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.

Biomechanical model of human cornea based on stromal microstructure

The optical characteristics of the human cornea depends on the mechanical balance between the intra-ocular pressure and intrinsic tissue stiffness. A wide range of ophthalmic surgical procedures alter corneal biomechanics to induce local or global curvature changes for the correction of visual acuity. Due to the large number of surgical interventions performed every day, a deeper understanding of corneal biomechanics is needed to improve the safety of these procedures and medical devices. The aim of this study is to propose a biomechanical model of the human cornea, based on stromal microstructure. The constitutive mechanical law includes collagen fiber distribution based on X-ray scattering analysis, collagen cross-linking, and fiber uncrimping. Our results showed that the proposed model reproduced inflation and extensiometry experimental data [Elsheikh et al., Curr. Eye Res., 2007; Elsheikh et al., Exp. Eye Res., 2008] successfully. The mechanical properties obtained for different age groups demonstrated an increase in collagen cross-linking for older specimens. In future work such a model could be used to simulate non-symmetric interventions, and provide better surgical planning.

Numerical model of the human cornea based on stromal microstructure: identification of mechanical properties for two age groups

The optical quality of the human eye mainly depends on the refractive performance of the cornea. The shape of the cornea is a mechanical balance between intraocular pressure and tissue intrinsic stiffness. Several surgical procedures in ophthalmology alter the biomechanics of the cornea to provoke local or global curvature changes for vision correction. Legitimated by the large number of surgical interventions performed every day, the demand for a deeper understanding of corneal biomechanics is rising to improve the safety of procedures and medical devices. The aim of our work is to propose a numerical model of corneal biomechanics, based on the stromal microstructure. Our novel anisotropic constitutive material law features a probabilistic weighting approach to model collagen fiber distribution as observed on human cornea by Xray scattering analysis (Aghamohammadzadeh et. al., Structure, February 2004). Furthermore, collagen cross-linking was explicitly included in the strain energy function. Results showed that the proposed model is able to successfully reproduce both inflation and extensiometry experimental data (Elsheikh et. al., Curr Eye Res, 2007; Elsheikh et. al., Exp Eye Res, May 2008). In addition, the mechanical properties calculated for patients of different age groups (Group A: 65-79 years; Group B: 80-95 years) demonstrate an increased collagen cross-linking, and a decrease in collagen fiber elasticity from younger to older specimen. These findings correspond to what is known about maturing fibrous biological tissue. Since the presented model can handle different loading situations and includes the anisotropic distribution of collagen fibers, it has the potential to simulate clinical procedures involving nonsymmetrical tissue interventions. In the future, such mechanical model can be used to improve surgical planning and the design of next generation ophthalmic devices.

A comparison of the conformability of everolimus-eluting bioresorbable vascular scaffolds to metal platform coronary stents

The aim of this study was to assess the differences in terms of curvature and angulation of the treated vessel after the deployment of either a metallic stent or a polymeric scaffold device.

Wetting and spreading of a surfactant film on solid particles: influence of sharp edges and surface irregularities

In addition to particle size and surface chemistry, the shape of particles plays an important role in their wetting and displacement by the surfactant film in the lung. The role of particle shape was the subject of our investigations using a model system consisting of a modified Langmuir-Wilhelmy surface balance. We measured the influence of sharp edges (lines) and other highly curved surfaces, including sharp corners or spikes, of different particles on the spreading of a dipalmitoylphosphatidyl (DPPC) film. The edges of cylindrical sapphire plates (circular curved edges, 1.65 mm radius) were wetted at a surface tension of 10.7 mJ/m2 (standard error (SE) = 0.45, n = 20) compared with that of 13.8 mJ/m2 (SE = 0.20, n = 20) for cubic sapphire plates (straight linear edges, edge length 3 mm) (p < 0.05). The top surfaces of the sapphire plates (cubic and cylindrical) were wetted at 8.4 mJ/m2 (SE = 0.54, n = 20) and 9.1 mJ/m2 (SE = 0.50, n = 20), respectively, but the difference was not significant (p > 0.05). The surfaces of the plates showed significantly higher resistance to spreading compared to that of the edges, as substantially lower surface tensions were required to initiate wetting (p < 0.05). Similar results were found for talc particles, were the edges of macro- and microcrystalline particles were wetted at 7.2 mJ/m2 (SE = 0.52, n = 20) and 8.2 mJ/m2 (SE = 0.30, n = 20) (p > 0.05), respectively, whereas the surfaces were wetted at 3.8 mJ/m2 (SE = 0.89, n = 20) and 5.8 mJ/m2 (SE = 0.52, n = 20) (p < 0.05), respectively. Further experiments with pollen of malvaceae and maize (spiky and fine knobbly surfaces) were wetted at 10.0 mJ/m2 (SE = 0.52, n = 10) and 22.75 mJ/m2 (SE = 0.81, n = 10), respectively (p < 0.05). These results show that resistance to spreading of a DPPC film on various surfaces is dependent on the extent these surfaces are curved. This is seen with cubic sapphire plates which have at their corners a radius of curvature of about 0.75 microm, spiky malvaceae pollen with an even smaller radius on top of their spikes, or talc with various highly curved surfaces. These highly curved surfaces resisted wetting by the DPPC film to a higher degree than more moderately curved surfaces such as those of cylindrical sapphire plates, maize pollens, or polystyrene spheres, which have a surface free energy similar to that of talc but a smooth surface. The macroscopic plane surfaces of the particles demonstrated the greatest resistance to spreading. This was explained by the extremely fine grooves in the nanometer range, as revealed by electron microscopy. In summary, to understand the effects of airborne particles retained on the surfaces of the respiratory tract, and ultimately their pathological potential, not only the particle size and surface chemistry but also the particle shape should be taken in consideration.

