Hierarchical Markov Random Fields Applied to Model Soft Tissue Deformations on Graphics Hardware

Many methodologies dealing with prediction or simulation of soft tissue deformations on medical image data require preprocessing of the data in order to produce a different shape representation that complies with standard methodologies, such as mass–spring networks, finite element method s (FEM). On the other hand, methodologies working directly on the image space normally do not take into account mechanical behavior of tissues and tend to lack physics foundations driving soft tissue deformations. This chapter presents a method to simulate soft tissue deformations based on coupled concepts from image analysis and mechanics theory. The proposed methodology is based on a robust stochastic approach that takes into account material properties retrieved directly from the image, concepts from continuum mechanics and FEM. The optimization framework is solved within a hierarchical Markov random field (HMRF) which is implemented on the graphics processor unit (GPU See Graphics processing unit ).

Strength of the Iberian intraplate lithosphere: Cenozoic deformations and seismicity

Previous studies about the strength of the lithosphere in the center of Iberia fail to resolve the depth of earthquakes because of the rheological uncertainties. Therefore, new contributions are considered (the crustal structure from a density model) and several parameters (tectonic regime, mantle rheology, strain rate) are checked in this paper to properly examine the role of lithospheric strength in the intraplate seismicity and the Cenozoic evolution. The strength distribution with depth, the integrated strength, the effective elastic thickness and the seismogenic thickness have been calculated by a finite element modelling of the lithosphere across the Central System mountain range and the bordering Duero and Madrid sedimentary basins. Only a dry mantle under strike-slip/extension and a strain rate of 10-15 s-1, or under extension and 10-16 s-1, causes a strong lithosphere. The integrated strength and the elastic thickness are lower in the mountain chain than in the basins. This heterogeneity has been maintained since the Cenozoic and determine the mountain uplift and the biharmonic folding of the Iberian lithosphere during the Alpine deformations. The seismogenic thickness bounds the seismic activity in the upper–middle crust, and the decreasing crustal strength from the Duero Basin towards the Madrid Basin is related to a parallel increase in Plio–Quaternary deformations and seismicity. However, elasto–plastic modelling shows that current African–Eurasian convergence is resolved elastically or ductilely, which accounts for the low seismicity recorded in this region.

Regional subsidence modelling in Murcia city (SE Spain) using 1-D vertical finite element analysis and 2-D interpolation of ground surface displacements

Subsidence is a hazard that may have natural or anthropogenic origin causing important economic losses. The area of Murcia city (SE Spain) has been affected by subsidence due to groundwater overexploitation since the year 1992. The main observed historical piezometric level declines occurred in the periods 1982–1984, 1992–1995 and 2004–2008 and showed a close correlation with the temporal evolution of ground displacements. Since 2008, the pressure recovery in the aquifer has led to an uplift of the ground surface that has been detected by the extensometers. In the present work an elastic hydro-mechanical finite element code has been used to compute the subsidence time series for 24 geotechnical boreholes, prescribing the measured groundwater table evolution. The achieved results have been compared with the displacements estimated through an advanced DInSAR technique and measured by the extensometers. These spatio-temporal comparisons have showed that, in spite of the limited geomechanical data available, the model has turned out to satisfactorily reproduce the subsidence phenomenon affecting Murcia City. The model will allow the prediction of future induced deformations and the consequences of any piezometric level variation in the study area.

A sensitivity study of the human crystalline lens using finite element analysis

Finite element analysis is a useful tool in understanding how the accommodation system of the eye works. Further to simpler FEA models that have been used hitherto, this paper describes a sensitivity study which aims to understand which parameters of the crystalline lens are key to developing an accurate model of the accommodation system. A number of lens models were created, allowing the mechanical properties, internal structure and outer geometry to be varied. These models were then spun about their axes, and the deformations determined. The results showed the mechanical properties are the critical parameters, with the internal structure secondary. Further research is needed to fully understand how the internal structure and properties interact to affect lens deformation.

Deformations of the pneumatic tyre

A mathematical model is developed for the general pneumatic tyre. The model will permit the investigations of tyre deformations produced by arbitrary external loading, and will enable estimates to be made of the distributions of applied and reactive forces. The principle of Finite Elements is used to idealise the composite tyre structure, each element consisting of a triangle of double curvature with varying thickness. Large deflections of' the structure are accomodated by the use of an iterative sequence of small incremental steps, each of' which obeys the laws of linear mechanics. The theoretical results are found to compare favourably with the experimental test data obtained from two different types of ttye construction. However, limitations in the discretisation process has prohibited accurate assessments to be made of stress distributions in the regions of high stress gradients ..

