Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Theoretical investigation of thermal tweezers for parallel manipulation of atoms and nanoparticles on surfaces

A major focus of research in nanotechnology is the development of novel, high throughput techniques for fabrication of arbitrarily shaped surface nanostructures of sub 100 nm to atomic scale. A related pursuit is the development of simple and efficient means for parallel manipulation and redistribution of adsorbed atoms, molecules and nanoparticles on surfaces – adparticle manipulation. These techniques will be used for the manufacture of nanoscale surface supported functional devices in nanotechnologies such as quantum computing, molecular electronics and lab-on-achip, as well as for modifying surfaces to obtain novel optical, electronic, chemical, or mechanical properties. A favourable approach to formation of surface nanostructures is self-assembly. In self-assembly, nanostructures are grown by aggregation of individual adparticles that diffuse by thermally activated processes on the surface. The passive nature of this process means it is generally not suited to formation of arbitrarily shaped structures. The self-assembly of nanostructures at arbitrary positions has been demonstrated, though these have typically required a pre-patterning treatment of the surface using sophisticated techniques such as electron beam lithography. On the other hand, a parallel adparticle manipulation technique would be suited for directing the selfassembly process to occur at arbitrary positions, without the need for pre-patterning the surface. There is at present a lack of techniques for parallel manipulation and redistribution of adparticles to arbitrary positions on the surface. This is an issue that needs to be addressed since these techniques can play an important role in nanotechnology. In this thesis, we propose such a technique – thermal tweezers. In thermal tweezers, adparticles are redistributed by localised heating of the surface. This locally enhances surface diffusion of adparticles so that they rapidly diffuse away from the heated regions. Using this technique, the redistribution of adparticles to form a desired pattern is achieved by heating the surface at specific regions. In this project, we have focussed on the holographic implementation of this approach, where the surface is heated by holographic patterns of interfering pulsed laser beams. This implementation is suitable for the formation of arbitrarily shaped structures; the only condition is that the shape can be produced by holographic means. In the simplest case, the laser pulses are linearly polarised and intersect to form an interference pattern that is a modulation of intensity along a single direction. Strong optical absorption at the intensity maxima of the interference pattern results in approximately a sinusoidal variation of the surface temperature along one direction. The main aim of this research project is to investigate the feasibility of the holographic implementation of thermal tweezers as an adparticle manipulation technique. Firstly, we investigate theoretically the surface diffusion of adparticles in the presence of sinusoidal modulation of the surface temperature. Very strong redistribution of adparticles is predicted when there is strong interaction between the adparticle and the surface, and the amplitude of the temperature modulation is ~100 K. We have proposed a thin metallic film deposited on a glass substrate heated by interfering laser beams (optical wavelengths) as a means of generating very large amplitude of surface temperature modulation. Indeed, we predict theoretically by numerical solution of the thermal conduction equation that amplitude of the temperature modulation on the metallic film can be much greater than 100 K when heated by nanosecond pulses with an energy ~1 mJ. The formation of surface nanostructures of less than 100 nm in width is predicted at optical wavelengths in this implementation of thermal tweezers. Furthermore, we propose a simple extension to this technique where spatial phase shift of the temperature modulation effectively doubles or triples the resolution. At the same time, increased resolution is predicted by reducing the wavelength of the laser pulses. In addition, we present two distinctly different, computationally efficient numerical approaches for theoretical investigation of surface diffusion of interacting adparticles – the Monte Carlo Interaction Method (MCIM) and the random potential well method (RPWM). Using each of these approaches we have investigated thermal tweezers for redistribution of both strongly and weakly interacting adparticles. We have predicted that strong interactions between adparticles can increase the effectiveness of thermal tweezers, by demonstrating practically complete adparticle redistribution into the low temperature regions of the surface. This is promising from the point of view of thermal tweezers applied to directed self-assembly of nanostructures. Finally, we present a new and more efficient numerical approach to theoretical investigation of thermal tweezers of non-interacting adparticles. In this approach, the local diffusion coefficient is determined from solution of the Fokker-Planck equation. The diffusion equation is then solved numerically using the finite volume method (FVM) to directly obtain the probability density of adparticle position. We compare predictions of this approach to those of the Ermak algorithm solution of the Langevin equation, and relatively good agreement is shown at intermediate and high friction. In the low friction regime, we predict and investigate the phenomenon of ‘optimal’ friction and describe its occurrence due to very long jumps of adparticles as they diffuse from the hot regions of the surface. Future research directions, both theoretical and experimental are also discussed.

