A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^

Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.

A multi-method approach for the assessment of composite indices and rankings

There is growing popularity in the use of composite indices and rankings for cross-organizational benchmarking. However, little attention has been paid to alternative methods and procedures for the computation of these indices and how the use of such methods may impact the resulting indices and rankings. This dissertation developed an approach for assessing composite indices and rankings based on the integration of a number of methods for aggregation, data transformation and attribute weighting involved in their computation. The integrated model developed is based on the simulation of composite indices using methods and procedures proposed in the area of multi-criteria decision making (MCDM) and knowledge discovery in databases (KDD). The approach developed in this dissertation was automated through an IT artifact that was designed, developed and evaluated based on the framework and guidelines of the design science paradigm of information systems research. This artifact dynamically generates multiple versions of indices and rankings by considering different methodological scenarios according to user specified parameters. The computerized implementation was done in Visual Basic for Excel 2007. Using different performance measures, the artifact produces a number of excel outputs for the comparison and assessment of the indices and rankings. In order to evaluate the efficacy of the artifact and its underlying approach, a full empirical analysis was conducted using the World Bank's Doing Business database for the year 2010, which includes ten sub-indices (each corresponding to different areas of the business environment and regulation) for 183 countries. The output results, which were obtained using 115 methodological scenarios for the assessment of this index and its ten sub-indices, indicated that the variability of the component indicators considered in each case influenced the sensitivity of the rankings to the methodological choices. Overall, the results of our multi-method assessment were consistent with the World Bank rankings except in cases where the indices involved cost indicators measured in per capita income which yielded more sensitive results. Low income level countries exhibited more sensitivity in their rankings and less agreement between the benchmark rankings and our multi-method based rankings than higher income country groups.

Multi-temporal monitoring of wetland water levels in the Florida Everglades using interferometric synthetic aperture radar (InSAR)

Interferometric synthetic aperture radar (InSAR) techniques can successfully detect phase variations related to the water level changes in wetlands and produce spatially detailed high-resolution maps of water level changes. Despite the vast details, the usefulness of the wetland InSAR observations is rather limited, because hydrologists and water resources managers need information on absolute water level values and not on relative water level changes. We present an InSAR technique called Small Temporal Baseline Subset (STBAS) for monitoring absolute water level time series using radar interferograms acquired successively over wetlands. The method uses stage (water level) observation for calibrating the relative InSAR observations and tying them to the stage's vertical datum. We tested the STBAS technique with two-year long Radarsat-1 data acquired during 2006–2008 over the Water Conservation Area 1 (WCA1) in the Everglades wetlands, south Florida (USA). The InSAR-derived water level data were calibrated using 13 stage stations located in the study area to generate 28 successive high spatial resolution maps (50 m pixel resolution) of absolute water levels. We evaluate the quality of the STBAS technique using a root mean square error (RMSE) criterion of the difference between InSAR observations and stage measurements. The average RMSE is 6.6 cm, which provides an uncertainty estimation of the STBAS technique to monitor absolute water levels. About half of the uncertainties are attributed to the accuracy of the InSAR technique to detect relative water levels. The other half reflects uncertainties derived from tying the relative levels to the stage stations' datum.

Characterization and modeling of multi-conductor transmission line using Finite-difference Time-Domain method

A two-dimensional, 2D, finite-difference time-domain (FDTD) method is used to analyze two different models of multi-conductor transmission lines (MTL). The first model is a two-conductor MTL and the second is a threeconductor MTL. Apart from the MTL's, a three-dimensional, 3D, FDTD method is used to analyze a three-patch microstrip parasitic array. While the MTL analysis is entirely in time-domain, the microstrip parasitic array is a study of scattering parameter Sn in the frequency-domain. The results clearly indicate that FDTD is an efficient and accurate tool to model and analyze multiconductor transmission line as well as microstrip antennas and arrays.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as "histogram binning" inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation.

Coral reef habitat maps derived from a high-spatial-resolution multi-spectral satellite image using object based image analysis

Coral reef maps at various spatial scales and extents are needed for mapping, monitoring, modelling, and management of these environments. High spatial resolution satellite imagery, pixel <10 m, integrated with field survey data and processed with various mapping approaches, can provide these maps. These approaches have been accurately applied to single reefs (10-100 km**2), covering one high spatial resolution scene from which a single thematic layer (e.g. benthic community) is mapped. This article demonstrates how a hierarchical mapping approach can be applied to coral reefs from individual reef to reef-system scales (10-1000 km**2) using object-based image classification of high spatial resolution images guided by ecological and geomorphological principles. The approach is demonstrated for three individual reefs (10-35 km**2) in Australia, Fiji, and Palau; and for three complex reef systems (300-600 km**2) one in the Solomon Islands and two in Fiji. Archived high spatial resolution images were pre-processed and mosaics were created for the reef systems. Georeferenced benthic photo transect surveys were used to acquire cover information. Field and image data were integrated using an object-based image analysis approach that resulted in a hierarchically structured classification. Objects were assigned class labels based on the dominant benthic cover type, or location-relevant ecological and geomorphological principles, or a combination thereof. This generated a hierarchical sequence of reef maps with an increasing complexity in benthic thematic information that included: 'reef', 'reef type', 'geomorphic zone', and 'benthic community'. The overall accuracy of the 'geomorphic zone' classification for each of the six study sites was 76-82% using 6-10 mapping categories. For 'benthic community' classification, the overall accuracy was 52-75% with individual reefs having 14-17 categories and reef systems 20-30 categories. We show that an object-based classification of high spatial resolution imagery, guided by field data and ecological and geomorphological principles, can produce consistent, accurate benthic maps at four hierarchical spatial scales for coral reefs of various sizes and complexities.

