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. ^

Multidimensional classification and diagnosis of leukemia in flow cytometry

This research is to establish new optimization methods for pattern recognition and classification of different white blood cells in actual patient data to enhance the process of diagnosis. Beckman-Coulter Corporation supplied flow cytometry data of numerous patients that are used as training sets to exploit the different physiological characteristics of the different samples provided. The methods of Support Vector Machines (SVM) and Artificial Neural Networks (ANN) were used as promising pattern classification techniques to identify different white blood cell samples and provide information to medical doctors in the form of diagnostic references for the specific disease states, leukemia. The obtained results prove that when a neural network classifier is well configured and trained with cross-validation, it can perform better than support vector classifiers alone for this type of data. Furthermore, a new unsupervised learning algorithm---Density based Adaptive Window Clustering algorithm (DAWC) was designed to process large volumes of data for finding location of high data cluster in real-time. It reduces the computational load to ∼O(N) number of computations, and thus making the algorithm more attractive and faster than current hierarchical algorithms.

Spatial variability in Florida Bay particulate organic matter composition: combining flow cytometry with stable isotope analyses

Long-term management plans for restoration of natural flow conditions through the Everglades increase the importance of understanding potential nutrient impacts of increased freshwater delivery on Florida Bay biogeochemistry. Planktonic communities respond quickly to changes in water quality, thus spatial variability in community composition and relationships to nutrient parameters must be understood in order to evaluate future downstream impacts of modifications to Everglades hydrology. Here we present initial results combining flow cytometry analyses of phytoplankton and bacterial populations (0.1–50 μm size fraction) with measurements of δ13C and δ15N composition and dissolved inorganic nutrient concentrations to explore proxies for planktonic species assemblage compositions and nutrient cycling. Particulate organic material in the 0.1–50 μm size fraction was collected from five stations in Northeastern and Western Florida Bay to characterize spatial variability in species assemblage and stable isotopic composition. A dense bloom of the picocyanobacterium, Synechococcus elongatus, was observed at Western Florida Bay sites. Smaller Synechococcus sp. were present at Northeast sites in much lower abundance. Bacteria and detrital particles were also more abundant at Western Florida Bay stations than in the northeast region. The highest abundance of detritus occurred at Trout Creek, which receives freshwater discharge from the Everglades through Taylor Slough. In terms of nutrient availability and stable isotopic values, the S. elongatus population in the Western bay corresponded to low DIN (0.5 μM NH 4 + ; 0.2 μM NO 3 − ) concentrations and depleted δ15N signatures ranging from +0.3 to +0.8‰, suggesting that the bloom supported high productivity levels through N2-fixation. δ15N values from the Northeast bay were more enriched (+2.0 to +3.0‰), characteristic of N-recycling. δ13C values were similar for all marine Florida Bay stations, ranging from −17.6 to −14.4‰, however were more depleted at the mangrove ecotone station (−25.5 to −22.3‰). The difference in the isotopic values reflects differences in carbon sources. These findings imply that variations in resource availability and nutrient sources exert significant control over planktonic community composition, which is reflected by stable isotopic signatures.

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.