Three dimensional study to quantify the relationship between facial hard and soft tissue movement as a result of orthognathic surgery

Introduction Prediction of soft tissue changes following orthognathic surgery has been frequently attempted in the past decades. It has gradually progressed from the classic “cut and paste” of photographs to the computer assisted 2D surgical prediction planning; and finally, comprehensive 3D surgical planning was introduced to help surgeons and patients to decide on the magnitude and direction of surgical movements as well as the type of surgery to be considered for the correction of facial dysmorphology. A wealth of experience was gained and numerous published literature is available which has augmented the knowledge of facial soft tissue behaviour and helped to improve the ability to closely simulate facial changes following orthognathic surgery. This was particularly noticed following the introduction of the three dimensional imaging into the medical research and clinical applications. Several approaches have been considered to mathematically predict soft tissue changes in three dimensions, following orthognathic surgery. The most common are the Finite element model and Mass tensor Model. These were developed into software packages which are currently used in clinical practice. In general, these methods produce an acceptable level of prediction accuracy of soft tissue changes following orthognathic surgery. Studies, however, have shown a limited prediction accuracy at specific regions of the face, in particular the areas around the lips. Aims The aim of this project is to conduct a comprehensive assessment of hard and soft tissue changes following orthognathic surgery and introduce a new method for prediction of facial soft tissue changes.   Methodology The study was carried out on the pre- and post-operative CBCT images of 100 patients who received their orthognathic surgery treatment at Glasgow dental hospital and school, Glasgow, UK. Three groups of patients were included in the analysis; patients who underwent Le Fort I maxillary advancement surgery; bilateral sagittal split mandibular advancement surgery or bimaxillary advancement surgery. A generic facial mesh was used to standardise the information obtained from individual patient’s facial image and Principal component analysis (PCA) was applied to interpolate the correlations between the skeletal surgical displacement and the resultant soft tissue changes. The identified relationship between hard tissue and soft tissue was then applied on a new set of preoperative 3D facial images and the predicted results were compared to the actual surgical changes measured from their post-operative 3D facial images. A set of validation studies was conducted. To include: • Comparison between voxel based registration and surface registration to analyse changes following orthognathic surgery. The results showed there was no statistically significant difference between the two methods. Voxel based registration, however, showed more reliability as it preserved the link between the soft tissue and skeletal structures of the face during the image registration process. Accordingly, voxel based registration was the method of choice for superimposition of the pre- and post-operative images. The result of this study was published in a refereed journal. • Direct DICOM slice landmarking; a novel technique to quantify the direction and magnitude of skeletal surgical movements. This method represents a new approach to quantify maxillary and mandibular surgical displacement in three dimensions. The technique includes measuring the distance of corresponding landmarks digitized directly on DICOM image slices in relation to three dimensional reference planes. The accuracy of the measurements was assessed against a set of “gold standard” measurements extracted from simulated model surgery. The results confirmed the accuracy of the method within 0.34mm. Therefore, the method was applied in this study. The results of this validation were published in a peer refereed journal. • The use of a generic mesh to assess soft tissue changes using stereophotogrammetry. The generic facial mesh played a major role in the soft tissue dense correspondence analysis. The conformed generic mesh represented the geometrical information of the individual’s facial mesh on which it was conformed (elastically deformed). Therefore, the accuracy of generic mesh conformation is essential to guarantee an accurate replica of the individual facial characteristics. The results showed an acceptable overall mean error of the conformation of generic mesh 1 mm. The results of this study were accepted for publication in peer refereed scientific journal. Skeletal tissue analysis was performed using the validated “Direct DICOM slices landmarking method” while soft tissue analysis was performed using Dense correspondence analysis. The analysis of soft tissue was novel and produced a comprehensive description of facial changes in response to orthognathic surgery. The results were accepted for publication in a refereed scientific Journal. The main soft tissue changes associated with Le Fort I were advancement at the midface region combined with widening of the paranasal, upper lip and nostrils. Minor changes were noticed at the tip of the nose and oral commissures. The main soft tissue changes associated with mandibular advancement surgery were advancement and downward displacement of the chin and lower lip regions, limited widening of the lower lip and slight reversion of the lower lip vermilion combined with minimal backward displacement of the upper lip were recorded. Minimal changes were observed on the oral commissures. The main soft tissue changes associated with bimaxillary advancement surgery were generalized advancement of the middle and lower thirds of the face combined with widening of the paranasal, upper lip and nostrils regions. In Le Fort I cases, the correlation between the changes of the facial soft tissue and the skeletal surgical movements was assessed using PCA. A statistical method known as ’Leave one out cross validation’ was applied on the 30 cases which had Le Fort I osteotomy surgical procedure to effectively utilize the data for the prediction algorithm. The prediction accuracy of soft tissue changes showed a mean error ranging between (0.0006mm±0.582) at the nose region to (-0.0316mm±2.1996) at the various facial regions.

