Bone Remodeling Adjacent to Morse Cone-Connection Implants with Platform Switch: A Fluorescence Study in the Dog Mandible

Purpose: The aim of this study was to evaluate, through fluorescence analysis, the effect that different interimplant distances, after prosthetic restoration, will have on bone remodeling in submerged and nonsubmerged implants restored with a ""platform switch."" Materials and Methods: Fifty-six Ankylos implants were placed 1.5 mm subcrestally in seven dogs. The implants were placed so that two fixed prostheses, with three interimplant contacts separated by 1-mm, 2-mm, and 3-mm distances, could be fabricated for each side of the mandible. The sides and the positions of the groups were selected randomly. To better evaluate bone remodeling, calcein green was injected 3 days before placement of the prostheses at 12 weeks postimplantation. At 3 days before sacrifice (8 weeks postloading), alizarin red was injected. The amounts of remodeled bone within the different interimplant areas were compared statistically before and after loading in submerged and nonsubmerged implants. Results: Statistically significant differences existed in the percentage of remodeled bone seen in the different regions. Mean percentages of remodeled bone in the submerged and nonsubmerged groups, respectively, were as follows: for the 1-mm distance, 23.0% +/- 0.05% and 23.1% +/- 0.03% preloading and 27.0% +/- 0.03% and 25.2% +/- 0.04% postloading, for the 2-mm distance, 18.2% +/- 0.05% and 18.1% +/- 0.04% preloading and 21.3% +/- 0.07% and 19.9% +/- 0.03% postloading, for the 3-mm distance, 18.3% +/- 0.03% and 18.3% +/- 0.03% preloading and 18.8% +/- 0.04% and 19.8% +/- 0.04% postloading, for distal-extension regions, 16.6% +/- 0.02% and 17.4% +/- 0.04% preloading and 17.0% +/- 0.04% and 18.4% +/- 0.04% postloading. Conclusions: Based upon this animal study, loading increases bone formation for submerged or nonsubmerged implants, and the interimplant distance of 1 mm appears to result in more pronounced bone remodeling than the 2-mm or 3-mm distances in implants with a ""platform switch."" INT J ORAL MAXILLOFAC IMPLANTS 2009;24:257-266

The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

Equicrestal and Subcrestal Dental Implants: A Histologic and Histomorphometric Evaluation of Nine Retrieved Human Implants

Background: Stability of pen-implant crestal bone plays a relevant role relative to the presence or absence of interdental papilla. Several factors can contribute to the crestal bone resorption observed around two-piece implants, such as the presence of a microgap at the level of the implant abutment junction, the type of connection between implant and prosthetic components, the implant positioning relative to the alveolar crest, and the interimplant distance. Subcrestal positioning of dental implants has been proposed to decrease the risk of exposure of the metal of the top of the implant or of the abutment margin, and to get enough space in a vertical dimension to create a harmoniously esthetic emergence profile. Methods: The present retrospective histologic study was performed to evaluate dental implants retrieved from human jaws that had been inserted in an equicrestal or subcrestal position. A total of nine implants were evaluated: five of these had been inserted in an equicrestal position, whereas the other four had been positioned subcrestally (1 to 3 mm). Results: In all subcrestally placed implants, preexisting and newly formed bone was found over the implant shoulder. In the equicrestal implants, crestal bone resorption (0.5 to 1.5 mm) was present around all implants. Conclusion: The subcrestal position of the implants resulted in bone located above the implant shoulder. J Periodontol 2011;82:708-715.

INFLUENCE OF INTERIMPLANT DISTANCES AND PLACEMENT DEPTH ON PAPILLA FORMATION AND CRESTAL RESORPTION: A CLINICAL AND RADIOGRAPHIC STUDY IN DOGS

Among the factors that contribute to the papilla formation and crestal bone preservation between contiguous implants, this animal study clinically and radiographically evaluated the interimplant distances (IDs) of 2 and 3 mm and the placement depths of Morse cone connection implants restored with platform switch. Bilateral mandibular premolars of 6 dogs were extracted, and after 12 weeks, the implants were placed. Four experimental groups were constituted: subcrestally with ID of 2 mm (2 SCL) and 3 mm (3 SCL) and crestally with ID of 2 mm (2 CL) and 3 mm (3 CL). Metallic crowns were immediately installed with a distance of 3 mm between the contact point and the bone crest. Eight weeks later, clinical measurements were performed to evaluate papilla formation, and radiographic images were taken to analyze the crestal bone remodeling. The subcrestal groups achieved better levels of papillae formation when compared with the crestal groups, with a significant difference between the 3 SCL and 3 CL groups (P = .026). Radiographically, the crestal bone preservation was also better in the subcrestal groups, with statistically significant differences between the 2SCL and 2CL groups (P = .002) and between the 3SCL and 3CL groups (P = .008). With the present conditions, it could be concluded that subcrestal implant placement had a positive impact on papilla formation and crestal bone preservation, which could favor the esthetic of anterior regions. However, the IDs of 2 and 3 mm did not show significantly different results.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Topological triangle characterization with application to object detection from images

A novel mathematical framework inspired on Morse Theory for topological triangle characterization in 2D meshes is introduced that is useful for applications involving the creation of mesh models of objects whose geometry is not known a priori. The framework guarantees a precise control of topological changes introduced as a result of triangle insertion/removal operations and enables the definition of intuitive high-level operators for managing the mesh while keeping its topological integrity. An application is described in the implementation of an innovative approach for the detection of 2D objects from images that integrates the topological control enabled by geometric modeling with traditional image processing techniques. (C) 2008 Published by Elsevier B.V.

The magnetized steel and scintillator calorimeters of the MINOS experiment

The Main Injector Neutrino Oscillation Search (MINOS) experiment uses an accelerator-produced neutrino beam to perform precision measurements of the neutrino oscillation parameters in the ""atmospheric neutrino"" sector associated with muon neutrino disappearance. This long-baseline experiment measures neutrino interactions in Fermilab`s NuMI neutrino beam with a near detector at Fermilab and again 735 km downstream with a far detector in the Soudan Underground Laboratory in northern Minnesota. The two detectors are magnetized steel-scintillator tracking calorimeters. They are designed to be as similar as possible in order to ensure that differences in detector response have minimal impact on the comparisons of event rates, energy spectra and topologies that are essential to MINOS measurements of oscillation parameters. The design, construction, calibration and performance of the far and near detectors are described in this paper. (C) 2008 Elsevier B.V. All rights reserved.

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

Spectral flow and iteration of closed semi-Riemannian geodesics

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.

Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.