A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Peer reviewed

Development of Multi-modal and Super-resolved Retinal Imaging Systems

Advancements in retinal imaging technologies have drastically improved the quality of eye care in the past couple decades. Scanning laser ophthalmoscopy (SLO) and optical coherence tomography (OCT) are two examples of critical imaging modalities for the diagnosis of retinal pathologies. However current-generation SLO and OCT systems have limitations in diagnostic capability due to the following factors: the use of bulky tabletop systems, monochromatic imaging, and resolution degradation due to ocular aberrations and diffraction.

Bulky tabletop SLO and OCT systems are incapable of imaging patients that are supine, under anesthesia, or otherwise unable to maintain the required posture and fixation. Monochromatic SLO and OCT imaging prevents the identification of various color-specific diagnostic markers visible with color fundus photography like those of neovascular age-related macular degeneration. Resolution degradation due to ocular aberrations and diffraction has prevented the imaging of photoreceptors close to the fovea without the use of adaptive optics (AO), which require bulky and expensive components that limit the potential for widespread clinical use.

In this dissertation, techniques for extending the diagnostic capability of SLO and OCT systems are developed. These techniques include design strategies for miniaturizing and combining SLO and OCT to permit multi-modal, lightweight handheld probes to extend high quality retinal imaging to pediatric eye care. In addition, a method for extending true color retinal imaging to SLO to enable high-contrast, depth-resolved, high-fidelity color fundus imaging is demonstrated using a supercontinuum light source. Finally, the development and combination of SLO with a super-resolution confocal microscopy technique known as optical photon reassignment (OPRA) is demonstrated to enable high-resolution imaging of retinal photoreceptors without the use of adaptive optics.

Dosimetric Evaluation of Metal Artefact Reduction using Metal Artefact Reduction (MAR) Algorithm and Dual-energy Computed Tomography (CT) Method

Purpose: Computed Tomography (CT) is one of the standard diagnostic imaging modalities for the evaluation of a patient’s medical condition. In comparison to other imaging modalities such as Magnetic Resonance Imaging (MRI), CT is a fast acquisition imaging device with higher spatial resolution and higher contrast-to-noise ratio (CNR) for bony structures. CT images are presented through a gray scale of independent values in Hounsfield units (HU). High HU-valued materials represent higher density. High density materials, such as metal, tend to erroneously increase the HU values around it due to reconstruction software limitations. This problem of increased HU values due to metal presence is referred to as metal artefacts. Hip prostheses, dental fillings, aneurysm clips, and spinal clips are a few examples of metal objects that are of clinical relevance. These implants create artefacts such as beam hardening and photon starvation that distort CT images and degrade image quality. This is of great significance because the distortions may cause improper evaluation of images and inaccurate dose calculation in the treatment planning system. Different algorithms are being developed to reduce these artefacts for better image quality for both diagnostic and therapeutic purposes. However, very limited information is available about the effect of artefact correction on dose calculation accuracy. This research study evaluates the dosimetric effect of metal artefact reduction algorithms on severe artefacts on CT images. This study uses Gemstone Spectral Imaging (GSI)-based MAR algorithm, projection-based Metal Artefact Reduction (MAR) algorithm, and the Dual-Energy method.

Materials and Methods: The Gemstone Spectral Imaging (GSI)-based and SMART Metal Artefact Reduction (MAR) algorithms are metal artefact reduction protocols embedded in two different CT scanner models by General Electric (GE), and the Dual-Energy Imaging Method was developed at Duke University. All three approaches were applied in this research for dosimetric evaluation on CT images with severe metal artefacts. The first part of the research used a water phantom with four iodine syringes. Two sets of plans, multi-arc plans and single-arc plans, using the Volumetric Modulated Arc therapy (VMAT) technique were designed to avoid or minimize influences from high-density objects. The second part of the research used projection-based MAR Algorithm and the Dual-Energy Method. Calculated Doses (Mean, Minimum, and Maximum Doses) to the planning treatment volume (PTV) were compared and homogeneity index (HI) calculated.

Results: (1) Without the GSI-based MAR application, a percent error between mean dose and the absolute dose ranging from 3.4-5.7% per fraction was observed. In contrast, the error was decreased to a range of 0.09-2.3% per fraction with the GSI-based MAR algorithm. There was a percent difference ranging from 1.7-4.2% per fraction between with and without using the GSI-based MAR algorithm. (2) A range of 0.1-3.2% difference was observed for the maximum dose values, 1.5-10.4% for minimum dose difference, and 1.4-1.7% difference on the mean doses. Homogeneity indexes (HI) ranging from 0.068-0.065 for dual-energy method and 0.063-0.141 with projection-based MAR algorithm were also calculated.