Thermal tweezers for manipulation of adatoms and nanoparticles on surfaces heated by interfering laser pulses

We conduct the detailed numerical investigation of a nanomanipulation and nanofabrication technique—thermal tweezers with dynamic evolution of surface temperature, caused by absorption of interfering laser pulses in a thin metalfilm or any other absorbing surface. This technique uses random Brownian forces in the presence of strong temperature modulation (surfacethermophoresis) for effective manipulation of particles/adatoms with nanoscale resolution. Substantial redistribution of particles on the surface is shown to occur with the typical size of the obtained pattern elements of ∼100 nm, which is significantly smaller than the wavelength of the incident pulses used (532 nm). It is also demonstrated that thermal tweezers based on surfacethermophoresis of particles/adatoms are much more effective in achieving permanent high maximum-to-minimum concentration ratios than bulk thermophoresis, which is explained by the interaction of diffusing particles with the periodic lattice potential on the surface. Typically required pulse regimes including pulse lengths and energies are also determined. The approach is applicable for reproducing any holographically achievable surfacepatterns, and can thus be used for engineering properties of surfaces including nanopatterning and design of surface metamaterials.

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.

Human osteoblast cell spreading and vinculin expression upon biomaterial surfaces

Any biomaterial implanted within the human body is influenced by the interactions that take place between its surface and the surrounding biological milieu. These interactions are known to influence the tissue interface dynamic, and thus act to emphasize the need to study cell-surface interactions as part of any biomaterial design process. The work described here investigates the relationship between human osteoblast attachment, spreading and focal contact formation on selected surfaces using immunostaining and digital image processing for vinculin, a key focal adhesion component. Our observations show that a relationship exists between levels of cell attachment, the degree of vinculin-associated plaque formation and biocompatibility. It also suggests that cell adhesion is not indicative of how supportive a substrate is to cell spreading, and that cell spreading

AFM study of forces between silicon oil and hydrophobic - hydrophylic surfaces in aqueous solutions

An investigation has been made of the interactions between silicone oil and various solid substrates immersed in aqueous solutions. Measurements were made using an atomic force microscope (AFM) using the colloid-probe method. The silicone oil drop is simulated by coating a small silica sphere with the oil, and measuring the force as this coated sphere is brought close to contact with a flat solid surface. It is found that the silicone oil surface is negatively charged, which causes a double-layer repulsion between the oil drop and another negatively charged surface such as mica. With hydrophilic solids, this repulsion is strong enough to prevent attachment of the drop to the solid. However, with hydrophobic surfaces there is an additional attractive force which overcomes the double-layer repulsion, and the silicone oil drop attaches to the solid. A "ramp" force appears in some, but not all, of the data sets. There is circumstantial evidence that this force results from compression of the silicone oil film coated on the glass sphere.

Understanding nutrient build-up on urban road surfaces

This paper discusses the outcomes of a research project on nutrients build-up on urban road surfaces. Nutrient build-up was investigated on road sites belonging to residential, industrial and commercial land use. Collected build-up samples were separated into five particle size ranges and were tested for total nitrogen (TN), total phosphorus (TP) and sub species of nutrients, namely, NO2-, NO3-, TKN and PO43-. Multivariate analytical techniques were used to analyse the data and to develop detailed understanding on build-up. Data analysis revealed that the solids loads on urban road surfaces are highly influenced by factors such as land use, antecedent dry period and traffic volume. However, the nutrient build-up process was found to be independent of the type of land use. It was solely dependent on the particle size of solids build-up. Most of the nutrients were associated with the particle size range <150 μm. Therefore, the removal of particles below 150 µm from road surfaces is of importance for the removal of nitrogen and phosphorus from road surface solids build-up. It is also important to consider the differences in the composition of nitrogen and phosphorus build-up in the context of designing effective stormwater quality mitigation strategies.

