Biomechanical function of the periodontal ligament in biting and orthodontic tooth movement

Alveolar bone remodelling is vital for the success of dental implants and orthodontic treatments. However, the underlying biomechanical mechanisms, in particular the function of the periodontal ligament (PDL) in bone remodelling, are not well understood. The PDL is a soft fibrous connective tissue that joins the tooth root to the alveolar bone and plays a critical role in the transmission of loads from the teeth to the surrounding bone. However, due to its complex structure, small size and location within the tooth socket it is difficult to study in vivo. Finite element analysis (FEA) is an ideal tool with which to investigate the role of the PDL, but inclusion of the PDL in FE models is complex and time consuming and most FE models that include teeth do not consider the PDL. The aim of this study was to investigate the effects of including the PDL and its fibrous structure in mandibular finite element models.This research involved the development of a novel method to include the fibres of the PDL in FE models. A simplified single tooth model was developed to assess the effects of modelling fibrous PDL compared to the traditional approach of representing the PDL as a simple layer of solid material and to an absent PDL. The same study design was then applied to a high-resolution model of the human molar region, which is the first time that the fibrous structure of the PDL has been included in a model with realistic tooth and bone geometry. Finally, molar region models of five additional species (cat, cercocebus, pig, rabbit and sheep) were tested with and without a PDL.The results from the research showed that omission of the PDL creates a more rigid model, reducing the strains observed in the mandibular corpus for all six species studied. This suggests that the results obtained are not specific to the human molar region, but may be true for the mammalian mandible in general. Compared to a solid PDL, the fibrous PDL altered the strains in the models, in particular increasing the strains observed in the tooth socket. This may be important for the management of orthodontic treatment, as strains in this region are thought to play an important role in bone remodelling during orthodontic tooth movement

Tissue Engineering for Periodontal Ligament Regeneration: Biomechanical Specifications

The periodontal biomechanical environment is very difficult to investigate. By the complex geometry and composition of the periodontal ligament, its mechanical behavior is very dependent on the type of loading (compressive vs. tensile loading; static vs. cyclic loading; uniaxial vs. multiaxial) and the location around the root (cervical, middle, or apical). These different aspects of the periodontal ligament make it difficult to develop a functional biomaterial to treat periodontal attachment due to periodontal diseases. This review aims to describe the structural and biomechanical properties of the periodontal ligament. Particular importance is placed in the close interrelationship that exists between structure and biomechanics: the periodontal ligament structural organization is specific to its biomechanical environment, and its biomechanical properties are specific to its structural arrangement. This balance between structure and biomechanics can be explained by a mechanosensitive periodontal cellular activity. These specifications have to be considered in the further tissue engineering strategies for the development of an efficient biomaterial for periodontal tissues regeneration

Моделирование напряженно-деформированного состояния периодонтальной связки при начальных перемещениях корня зуба

Определены гидростатические напряжения, возникающие в тканях периодонта, при поступательных перемещениях корня зуба. Внешняя поверхность корня зуба и внутренняя поверхность периодонтальной связки описываются уравнением двуполостного гиперболоида. Толщина периодонта по нормали к поверхности является постоянной величиной. Корень зуба предполагается абсолютно твердым телом. На основании значений, благоприятных для перестройки костной ткани напряжений, установлены диапазоны нагрузки для поступательного ортодонтического перемещения зубов. Показано, что полученные значения нагрузки приводят к деформациям тканей периодонта, которые соответствуют линейно-упругой модели периодонтальной связки. Проведен сравнительный анализ результатов расчета нормальных напряжений на основании аналитической и конечно-элементной моделей. = Hydrostatic stresses in the periodontal ligament under translational displacement of the tooth root were defined. The external surface of the tooth root and the internal surface of the periodontal ligament were described by the equation of a two-sheet hyperboloid. The thickness of the periodontal ligament along normal to the tooth root surface is constant. The tooth root was assumed to be rigid. The system of equations for the translational displacements and rotation angles of the tooth root in periodontal ligament was formulated. Load ranges for translational orthodontic tooth movement were defined based on the magnitudes of stresses favorable to bone remodelling. The obtained values of the load lead to the appearance of the periodontal tissue strains, corresponding to a linear elastic model of the periodontal ligament. Comparative analysis of the results of the calculation of normal stresses on the basis of analytical and finite element models was carried out

