The influence of yield surface shape and damage in the depth-dependent response of bone tissue to nanoindentation using spherical and Berkovich indenters

Prevention and treatment of osteoporosis rely on understanding of the micromechanical behaviour of bone and its influence on fracture toughness and cell-mediated adaptation processes. Postyield properties may be assessed by nonlinear finite element simulations of nanoindentation using elastoplastic and damage models. This computational study aims at determining the influence of yield surface shape and damage on the depth-dependent response of bone to nanoindentation using spherical and conical tips. Yield surface shape and damage 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 is well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not statistically significant (p<0.0001). For spherical tips, damage was not a significant parameter (p<0.0001). The gained knowledge can be used for developing an inverse method for identification of postelastic properties of bone from nanoindentation.

Isolation of Lautropia mirabilis from oral cavities of human immunodeficiency virus-infected children.

Lautropia mirabilis, a pleomorphic, motile, gram-negative coccus, has been isolated from the oral cavities of 32 of 60 (53.3%) children infected with human immunodeficiency virus (HIV) and 3 of 25 (12.0%) HIV-uninfected controls; the association of L. mirabilis isolation with HIV infection is significant (P < 0.001). All children in the study, both HIV-infected children and controls, were born to HIV-infected mothers. The presence of this bacterium was not associated with clinical disease in these children. The HIV-infected children with L. mirabilis did not differ from the HIV-infected children without L. mirabilis in immunological status, clinical status, or systemic medications. The role of HIV infection itself or concomitant factors in the establishment of L. mirabilis in the oral cavity remains to be elucidated.

Minimally invasive photopolymerization in intervertebral disc tissue cavities

Photopolymerized hydrogels are commonly used for a broad range of biomedical applications. As long as the polymer volume is accessible, gels can easily be hardened using light illumination. However, in clinics, especially for minimally invasive surgery, it becomes highly challenging to control photopolymerization. The ratios between polymerization- volume and radiating-surface-area are several orders of magnitude higher than for ex-vivo settings. Also tissue scattering occurs and influences the reaction. We developed a Monte Carlo model for photopolymerization, which takes into account the solid/liquid phase changes, moving solid/liquid-boundaries and refraction on these boundaries as well as tissue scattering in arbitrarily designable tissue cavities. The model provides a tool to tailor both the light probe and the scattering/absorption properties of the photopolymer for applications such as medical implants or tissue replacements. Based on the simulations, we have previously shown that by adding scattering additives to the liquid monomer, the photopolymerized volume was considerably increased. In this study, we have used bovine intervertebral disc cavities, as a model for spinal degeneration, to study photopolymerization in-vitro. The cavity is created by enzyme digestion. Using a custom designed probe, hydrogels were injected and photopolymerized. Magnetic resonance imaging (MRI) and visual inspection tools were employed to investigate the successful photopolymerization outcomes. The results provide insights for the development of novel endoscopic light-scattering polymerization probes paving the way for a new generation of implantable hydrogels.

Fate of accidental symmetries of the relativistic hydrogen atom in a spherical cavity

The non-relativistic hydrogen atom enjoys an accidental SO(4) symmetry, that enlarges the rotational SO(3) symmetry, by extending the angular momentum algebra with the Runge–Lenz vector. In the relativistic hydrogen atom the accidental symmetry is partially lifted. Due to the Johnson–Lippmann operator, which commutes with the Dirac Hamiltonian, some degeneracy remains. When the non-relativistic hydrogen atom is put in a spherical cavity of radius R with perfectly reflecting Robin boundary conditions, characterized by a self-adjoint extension parameter γ, in general the accidental SO(4) symmetry is lifted. However, for R=(l+1)(l+2)a (where a is the Bohr radius and l is the orbital angular momentum) some degeneracy remains when γ=∞ or γ = 2/R. In the relativistic case, we consider the most general spherically and parity invariant boundary condition, which is characterized by a self-adjoint extension parameter. In this case, the remnant accidental symmetry is always lifted in a finite volume. We also investigate the accidental symmetry in the context of the Pauli equation, which sheds light on the proper non-relativistic treatment including spin. In that case, again some degeneracy remains for specific values of R and γ.

