Estrogen deficiency-associated bone loss in the maxilla: A methodology to quantify the changes in the maxillary intra-radicular alveolar bone in an ovariectomized rat osteoporosis model

The effects of estrogen deficiency on bone characteristics are site-dependent, with the most commonly studied sites being appendicular long bones (proximal femur and tibia) and axial bones (vertebra). The effect on the maxillary and mandibular bones is still inconsistent and requires further investigation. This study was designed to evaluate bone quality in the posterior maxilla of ovariectomized rats in order to validate this site as an appropriate model to study the effect of osteoporotic changes. Methods: Forty-eight 3-month-old female Sprague-Dawley rats were randomly divided into two groups: an ovariectomized group (OVX, n=24) and Sham-operated group (SHAM, n=24). Six rats were randomly sacrificed from both groups at time points 8, 12, 16 and 20 weeks. The samples from tibia and maxilla were collected for Micro CT and histological analysis. For the maxilla, the volume of interest (VOI) area focused on the furcation areas of the first and second molar. Trabecular bone volume fraction (BV/TV, %), trabecular thickness (Tb.Th.), trabecular number (Tb.N.), trabecular separation (Tb.Sp.), and connectivity density (Conn.Dens) were analysed after Micro CT scanning. Results: At 8 weeks the indices BV/TV, Tb.Sp, Tb.N and Conn.Dens showed significant differences (P<0.05) between the OVX and SHAM groups in the tibia. Compared with the tibia, the maxilla developed osteoporosis at a later stage, with significant changes in maxillary bone density only occurring after 12 weeks. Compared with the SHAM group, both the first and second molars of the OVX group showed significantly decreased BV/TV values from 12 weeks, and these changes were sustained through 16 and 20 weeks. For Tb.Sp, there were significant increases in bone values for the OVX group compared with the SHAM group at 12, 16 and 20 weeks. Histological changes were highly consistent with Micro CT results. Conclusion: This study established a method to quantify the changes of intra-radicular alveolar bone in the posterior maxilla in an accepted rat osteoporosis model. The degree of the osteoporotic changes to trabecular bone architecture is site-dependent and at least 3 months are required for the osteoporotic effects to be apparent in the posterior maxilla following rat OVX.

Capacity determination and expansion models for rail networks

This thesis focused upon the development of improved capacity analysis and capacity planning techniques for railways. A number of innovations were made and were tested on a case study of a real national railway. These techniques can reduce the time required to perform decision making activities that planners and managers need to perform. As all railways need to be expanded to meet increasing demands, the presumption that analytical capacity models can be used to identify how best to improve an existing network at least cost, was fully investigated. Track duplication was the mechanism used to expanding a network's capacity, and two variant capacity expansion models were formulated. Another outcome of this thesis is the development and validation of bi objective models for capacity analysis. These models regulate the competition for track access and perform a trade-off analysis. An opportunity to develop more general mulch-objective approaches was identified.

Melanoma cell colony expansion parameters revealed by approximate Bayesian computation

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ.

The effects of osteoporosis on osseointegration in the rat maxilla

The study investigated the effects of oestrogen deficiency on dental implant in a rat model. An osteoporosis rat model was successfully established for dental implant research and it was noted that bone cells functioned differently in osteoporotic condition during the healing of dental implant. The study further demonstrated that implant surface roughness could stimulate bone formation, therefore, improve the bone healing in osteoporotic condition.

Analytical study of osteoporosis of maxilla in ovariectomized rats

The project applied analytical facilities to characterize the composition and mechanical properties of osteoporosis in maxillary bone using an ovariectomized rat model. It was found that osteoporotic jaw bone contained different amount of trace elements in comparison with the normal bone, which plays a significant role in bone quality. The knowledge generated from the study will assist the treatment of jaw bone fracture and dental implant placement.

Birth and expansion of innovation ecosystems: A case study of copper production

Despite the growing attention innovation ecosystems have received from scholars and practitioners, rather little is known about the crucial birth and expansion phases that these ecosystems experience. Through a single case in the complex product system (CoPS) environment, this paper investigates the development of an innovation ecosystem between 1980 and 2007. The findings demonstrate that the ecosystem’s birth phase includes sub-phases, namely, invention and start-up, where the ecosystem is reconfigured to find the appropriate form and the proper actors to satisfy the first customer’s requirements. Moreover, the duration of the expansion phase is found to be remarkably long, suggesting that within the CoPS setting, expansion may also include two or more sub-phases.

Homogeneous isotropic turbulence: large momentum expansion

High temperature expansion is an effective tool for studying second order phase transitions. With this in mind, we have looked at a high momentum expansion for homogeneous isotropic turbulence. Combining our results with those of the inertial range, we give another view of extended self-similarity (ESS).