Pollutant characteristics on roof surfaces for evaluation as a stormwater harvesting catchment

This paper presents the outcomes of a study which focused on evaluating roof surfaces as stormwater harvesting catchments. Build-up and wash-off samples were collected from model roof surfaces. The collected build-up samples were separated into five different particle size ranges prior to the analysis of physico-chemical parameters. Study outcomes showed that roof surfaces are efficient catchment surfaces for the deposition of fine particles which travel over long distances. Roof surfaces contribute relatively high pollutant loads to the runoff and hence significantly influence the quality of the harvested rainwater. Pollutants associated with solids build-up on roof surfaces can vary with time, even with minimal changes to total solids load and particle size distribution. It is postulated that this variability is due to changes in distant atmospheric pollutant sources and wind patterns. The study highlighted the requirement for first flush devices to divert the highly polluted initial portion of roof runoff. Furthermore, it is highly recommended to not to harvest runoff from small intensity rainfall events since there is a high possibility that the runoff would contain a significant amount of pollutants even after the initial runoff fraction.

Fumaric acid monoethyl ester-functionalized poly(D,L-Lactide)/N-vinyl-2- pyrrolidone Resins for the preparation of tissue engineering scaffolds by stereolithography

Polymer networks were prepared by photocross-linking fumaric acid monoethyl ester (FAME) functionalized, three-armed poly(D,L-lactide) oligomers using Af-vinyl-2-pyrrolidone (NVP) as diluent and comonomer. The use of NVP together with FAME-functionalized oligomers resulted in copolymerization at high rates, and networks with gel contents in excess of 90 were obtained. The hydrophilicity of the poly(D,L-lactide) networks increases with increasing amounts of NVP, networks containing 50 wt of NVP absorbed 40 of water. As the amount of NVP was increased from 30 to 50 wt , the Young's modulus after equilibration in water decreased from 0.8 to 0.2 GPa, as opposed to an increase from 1.5 to 2.1 GPa in the dry state. Mouse preosteoblasts readily adhered and spread onto all prepared networks. Using stereolithography, porous structures with a well-defined gyroid architecture were prepared from these novel materials. This allows the preparation of tissue engineering scaffolds with optimized pore architecture and tunable material properties.

Methacrylate-functionalized oligomers based on lactide, E-caprolactone and trimethylene carbonate for application in stereo-lithography

Photo-curable biodegradable macromers were prepared by ring opening polymerization of D,L-lactide (DLLA), (similar to)-caprolactone (CL) and 1,3-trimethylene carbonate (TMC) in the presence of glycerol or sorbitol as initiator and stannous octoate as catalyst, and subsequent methacrylation of the terminal hydroxyl groups. These methacrylated macromers, ranging in molecular weight from approximately 700 to 6000 g/mol, were cross-linked using ultraviolet (UV) light to form biodegradable networks. Homogeneous networks with high gel contents were prepared. One of the resins based on PTMC was used to prepare three-dimensional structures by stereo-lithography using a commercially available apparatus.

Methacrylate-functionalized oligomers based on lactide, ε- caprolactone and trimethylene carbonate for application in stereo-lithography

Photo-curable biodegradable macromers were prepared by ring opening polymerization of D,L-lactide (DLLA), ε-caprolactone (CL) and 1,3-trimethylene carbonate (TMC) in the presence of glycerol or sorbitol as initiator and stannous octoate as catalyst, and subsequent methacrylation of the terminal hydroxyl groups. These methacrylated macromers, ranging in molecular weight from approximately 700 to 6000 g/mol, were cross-linked using ultraviolet (UV) light to form biodegradable networks. Homogeneous networks with high gel contents were prepared. One of the resins based on PTMC was used to prepare three-dimensional structures by stereo-lithography using a commercially available apparatus.