Finite element analysis in implant dentistry: State of the art and future directions.

OBJECTIVE: To discuss the state of the art of Finite Element (FE) modeling in implant dentistry, to highlight the principal features and the current limitations, and giving recommendations to pave the way for future studies. METHODS: The articles' search was performed through PubMed, Web of Science, Scopus, Science Direct, and Google Scholar using specific keywords. The articles were selected based on the inclusion and exclusion criteria, after title, abstract and full-text evaluation. A total of 147 studies were included in this review. RESULTS: To date, the FE analysis of the bone-dental implant system has been investigated by analyzing several types of implants; modeling only a portion of bone considered as isotropic material, despite its anisotropic behavior; assuming in most cases complete osseointegration; considering compressive or oblique forces acting on the implant; neglecting muscle forces and the bone remodeling process. Finally, there is no standardized approach for FE modeling in the dentistry field. SIGNIFICANCE: FE modeling is an effective computational tool to investigate the long-term stability of implants. The ultimate aim is to transfer such technology into clinical practice to help dentists in the diagnostic and therapeutic phases. To do this, future research should deeply investigate the loading influence on the bone-implant complex at a microscale level. This is a key factor still not adequately studied. Thus, a multiscale model could be useful, allowing to account for this information through multiple length scales. It could help to obtain information about the relationship among implant design, distribution of bone stress, and bone growth. Finally, the adoption of a standardized approach will be necessary, in order to make FE modeling highly predictive of the implant's long-term stability.

Coupled electro-mechanical models of fiber-distributed active tissues.

We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.