On the development of an integrated bone remodeling law for orthodontic tooth movements models using the Finite Element Method.

Doctoral thesis (2012)

One of the guiding principles in orthodontics is to gradually impose progressive and irreversible bone deformations due to remodeling using specific force systems on the teeth. Bone remodeling leads the ... [more ▼]

One of the guiding principles in orthodontics is to gradually impose progressive and irreversible bone deformations due to remodeling using specific force systems on the teeth. Bone remodeling leads the teeth into new positions with two tissues having a major influence: the periodontal ligament and the alveolar bone. Their mechanical and biological/physiological reactions to orthodontic forces are tightly linked. This mechanical biological coupling can be treated in biomechanical models, focusing on the mechanics and considering the phenomenological aspects of the biology/physiology. The development of such a model for bone tissue within a Finite Element framework is the core of this work. We propose to reconcile two approaches of bone modeling (small strains linear elasticity for remodeling problems and complex constitutive models for other applications) by writing a constitutive model for trabecular bone at macroscopic level, built on morphological parameters to describe the anisotropy, and accounting for effects such as plasticity of the trabeculae. The continuum parameters such as the stiffness can evolve with morphology as remodeling occurs in the tissue. For this, we extend and enhance Doblaré and Garcia's remodeling phenomenological model. The remodeling process corresponds to an evolution of a damage tensor representing the bone morphology. To do so, we propose an integration method for an anisotropic Continuum Damage model coupled to plasticity. Adapting Doblaré and Garcia's remodeling law to our constitutive model, we extend it so that it can be used in the specific case of orthodontic tooth movement, still following Frost's mechanostat theory. We propose to include the hydrostatic pressure dependency of remodeling, due to the presence of the periodontal ligament, within the bone remodeling law. We finally present a validation method for the mechanical representation of the bone matrix through the knowledge of its morphology, both on engineered cellular solids with bone-like morphology (aluminum and polymeric foams) and on bone (Deer antler) samples. Applying the model on the benchmark problem of the proximal femur remodeling, leads to results that are comparable to other models of the literature. We can therefore assume the way the remodeling model is built is valid. We finally apply the developed model to orthodontic tooth movement simulations. First we propose a model accounting for the non-linear mechanical response of the PdL through either bilateral contact conditions or spring models. We then present applications of orthodontic tooth movement, either displacement driven or force driven, both 2D and 3D. We thus show we can qualitatively represent the tooth movement, however outlining some of the drawbacks of the models (an unphysiological density distribution can arise due to the poor representation of the actual loads and a strong dependence on the boundary conditions is pointed out). However, we can represent the formation and resorption of hyaline areas, the non-linearity of the force/displacement relationship, and that applying a stepwise increasing force leads to higher displacements than a high initial force as there is no hyaline zone to resorb. [less ▲]

Development of a biomechanical model of deer antler cancellous bone based on X-ray microtomographic images

in Micro-CT User Meeting 2012 - Abstract Book (2012, April)

Finite element models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. The aim of this paper is to develop and validate a ... [more ▼]

Finite element models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. The aim of this paper is to develop and validate a biomechanical model for deer antler cancellous bone tissue based on X-ray microtomographic images. In order to simulate the mechanical behavior under compressive load using a finite element model, images obtained by X-ray microtomography were exported into Metafor, which is an non-linear finite element software initially developed at University of Liège for metal forming processes. This software has recently found biomedical applications. The ultimate goal is to compare model predictions with the mechanical behavior observed experimentally using the Skyscan material testing stage under compression mode. The creation of the biomechanical model mesh from segmented μCT images, its integration into the software Metafor and the simulation of a compression test are described in this paper. [less ▲]

A non-linear homogeneous model for bone-like materials under compressive load.

in International Journal for Numerical Methods in Biomedical Engineering (2012), 28(2), 334-348

Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which ... [more ▼]

Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strains framework. This material model was implemented into Metafor, a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested : aluminum foams of variable density (ERG, Oakland, CA), PLA (polylactic acid) foam (CERM, University of Liège) and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège). [less ▲]

On the periodontal ligament representation in 3D finite element analysis for orthodontic tooth movement models

Conference (2011, November)

A non-linear homogeneous model for bone-like materials under compressive load.

in Nithiarasu, P.; Löhner, R.; van Loon, R. (Eds.) et al Conference Proceedings - 2nd International Conference on Computational & Mathematical Biomedical Engineering (2011)

Using morphological data provided by computed tomography, finite element (FE) models can be used to compute the mechanical response of bone and bone-like materials without describing the complex local ... [more ▼]

Using morphological data provided by computed tomography, finite element (FE) models can be used to compute the mechanical response of bone and bone-like materials without describing the complex local microarchitecture. A constitutive law is here developed and proposed for this purpose. It captures the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using a plastic material model, allowing hardening of the yield parameters. These characteristics are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strains framework. This law is implemented into Metafor, a non-linear FE software. Simulations of cylindrical samples undergoing stepwise compression are presented. [less ▲]

Isotropic continuum damage/repair model for alveolar bone remodelling

in Journal of Computational & Applied Mathematics (2010), 234

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an ... [more ▼]

Several authors have proposed mechanical models to predict long term tooth movement, considering both the tooth and its surrounding bone tissue as isotropic linear elastic materials coupled to either an adaptative elasticity behavior or an update of the elasticity constants with density evolution. However, tooth movements obtained through orthodontic appliances result from a complex biochemical process of bone structure and density adaptation to its mechanical environment, called bone remodeling. This process is far from linear reversible elasticity. It leads to permanent deformations due to biochemical actions. The proposed biomechanical constitutive law, inspired from Doblaré and García (2002) [30], is based on a elasto-viscoplastic material coupled with Continuum isotropic Damage Mechanics (Doblaré and García (2002) [30] considered only the case of a linear elastic material coupled with damage). The considered damage variable is not actual damage of the tissue but a measure of bone density. The damage evolution law therefore implies a density evolution. It is here formulated as to be used explicitly for alveolar bone, whose remodeling cells are considered to be triggered by the pressure state applied to the bone matrix. A 2D model of a tooth submitted to a tipping movement, is presented. Results show a reliable qualitative prediction of bone density variation around a tooth submitted to orthodontic forces. [less ▲]

Anisotropic continuum damage model coupled to viscoplasticity for a pressure dependent alveolar bone remodeling law

in National Congress on Theoretical and Applied Mechanics (2009, May)

A pressure dependent bone remodeling model for application in orthodontics

in XXIInd Congress of the International Society of Biomechanics (2009)

A damage/repair model for alveolar bone remodeling

in Middleton; Evans; Holt (Eds.) et al 8th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering : CMBBE2008, Porto, Porugal (2008)

Contribution to a bone deformation study in orthodontics

Poster (2006, July)