Strength of the Iberian intraplate lithosphere: Cenozoic deformations and seismicity

Previous studies about the strength of the lithosphere in the Iberia centre fail to resolve the depth of earthquakes because of the rheological uncertainties. Therefore, new contributions are considered (the crustal structure from a density model) and several parameters (tectonic regime, mantle rheology, strain rate) are checked in this paper to properly examine the role of lithospheric strength in the intraplate seismicity and the Cenozoic evolution. The strength distribution with depth, the integrated strength, the effective elastic thickness and the seismogenic thickness have been calculated by a finite element modelling of the lithosphere across the Central System mountain range and the bordering Duero and Madrid sedimentary basins. Only a dry mantle under strike-slip/extension and a strain rate of 10-15 s-1, or under extension and 10-16 s-1, causes a strong lithosphere. The integrated strength and the elastic thickness are lower in the mountain chain than in the basins. These anisotropies have been maintained since the Cenozoic and determine the mountain uplift and the biharmonic folding of the Iberian lithosphere during the Alpine deformations. The seismogenic thickness bounds the seismic activity in the upper–middle crust, and the decreasing crustal strength from the Duero Basin towards the Madrid Basin is related to a parallel increase in Plio–Quaternary deformations and seismicity. However, elasto–plastic modelling shows that current African–Eurasian convergence is resolved elastically or ductilely, which accounts for the low seismicity recorded in this region.

SIMULATING LARGE DEFORMATION OF INTRANEURAL GANGLION CYST USING FINITE ELEMENT METHOD

Intraneural Ganglion Cyst is disorder observed in the nerve injury, it is still unknown and very difficult to predict its propagation in the human body so many times it is referred as an unsolved history. The treatments for this disorder are to remove the cystic substance from the nerve by a surgery. However these treatments may result in neuropathic pain and recurrence of the cyst. The articular theory proposed by Spinner et al., (Spinner et al. 2003) considers the neurological deficit in Common Peroneal Nerve (CPN) branch of the sciatic nerve and adds that in addition to the treatment, ligation of articular branch results into foolproof eradication of the deficit. Mechanical modeling of the affected nerve cross section will reinforce the articular theory (Spinner et al. 2003). As the cyst propagates, it compresses the neighboring fascicles and the nerve cross section appears like a signet ring. Hence, in order to mechanically model the affected nerve cross section; computational methods capable of modeling excessively large deformations are required. Traditional FEM produces distorted elements while modeling such deformations, resulting into inaccuracies and premature termination of the analysis. The methods described in research report have the capability to simulate large deformation. The results obtained from this research shows significant deformation as compared to the deformation observed in the conventional finite element models. The report elaborates the neurological deficit followed by detail explanation of the Smoothed Particle Hydrodynamic approach. Finally, the results show the large deformation in stages and also the successful implementation of the SPH method for the large deformation of the biological organ like the Intra-neural ganglion cyst.

Finite element modeling of tube deformation during cold pilgering

A three-dimensional finite element model of cold pilgering of stainless steel tubes is developed in this paper. The objective is to use the model to increase the understanding of forces and deformations in the process. The focus is on the influence of vertical displacements of the roll stand and axial displacements of the mandrel and tube. Therefore, the rigid tools and the tube are supported with elastic springs. Additionally, the influences of friction coefficients in the tube/mandrel and tube/roll interfaces are examined. A sensitivity study is performed to investigate the influences of these parameters on the strain path and the roll separation force. The results show the importance of accounting for the displacements of the tube and rigid tools on the roll separation force and the accumulative plastic strain.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

Connected Hopf algebras of finite Gelfand-Kirillov dimension

Following the seminal work of Zhuang, connected Hopf algebras of finite GK-dimension over algebraically closed fields of characteristic zero have been the subject of several recent papers. This thesis is concerned with continuing this line of research and promoting connected Hopf algebras as a natural, intricate and interesting class of algebras. We begin by discussing the theory of connected Hopf algebras which are either commutative or cocommutative, and then proceed to review the modern theory of arbitrary connected Hopf algebras of finite GK-dimension initiated by Zhuang. We next focus on the (left) coideal subalgebras of connected Hopf algebras of finite GK-dimension. They are shown to be deformations of commutative polynomial algebras. A number of homological properties follow immediately from this fact. Further properties are described, examples are considered and invariants are constructed. A connected Hopf algebra is said to be "primitively thick" if the difference between its GK-dimension and the vector-space dimension of its primitive space is precisely one . Building on the results of Wang, Zhang and Zhuang,, we describe a method of constructing such a Hopf algebra, and as a result obtain a host of new examples of such objects. Moreover, we prove that such a Hopf algebra can never be isomorphic to the enveloping algebra of a semisimple Lie algebra, nor can a semisimple Lie algebra appear as its primitive space. It has been asked in the literature whether connected Hopf algebras of finite GK-dimension are always isomorphic as algebras to enveloping algebras of Lie algebras. We provide a negative answer to this question by constructing a counterexample of GK-dimension 5. Substantial progress was made in determining the order of the antipode of a finite dimensional pointed Hopf algebra by Taft and Wilson in the 1970s. Our final main result is to show that the proof of their result can be generalised to give an analogous result for arbitrary pointed Hopf algebras.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Photoelastic And Finite Element Analyses Of Occlusal Loads In Mandibular Body.

