Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Comparison of bacterial plaque samples from titanium implant and tooth surfaces by different methods

Studies have shown similarities in the microflora between titanium implants or tooth sites when samples are taken by gingival crevicular fluid (GCF) sampling methods. The purpose of the present study was to study the microflora from curette and GCF samples using the checkerboard DNA-DNA hybridization method to assess the microflora of patients who had at least one oral osseo-integrated implant and who were otherwise dentate. Plaque samples were taken from tooth/implant surfaces and from sulcular gingival surfaces with curettes, and from gingival fluid using filter papers. A total of 28 subjects (11 females) were enrolled in the study. The mean age of the subjects was 64.1 years (SD+/-4.7). On average, the implants studied had been in function for 3.7 years (SD+/-2.9). The proportion of Streptococcus oralis (P<0.02) and Fusobacterium periodonticum (P<0.02) was significantly higher at tooth sites (curette samples). The GCF samples yielded higher proportions for 28/40 species studies (P-values varying between 0.05 and 0.001). The proportions of Tannerella forsythia (T. forsythensis), and Treponema denticola were both higher in GCF samples (P<0.02 and P<0.05, respectively) than in curette samples (implant sites). The microbial composition in gingival fluid from samples taken at implant sites differed partly from that of curette samples taken from implant surfaces or from sulcular soft tissues, providing higher counts for most bacteria studied at implant surfaces, but with the exception of Porphyromonas gingivalis. A combination of GCF and curette sampling methods might be the most representative sample method.

Bone apposition around two different sandblasted and acid-etched titanium implant surfaces: a histomorphometric study in canine mandibles

PURPOSE: The aim of this study was to evaluate bone apposition to a modified sandblasted and acid-etched (SLA) implant surface (modSLA) in the canine mandible as compared with the standard SLA surface. MATERIAL AND METHODS: In this experimental study, all mandibular premolars and first molars were extracted bilaterally in five foxhounds. After a healing period of 6 months, each side of the mandible received six randomly assigned dental implants alternating between the standard SLA and modSLA surface. The dogs were sacrificed at 2 weeks (n=2) or 4 weeks (n=3) after implant placement. Histologic and histomorphometric analyses were then performed for each implant. RESULTS: The microscopic healing patterns at weeks 2 and 4 for the two implant types with the standard SLA and modSLA surfaces showed similar qualitative findings. New bone tissue had already established direct contact with implant surfaces after 2 weeks of healing. The mean percentage of newly formed bone in contact with the implant (BIC) was significantly greater for modSLA (28.2+/-7.9%) than for SLA (22.2+/-7.3%) (P<0.05). This difference was no longer evident after 4 weeks. An increase in BIC for both implant surface types occurred from weeks 2 to 4. This increase was statistically significant when compared with SLA at 2 weeks (P<0.05), but not when compared with modSLA at 2 weeks. CONCLUSION: The data from the present study demonstrate significantly more bone apposition for the modSLA surface than the standard SLA surface after 2 weeks of healing. This increased bone apposition may allow a further reduction of the healing period following implant placement for patients undergoing early loading procedures.

A stereological comparison of villous and microvillous surfaces in small intestines of frugivorous and entomophagous bats: species, inter-individual and craniocaudal differences

The extents of functional surfaces (villi, microvilli) have been estimated at different longitudinal sites, and in the entire small intestine, for three species of bats belonging to two feeding groups: insect- and fruit-eaters. In all species, surface areas and other structural quantities tended to be greatest at more cranial sites and to decline caudally. The entomophagous bat (Miniopterus inflatus) had a mean body mass (coefficient of variation) of 8.9 g (5%) and a mean intestinal length of 20 cm (6%). The surface area of the basic intestinal tube (primary mucosa) was 9.1 cm2 (10%) but this was amplified to 48 cm2 (13%) by villi and to 0.13 m2 (20%) by microvilli. The total number of microvilli per intestine was 4 x 10(11) (20%). The average microvillus had a diameter of 8 nm (10%), a length of 1.1 microns (22%) and a membrane surface area of 0.32 micron 2 (31%). In two species of fruit bats (Epomophorus wahlbergi and Lisonycteris angolensis), body masses were greater and intestines longer, the values being 76.0 g (18%) and 76.9 g (4%), and 73 cm (16%) and 72 cm (7%), respectively. Surface areas were also greater, amounting to 76 cm2 (26%) and 45 cm2 (8%) for the primary mucosa, 547 cm2 (29%) and 314 cm2 (16%) for villi and 2.7 m2 (23%) and 1.5 m2 (18%) for microvilli. An increase in the number of microvilli, 33 x 10(11) (19%) and 15 x 10(11) (24%) per intestine, contributed to the more extensive surface area but there were concomitant changes in the dimensions of microvilli. Mean diameters were 94 nm (8%) and 111 nm (4%), and mean lengths were 2.8 microns (12%) and 2.9 microns (10%), respectively. Thus, an increase in the surface area of the average microvillus to 0.83 micron 2 (12%) and 1.02 microns 2 (11%) also contributed to the greater total surface area of microvilli. The lifestyle-related differences in total microvillous surface areas persisted when structural quantities were normalised for the differences in body masses. The values for total microvillous surface area were 148 cm2g-1 (20%) in the entomophagous bat, 355 cm2g-1 (20%) in E. wahlbergi and 192 cm2g-1 (17%) in L. angolensis. This was true despite the fact that the insecteater possessed a greater length of intestine per unit of body mass: 22 mm g-1 (8%) versus 9-10 mm g-1 (9-10%) for the fruit-eaters.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Early bone apposition to hydrophilic and hydrophobic titanium implant surfaces: a histologic and histomorphometric study in minipigs.

