Modeling corneal surfaces with three-dimensional basis functions

Purpose: To ascertain the effectiveness of object-centered three-dimensional representations for the modeling of corneal surfaces. Methods: Three-dimensional (3D) surface decomposition into series of basis functions including: (i) spherical harmonics, (ii) hemispherical harmonics, and (iii) 3D Zernike polynomials were considered and compared to the traditional viewer-centered representation of two-dimensional (2D) Zernike polynomial expansion for a range of retrospective videokeratoscopic height data from three clinical groups. The data were collected using the Medmont E300 videokeratoscope. The groups included 10 normal corneas with corneal astigmatism less than −0.75 D, 10 astigmatic corneas with corneal astigmatism between −1.07 D and 3.34 D (Mean = −1.83 D, SD = ±0.75 D), and 10 keratoconic corneas. Only data from the right eyes of the subjects were considered. Results: All object-centered decompositions led to significantly better fits to corneal surfaces (in terms of the RMS error values) than the corresponding 2D Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters (2, 4, 6, and 8 mm), and model orders (4th to 10th radial orders) The best results (smallest RMS fit error) were obtained with spherical harmonics decomposition which lead to about 22% reduction in the RMS fit error, as compared to the traditional 2D Zernike polynomials. Hemispherical harmonics and the 3D Zernike polynomials reduced the RMS fit error by about 15% and 12%, respectively. Larger reduction in RMS fit error was achieved for smaller corneral diameters and lower order fits. Conclusions: Object-centered 3D decompositions provide viable alternatives to traditional viewer-centered 2D Zernike polynomial expansion of a corneal surface. They achieve better fits to videokeratoscopic height data and could be particularly suited to the analysis of multiple corneal measurements, where there can be slight variations in the position of the cornea from one map acquisition to the next.

Free surface flow into a horizontal slot with zero gravity

The two-dimensional free surface flow of a finite-depth fluid into a horizontal slot is considered. For this study, the effects of viscosity and gravity are ignored. A generalised Schwarz-Christoffel mapping is used to formulate the problem in terms of a linear integral equation, which is solved exactly with the use of a Fourier transform. The resulting free surface profile is given explicitly in closed-form.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

An extension to the rank constraint for improving the reliability of stereo matching algorithms using the rank transform

The rank transform is one non-parametric transform which has been applied to the stereo matching problem The advantages of this transform include its invariance to radio metric distortion and its amenability to hardware implementation. This paper describes the derivation of the rank constraint for matching using the rank transform Previous work has shown that this constraint was capable of resolving ambiguous matches thereby improving match reliability A new matching algorithm incorporating this constraint was also proposed. This paper extends on this previous work by proposing a matching algorithm which uses a dimensional match surface in which the match score is computed for every possible template and match window combination. The principal advantage of this algorithm is that the use of the match surface enforces the left�right consistency and uniqueness constraints thus improving the algorithms ability to remove invalid matches Experimental results for a number of test stereo pairs show that the new algorithm is capable of identifying and removing a large number of in incorrect matches particularly in the case of occlusions

