Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.Comment: 10 page

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed

Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol

The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data

Reaction diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates, however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of Glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models' performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use $k$-means clustering to predict the number of subpopulations based on the recovered distributions

Personalised antimicrobial management in secondary care

Background: The growing threat of Antimicrobial Resistance (AMR) requires innovative methods to promote the sustainable effectiveness of antimicrobial agents. Hypothesis: This thesis aimed to explore the hypothesis that personalised decision support interventions have the utility to enhance antimicrobial management across secondary care. Methods: Different research methods were used to investigate this hypothesis. Individual physician decision making was mapped and patient experiences of engagement with decision making explored using semi-structured interviews. Cross-specialty engagement with antimicrobial management was investigated through cross-sectional analysis of conference abstracts and educational training curricula. Artificial intelligence tools were developed to explore their ability to predict the likelihood of infection and provide individualised prescribing recommendations using routine patient data. Dynamic, individualised dose optimisation was explored through: (i) development of a microneedle based, electrochemical biosensor for minimally invasive monitoring of beta-lactams; and (ii) pharmacokinetic (PK)-pharmacodynamic (PD) modelling of a new PK-PD index using C-Reactive protein (CRP) to predict the pharmacodynamics of vancomycin. Ethics approval was granted for all aspects of work explored within this thesis. Results: Mapping of individual physician decision making during infection management demonstrated several areas where personalised, technological interventions could enhance antimicrobial management. At specialty level, non-infection specialties have little engagement with antimicrobial management. The importance of engaging surgical specialties, who have relatively high rates of antimicrobial usage and healthcare associated infections, was observed. An individualised information leaflet, co-designed with patients, to provide personalised infection information to in-patients receiving antibiotics significantly improved knowledge and reported engagement with decision making. Artificial intelligence was able to enhance the prediction of infection and the prescribing of antimicrobials using routinely available clinical data. Real-time, continuous penicillin monitoring was demonstrated using a microneedle based electrochemical sensor in-vivo. A new PK-PD index, using C-Reactive Protein, was able to predict individual patient response to vancomycin therapy at 96-120 hours of therapy. Conclusion: Through co-design and the application of specific technologies it is possible to provide personalised antimicrobial management within secondary care.Open Acces

A Functionalised Aptamer Electrochemical Biosensor Platform

The ability to utilise new knowledge of biomarkers from genomic and proteomic data will have a great impact on molecular diagnosis. Biomarker detection could be achieved by utilising a capture molecule that associates specifically with the target biomarker. The work described in this thesis focuses on a platform comprising a lysozyme binding aptamer and an amperometric electrode (an electrochemical aptasensor). To couple the binding reaction to a change in current, the aptamer is modified with a redox group, ferrocene. Two types of signalling aptamer were constructed, one comprised the aptamer self-assembled on gold and hybridised to a short complementary oligonucleotide carrying a ferrocene group. The second incorporated the binding sequence into a molecular beacon, one end of which self-assembled onto the electrode, the other end carried the ferrocene group. Both of these showed a lysozyme dependent change in current on a gold electrode. Further characterisation of the first aptasensor suggested that the nucleic acid formed a multilayer structure on the electrode surface and that lysozyme binding induced conformational change moved ferrocene close to the surface, increasing the current. In contrast, the second aptamer usually showed a decrease in current in the presence of lysozyme suggesting that the binding resulted in the ferrocene moving away from the surface. In order to evaluate the possible use of these aptasensors for continuous in vivo measurement, needle shaped microelectrodes arrays were produced and the beacon aptamer immobilised on the surface. These electrodes had high impedance which resulted in low sensitivity, however lysozyme binding could still be detected using electrochemical impedance spectroscopy with ferrocyanide in solution. These microspike arrays could also be used for glucose sensing following modification with glucose oxidase