Bayesian mixtures for modelling complex medical data : a case study in Parkinson’s disease

Mixture models are a flexible tool for unsupervised clustering that have found popularity in a vast array of research areas. In studies of medicine, the use of mixtures holds the potential to greatly enhance our understanding of patient responses through the identification of clinically meaningful clusters that, given the complexity of many data sources, may otherwise by intangible. Furthermore, when developed in the Bayesian framework, mixture models provide a natural means for capturing and propagating uncertainty in different aspects of a clustering solution, arguably resulting in richer analyses of the population under study. This thesis aims to investigate the use of Bayesian mixture models in analysing varied and detailed sources of patient information collected in the study of complex disease. The first aim of this thesis is to showcase the flexibility of mixture models in modelling markedly different types of data. In particular, we examine three common variants on the mixture model, namely, finite mixtures, Dirichlet Process mixtures and hidden Markov models. Beyond the development and application of these models to different sources of data, this thesis also focuses on modelling different aspects relating to uncertainty in clustering. Examples of clustering uncertainty considered are uncertainty in a patient’s true cluster membership and accounting for uncertainty in the true number of clusters present. Finally, this thesis aims to address and propose solutions to the task of comparing clustering solutions, whether this be comparing patients or observations assigned to different subgroups or comparing clustering solutions over multiple datasets. To address these aims, we consider a case study in Parkinson’s disease (PD), a complex and commonly diagnosed neurodegenerative disorder. In particular, two commonly collected sources of patient information are considered. The first source of data are on symptoms associated with PD, recorded using the Unified Parkinson’s Disease Rating Scale (UPDRS) and constitutes the first half of this thesis. The second half of this thesis is dedicated to the analysis of microelectrode recordings collected during Deep Brain Stimulation (DBS), a popular palliative treatment for advanced PD. Analysis of this second source of data centers on the problems of unsupervised detection and sorting of action potentials or "spikes" in recordings of multiple cell activity, providing valuable information on real time neural activity in the brain.

Non-invasive, quantitative analysis of drug mixtures in containers using spatially offset Raman spectroscopy (SORS) and multivariate statistical analysis

In this paper, spatially offset Raman spectroscopy (SORS) is demonstrated for non-invasively investigating the composition of drug mixtures inside an opaque plastic container. The mixtures consisted of three components including a target drug (acetaminophen or phenylephrine hydrochloride) and two diluents (glucose and caffeine). The target drug concentrations ranged from 5% to 100%. After conducting SORS analysis to ascertain the Raman spectra of the concealed mixtures, principal component analysis (PCA) was performed on the SORS spectra to reveal trends within the data. Partial least squares (PLS) regression was used to construct models that predicted the concentration of each target drug, in the presence of the other two diluents. The PLS models were able to predict the concentration of acetaminophen in the validation samples with a root-mean-square error of prediction (RMSEP) of 3.8% and the concentration of phenylephrine hydrochloride with an RMSEP of 4.6%. This work demonstrates the potential of SORS, used in conjunction with multivariate statistical techniques, to perform non-invasive, quantitative analysis on mixtures inside opaque containers. This has applications for pharmaceutical analysis, such as monitoring the degradation of pharmaceutical products on the shelf, in forensic investigations of counterfeit drugs, and for the analysis of illicit drug mixtures which may contain multiple components.

Kinetic energy of He atoms in liquid He-4-He-3 mixtures

Deep inelastic neutron scattering measurements on liquid 3He-4He mixtures in the normal phase have been performed on the VESUVIO spectrometer at the ISIS pulsed neutron source at exchanged wave vectors of about q≃120.0Å-1. The neutron Compton profiles J(y) of the mixtures were measured along the T=1.96K isotherm for 3He concentrations, x, ranging from 0.1 to 1.0 at saturated vapor pressures. Values of kinetic energies 〈T〉 of 3He and 4He atoms as a function of x, 〈T〉(x), were extracted from the second moment of J(y). The present determinations of 〈T〉(x) confirm previous experimental findings for both isotopes and, in the case of 3He, a substantial disagreement with theory is found. In particular 〈T〉(x) for the 3He atoms is found to be independent of concentration yielding a value 〈T〉3(x=0.1)≃12K, much lower than the value suggested by the most recent theoretical estimates of approximately 19 K.

Effect of pretreatment on saccharification of sugarcane bagasse by complex and simple enzyme mixtures

Saccharification of sugarcane bagasse pretreated at the pilot-scale with different processes (in combination with steam-explosion) was evaluated. Maximum glucan conversion with Celluclast 1.5 L (15–25 FPU/g glucan) was in the following order: glycerol/HCl > HCl > H2SO4 > NaOH, with the glycerol system achieving ∼100% conversion. Surprisingly, the NaOH substrate achieved optimum saccharification with only 8 FPU/g glucan. Glucan conversions (3.6–6%) obtained with mixtures of endo-1,4-β-glucanase (EG) and β-glucosidase (βG) for the NaOH substrate were 2–6 times that of acid substrates. However, glucan conversions (15–60%) obtained with mixtures of cellobiohydrolase (CBH I) and βG on acidified glycerol substrate were 10–30% higher than those obtained for NaOH and acid substrates. The susceptibility of the substrates to enzymatic saccharification was explained by their physical and chemical attributes. Acidified glycerol pretreatment offers the opportunity to simplify the complexity of enzyme mixtures required for saccharification of lignocellulosics.