Morphology of osteocyte cells in normal and hyper-gravity

Osteocyte cells are the most abundant cells in human bone tissue. Due to their unique morphology and location, osteocyte cells are thought to act as regulators in the bone remodelling process, and are believed to play an important role in astronauts’ bone mass loss after long-term space missions. There is increasing evidence showing that an osteocyte’s functions are highly affected by its morphology. However, changes in an osteocyte’s morphology under an altered gravity environment are still not well documented. Several in vitro studies have been recently conducted to investigate the morphological response of osteocyte cells to the microgravity environment, where osteocyte cells were cultured on a two-dimensional flat surface for at least 24 hours before microgravity experiments. Morphology changes of osteocyte cells in microgravity were then studied by comparing the cell area to 1g control cells. However, osteocyte cells found in vivo are with a more 3D morphology, and both cell body and dendritic processes are found sensitive to mechanical loadings. A round shape osteocyte’s cells support a less stiff cytoskeleton and are more sensitive to mechanical stimulations compared with flat cellular morphology. Thus, the relative flat and spread shape of isolated osteocytes in 2D culture may greatly hamper their sensitivity to a mechanical stimulus, and the lack of knowledge on the osteocyte’s morphological characteristics in culture may lead to subjective and noncomprehensive conclusions of how altered gravity impacts on an osteocyte’s morphology. Through this work empirical models were developed to quantitatively predicate the changes of morphology in osteocyte cell lines (MLO-Y4) in culture, and the response of osteocyte cells, which are relatively round in shape, to hyper-gravity stimulation has also been investigated. The morphology changes of MLO-Y4 cells in culture were quantified by measuring cell area and three dimensionless shape features including aspect ratio, circularity and solidity by using widely accepted image analysis software (ImageJTM). MLO-Y4 cells were cultured at low density (5×103 per well) and the changes in morphology were recorded over 10 hours. Based on the data obtained from the imaging analysis, empirical models were developed using the non-linear regression method. The developed empirical models accurately predict the morphology of MLO-Y4 cells for different culture times and can, therefore, be used as a reference model for analysing MLO-Y4 cell morphology changes within various biological/mechanical studies, as necessary. The morphological response of MLO-Y4 cells with a relatively round morphology to hyper-gravity environment has been investigated using a centrifuge. After 2 hours culture, MLO-Y4 cells were exposed to 20g for 30mins. Changes in the morphology of MLO-Y4 cells are quantitatively analysed by measuring the average value of cell area and dimensionless shape factors such as aspect ratio, solidity and circularity. In this study, no significant morphology changes were detected in MLO-Y4 cells under a hyper-gravity environment (20g for 30 mins) compared with 1g control cells.

Metal hexaborides with Sc, Ti or Mn

Comparison of well-determined single crystal data for stoichiometric, or near-stoichiometric, metal hexaborides con-firm previously identified lattice parameter trends using powder diffraction. Trends for both divalent and trivalent forms suggest that potential new forms for synthesis include Sc and Mn hexaborides. Density Functional Theory (DFT) calculations for KB6, CaB6, YB6, LaB6, boron octahedral clusters and Sc and Mn forms, show that the shapes of bonding orbitals are defined by the boron framework. Inclusion of metal into the boron framework induces a reduction in energy ranging from 1 eV to 6 eV increasing with ionic charge. For metals with d1 character, such a shift in energy brings a doubly degenerate band section along the G-M reciprocal space direction within the conduction bands tangential to the Fermi surface. ScB6 band structure and density of states calculations show directional and gap characteristics similar to those of YB6 and LaB6. These calculations for ScB6 suggest it may be possible to realize superconductivity in this compound if synthesized.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Surface reconstruction of wheat leaf morphology from three-dimensional scanned data

Realistic virtual models of leaf surfaces are important for a number of applications in the plant sciences, such as modelling agrichemical spray droplet movement and spreading on the surface. In this context, the virtual surfaces are required to be sufficiently smooth to facilitate the use of the mathematical equations that govern the motion of the droplet. While an effective approach is to apply discrete smoothing D2-spline algorithms to reconstruct the leaf surfaces from three-dimensional scanned data, difficulties arise when dealing with wheat leaves that tend to twist and bend. To overcome this topological difficulty, we develop a parameterisation technique that rotates and translates the original data, allowing the surface to be fitted using the discrete smoothing D2-spline methods in the new parameter space. Our algorithm uses finite element methods to represent the surface as a linear combination of compactly supported shape functions. Numerical results confirm that the parameterisation, along with the use of discrete smoothing D2-spline techniques, produces realistic virtual representations of wheat leaves.

Three-dimensional reconstruction of an ancient Egyptian mummy

A complete series of cross-sectional computed tomography (CT) scans were obtained of a mummy of an Egyptian priestess, Tjenmutengebtiu, (Jeni), who lived in the twenty-second Dynasty (c. 945-715 BC). The purpose of this joint British Museum and St. Thomas’ Hospital project was effectively to ‘unwrap’ a mummy using cross-sectional X-rays. Jeni is encased in a beautifully decorated anthropomorphic cartonnage coffin. The head and neck were scanned with 2mm slices, the teeth with 1mm slices and the rest of the body with 4 mm slices, a 512 x 512 matrix was used. The 2D CT images, and 3D surface reconstruction’s, demonstrate many features of the embalming techniques and funerary customs of the XXII Dynasty. The presence of cloth protruding from the nasal cavities into the otherwise empty cranial cavity indicates that the brain was extracted via the nose. The remains of the heart can be seen as well as four organ packs corresponding to the mummified and repackaged lungs, intestines, stomach and liver. Each of the organ packs encloses a wax figurine representing one of the four sons of Horus. The teeth are in very good condition with little signs of wear, which, considering the gritty diet of the Egyptians, indicates that Jeni must have been very young when she died. A young age of death is also suggested by analysis of the shape of the molar teeth. The body is generally in very good condition demonstrating the consummate skill of the twenty-second Dynasty embalmers.