Conclusion: (1) Percent error without using the GSI-based MAR algorithm may deviate as high as 5.7%. This error invalidates the goal of Radiation Therapy to provide a more precise treatment. Thus, GSI-based MAR algorithm was desirable due to its better dose calculation accuracy. (2) Based on direct numerical observation, there was no apparent deviation between the mean doses of different techniques but deviation was evident on the maximum and minimum doses. The HI for the dual-energy method almost achieved the desirable null values. In conclusion, the Dual-Energy method gave better dose calculation accuracy to the planning treatment volume (PTV) for images with metal artefacts than with or without GE MAR Algorithm.

Multi-scale colorectal tumour segmentation using a novel coarse to fine strategy

This paper addresses the problem of colorectal tumour segmentation in complex real world imagery. For efficient segmentation, a multi-scale strategy is developed for extracting the potentially cancerous region of interest (ROI) based on colour histograms while searching for the best texture resolution. To achieve better segmentation accuracy, we apply a novel bag-of-visual-words method based on rotation invariant raw statistical features and random projection based l2-norm sparse representation to classify tumour areas in histopathology images. Experimental results on 20 real world digital slides demonstrate that the proposed algorithm results in better recognition accuracy than several state of the art segmentation techniques.

High resolution Thomson Parabola Spectrometer for full spectral capture of multi-species ion beams

We report on the experimental characterisation of laser-driven ion beams using a Thomson Parabola Spectrometer (TPS) equipped with trapezoidally shaped electric plates, proposed by Gwynne et al. [Rev. Sci. Instrum. 85, 033304 (2014)]. While a pair of extended (30 cm long) electric plates was able to produce a significant increase in the separation between neighbouring ion species at high energies, deploying a trapezoidal design circumvented the spectral clipping at the low energy end of the ion spectra. The shape of the electric plate was chosen carefully considering, for the given spectrometer configuration, the range of detectable ion energies and species. Analytical tracing of the ion parabolas matches closely with the experimental data, which suggests a minimal effect of fringe fields on the escaping ions close to the wedged edge of the electrode. The analytical formulae were derived considering the relativistic correction required for the high energy ions to be characterised using such spectrometer.

Defining the Resolution of a Network for Transportation Analyses: a New Method to Improve Transportation Planning Decisions

Travel demand models are important tools used in the analysis of transportation plans, projects, and policies. The modeling results are useful for transportation planners making transportation decisions and for policy makers developing transportation policies. Defining the level of detail (i.e., the number of roads) of the transport network in consistency with the travel demand model’s zone system is crucial to the accuracy of modeling results. However, travel demand modelers have not had tools to determine how much detail is needed in a transport network for a travel demand model. This dissertation seeks to fill this knowledge gap by (1) providing methodology to define an appropriate level of detail for a transport network in a given travel demand model; (2) implementing this methodology in a travel demand model in the Baltimore area; and (3) identifying how this methodology improves the modeling accuracy. All analyses identify the spatial resolution of the transport network has great impacts on the modeling results. For example, when compared to the observed traffic data, a very detailed network underestimates traffic congestion in the Baltimore area, while a network developed by this dissertation provides a more accurate modeling result of the traffic conditions. Through the evaluation of the impacts a new transportation project has on both networks, the differences in their analysis results point out the importance of having an appropriate level of network detail for making improved planning decisions. The results corroborate a suggested guideline concerning the development of a transport network in consistency with the travel demand model’s zone system. To conclude this dissertation, limitations are identified in data sources and methodology, based on which a plan of future studies is laid out.

A multi-method study of the transformation of the carbonaceous skeleton of a polymer-based nanoporous carbon along the activation pathway

The change in the carbonaceous skeleton of nanoporous carbons during their activation has received limited attention, unlike its counterpart process in the presence of an inert atmosphere. Here we adopt a multi-method approach to elucidate this change in a poly(furfuryl alcohol)-derived carbon activated using cyclic application of oxygen saturation at 250 °C before its removal (with carbon) at 800 °C in argon. The methods used include helium pycnometry, synchrotron-based X-ray diffraction (XRD) and associated radial distribution function (RDF) analysis, transmission electron microscopy (TEM) and, uniquely, electron energy-loss spectroscopy spectrum-imaging (EELS-SI), electron nanodiffraction and fluctuation electron microscopy (FEM). Helium pycnometry indicates the solid skeleton of the carbon densifies during activation from 78% to 93% of graphite. RDF analysis, EELS-SI, and FEM all suggest this densification comes through an in-plane growth of sp2 carbon out to the medium range without commensurate increase in order normal to the plane. This process could be termed ‘graphenization’. The exact way in which this process occurs is not clear, but TEM images of the carbon before and after activation suggest it may come through removal of the more reactive carbon, breaking constraining cross-links and creating space that allows the remaining carbon material to migrate in an annealing-like process.