Ocular pulse amplitude in healthy subjects as measured by dynamic contour tonometry

OBJECTIVES: To test whether dynamic contour tonometry yields ocular pulse amplitude (OPA) measurements that are independent of corneal thickness and curvature, and to assess variables of observer agreement. METHODS: In a multivariate cluster analysis on 223 eyes, the relationship between central corneal thickness, corneal curvature, axial length, anterior chamber depth, intraocular pressure, sex, age, and OPA measurements was assessed. Intraobserver and interobserver variabilities were calculated from repeated measurements obtained from 8 volunteers by 4 observers. RESULTS: The OPA readings were not affected by central corneal thickness (P = .08), corneal curvature (P = .47), anterior chamber depth (P = .80), age (P = .60), or sex (P = .73). There was a positive correlation between OPA and intraocular pressure (0.12 mm Hg/1 mm Hg of intraocular pressure; P<.001) and a negative correlation between OPA and axial length (0.27 mm Hg/1 mm of length; P<.001). Intraobserver and interobserver variabilities were 0.08 and 0.02 mm Hg, respectively, and the intraclass correlation coefficient was 0.89. CONCLUSIONS: The OPA readings obtained with dynamic contour tonometry in healthy subjects are not influenced by the structure of the anterior segment of the eye but are affected by intraocular pressure and axial length. We found a high amount of agreement within and between observers.

Prevalence of bone attrition on knee radiographs and MRI in a community-based cohort

OBJECTIVES: Bone attrition probably constitutes remodeling of the bone, resulting in flattening or depression of the articular surfaces. Defining bone attrition is challenging because it is an accentuation of the normal curvature of the tibial plateaus. We aimed to define bone attrition on magnetic resonance imaging (MRI) of the knee using information from both radiographs and MRIs, and to assess whether bone attrition is common prior to end stage disease osteoarthritis (OA) in the tibio-femoral joint. METHODS: All knees of participants in the community-based sample of the Framingham OA Study were evaluated for bone attrition in radiographs and MRIs. Radiographs were scored based on templates designed to outline the normal contours of the tibio-femoral joint. MRIs were analyzed using the semi-quantitative Whole-Organ Magnetic Resonance Imaging Scoring (WORMS) method. The prevalence of bone attrition was calculated using two different thresholds for MRI scores. RESULTS: Inter-observer agreement for identification of bone attrition was substantial for the radiographs (kappa=0.71, 95% CI 0.67-0.81) and moderate for MRI (kappa=0.56, 95% CI 0.40-0.72). Of 964 knees, 5.7% of the radiographs showed bone attrition. Of these, 91% of MRIs were also read as showing bone attrition. We selected a conservative threshold for bone attrition on MRI scoring (> or = 2 on a 0-3 scale) based on agreement with attrition on the radiograph or when bone attrition on MRI co-occurred with cartilage loss on OA. Using this threshold for bone attrition on MRI, bone attrition was common in knees with OA. For example, in knees with mild OA but no joint space narrowing, 13 of 88 MRIs (14.8%) showed bone attrition. CONCLUSIONS: Using MRI we found that many knees with mild OA without joint narrowing on radiographs had bone attrition, even using conservative definitions. The validity of our definition of bone attrition should be evaluated in further studies. Bone attrition may occur in milder OA and at earlier stages of disease than previously thought.