Probabilistic Evaluation of Three-Dimensional Reconstructions from X-Ray Images Spanning a Limited Angle

An important part of computed tomography is the calculation of a three-dimensional reconstruction of an object from series of X-ray images. Unfortunately, some applications do not provide sufficient X-ray images. Then, the reconstructed objects no longer truly represent the original. Inside of the volumes, the accuracy seems to vary unpredictably. In this paper, we introduce a novel method to evaluate any reconstruction, voxel by voxel. The evaluation is based on a sophisticated probabilistic handling of the measured X-rays, as well as the inclusion of a priori knowledge about the materials that the object receiving the X-ray examination consists of. For each voxel, the proposed method outputs a numerical value that represents the probability of existence of a predefined material at the position of the voxel while doing X-ray. Such a probabilistic quality measure was lacking so far. In our experiment, false reconstructed areas get detected by their low probability. In exact reconstructed areas, a high probability predominates. Receiver Operating Characteristics not only confirm the reliability of our quality measure but also demonstrate that existing methods are less suitable for evaluating a reconstruction.

Three dimensional numerical simulation of thermohaline currents of the Persian Gulf

Observational data and a three dimensional numerical model (POM) are used to investigate the Persian Gulf outflow structure and its spreading pathway into the Oman Sea. The model is based on orthogonal curvilinear coordinate system in horizontal and train following coordinate (sigma coordinate) system in vertical. In the simulation, the horizontal diffusivity coefficients are calculated form Smogorinsky diffusivity formula and the eddy vertical diffusivities are obtained from a second turbulence closure model (namely Mellor-Yamada level 2.5 model of turbulence). The modeling area includes the east of the Persian Gulf, the Oman Sea and a part of the north-east of the Indian Ocean. In the model, the horizontal grid spacing was assumed to be about 3.5 km and the number of vertical levels was set to 32. The simulations show that the mean salinity of the PG outflow does not change substantially during the year and is about 39 psu, while its temperature exhibits seasonal variations. These lead to variations in outflow density in a way that is has its maximum density in late winter (March) and its minimum in mid-summer (August). At the entrance to the Oman Sea, the PG outflow turns to the right due to Coriolis Effect and falls down on the continental slope until it gains its equilibrium depth. The highest density of the outflow during March causes it to sink more into the deeper depths in contrast to that of August which the density is the lowest one. Hence, the neutral buoyancy depths of the outflow are about 500 m and 250 m for March and August respectively. Then, the outflow spreads in its equilibrium depths in the Oman Sea in vicinity of western and southern boundaries until it approach the Ras al Hamra Cape where the water depth suddenly begins to increase. Therefore, during March, the outflow that is deeper and wider relative to August, is more affected by the steep slope topography and as a result of vortex stretching mechanism and conservation of potential vorticity it separates from the lateral boundaries and finally forms an anti-cyclonic eddy in the Oman Sea. But during August the outflow moves as before in vicinity of lateral boundaries. In addition, the interaction of the PG outflow with tide in the Strait of Hormuz leads to intermittency in outflow movement into the Oman Sea and it could be the major reason for generations of Peddy (Peddies) in the Oman Sea.

Fully Anisotropic Solution of the Three Dimensional Boltzmann Transport Equation

The development of accurate modeling techniques for nanoscale thermal transport is an active area of research. Modern day nanoscale devices have length scales of tens of nanometers and are prone to overheating, which reduces device performance and lifetime. Therefore, accurate temperature profiles are needed to predict the reliability of nanoscale devices. The majority of models that appear in the literature obtain temperature profiles through the solution of the Boltzmann transport equation (BTE). These models often make simplifying assumptions about the nature of the quantized energy carriers (phonons). Additionally, most previous work has focused on simulation of planar two dimensional structures. This thesis presents a method which captures the full anisotropy of the Brillouin zone within a three dimensional solution to the BTE. The anisotropy of the Brillouin zone is captured by solving the BTE for all vibrational modes allowed by the Born Von-Karman boundary conditions.