OBJECTIVE The first objective of this pilot study was to evaluate the impact of the hydrophilicity on the early phases of osseointegration. The second objective was to compare two hydrophilic implant surfaces with different geometries, surface roughness, and technologies achieving hydrophilicity. MATERIAL AND METHODS Twelve weeks after extraction, all four quadrants of nine minipigs received three dental implants, alternating between hydrophilic microrough surfaces (INICELL and SLActive) and a conventional hydrophobic microrough surface. After 5, 10, and 15 days of submerged healing, ground sections were prepared and subjected to histologic and histomorphometric analysis. RESULTS The histologic analysis revealed a similar healing pattern among the hydrophilic and hydrophobic implant surfaces, with extensive bone formation occurring between day 5 and day 10. With BIC values of greater than 50% after 10 days, all examined surfaces indicated favorable osseointegration at this very early point in healing. At day 15, the mean new bone-to-implant contact (newBIC) of one hydrophilic surface (INICELL; 55.8 ± 14.4%) was slightly greater than that of the hydrophobic microrough surface (40.6 ± 20.2%). At day 10 and day 15, an overall of 21% of the implants had to be excluded from analysis due to inflammations primarily caused by surgical complications. CONCLUSION Substantial bone apposition occurs between day 5 and day 10. The data suggest that the hydrophilic surface can provoke a slight tendency toward increased bone apposition in minipigs after 15 days. A direct comparison of two hydrophilic surfaces with varying geometries is of limited relevance.

Experimental peri-implant mucositis at different implant surfaces

OBJECTIVES To histologically and immunologically assess experimental peri-implant mucositis at surface enhanced modified (mod) hydrophilic titanium implants. MATERIALS AND METHODS In a split-mouth design (n = 6 foxhounds), four different implants were inserted on each side of the maxilla: three titanium-zirconium alloy implants (TiZr) with either modSLA (sand-blasted, acid etched and chemically mod), modMA (machined, acid etched and chemically mod), or M (machined) surfaces in the transmucosal portion, and one titanium implant with a machined transmucosal portion (TiM). Experimental mucositis was induced at one randomly assigned side (NPC), whereas the contra-lateral maxillary side received mechanical plaque removal three times per week (PC). At 16 weeks, tissue biopsies were processed for histological (primary outcome: apical extension of the inflammatory cell infiltrate measured from the mucosal margin - PM-aICT) and immunohistochemical (CD68 antigen reactivity) analyses. Peri-implant sulcus fluid was analysed for interleukin (IL)-1β, IL-8, matrix metalloproteinase (MMP)-8 and myeloperoxidase (MPO). RESULTS Mean PM-aICT values varied between 1.86 (TiZrmodSLA) and 3.40 mm (TiM) in the UPC group, and between 0.88 (TiZrmodSLA) and 2.08 mm (TiZrM) in the PC group. Mean CD68, IL-1β, IL-8, MMP-8 and MPO values were equally distributed between mod- and control implants in both NPC and PC groups. CONCLUSIONS The progression of experimental mucositis was comparable at all implant surfaces investigated.

The deglaciation history of the Simplon region (southern Swiss Alps) constrained by 10Be exposure dating of ice-molded bedrock surfaces

The deglaciation history of the Swiss Alps after the Last Glacial Maximum involved the decay of several ice domes and the subsequent disintegration of valley glaciers at high altitude. Here we use bedrock exposure dating to reconstruct the temporal and spatial pattern of ice retreat at the Simplon Pass (altitude: ∼2000 m) located 40 km southwest of the ‘Rhône ice dome’. Eleven 10Be exposure ages from glacially polished quartz veins and ice-molded bedrock surfaces cluster tightly between 13.5 ± 0.6 ka and 15.4 ± 0.6 ka (internal errors) indicating that the Simplon Pass depression became ice-free at 14.1 ± 0.4 ka (external error of mean age). This age constraint is interpreted to record the melting of the high valley glaciers in the Simplon Pass region during the warm Bølling–Allerød interstadial shortly after the Oldest Dryas stadial. Two bedrock samples collected a few hundred meters above the pass depression yield older 10Be ages of 17.8 ± 0.6 ka and 18.0 ± 0.6 ka. These ages likely reflect the initial downwasting of the Rhône ice dome and the termination of the ice transfluence from the ice dome across the Simplon Pass toward the southern foreland. There, the retreat of the piedmont glacier in Val d’Ossola was roughly synchronous with the decay of the Rhône ice dome in the interior of the mountain belt, as shown by 10Be ages of 17.7 ± 0.9 ka and 16.1 ± 0.6 ka for a whaleback at ∼500 m elevation near Montecrestese in northern Italy. In combination with well-dated paleoclimate records derived from lake sediments, our new age data suggest that during the deglaciation of the European Alps the decay of ice domes was approximately synchronous with the retreat of piedmont glaciers in the foreland and was followed by the melting of high-altitude valley glaciers after the transition from the Oldest Dryas to the Bølling–Allerød, when mean annual temperatures rose rapidly by ∼3 °C.