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.

Determining the zone of reflection for posterior corneal surface comparison phakometry

Although comparison phakometry has been used by a number of studies to measure posterior corneal shape, these studies have not calculated the size of the posterior corneal zones of reflection they assessed. This paper develops paraxial equations for calculating posterior corneal zones of reflection, based on standard keratometry equations and equivalent mirror theory. For targets used in previous studies, posterior corneal reflection zone sizes were calculated using paraxial equations and using exact ray tracing, assuming spherical and aspheric corneal surfaces. Paraxial methods and exact ray tracing methods give similar estimates for reflection zone sizes less than 2 mm, but for larger zone sizes ray tracing methods should be used.

Ultrasonic measurement of fine head movements in a standard ophthalmic headrest

We aimed to investigate the naturally occurring horizontal plane movements of a head stabilized in a standard ophthalmic headrest and to analyze their magnitude, velocity, spectral characteristics, and correlation to the cardio pulmonary system. Two custom-made air-coupled highly accurate (±2 μm)ultrasound transducers were used to measure the displacements of the head in different horizontal directions with a sampling frequency of 100 Hz. Synchronously to the head movements, an electrocardiogram (ECG) signal was recorded. Three healthy subjects participated in the study. Frequency analysis of the recorded head movements and their velocities was carried out, and functions of coherence between the two displacements and the ECG signal were calculated. Frequency of respiration and the heartbeat were clearly visible in all recorded head movements. The amplitude of head displacements was typically in the range of ±100 μm. The first harmonic of the heartbeat (in the range of 2–3 Hz), rather than its principal frequency, was found to be the dominant frequency of both head movements and their velocities. Coherence analysis showed high interdependence between the considered signals for frequencies of up to 20 Hz. These findings may contribute to the design of better ophthalmic headrests and should help other studies in the decision making of whether to use a heavy headrest or a bite bar.

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.

Corneal sensitivity as an ophthalmic marker of diabetic neuropathy

Purpose. The objective of this study was to explore the discriminative capacity of non-contact corneal esthesiometry (NCCE) when compared with the neuropathy disability score (NDS) score—a validated, standard method of diagnosing clinically significant diabetic neuropathy. Methods. Eighty-one participants with type 2 diabetes, no history of ocular disease, trauma, or surgery and no history of systemic disease that may affect the cornea were enrolled. Participants were ineligible if there was history of neuropathy due to non-diabetic cause or current diabetic foot ulcer or infection. Corneal sensitivity threshold was measured on the eye of dominant hand side at a distance of 10 mm from the center of the cornea using a stimulus duration of 0.9 s. The NDS was measured producing a score ranging from 0 to 10. To determine the optimal cutoff point of corneal sensitivity that identified the presence of neuropathy (diagnosed by NDS), the Youden index and “closest-to-(0,1)” criteria were used. Results. The receiver-operator characteristic curve for NCCE for the presence of neuropathy (NDS ≥3) had an area under the curve of 0.73 (p = 0.001) and, for the presence of moderate neuropathy (NDS ≥6), area of 0.71 (p = 0.003). By using the Youden index, for an NDS ≥3, the sensitivity of NCCE was 70% and specificity was 75%, and a corneal sensitivity threshold of 0.66 mbar or higher indicated the presence of neuropathy. When NDS ≥6 (indicating risk of foot ulceration) was applied, the sensitivity was 52% with a specificity of 85%. Conclusions. NCCE is a sensitive test for the diagnosis of minimal and more advanced diabetic neuropathy and may serve as a useful surrogate marker for diabetic and perhaps other neuropathies.