Transmission electron tomography: quality assessment and enhancement for three-dimensional imaging of nanostructures

Nanotechnology has revolutionised humanity's capability in building microscopic systems by manipulating materials on a molecular and atomic scale. Nan-osystems are becoming increasingly smaller and more complex from the chemical perspective which increases the demand for microscopic characterisation techniques. Among others, transmission electron microscopy (TEM) is an indispensable tool that is increasingly used to study the structures of nanosystems down to the molecular and atomic scale. However, despite the effectivity of this tool, it can only provide 2-dimensional projection (shadow) images of the 3D structure, leaving the 3-dimensional information hidden which can lead to incomplete or erroneous characterization. One very promising inspection method is Electron Tomography (ET), which is rapidly becoming an important tool to explore the 3D nano-world. ET provides (sub-)nanometer resolution in all three dimensions of the sample under investigation. However, the fidelity of the ET tomogram that is achieved by current ET reconstruction procedures remains a major challenge. This thesis addresses the assessment and advancement of electron tomographic methods to enable high-fidelity three-dimensional investigations. A quality assessment investigation was conducted to provide a quality quantitative analysis of the main established ET reconstruction algorithms and to study the influence of the experimental conditions on the quality of the reconstructed ET tomogram. Regular shaped nanoparticles were used as a ground-truth for this study. It is concluded that the fidelity of the post-reconstruction quantitative analysis and segmentation is limited, mainly by the fidelity of the reconstructed ET tomogram. This motivates the development of an improved tomographic reconstruction process. In this thesis, a novel ET method was proposed, named dictionary learning electron tomography (DLET). DLET is based on the recent mathematical theorem of compressed sensing (CS) which employs the sparsity of ET tomograms to enable accurate reconstruction from undersampled (S)TEM tilt series. DLET learns the sparsifying transform (dictionary) in an adaptive way and reconstructs the tomogram simultaneously from highly undersampled tilt series. In this method, the sparsity is applied on overlapping image patches favouring local structures. Furthermore, the dictionary is adapted to the specific tomogram instance, thereby favouring better sparsity and consequently higher quality reconstructions. The reconstruction algorithm is based on an alternating procedure that learns the sparsifying dictionary and employs it to remove artifacts and noise in one step, and then restores the tomogram data in the other step. Simulation and real ET experiments of several morphologies are performed with a variety of setups. Reconstruction results validate its efficiency in both noiseless and noisy cases and show that it yields an improved reconstruction quality with fast convergence. The proposed method enables the recovery of high-fidelity information without the need to worry about what sparsifying transform to select or whether the images used strictly follow the pre-conditions of a certain transform (e.g. strictly piecewise constant for Total Variation minimisation). This can also avoid artifacts that can be introduced by specific sparsifying transforms (e.g. the staircase artifacts the may result when using Total Variation minimisation). Moreover, this thesis shows how reliable elementally sensitive tomography using EELS is possible with the aid of both appropriate use of Dual electron energy loss spectroscopy (DualEELS) and the DLET compressed sensing algorithm to make the best use of the limited data volume and signal to noise inherent in core-loss electron energy loss spectroscopy (EELS) from nanoparticles of an industrially important material. Taken together, the results presented in this thesis demonstrates how high-fidelity ET reconstructions can be achieved using a compressed sensing approach.

A three-dimensional representation method for noisy point clouds based on growing self-organizing maps accelerated on GPUs

The research described in this thesis was motivated by the need of a robust model capable of representing 3D data obtained with 3D sensors, which are inherently noisy. In addition, time constraints have to be considered as these sensors are capable of providing a 3D data stream in real time. This thesis proposed the use of Self-Organizing Maps (SOMs) as a 3D representation model. In particular, we proposed the use of the Growing Neural Gas (GNG) network, which has been successfully used for clustering, pattern recognition and topology representation of multi-dimensional data. Until now, Self-Organizing Maps have been primarily computed offline and their application in 3D data has mainly focused on free noise models, without considering time constraints. It is proposed a hardware implementation leveraging the computing power of modern GPUs, which takes advantage of a new paradigm coined as General-Purpose Computing on Graphics Processing Units (GPGPU). The proposed methods were applied to different problem and applications in the area of computer vision such as the recognition and localization of objects, visual surveillance or 3D reconstruction.

Noninvasive imaging of three-dimensional micro and nanostructures by topological methods

We present topological derivative and energy based procedures for the imaging of micro and nano structures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located and their position tracked with nanometer precision. Multiple objects dis-tributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and nonconvex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by gluing together two-dimensional horizontal slices between axial peaks or by locating objects at three-dimensional peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the lo-cation, size, and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective.