Biomechanics of the Spine

The human spinal column is a complex structure composed of 24 individual vertebrae plus the sacrum. The principal functions of the spine are to protect the spinal cord, to provide mobility to the trunk and to transfer loads from the head and trunk to the pelvis. By nature of a natural sagittal curvature and the relatively flexible intervertebral discs interposed between semi-rigid vertebrae, the spinal column is a compliant structure which can filter out shock and vibrations before they reach the brain. The intrinsic, passive stability of the spine is provided by the discs and surrounding ligamentous structures, and supplemented by the actions of the spinal muscles. The seven intervertebral ligaments which span each pair of adjacent vertebrae and the two synovial joints on each vertebra (facets or zygapophyseal joints) allow controlled, fully three-dimensional motion.

Outcome evaluation of early placed maxillary anterior single-tooth implants using objective esthetic criteria: a cross-sectional, retrospective study in 45 patients with a 2- to 4-year follow-up using pink and white esthetic scores

BACKGROUND: To validate the concept of early implant placement for use in the esthetically sensitive anterior maxilla, clinical trials should ideally include objective esthetic criteria when assessing outcome parameters. METHODS: In this cross-sectional, retrospective 2- to 4-year study involving 45 patients treated with maxillary anterior single-tooth implants according to the concept of early implant placement, a novel comprehensive index, comprising pink esthetic score and white esthetic score (PES/WES; the highest possible combined score is 20), was applied for the objective esthetic outcome assessment of anterior single-tooth implants. RESULTS: All 45 anterior maxillary single-tooth implants fulfilled strict success criteria for dental implants with regard to osseointegration, including the absence of peri-implant radiolucency, implant mobility, suppuration, and pain. The mean total PES/WES was 14.7 +/- 1.18 (range: 11 to 18). The mean total PES of 7.8 +/- 0.88 (range: 6 to 9) documents favorable overall peri-implant soft tissue conditions. The two PES variables facial mucosa curvature (1.9 +/- 0.29) and facial mucosa level (1.8 +/- 0.42) had the highest mean values, whereas the combination variable root convexity/soft tissue color and texture (1.2 +/- 0.53) proved to be the most difficult to fully satisfy. Mean scores were 1.6 +/- 0.5 for the mesial papilla and 1.3 +/- 0.5 for the distal papilla. A mean value of 6.9 +/- 1.47 (range: 4 to 10) was calculated for WES. CONCLUSIONS: This study demonstrated that anterior maxillary single-tooth replacement, according to the concept of early implant placement, is a successful and predictable treatment modality, in general, and from an esthetic point of view, in particular. The suitability of the PES/WES index for the objective outcome assessment of the esthetic dimension of anterior single-tooth implants was confirmed. However, prospective clinical trials are needed to further validate and refine this index.

Strong Down-Valley Low-Level Jets over the Atacama Desert: Observational Characterization

The near-surface wind and temperature regime at three points in the Atacama Desert of northern Chile is described using two-year multi-level measurements from 80-m towers located in an altitude range between 2100 and 2700 m ASL. The data reveal the frequent development of strong nocturnal drainage flows at all sites. Down-valley nose-shaped wind speed profiles are observed with maximum values occurring at heights between 20 m and 60 m AGL. The flow intensity shows considerable inter-daily variability and a seasonal modulation of maximum speeds, which in the cold season can attain hourly average values larger than 20 m s−1. Turbulent mixing appears significant over the full tower layer, affecting the curvature of the nighttime temperature profile and possibly explaining the observed increase of surface temperatures in the down-valley direction. Nocturnal valley winds and temperatures are weakly controlled by upper-air conditions observed at the nearest aerological station. Estimates of terms in the momentum budget for the development and the quasi-stationary phases of the down-valley flows suggest that the pressure gradient force due to the near-surface cooling along the sloping valley axes plays an important role in these drainage flows. A scale for the jet nose height of equilibrium turbulent down-slope jets is proposed, based on surface friction velocity and surface inversion intensity. At one of the sites this scale explains about 70% of the case-to-case observed variance of jet nose heights. Further modeling and observational work is needed, however, in order to better define the dynamics, extent and turbulence structure of this flow system, which has significant wind-energy, climatic and environmental implications.