Porous polyurethane coatings bonded onto surface-modified titanium substrates for the growth of an endothelial cell layer

Cardiovascular diseases refer to the class of diseases that involve the heart or blood vessels (arteries and veins). Examples of medical devices for treating the cardiovascular diseases include ventricular assist devices (VADs), artificial heart valves and stents. Metallic biomaterials such as titanium and its alloy are commonly used for ventricular assist devices. However, titanium and its alloy show unacceptable thrombosis, which represents a major obstacle to be overcome. Polyurethane (PU) polymer has better blood compatibility and has been used widely in cardiovascular devices. Thus one aim of the project was to coat a PU polymer onto a titanium substrate by increasing the surface roughness, and surface functionality. Since the endothelium of a blood vessel has the most ideal non-thrombogenic properties, it was the target of this research project to grow an endothelial cell layer as a biological coating based on the tissue engineering strategy. However, seeding endothelial cells on the smooth PU coating surfaces is problematic due to the quick loss of seeded cells which do not adhere to the PU surface. Thus it was another aim of the project to create a porous PU top layer on the dense PU pre-layer-coated titanium substrate. The method of preparing the porous PU layer was based on the solvent casting/particulate leaching (SCPL) modified with centrifugation. Without the step of centrifugation, the distribution of the salt particles was not uniform within the polymer solution, and the degree of interconnection between the salt particles was not well controlled. Using the centrifugal treatment, the pore distribution became uniform and the pore interconnectivity was improved even at a high polymer solution concentration (20%) as the maximal salt weight was added in the polymer solution. The titanium surfaces were modified by alkli and heat treatment, followed by functionlisation using hydrogen peroxide. A silane coupling agent was coated before the application of the dense PU pre-layer and the porous PU top layer. The ability of the porous top layer to grow and retain the endothelial cells was also assessed through cell culture techniques. The bonding strengths of the PU coatings to the modified titanium substrates were measured and related to the surface morphologies. The outcome of the project is that it has laid a foundation to achieve the strategy of endothelialisation for the blood compatibility of medical devices. This thesis is divided into seven chapters. Chapter 2 describes the current state of the art in the field of surface modification in cardiovascular devices such as ventricular assist devices (VADs). It also analyses the pros and cons of the existing coatings, particularly in the context of this research. The surface coatings for VADs have evolved from early organic/ inorganic (passive) coatings, to bioactive coatings (e.g. biomolecules), and to cell-based coatings. Based on the commercial applications and the potential of the coatings, the relevant review is focused on the following six types of coatings: (1) titanium nitride (TiN) coatings, (2) diamond-like carbon (DLC) coatings, (3) 2-methacryloyloxyethyl phosphorylcholine (MPC) polymer coatings, (4) heparin coatings, (5) textured surfaces, and (6) endothelial cell lining. Chapter 3 reviews the polymer scaffolds and one relevant fabrication method. In tissue engineering, the function of a polymeric material is to provide a 3-dimensional architecture (scaffold) which is typically used to accommodate transplanted cells and to guide their growth and the regeneration of tissue. The success of these systems is dependent on the design of the tissue engineering scaffolds. Chapter 4 describes chemical surface treatments for titanium and titanium alloys to increase the bond strength to polymer by altering the substrate surface, for example, by increasing surface roughness or changing surface chemistry. The nature of the surface treatment prior to bonding is found to be a major factor controlling the bonding strength. By increasing surface roughness, an increase in surface area occurs, which allows the adhesive to flow in and around the irregularities on the surface to form a mechanical bond. Changing surface chemistry also results in the formation of a chemical bond. Chapter 5 shows that bond strengths between titanium and polyurethane could be significantly improved by surface treating the titanium prior to bonding. Alkaline heat treatment and H2O2 treatment were applied to change the surface roughness and the surface chemistry of titanium. Surface treatment increases the bond strength by altering the substrate surface in a number of ways, including increasing the surface roughness and changing the surface chemistry. Chapter 6 deals with the characterization of the polyurethane scaffolds, which were fabricated using an enhanced solvent casting/particulate (salt) leaching (SCPL) method developed for preparing three-dimensional porous scaffolds for cardiac tissue engineering. The enhanced method involves the combination of a conventional SCPL method and a step of centrifugation, with the centrifugation being employed to improve the pore uniformity and interconnectivity of the scaffolds. It is shown that the enhanced SCPL method and a collagen coating resulted in a spatially uniform distribution of cells throughout the collagen-coated PU scaffolds.In Chapter 7, the enhanced SCPL method is used to form porous features on the polyurethane-coated titanium substrate. The cavities anchored the endothelial cells to remain on the blood contacting surfaces. It is shown that the surface porosities created by the enhanced SCPL may be useful in forming a stable endothelial layer upon the blood contacting surface. Chapter 8 finally summarises the entire work performed on the fabrication and analysis of the polymer-Ti bonding, the enhanced SCPL method and the PU microporous surface on the metallic substrate. It then outlines the possibilities for future work and research in this area.