Three-dimensional kinetic adaptations of gait throughout pregnancy and postpartum

Biomechanical adaptations that occur during pregnancy can lead to changes on gait pattern. Nevertheless, these adaptations of gait are still not fully understood. The purpose was to determine the effect of pregnancy on the biomechanical pattern of walking, regarding the kinetic parameters. A three-dimensional analysis was performed in eleven participants. The kinetic parameters in the joints of the lower limb during gait were compared at the end of the first, second, and third trimesters of pregnancy and in the postpartum period, in healthy pregnant women. The main results showed a reduction in the normalized vertical reaction forces, throughout pregnancy, particularly the third peak. Pregnant women showed, during most of the stance phase, medial reaction forces as a motor response to promote the body stability. Bilateral changes were observed in hip joint, with a decrease in the participation of the hip extensors and in the eccentric contraction of hip flexors. In ankle joint a decrease in the participation of ankle plantar flexors was found. In conclusion, the overall results point to biomechanical adjustments that showed a decrease of the mechanical load of women throughout pregnancy, with exception for few unilateral changes of hip joint moments.

Critical behavior of the three-dimensional Ising spin glass

We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L520) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a KosterlitzThouless phase transition. Precise values for the ν and ƞ critical exponents are also presented.

Critical behavior in the site-diluted three-dimensional three-state Potts model

We have studied numerically the effect of quenched site dilution on a weak first-order phase transition in three dimensions. We have simulated the site diluted three-states Potts model studying in detail the secondorder region of its phase diagram. We have found that the n exponent is compatible with the one of the three-dimensional diluted Ising model, whereas the h exponent is definitely different.

Three-dimensional kinetic adaptations of gait throughout pregnancy and postpartum

Biomechanical adaptations that occur during pregnancy can lead to changes on gait pattern. Nevertheless, these adaptations of gait are still not fully understood. The purpose was to determine the effect of pregnancy on the biomechanical pattern of walking, regarding the kinetic parameters. A three-dimensional analysis was performed in eleven participants. The kinetic parameters in the joints of the lower limb during gait were compared at the end of the first, second, and third trimesters of pregnancy and in the postpartum period, in healthy pregnant women. The main results showed a reduction in the normalized vertical reaction forces, throughout pregnancy, particularly the third peak. Pregnant women showed, during most of the stance phase, medial reaction forces as a motor response to promote the body stability. Bilateral changes were observed in hip joint, with a decrease in the participation of the hip extensors and in the eccentric contraction of hip flexors. In ankle joint a decrease in the participation of ankle plantar flexors was found. In conclusion, the overall results point to biomechanical adjustments that showed a decrease of the mechanical load of women throughout pregnancy, with exception for few unilateral changes of hip joint moments.

In vitro characterization of the three-dimensional strain pattern in human vertebrae affected by metastases

La colonna vertebrale è la principale sede di metastasi, le quali possono alterare la normale distribuzione dei tessuti ossei e ridurre la capacità della vertebra di sostenere carichi. L’instabilità spinale causata dalle metastasi, tuttavia, è di difficile determinazione. La caratterizzazione meccanica delle vertebre metastatiche permetterebbe di identificare e, di conseguenza trattare, quelle ad alto rischio di frattura. In questo studio, ho valutato il comportamento meccanico a rottura di vertebre umane affette da metastasi misurando in vitro il campo di deformazione. Undici provini, costituiti da due vertebre centrali, una metastatica e una sana, sono stati preparati e scansionati applicando carichi graduali di compressione in una micro-tomografia computerizzata (μCT). Le deformazioni principali sono state misurate attraverso un algoritmo globale di Digital Volume Correlation (DVC) e successivamente sono state analizzate. Lo studio ha rivelato che le vertebre con metastasi litiche raggiungono deformazioni maggiori delle vertebre sane. Invece, le metastasi miste non assicurano un comportamento univoco in quanto combinano gli effetti antagonisti delle lesioni litiche e blastiche. Dunque la valutazione è stata estesa a possibili correlazioni tra il campo di deformazione e la microstruttura della vertebra. L'analisi ha identificato le regioni in cui parte la frattura (a più alta deformazione), senza identificare, in termini microstrutturali, una zona preferenziale di rottura a priori. Infatti, alcune zone con un pattern trabecolare denso, presunte più rigide, hanno mostrato deformazioni maggiori di quelle dei tessuti sani, sottolineando l’importanza della valutazione della qualità del tessuto osseo. Questi risultati, generalizzati su un campione più ampio, potrebbero essere utilizzati per implementare nuovi criteri negli attuali sistemi di valutazione dell'instabilità spinale.

The three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests.