Computational strategies for surface fitting using thin plate spline finite element methods

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

Classificação da curvatura de vertentes em perfil via Thin Plate Spline e Inferência Fuzzy

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Morphometric analysis of long-term dentoskeletal effects induced by treatment with Balters bionator

Objective: To evaluate the long-term effects of the standard (Class II) Balters bionator in growing patients with Class II malocclusion with mandibular retrusion by using morphometrics (thin-plate spline [TPS] analysis). Materials and Methods: Twenty-three Class II patients (8 male, 15 female) were treated consecutively with the Balters bionator (bionator group). The sample was evaluated at T0, start of treatment; T1, end of bionator therapy; and T2, long-term observation (including fixed appliances). Mean age at the start of treatment was 10 years 2 months (T0); at posttreatment, 12 years 3 months (T1); and at long-term follow-up, 18 years 2 months (T2). The control group consisted of 22 subjects (11 male, 11 female) with untreated Class II malocclusion. Lateral cephalograms were analyzed at the three time points for all groups. TPS analysis evaluated statistical differences (permutation tests) in the craniofacial shape and size between the bionator and control groups. Results: TPS analysis showed that treatment with the bionator is able to produce favorable mandibular shape changes (forward and downward displacement) that contribute significantly to the correction of the Class II dentoskeletal imbalance. These results are maintained at a long-term observation after completion of growth. The control group showed no statistically significant differences in the correction of Class II malocclusion. Conclusions: This study suggests that bionator treatment of Class II malocclusion produces favorable results over the long term with a combination of skeletal and dentoalveolar shape changes.

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Simulation of AE wave propagation in thin plate for source identification

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in wide spectrum areas, ranging from non-destructive testing for the detection of materials defects to monitoring of microeismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary/longitudinal waves), S waves (shear/transverse waves) and Rayleight (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use the acoustic emission technique for accurate identification of source location, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.

Variation in mandible shape in Thrichomys apereoides (Mammalia: Rodentia): Geometric analysis of a complex morphological structure

The model of development and evolution of complex morphological structures conceived by Atchley and Hall in 1991 (Biol. Rev. 66:101-157), which establishes that changes at the macroscopic, morphogenetic level can be statistically detected as variation in skeletal units at distinct scales, was applied in combination with the formalism of geometric morphometrics to study variation in mandible shape among populations of the rodent species Thrichomys apereoides. The thin-plate spline technique produced geometric descriptors of shape derived from anatomical landmarks in the mandible, which we used with graphical and inferential approaches to partition the contribution of global and localized components to the observed differentiation in mandible shape. A major pattern of morphological differentiation in T. apereoides is attributable to localized components of shape at smaller geometric scales associated with specific morphogenetic units of the mandible. On the other hand, a clinal trend of variation is associated primarily with localized components of shape at larger geometric scales. Morphogenetic mechanisms assumed to be operating to produce the observed differentiation in the specific units of the mandible include mesenchymal condensation differentiation, muscle hypertrophy, and tooth growth. Perspectives for the application of models of morphological evolution and geometric morphometrics to morphologically based systematic biology are considered.

Morphometric analysis of treatment effects of the Balters bionator in growing Class II patients

Objective: To investigate the effects of the standard (Class II) Balters bionator in growing patients with Class II malocclusion with mandibular retrusion by using morphometrics (thin-plate spline [TPS] analysis). Materials and Methods: Thirty-one Class II patients (17 male and 14 female) were treated with the Balters bionator (bionator group). Mean age at the start of treatment (T0) was 10.3 years, while it was 13 years at the end of treatment (T1). Mean treatment time was 2 years and 2 months. The control group consisted of 22 subjects (14 male and 8 female) with untreated Class II malocclusion. Mean age at T0 was 10.2 years, while it was 12.2 years at T1. The observation period lasted 2 years on average. TPS analysis evaluated statistical (permutation tests) differences in the craniofacial shape and size between the bionator and control groups. Results: Through TPS analysis (deformation grids) the bionator group showed significant shape changes in the mandible that could be described as a mandibular forward and downward displacement. The control group showed no statistically significant differences in the correction of Class II malocclusion. Conclusions: Bionator appliance is able to induce significant mandibular shape changes that lead to the correction of Class II dentoskeletal disharmony. © 2013 by The EH Angle Education and Research Foundation, Inc.

Transformação de coordenadas com modelagem de distorções entre SAD69 e SIRGAS2000 com o uso de Thin-Plate Splines

Several countries have been passed by change processes in their fundamental geodesic structure with the focus on the adoption of geocentric reference systems. In Brazil, the adoption of the SIRGAS2000 evolves the coexistence of two realizations from the COrrego Alegre system, two realizations from the SAD69 system and one realization from the SIRGAS2000 system. To make use of products in the old reference systems, methods of coordinate transformation between the existent reference frames are necessary. So, in this paper one solution for the transformation between coordinates from different reference frames, based on Thin-Plate Splines (TPS), that allows the estimation of parameters from one linear transformation and also one non-linear model is presented. The TPS model was developed to work with tridimensional coordinates and in this paper the results and analysis are performed with simulated data and also with data from the official Brazilian Geodetic System (SGB). In the check points from SAD69 stations (realization of 1996 - SAD69/96), the values of RMSE obtained were of 78,2 mm in latitude and 67,5 mm in longitude, before the transformation to the SIRGAS2000. In the comparison between the TPS model and ProGriD (Brazilian software provided by IBGE), the statistical indicators were reduced in 97%, by using the TPS model. Based in the obtained results from real dataset, the TPS model appears to be promising, since it allows improving the quality of transformation process with simultaneous distortion modeling.

Articulated Model Registration of MRI/X-Ray Spine Data

This paper presents a method based on articulated models for the registration of spine data extracted from multimodal medical images of patients with scoliosis. With the ultimate aim being the development of a complete geometrical model of the torso of a scoliotic patient, this work presents a method for the registration of vertebral column data using 3D magnetic resonance images (MRI) acquired in prone position and X-ray data acquired in standing position for five patients with scoliosis. The 3D shape of the vertebrae is estimated from both image modalities for each patient, and an articulated model is used in order to calculate intervertebral transformations required in order to align the vertebrae between both postures. Euclidean distances between anatomical landmarks are calculated in order to assess multimodal registration error. Results show a decrease in the Euclidean distance using the proposed method compared to rigid registration and more physically realistic vertebrae deformations compared to thin-plate-spline (TPS) registration thus improving alignment.

Identification of Mycobacteria by Thin Layer Chromatographic Analysis of Mycolic Acids and Conventional Biochemical Method: Four Years of Experience

Mycolic acids analysis by thin-layer chromatography (TLC) has been employed by several laboratories worldwide as a method for fast identification of mycobacteria. This method was introduced in Brazil by our laboratory in 1992 as a routine identification technique. Up to the present, 861 strains isolated were identified by mycolic acids TLC and by standard biochemical tests; 61% out of these strains came as clinical samples, 4% isolated from frogs and 35% as environmental samples. Mycobacterium tuberculosis strains identified by classical methods were confirmed by their mycolic acids contents (I, III and IV). The method allowed earlier differentiation of M. avium complex - MAC (mycolic acids I, IV and VI) from M. simiae (acids I, II and IV), both with similar biochemical properties. The method also permitted to distinguish M. fortuitum (acids I and V) from M. chelonae (acids I and II) , and to detect mixed mycobacterial infections cases as M. tuberculosis with MAC and M. fortuitum with MAC. Concluding, four years experience shows that mycolic acids TLC is an easy, reliable, fast and inexpensive method, an important tool to put together conventional mycobacteria identification methods.

Estudo longitudinal das alterações dentoesqueléticas à longo prazo da má oclusão de classe II, divisão 1ª tratada com o Bionator de Balters utilizando-se a cefalometria radiográfica e a morfometria geométrica

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