Biomechanical Modeling of Canine Retraction

Objective: To create a comprehensive finite element model capable of analyzing the biomechanics of canine retraction. Methods: A half maxilla virtual model with an extracted first premolar was created from human computed tomography data. Accurate brackets and an 0.018 archwire were placed to model canine retraction under 0.5N and 1.0N of retraction force. A two-tooth substructural model was isolated to examine the importance of surrounding geometry. Additionally, mesh size and periodontal ligament (PDL) elastic modulus were varied to examine the effect on predictions. Comparisons were made to previously published clinical data. Results: The substructural model decreased computational load, but altered maximum stress up to 16.4%. Coarse mesh sizing affected displacement results up to 22% and maximum stress up to 47%. No PDL stiffness was able to accurately represent the clinical data. Conclusions: Modeling canine retraction was partially achieved, highlighting the importance of mesh sizing and the need to incorporate remodeling.Master of Scienc

Explore the Dynamic Characteristics of Dental Structures: Modelling, Remodelling, Implantology and Optimisation

The properties of a structure can be both narrowly and broadly described. The mechanical properties, as a narrow sense of property, are those that are quantitative and can be directly measured through experiments. They can be used as a metric to compare the benefits of one material versus another. Examples include Young’s modulus, tensile strength, natural frequency, viscosity, etc. Those with a broader definition, can be hardly measured directly. This thesis aims to study the dynamic properties of dental complex through experiments, clinical trials and computational simulations, thereby bridging some gaps between the numerical study and clinical application. The natural frequency and mode shapes, of human maxilla model with different levels of integrities and properties of the periodontal ligament (PDL), are obtained through the complex modal analysis. It is shown that the comprehensiveness of a computational model significantly affects the characterisation of dynamic behaviours, with decreasing natural frequencies and changed mode shapes as a result of the models with higher extents of integrity and preciseness. It is also found that the PDL plays a very important role in quantifying natural frequencies. Meanwhile, damping properties and the heterogeneity of materials also have an influence on the dynamic properties of dental structures. The understanding of dynamic properties enables to further investigate how it can influence the response when applying an external stimulus. In a parallel preliminary clinical trial, 13 patients requiring bilateral maxillary premolar extractions were recruited and applied with mechanical vibrations of approximately 20 g and 50 Hz, using a split mouth design. It is found that both the space closure and canine distalisation of the vibration group are significantly faster and higher than those of the control group (p<0.05). The pressure within the PDL is computationally calculated to be higher with the vibration group for maxillary teeth for both linguo-buccal and mesial-distal directions. A further increased PDL response can be observed if increasing the frequency until reaching a local natural frequency. The vibration of 50 Hz or higher is thus approved to be a potential stimulus accelerating orthodontic treatment. The pivotal role of soft tissue the PDL is further studied by quantitatively establishing pressure thresholds regulating orthodontic tooth movement (OTM). The centre of resistance and moment to force ratio are also examined via simulation. Distally-directed tipping and translational forces, ranging from 7.5 g to 300 g, are exerted onto maxillary teeth. The hydrostatic stress is quantified from nonlinear finite element analysis (FEA) and compared with normal capillary and systolic blood pressure for driving the tissue remodelling. Localised and volume-averaged hydrostatic stress are introduced to describe OTM. By comparing with clinical results in past literature, the volume average of hydrostatic stress in PDL was proved to describe the process of OTM more indicatively. Global measurement of hydrostatic pressure in the PDL better characterised OTM, implying that OTM occurs only when the majority of PDL volume is critically stressed. The FEA results provide new insights into relevant orthodontic biomechanics and help establish optimal orthodontic force for a specific patient. Implant-supported fixed partial denture (FPD) with cantilever extension can transfer excessive load to the bone surrounding implants and stress/strain concentration which potentially leads to bone resorption. The immediate biomechanical response and long-term bone remodelling outcomes are examined. It is indicated that during the chewing cycles, the regions near implant necks and apexes experience high von Mises stress (VMS) and equivalent strain (EQS) than the middle regions in all configurations, with or without the cantilever. The patient-specific dynamic loading data and CT based mandibular model allow us to model the biomechanical responses more realistically. The results provide the data for clinical assessment of implant configuration to improve longevity and reliability of the implant-supported FPD restoration. On the other hand, the results show that the three-implant supported and distally cantilevered FPDs see noticeable and continuous bone apposition, mainly adjacent to the cervical and apical regions. The bridged and mesially cantilevered FPDs show bone resorption or no visible bone formation in some areas. Caution should be taken when selecting the FPD with cantilever due to the risk of overloading bone resorption. The position of FPD pontics plays a critical role in mechanobiological functionality and bone remodelling. As an important loading condition of dental biomechanics, the accurate assignment of masticatory loads has long been demanded. Methods involving different principles have been applied to acquire or assess the muscular co-activation during normal or unhealthy stomatognathic functioning. Their accuracy and capability of direct quantification, especially when using alone, are however questioned. We establish a clinically validated Sequential Kriging Optimisation (SKO) model, coupled with the FEM and in vivo occlusal records, to further the understanding of muscular functionality following a fibula free flap (FFF) surgery. The results, within the limitations of the current study, indicates the statistical advantage of agreeing occlusal measurements and hence the reliability of using the SKO model over the traditionally adopted optimality criteria. It is therefore speculated that mastication is not optimally controlled to a definite degree. It is also found that the maximum muscular capacity slightly decreases whereas the actual muscle forces fluctuate over the 28-month period

