A visco-elastic model for the prediction of orthodontic tooth movement.

in Computer Methods in Biomechanics & Biomedical Engineering (2012)

This study presents a biomechanical model of orthodontic tooth movement. Although such models have already been presented in the literature, most of them incorporate computationally expensive finite ... [more ▼]

This study presents a biomechanical model of orthodontic tooth movement. Although such models have already been presented in the literature, most of them incorporate computationally expensive finite elements (FE) methods to determine the strain distribution in the periodontal ligament (PDL). In contrast, the biomechanical model presented in this work avoids the use of FE methods. The elastic deformation of the PDL is modelled using an analytical approach, which does not require setting up a 3D model of the tooth. The duration of the lag phase is estimated using the calculated hydrostatic stresses, and bone remodelling is predicted by modelling the alveolar bone as a viscous material. To evaluate the model, some typically used motion patterns were simulated and a sensitivity analysis was carried out on the parameters. Results show that despite some shortcomings, the model is able to describe commonly used motion patterns in orthodontic tooth movement, in both single- and multi-rooted teeth. [less ▲]

Connecting biology and mechanics in fracture healing: an integrated mathematical modeling framework for the study of nonunions

in Biomechanics & Modeling in Mechanobiology (2010), 9(6), 713-724

Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are ... [more ▼]

Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are included. Mechanics and biology are coupled by making certain parameters of a previously established bioregulatory model dependent on local mechanical stimuli. To illustrate the potential added value of such a framework, this coupled model was applied to investigate whether local mechanical stimuli influencing only the angiogenic process can explain normal healing as well as overload-induced nonunion development. Simulation results showed that mechanics acting directly on angiogenesis alone was not able to predict the formation of overload-induced onunions. However, the direct action of mechanics on both angiogenesis and osteogenesis was able to predict overload-induced nonunion formation, confirming the hypotheses of several experimental studies investigating the interconnection between angiogenesis and osteogenesis. This study shows that mathematical models can assist in testing hypothesis on the nature of the interaction between biology and mechanics. [less ▲]

Mechanical loading affects angiogenesis and osteogenesis in an in vivo bone chamber: a modeling study.

in Tissue Engineering. Part A (2010), 16(11), 3353-3361

Despite a myriad of studies confirming the interaction between biology and mechanics, the exact nature of the main mechanical stimuli and their influence on the bone regeneration processes are still ... [more ▼]

Despite a myriad of studies confirming the interaction between biology and mechanics, the exact nature of the main mechanical stimuli and their influence on the bone regeneration processes are still unclear. The hypothesis of this study was that the outcome of peri-implant healing under different implant loading regimens can be explained by the influence of fluid flow on the combination of angiogenesis and osteogenesis through its influence on cell proliferation and differentiation. To investigate this hypothesis a mathematical model of bone regeneration was applied to simulate the peri-implant healing in an in vivo repeated sampling bone chamber for different axial micromechanical implant loading regimes. When mechanical loading was modeled to influence both osteogenic and angiogenic processes, a good agreement was observed between simulations and experiments concerning the amount of bone in the bone chamber, its radial and longitudinal distribution, and the bone-implant contact for different implant displacement magnitudes. [less ▲]

Design of treatment strategies for an atrophic nonunion case in fracture healing

in proceedings of the IVth International Conference on Computational Bioengineering (2009)

Biomaterial Surface Characteristics Modulate the Outcome of Bone Regeneration around Endosseous Oral Implants: In Silico Modeling

in Miller, Karol; Nielsen, Poul M.F. (Eds.) MICCAI 2009 Workshop Proceedings (2009)

Experimental investigations have demonstrated the importance of platelets and their activation for bone regeneration around oral implants. This study aimed to numerically demonstrate the key role of ... [more ▼]

Experimental investigations have demonstrated the importance of platelets and their activation for bone regeneration around oral implants. This study aimed to numerically demonstrate the key role of activated platelets which is controlled by implant surface characteristics. The cellular activities involved in the process of peri-implant endosseous healing can be represented by migration, proliferation, differentiation, removal, extracellular matrix synthesis and degradation, and growth factor production/release and decay. These activities are described by a system of highly coupled non-linear partial differential equations of taxis–diffusion–reaction type. Moreover, cell–biomaterial interactions were treated by including surface-specific model parameters. A well-designed in vivo model that looked at healing around oral implants with different surface properties was selected from literature to validate the results. Numerical simulations agreed well with the experimentally observed healing response and demonstrated that platelet-related model parameters, which were dependent on implant surface characteristics, modulate the pattern of healing. [less ▲]

A mechanobioregulatory model for the study of bone fracture healing

in Proceedings of the European Conference on Mathematical and Theoretical Biology (2008)

A mathematical model of bone regeneration including angiogenesis: relevance for tissue engineering strategies

in European Cells and Materials (2008), Vol. 14(Suppl. 1,), 29

Mathematical modelling of bone regeneration including angiogenesis: design of treatment strategies for atrophic non-unions

in Proceedings of the 54th Annual Meeting of the Orthopaedic Research Society (2008)

Mathematical modeling of fracture healing: coupling between mechanics, angiogenesis and osteogenesis

in IFMBE Proceedings 22 (2008)

Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are ... [more ▼]

Both mechanical and biological factors play an important role in normal as well as impaired fracture healing. This study aims to provide a mathematical framework in which both regulatory mechanisms are included and angiogenesis is explicitly incorporated. To illustrate the added value of such a framework, a coupled mechanobioregulatory model was proposed. This model was based on a previously developed bioregulatory model [1], using a simple coupling between mechanics and biology whereby certain parameters of the bioregulatory model were made dependent on local mechanical stimuli. As a first example, in this study, the proliferation of osteoblasts and endothelial cells were made dependent on the local fluid flow [2]. Various loading situations, ranging from non-loading to overloading, were simulated. Simulations of adverse mechanical circumstances predicted the formation of avascular nonunions, a result that was corroborated by various experimental observations. This model allows testing various hypotheses concerning the nature of the mechanical stimulus influencing the healing process, as well as the most important cellular processes influenced by mechanical loading. It is one of the first models that provides an explicit coupling between mechanical and angiogenic factors. As both factors have been identified to play a key role in the occurrence of delayed and nonunions, the model allows to further explore their etiology and treatment. [less ▲]

Computational modelling of peri-implant healing

in Middleton, J.; Jones, M. L.; Shrive, N. (Eds.) Proceedings of the 8th interantional symposium on Computer Methods in Biomechanics and Biomedical Engineering (2008)