This study proposed to evaluate the mandibular biomechanics in the posterior dentition based on experimental and computational analyses. The analyses were performed on a model of human mandible, which was modeled by epoxy resin for photoelastic analysis and by computer-aided design for finite element analysis. To standardize the evaluation, specific areas were determined at the lateral surface of mandibular body. The photoelastic analysis was configured through a vertical load on the first upper molar and fixed support at the ramus of mandible. The same configuration was used in the computer simulation. Force magnitudes of 50, 100, 150, and 200 N were applied to evaluate the bone stress. The stress results presented similar distribution in both analyses, with the more intense stress being at retromolar area and oblique line and alveolar process at molar level. This study presented the similarity of results in the experimental and computational analyses and, thus, showed the high importance of morphology biomechanical characterization at posterior dentition.

Finite-element Analysis Of 3 Situations Of Trauma In The Human Edentulous Mandible.

Maxillofacial trauma resulting from falls in elderly patients is a major social and health care concern. Most of these traumatic events involve mandibular fractures. The aim of this study was to analyze stress distributions from traumatic loads applied on the symphyseal, parasymphyseal, and mandibular body regions in the elderly edentulous mandible using finite-element analysis (FEA). Computerized tomographic analysis of an edentulous macerated human mandible of a patient approximately 65 years old was performed. The bone structure was converted into a 3-dimensional stereolithographic model, which was used to construct the computer-aided design (CAD) geometry for FEA. The mechanical properties of cortical and cancellous bone were characterized as isotropic and elastic structures, respectively, in the CAD model. The condyles were constrained to prevent free movement in the x-, y-, and z-axes during simulation. This enabled the simulation to include the presence of masticatory muscles during trauma. Three different simulations were performed. Loads of 700 N were applied perpendicular to the surface of the cortical bone in the symphyseal, parasymphyseal, and mandibular body regions. The simulation results were evaluated according to equivalent von Mises stress distributions. Traumatic load at the symphyseal region generated low stress levels in the mental region and high stress levels in the mandibular neck. Traumatic load at the parasymphyseal region concentrated the resulting stress close to the mental foramen. Traumatic load in the mandibular body generated extensive stress in the mandibular body, angle, and ramus. FEA enabled precise mapping of the stress distribution in a human elderly edentulous mandible (neck and mandibular angle) in response to 3 different traumatic load conditions. This knowledge can help guide emergency responders as they evaluate patients after a traumatic event.

Keratoconus prediction using a finite element model of the cornea with local biomechanical properties

PURPOSE: The ability to predict and understand which biomechanical properties of the cornea are responsible for the stability or progression of keratoconus may be an important clinical and surgical tool for the eye-care professional. We have developed a finite element model of the cornea, that tries to predicts keratoconus-like behavior and its evolution based on material properties of the corneal tissue. METHODS: Corneal material properties were modeled using bibliographic data and corneal topography was based on literature values from a schematic eye model. Commercial software was used to simulate mechanical and surface properties when the cornea was subject to different local parameters, such as elasticity. RESULTS: The simulation has shown that, depending on the corneal initial surface shape, changes in local material properties and also different intraocular pressures values induce a localized protuberance and increase in curvature when compared to the remaining portion of the cornea. CONCLUSIONS: This technique provides a quantitative and accurate approach to the problem of understanding the biomechanical nature of keratoconus. The implemented model has shown that changes in local material properties of the cornea and intraocular pressure are intrinsically related to keratoconus pathology and its shape/curvature.

Stress distribution in the cervical region of an upper central incisor in a 3D finite element model

The aim of this study was to evaluate the stress distribution in the cervical region of a sound upper central incisor in two clinical situations, standard and maximum masticatory forces, by means of a 3D model with the highest possible level of fidelity to the anatomic dimensions. Two models with 331,887 linear tetrahedral elements that represent a sound upper central incisor with periodontal ligament, cortical and trabecular bones were loaded at 45º in relation to the tooth's long axis. All structures were considered to be homogeneous and isotropic, with the exception of the enamel (anisotropic). A standard masticatory force (100 N) was simulated on one of the models, while on the other one a maximum masticatory force was simulated (235.9 N). The software used were: PATRAN for pre- and post-processing and Nastran for processing. In the cementoenamel junction area, tensile forces reached 14.7 MPa in the 100 N model, and 40.2 MPa in the 235.9 N model, exceeding the enamel's tensile strength (16.7 MPa). The fact that the stress concentration in the amelodentinal junction exceeded the enamel's tensile strength under simulated conditions of maximum masticatory force suggests the possibility of the occurrence of non-carious cervical lesions such as abfractions.