Biomedical Engineering Reference
In-Depth Information
Figure 2.1
Total hip arthroplasty (THA).
homeostatic equilibrium state
relating a stress-strain state to a specific bone density
distribution. Any local perturbation in the mechanical state would promote a
driving force for local changes in bone density in such a way that the equilibrium is
recovered [2-7]. Owing to their nature, these models are named
error-driven
models.
On the basis of a similar equilibrium concept and introducing continuum damage
as a driving force, a group of studies treated remodeling as a continuous process
of simultaneous damage and healing, the rates of which depend on local stress
and strain levels. Owing to the possibility of including different phenomenological
effects within a thermodynamically consistent framework, this approach has been
increasingly investigated, for example, in [8-15] among others.
On the basis of the observations of Meyer, Culmann, and Wolf in the second
half of the nineteenth century, a set of models described adaptation as a path
toward a stable minimum (or maximum) condition, in which the bone behaves
as an optimal structure. Later, several studies derived adaptation laws based on
optimality conditions of a minimization problem, among them being [16-20]. It is
worth mentioning that strong interconnection exists among all these approaches
and thus the short classification presented is not strict.
Most of these computational techniques allow an approximate representation
of the long-term structural behavior of the bone-implant system. In fact, it has
beenshownthatthesemodelsareabletoreproducethenormalarchitectureof
bone. The studies [4, 5, 9, 10, 21, 22] are examples of bidimensional simulations,
while in [16, 18, 23, 24]
3D
results are found. These models have also been used
to predict the osteoporosis process [25] as well as effects related to the resorption
phenomenon in host bone due to orthopedic implants [3, 6, 8, 11, 26-29]. The
objectives of all these efforts are clearly a better understanding of the mechanisms
that control the adaptive bone response, as well as the selection of the most
appropriate prosthesis for a given bone state (obtained from personalized digital
medical images - computational tomography).
Nevertheless, the problem of long-term stability of orthopedic implants has not
been satisfactorily solved yet [30]. Besides the problems related to the resorption