Modeliranje iniciranja koštane pregradnje kod ortodontske terapije

Cilj istraživanja doktorskoga rada bio je može li se ortodontska koštana pregradnja predvidjeti koristeći teorije koštane pregradnje koje se temelje na prilagodbi kosti opterećenju razvijene u ortopedskoj biomehanici, gdje je gustoća energije deformiranja mehanički stimulus za kost i povezana je s gustoćom kosti. Hipoteza je da zub "visi" u vlaknastom PDL-u te da će ortodontsko opterećenje smanjiti opterećenje u vlaknima na gurnutoj strani i povećati na suprotnoj strani. U procesu, alveolna kost i parodontni ligament reagiraju na opterećenje mehanički i biološki. Fokus istraživanja bio je na mehanici i fenomenološkim aspektima biologije opisanima pomoću metode konačnih elemenata. Žvačna sila predstavlja dnevno opterećenje u ustima te referentnu vrijednost stimulusa. 3D model razvijen je iz CT snimki pacijenta kojemu je preporučena ortodontska terapija te je napravljen u softveru Mimics, koji omogućuje očitanje gustoće kosti s CT snimaka. 3D numerička analiza napravljena je u Marc Mentatu, gdje su različita ortodontska opterećenja analizirana. Zadnji korak bila je implementacija algoritma koštane pregradnje napisanog u programskom jeziku Fortran u Marc Mentat pomoću specijalnih rutina. Predloženi opis inicijacije koštane pregradnje može predvidjeti podopterećene i preopterećene uvjete koji vode ka koštanoj resorpciji i formiranju oponašajući biološki proces. Glavni je doprinos dokorskoga rada razvoj numeričkoga modela inicijacije koštane pregradnje, koji uključuje utjecaj žvačne sile, vlaknastoga parodontnoga ligamenta, personaliziranu geometriju te postavljanje gustoće energije deformiranja kao mehaničkoga stimulusa

A study of the Rapid Maxillary Expansion with the use of the finite element method

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