Low temperature pretreatment of sugarcane bagasse at atmospheric pressure using mixtures of ethylene carbonate and ethylene glycol

A low temperature lignocellulose pretreatment process was developed using acid-catalysed mixtures of alkylene carbonate and alkylene glycol. Pretreatment of sugarcane bagasse with mixtures of ethylene carbonate (EC) and ethylene glycol (EG) was more effective than that with mixtures of propylene carbonate (PC) and propylene glycol (PG). These mixtures were more effective than the individual components in making bagasse cellulose more amenable to cellulase digestion. Glucan digestibilities of ≥87% could be achieved with a wide range of EC to EG ratios from 9:1 to 1:1 (w/w). Pretreatment of bagasse by the EC/EG mixture with a ratio of 4:1 in the presence of 1.2% H2SO4 at 90 °C for 30 min led to the highest glucan enzymatic digestibility of 93%. The high glucan digestibilities obtained under these acidic conditions were due to (a) the ability of alkylene carbonate to cause significant biomass size reduction, (b) the ability of alkylene glycol to cause biomass defibrillation, (c) the ability of alkylene carbonate and alkylene glycol to remove xylan and lignin, and (d) the magnified above attributes in the mixtures of alkylene carbonate and alkylene glycol.

Foil-based atom chip for Bose-Einstein condensates

We describe a novel method of fabricating atom chips that are well suited to the production and manipulation of atomic Bose–Einstein condensates. Our chip was created using a silver foil and simple micro-cutting techniques without the need for photolithography. It can sustain larger currents than conventional chips, and is compatible with the patterning of complex trapping potentials. A near pure Bose–Einstein condensate of 4 × 104 87Rb atoms has been created in a magnetic microtrap formed by currents through wires on the chip. We have observed the fragmentation of atom clouds in close proximity to the silver conductors. The fragmentation has different characteristic features to those seen with copper conductors.

Methanesulfonic acid-catalyzed conversion of glucose and xylose mixtures to levulinic acid and furfural

Methanesulfonic acid (MSA) was compared with sulfuric acid for the conversion of glucose and xylose mixtures to produce levulinic acid and furfural. The interactions of glucose and xylose, the predominant sugars found in biomass, were found to influence product yields with furfural degradation reactions enhanced under higher reactant loadings. Fast heating rates allowed maximal yields (>60 mol%) of levulinic acid and furfural to be achieved under short reaction times. Under the range of conditions examined, sulfuric acid produced a slight increase in levulinic acid yield by 6% (P = 0.02), although there was no significant difference (P = 0.11) between MSA and sulfuric acid in levulinic acid formed from glucose alone. The amount and type of the solid residue is similar between MSA and sulfuric acid. As such, MSA is a suitable alternative because its use minimizes corrosion and disposal issues associated with mineral acid catalysts. The heating value of the residue was 22 MJ/kg implying that it is a suitable source of fuel. On the basis of these results, a two-stage processing strategy is proposed to target high levulinic acid and furfural yields, and other chemical products (e.g., lactic acid, xylitol, acetic acid and formic acid). This will result in full utilization of bagasse components.

CFD convective flow simulation of the varying properties of CO2-H20 mixtures in geothermal systems

Numerical simulation of a geothermal reservoir, modelled as a bottom-heated square box, filled with water-CO2 mixture is presented in this work. Furthermore, results for two limiting cases of a reservoir filled with either pure water or CO2 are presented. Effects of different parameters including CO2 concentration as well as reservoir pressure and temperature on the overall performance of the system are investigated. It has been noted that, with a fixed reservoir pressure and temperature, any increase in CO2concentration leads to better performance, i.e. stronger convection and higher heat transfer rates. With a fixed CO2 concentration, however, the reservoir pressure and temperature can significantly affect the overall heat transfer and flow rate from the reservoir. Details of such variations are documented and discussed in the present paper.

Using informative priors in the estimation of mixtures over time with application to aerosol particle size distributions

The issue of using informative priors for estimation of mixtures at multiple time points is examined. Several different informative priors and an independent prior are compared using samples of actual and simulated aerosol particle size distribution (PSD) data. Measurements of aerosol PSDs refer to the concentration of aerosol particles in terms of their size, which is typically multimodal in nature and collected at frequent time intervals. The use of informative priors is found to better identify component parameters at each time point and more clearly establish patterns in the parameters over time. Some caveats to this finding are discussed.