Formation of one-dimensional capped ZnO nanoparticle assemblies at the air/water interface

The self-assembling behavior and microscopic structure of zinc oxide nanoparticle Langmuir-Blodgett monolayer films were investigated for the case of zinc oxide nanoparticles coated with a hydrophobic layer of dodecanethiol. Evolution of nanoparticle film structure as a function of surface pressure (π) at the air-water interface was monitored in situ using Brewster’s angle microscopy, where it was determined that π=16 mN/m produced near-defect-free monolayer films. Transmission electron micrographs of drop-cast and Langmuir-Schaefer deposited films of the dodecanethiol-coated zinc oxide nanoparticles revealed that the nanoparticle preparation method yielded a microscopic structure that consisted of one-dimensional rodlike assemblies of nanoparticles with typical dimensions of 25 x 400 nm, encased in the organic dodecanethiol layer. These nanoparticle-containing rodlike micelles were aligned into ordered arrangements of parallel rods using the Langmuir-Blodgett technique.

Radiation effect on free convection laminar flow along a vertical flat plate with streamwise sinusoidal surface temperature

The effect of thermal radiation on a steady two-dimensional natural convection laminar flow of viscous incompressible optically thick fluid along a vertical flat plate with streamwise sinusoidal surface temperature has been investigated in this study. Using the appropriate variables; the basic governing equations are transformed to convenient form and then solved numerically employing two efficient methods, namely, Implicit finite difference method (IFD) together with Keller box scheme and Straight forward finite difference (SFFD) method. Effects of the variation of the physical parameters, for example, conduction-radiation parameter (Planck number), surface temperature parameter, and the amplitude of the surface temperature, are shown on the skin friction and heat transfer rate quantitatively are shown numerically. Velocity and temperature profiles as well as streamlines and isotherms are also presented and discussed for the variation of conduction-radiation parameter. It is found that both skin-friction and rate of heat transfer are enhanced considerably by increasing the values of conduction radiation parameter, Rd.

Effects of corrugation frequency and aspect ratio on natural convection within an enclosure having sinusoidal corrugation over a heated top surface

Natural convection of a two-dimensional laminar steady-state incompressible fluid flow in a modified rectangular enclosure with sinusoidal corrugated top surface has been investigated numerically. The present study has been carried out for different corrugation frequencies on the top surface as well as aspect ratios of the enclosure in order to observe the change in hydrodynamic and thermal behavior with constant corrugation amplitude. A constant flux heat source is flush mounted on the top sinusoidal wall, modeling a wavy sheet shaded room exposed to sunlight. The flat bottom surface is considered as adiabatic, while the both vertical side walls are maintained at the constant ambient temperature. The fluid considered inside the enclosure is air having Prandtl number of 0.71. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results in terms of isotherms, streamlines and average Nusselt numbers are obtained for the Rayleigh number ranging from 10^3 to 10^6 with constant physical properties for the fluid medium considered. It is found that the convective phenomena are greatly influenced by the presence of the corrugation and variation of aspect ratios.

Mixed convection laminar flow along a horizontal plate subject to streamwise sinusoidal surface temperature

Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.