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

presented system - parallelization of the Finite Element Method mesh generation. Also
the performance tests of the parallel mesh generation tool are presented.
3. SIMULATION OF TRABECULAR BONE ADAPTATION
For the simulations of trabecular bone adaptation phenomenon the model developed by
Huiskes [2,4] is used. The key assumption of this model is existence of homeostasis
(perfect balance between bone gain and loss). This equilibrium can occur only in the
presence of mechanical stimulation. The network of osteocytes plays the role of sensors
of the mechanical energy distribution throughout the trabecular bone tissue. The model
postulates strain energy density (SED), as a scalar measure of the mechanical
stimulation and distinguishes single value of SED corresponding to trabecular bone
remodeling homeostasis with the 'lazy zone' assumption - only a significant change in
mechanical stimulation results in bone loss or gain. The phenomenon of trabecular bone
adaptation has two important attributes. Firstly, mechanical stimulation is needed to
maintain the rebuilding balance. Secondly, the process of resorption and formation
occurs on the trabecular bone surface only. These factors together with the ‘regulatory
model’ concept were the basis for the generic, three-dimensional system for biomimetic
structural optimisation [5,6]. The developed method mimics the geometry evolution of
the real bone, where the volumetric finite elements mesh and the surface of the
trabecular network are controlled during the simulation with the following assumptions:
where:
Add an amount of material for U > (Uh + s) (1)
No action - ‘lazy zone’ for (Uh – s) < U < ( Uh + s) (2)
Remove an amount of material for U < ( Uh – s) (3)
− Uh is the SED value corresponding to homeostasis of bone loss and gain
− 2s is the size of the ‘lazy zone’
The material in virtual space is added onto or removed from the surface of the structure.
The structural form is changed imitating the behavior of Basic Multicellular Units
(BMU), thus the change concerns always the same amount of material (tissue),
independently of current values of SED according to formulas (1-3). Such a mechanism
secures stability of the process and prevents rapid change in the form of the structure.
The simulated remodeling process stops, if SED values on the whole surface of the
structure are included into the ‘lazy zone’. The beams of trabecular bone are assumed to
be made of isotropic linear elastic material, where the marrow space is treated as voids.
Because the remodeling process occurs only on the surface of the trabecular bone, only
the 'surface' layer of the structure is taken into consideration during the simulation
process. In contrast to other voxel models, the approach adopted in this system does not
relay on earlier voxel discretization, but mimics the natural evolution of the bone tissue
as the biological process of bone formation and resorption. Adaptation to the
mechanical stimulation results in adaptation of the trabecular bone surface position in
the virtual space.