Association between aneurysm shoulder stress and abdominal aortic aneurysm expansion: A longitudinal follow-up study

Background Aneurysm expansion rate is an important indicator of the potential risk of abdominal aortic aneurysm (AAA) rupture. Stress within the AAA wall is also thought to be a trigger for its rupture. However, the association between aneurysm wall stresses and expansion of AAA is unclear. Methods and Results Forty-four patients with AAAs were included in this longitudinal follow-up study. They were assessed by serial abdominal ultrasonography and computed tomography scans if a critical size was reached or a rapid expansion occurred. Patient-specific 3-dimensional AAA geometries were reconstructed from the follow-up computed tomography images. Structural analysis was performed to calculate the wall stresses of the AAA models at both baseline and final visit. A nonlinear large-strain finite element method was used to compute the wall-stress distribution. The relationship between wall stresses and expansion rate was investigated. Slowly and rapidly expanding aneurysms had comparable baseline maximum diameters (median, 4.35 cm [interquartile range, 4.12 to 5.0 cm] versus 4.6 cm [interquartile range, 4.2 to 5.0 cm]; P=0.32). Rapidly expanding AAAs had significantly higher shoulder stresses than slowly expanding AAAs (median, 300 kPa [interquartile range, 280 to 320 kPa] versus 225 kPa [interquartile range, 211 to 249 kPa]; P=0.0001). A good correlation between shoulder stress at baseline and expansion rate was found (r=0.71; P=0.0001). Conclusion A higher shoulder stress was found to have an association with a rapidly expanding AAA. Therefore, it may be useful for estimating the expansion of AAAs and improve risk stratification of patients with AAAs.

Transmission loss analysis of rectangular expansion chamber with arbitrary location of inlet/outlet by means of Green's functions

Transmission loss of a rectangular expansion chamber, the inlet and outlet of which are situated at arbitrary locations of the chamber, i.e., the side wall or the face of the chamber, are analyzed here based on the Green's function of a rectangular cavity with homogeneous boundary conditions. The rectangular chamber Green's function is expressed in terms of a finite number of rigid rectangular cavity mode shapes. The inlet and outlet ports are modeled as uniform velocity pistons. If the size of the piston is small compared to wavelength, then the plane wave excitation is a valid assumption. The velocity potential inside the chamber is expressed by superimposing the velocity potentials of two different configurations. The first configuration is a piston source at the inlet port and a rigid termination at the outlet, and the second one is a piston at the outlet with a rigid termination at the inlet. Pressure inside the chamber is derived from velocity potentials using linear momentum equation. The average pressure acting on the pistons at the inlet and outlet locations is estimated by integrating the acoustic pressure over the piston area in the two constituent configurations. The transfer matrix is derived from the average pressure values and thence the transmission loss is calculated. The results are verified against those in the literature where use has been made of modal expansions and also numerical models (FEM fluid). The transfer matrix formulation for yielding wall rectangular chambers has been derived incorporating the structural–acoustic coupling. Parametric studies are conducted for different inlet and outlet configurations, and the various phenomena occurring in the TL curves that cannot be explained by the classical plane wave theory, are discussed.

Phosphorus nutrition and tolerance of cotton to water stress: II. Water relations, free and bound water and leaf expansion rate

In previous experiments, increased leaf-Phosphorus (P) content with increasing P supply enhanced the individual leaf expansion and water content of fresh cotton leaves in a severely drying soil. In this paper, we report on the bulk water content of leaves and its components, free and bound water, along with other measures of plant water status, in expanding cotton leaves of various ages in a drying soil with different P concentrations. The bound water in living tissue is more likely to play a major role in tolerance to abiotic stresses by maintaining the structural integrity and/or cell wall extensibility of the leaves, whilst an increased amount of free water might be able to enhance solute accumulation, leading to better osmotic adjustment and tolerance to water stress, and maintenance of the volumes of sub-cellular compartments for expansive leaf growth. There were strong correlations between leaf-P%, leaf water (total, free and bound water) and leaf expansion rate (LER) under water stress conditions in a severely drying soil. Increased soil-P enhanced the uptake of P from a drying soil, leading to increased supply of osmotically active inorganic solutes to the cells in growing leaves. This appears to have led to the accumulation of free water and more bound water, ultimately leading to increased leaf expansion rates as compared to plants in low P soil under similar water stress conditions. The greater amount of bound and free water in the high-P plants was not necessarily associated with changes in cell turgor, and appears to have maintained the cell-wall properties and extensibility under water stressed conditions in soils that are nutritionally P-deficient.

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.