Periacetabular osteotomy restores the typically excessive range of motion in dysplastic hips with a spherical head

BACKGROUND Residual acetabular dysplasia is seen in combination with femoral pathomorphologies including an aspherical femoral head and valgus neck-shaft angle with high antetorsion. It is unclear how these femoral pathomorphologies affect range of motion (ROM) and impingement zones after periacetabular osteotomy. QUESTIONS/PURPOSES (1) Does periacetabular osteotomy (PAO) restore the typically excessive ROM in dysplastic hips compared with normal hips; (2) how do impingement locations differ in dysplastic hips before and after PAO compared with normal hips; (3) does a concomitant cam-type morphology adversely affect internal rotation; and (4) does a concomitant varus-derotation intertrochanteric osteotomy (IO) affect external rotation? METHODS Between January 1999 and March 2002, we performed 200 PAOs for dysplasia; of those, 27 hips (14%) met prespecified study inclusion criteria, including availability of a pre- and postoperative CT scan that included the hip and the distal femur. In general, we obtained those scans to evaluate the pre- and postoperative acetabular and femoral morphology, the degree of acetabular reorientation, and healing of the osteotomies. Three-dimensional surface models based on CT scans of 27 hips before and after PAO and 19 normal hips were created. Normal hips were obtained from a population of CT-based computer-assisted THAs using the contralateral hip after exclusion of symptomatic hips or hips with abnormal radiographic anatomy. Using validated and computerized methods, we then determined ROM (flexion/extension, internal- [IR]/external rotation [ER], adduction/abduction) and two motion patterns including the anterior (IR in flexion) and posterior (ER in extension) impingement tests. The computed impingement locations were assigned to anatomical locations of the pelvis and the femur. ROM was calculated separately for hips with (n = 13) and without (n = 14) a cam-type morphology and PAOs with (n = 9) and without (n = 18) a concomitant IO. A post hoc power analysis based on the primary research question with an alpha of 0.05 and a beta error of 0.20 revealed a minimal detectable difference of 4.6° of flexion. RESULTS After PAO, flexion, IR, and adduction/abduction did not differ from the nondysplastic control hips with the numbers available (p ranging from 0.061 to 0.867). Extension was decreased (19° ± 15°; range, -18° to 30° versus 28° ± 3°; range, 19°-30°; p = 0.017) and ER in 0° flexion was increased (25° ± 18°; range, -10° to 41° versus 38° ± 7°; range, 17°-41°; p = 0.002). Dysplastic hips had a higher prevalence of extraarticular impingement at the anteroinferior iliac spine compared with normal hips (48% [13 of 27 hips] versus 5% [one of 19 hips], p = 0.002). A PAO increased the prevalence of impingement for the femoral head from 30% (eight of 27 hips) preoperatively to 59% (16 of 27 hips) postoperatively (p = 0.027). IR in flexion was decreased in hips with a cam-type deformity compared with those with a spherical femoral head (p values from 0.002 to 0.047 for 95°-120° of flexion). A concomitant IO led to a normalization of ER in extension (eg, 37° ± 7° [range, 21°-41°] of ER in 0° of flexion in hips with concomitant IO compared with 38° ± 7° [range, 17°-41°] in nondysplastic control hips; p = 0.777). CONCLUSIONS Using computer simulation of hip ROM, we could show that the PAO has the potential to restore the typically excessive ROM in dysplastic hips. However, a PAO can increase the prevalence of secondary intraarticular impingement of the aspherical femoral head and extraarticular impingement of the anteroinferior iliac spines in flexion and internal rotation. A cam-type morphology can result in anterior impingement with restriction of IR. Additionally, a valgus hip with high antetorsion can result in posterior impingement with decreased ER in extension, which can be normalized with a varus derotation IO of the femur. However, indication of an additional IO needs to be weighed against its inherent morbidity and possible complications. The results are based on a limited number of hips with a pre- and postoperative CT scan after PAO. Future prospective studies are needed to verify the current results based on computer simulation and to test their clinical importance.

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Gravity potential spherical harmonic series

Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.