Quantification of Popliteal Artery Deformation During Leg Flexion in Subjects With Peripheral Artery Disease: A Pilot Study

Purpose: To quantify the in vivo deformations of the popliteal artery during leg flexion in subjects with clinically relevant peripheral artery disease (PAD). Methods: Five patients (4 men; mean age 69 years, range 56–79) with varying calcification levels of the popliteal artery undergoing endovascular revascularization underwent 3-dimensional (3D) rotational angiography. Image acquisition was performed with the leg straight and with a flexion of 70°/20° in the knee/hip joints. The arterial centerline and the corresponding branches in both positions were segmented to create 3D reconstructions of the arterial trees. Axial deformation, twisting, and curvatures were quantified. Furthermore, the relationships between the calcification levels and the deformations were investigated. Results: An average shortening of 5.9%±2.5% and twist rate of 3.8±2.2°/cm in the popliteal artery were observed. Maximal curvatures in the straight and flexed positions were 0.12±0.04 cm−1 and 0.24±0.09 cm−1, respectively. As the severity of calcification increased, the maximal curvature in the straight position increased from 0.08 to 0.17 cm−1, while an increase from 0.17 to 0.39 cm−1 was observed for the flexed position. Axial elongations and arterial twisting were not affected by the calcification levels. Conclusion: The popliteal artery of patients with symptomatic PAD is exposed to significant deformations during flexion of the knee joint. The severity of calcification directly affects curvature, but not arterial length or twisting angles. This pilot study also showed the ability of rotational angiography to quantify the 3D deformations of the popliteal artery in patients with various levels of calcification.

Patient-specific finite-element simulation of the human cornea: A clinical validation study on cataract surgery

The planning of refractive surgical interventions is a challenging task. Numerical modeling has been proposed as a solution to support surgical intervention and predict the visual acuity, but validation on patient specific intervention is missing. The purpose of this study was to validate the numerical predictions of the post-operative corneal topography induced by the incisions required for cataract surgery. The corneal topography of 13 patients was assessed preoperatively and postoperatively (1-day and 30-day follow-up) with a Pentacam tomography device. The preoperatively acquired geometric corneal topography – anterior, posterior and pachymetry data – was used to build patient-specific finite element models. For each patient, the effects of the cataract incisions were simulated numerically and the resulting corneal surfaces were compared to the clinical postoperative measurements at one day and at 30-days follow up. Results showed that the model was able to reproduce experimental measurements with an error on the surgically induced sphere of 0.38D one day postoperatively and 0.19D 30 days postoperatively. The standard deviation of the surgically induced cylinder was 0.54D at the first postoperative day and 0.38D 30 days postoperatively. The prediction errors in surface elevation and curvature were below the topography measurement device accuracy of ±5μm and ±0.25D after the 30-day follow-up. The results showed that finite element simulations of corneal biomechanics are able to predict post cataract surgery within topography measurement device accuracy. We can conclude that the numerical simulation can become a valuable tool to plan corneal incisions in cataract surgery and other ophthalmosurgical procedures in order to optimize patients' refractive outcome and visual function.

How fluids bend: the elastic expansion for higher-dimensional black holes

Hydrodynamics can be consistently formulated on surfaces of arbitrary co-dimension in a background space-time, providing the effective theory describing long-wavelength perturbations of black branes. When the co-dimension is non-zero, the system acquires fluid-elastic properties and constitutes what is called a fluid brane. Applying an effective action approach, the most general form of the free energy quadratic in the extrinsic curvature and extrinsic twist potential of stationary fluid brane configurations is constructed to second order in a derivative expansion. This construction generalizes the Helfrich-Canham bending energy for fluid membranes studied in theoretical biology to the case in which the fluid is rotating. It is found that stationary fluid brane configurations are characterized by a set of 3 elastic response coefficients, 3 hydrodynamic response coefficients and 1 spin response coefficient for co-dimension greater than one. Moreover, the elastic degrees of freedom present in the system are coupled to the hydrodynamic degrees of freedom. For co-dimension-1 surfaces we find a 8 independent parameter family of stationary fluid branes. It is further shown that elastic and spin corrections to (non)-extremal brane effective actions can be accounted for by a multipole expansion of the stress-energy tensor, therefore establishing a relation between the different formalisms of Carter, Capovilla-Guven and Vasilic-Vojinovic and between gravity and the effective description of stationary fluid branes. Finally, it is shown that the Young modulus found in the literature for black branes falls into the class predicted by this approach - a relation which is then used to make a proposal for the second order effective action of stationary blackfolds and to find the corrected horizon angular velocity of thin black rings.