directions have been applied to
one single node in order to prevent rigid body motions. To account for the ambient
region of the vertebral body, thermal boundary conditions have been adopted by
applying heat convection on the cortical shell with an ambient temperature of θ∞ = 37°C
and a film coefficient of hc = 1 mW/m 2 K.