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

cement volume fraction (CVF), the pore ratio in the cement bulk (PR) and a stiffness
correction factor that relates the cement stiffness to the (negatively correlated) cement
temperature [5]. The hydraulic permeability of the bone was calculated based on the
element bone volume ratio, the degree of anisotropy (DA) and the trabecular spacing
(Tb.Sp) according to [6]:
s ( ) = α + α ⋅ BVTV + α ⋅ DA + α ⋅Tb.Sp
log10 0 1
2
3
k , (1)
s
where k refers to the intrinsic permeability and α0 K α3
to the fitting coefficient of the
log-linear regression model. The apparent dynamic viscosity µ of the cement was
updated according to the Ostwald-de Waele equation
= C ⋅γ
r −1
µ & , (2)
where C and r are the time-dependent consistency and power-law indices, respectively,
and γ& refers to the local fluid shearing rate.
3.3 Finite Element analyses, Monte Carlo simulation and bone strength assessment
For all simulations, a tetrahedral FE mesh (approx. 50000 elements), representing the
vertebral body, was used. The multicomponent (bone marrow/ bone cement) flow was
governed by a mixed-boundary formulation [7]. For the mechanical stress assessment, a
load of 1.09 MPa uniformly distributed over the nucleus pulposus area was applied. The
cement injections were virtually performed at 15 randomly chosen and evenly
distributed locations within the vertebral body. The strength assessment indicator SAI
was computed as the ratio of effective local strain and predicted failure strain. The
organ strength improvement OSI was calculated according to
( SAI post )
( SAI )
max
Ω
OSI = 1 −
max
, (3)
Ω
pre
where Ω refers to the computational domain and SAIpre and SAIpost refer to the pre- and
post-augmentation strength assessment indicator, respectively.
4. RESULTS
The predicted values of SAI were 1.1887e-4≤SAIpre≤4.8499 and 2.3702e-
5≤SAIpost≤8.1456. The organ strength improvement indicator was found to be -
79.71%≤OSI≤ 94.13%, depending on the injection volume and the cement type. The
spreading pattern and local SAI-distribution for the pre-augmentation case, two
positions and two injection volumes are shown in Figure 1. Figure 2 shows OSI as a
function of the injected volume (positive correlation) and the cement type. The cement
type A has the highest and the cement type F the smallest Young’s modulus.