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

Sieve Inference on Semi-nonparametric Time Series Models

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a "pre-asymptotic" sieve variance estimator that captures temporal dependence. We construct a "pre-asymptotic" Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled "pre-asymptotic" Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled "pre-asymptotic" Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values.Weak dependence, Sieve M estimation, Sieve Riesz representor, Irregular functional, Misspecification, Pre-asymptotic variance, Orthogonal series long run variance estimation, F distribution

Sieve Semiparametric Two-Step GMM under Weak Dependence

This paper considers semiparametric two-step GMM estimation and inference with weakly dependent data, where unknown nuisance functions are estimated via sieve extremum estimation in the first step. We show that although the asymptotic variance of the second-step GMM estimator may not have a closed form expression, it can be well approximated by sieve variances that have simple closed form expressions. We present consistent or robust variance estimation, Wald tests and Hansen’s (1982) over-identification tests for the second step GMM that properly reflect the first-step estimated functions and the weak dependence of the data. Our sieve semiparametric two-step GMM inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric. A new consistent random-perturbation estimator of the derivative of the expectation of the non-smooth moment function is also provided

Series Estimation of Stochastic Processes: Recent Developments and Econometric Applications

This paper overviews recent developments in series estimation of stochastic processes and some of their applications in econometrics. Underlying this approach is the idea that a stochastic process may under certain conditions be represented in terms of a set of orthonormal basis functions, giving a series representation that involves deterministic functions. Several applications of this series approximation method are discussed. The first shows how a continuous function can be approximated by a linear combination of Brownian motions (BMs), which is useful in the study of the spurious regressions. The second application utilizes the series representation of BM to investigate the effect of the presence of deterministic trends in a regression on traditional unit-root tests. The third uses basis functions in the series approximation as instrumental variables (IVs) to perform efficient estimation of the parameters in cointegrated systems. The fourth application proposes alternative estimators of long-run variances in some econometric models with dependent data, thereby providing autocorrelation robust inference methods in these models. We review some work related to these applications and some ongoing research involving series approximation methods

Sieve Inference on Semi-nonparametric Time Series Models

The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a “pre-asymptotic” sieve variance estimator that captures temporal dependence. We construct a “pre-asymptotic” Wald statistic using an orthonormal series long run variance (OS-LRV) estimator. For sieve M estimators of both regular (i.e., root-T estimable) and irregular functionals, a scaled “pre-asymptotic” Wald statistic is asymptotically F distributed when the series number of terms in the OS-LRV estimator is held fixed. Simulations indicate that our scaled “pre-asymptotic” Wald test with F critical values has more accurate size in finite samples than the usual Wald test with chi-square critical values

Asymptotic Efficiency of Semiparametric Two-step GMM

In this note, we characterize the semiparametric efficiency bound for a class of semiparametric models in which the unknown nuisance functions are identified via nonparametric conditional moment restrictions with possibly non-nested or over-lapping conditioning sets, and the finite dimensional parameters are potentially over-identified via unconditional moment restrictions involving the nuisance functions. We discover a surprising result that semiparametric two-step optimally weighted GMM estimators achieve the efficiency bound, where the nuisance functions could be estimated via any consistent nonparametric procedures in the first step. Regardless of whether the efficiency bound has a closed form expression or not, we provide easy-to-compute sieve based optimal weight matrices that lead to asymptotically efficient two-step GMM estimators

Efficient Semi-Supervised Federated Learning for Heterogeneous Participants

Federated Learning (FL) has emerged to allow multiple clients to collaboratively train machine learning models on their private data. However, training and deploying large-scale models on resource-constrained clients is challenging. Fortunately, Split Federated Learning (SFL) offers a feasible solution by alleviating the computation and/or communication burden on clients. However, existing SFL works often assume sufficient labeled data on clients, which is usually impractical. Besides, data non-IIDness across clients poses another challenge to ensure efficient model training. To our best knowledge, the above two issues have not been simultaneously addressed in SFL. Herein, we propose a novel Semi-SFL system, which incorporates clustering regularization to perform SFL under the more practical scenario with unlabeled and non-IID client data. Moreover, our theoretical and experimental investigations into model convergence reveal that the inconsistent training processes on labeled and unlabeled data have an influence on the effectiveness of clustering regularization. To this end, we develop a control algorithm for dynamically adjusting the global updating frequency, so as to mitigate the training inconsistency and improve training performance. Extensive experiments on benchmark models and datasets show that our system provides a 3.0x speed-up in training time and reduces the communication cost by about 70.3% while reaching the target accuracy, and achieves up to 5.1% improvement in accuracy under non-IID scenarios compared to the state-of-the-art baselines.Comment: 16 pages, 12 figures, conferenc