Hyperglycaemia in critical care is common and has been linked to increased mortality and morbidity. Tight control of blood glucose concentrations to more normal levels can significantly reduce the negative outcomes associated with hyperglycaemia. However, hypoglycaemia and glycaemic variability have also been independently shown to increase mortality in critically ill patients. Further complicating the matter, critically ill patients exhibit high inter- and intra patient metabolic variability and thus consistent, safe control of glycaemia has proved very difficult. Model-based and model-derived tight glycaemic control methods have shown significant ability to provide very tight control with little or no hypoglycaemia in the intensive care unit (ICU). The model-based control practised in the Christchurch Hospital ICU uses a physiological model that relies on a single, time-varying parameter, SI, to capture the patient-specific glycaemic response to insulin. As an identified parameter, SI is prone to also capturing other, unintended, dynamics that add variability on multiple timescales. The objective of this research was to enable enhanced glycaemic control by addressing this variability of the SI parameter through better modelling and implementation. An improved model of insulin secretion as a function of blood glucose concentration was developed using data collected from a recent study at the Christchurch Hospital ICU. Separate models were identified for non-diabetic patients and diagnosed, or suspected type II diabetic patients, with R2 = 0.61 and 0.69, respectively. The gradients of the functions identified were comparable to data published in a number of other studies on healthy and diabetic subjects. The transcapilliary diffusion (nI) and cellular clearance (nC) rate parameters were optimised using data from published microdialysis studies. Interactions between these key parameters determine maximum interstitial insulin concentrations available for glucose disposal, and thus directly influence SI. The optimal values of these parameters were determined to be nI = nC = 0.0060 1/min. Models of endogenous glucose production (EGP), as functions of blood glucose concentration and time, were assessed. These models proved unsatisfactory due to difficulties in identifying reliable functions with the available data set. Thus, it was determined that EGP should continue to be treated as a population constant, except during real-time glycaemic control, where the value may be adjusted temporarily to ensure valid SI values. The first 24 hours of ICU stay proved to be a period of significantly increased SI variability, both in terms of hour-to-hour changes and longer-term evolution of level. This behaviour was evident for the entire study cohort as a whole and was particularly pronounced during the first 12-18 hours. The subgroup of cardiovascular surgery patients, in which there was sufficient data for analysis, mirrored the results of the whole cohort, but was found to have even lower and more variable SI. Glucocorticoid steroids were also found to be associated with clinically significant reductions in overall level and increases in hour-to-hour variability of SI. To manage variability caused by factors external to the physiological model, the use of several stochastic models was proposed. Using different models for the early part of ICU stay and for different diagnostic subgroups as well as when patients were receiving certain drug therapies would permit control algorithms to reduce the impact of the SI variability on outcome glycaemia. The impact of measurement timing and BG concentration errors on the variability of SI was assessed. Results indicated that the impact of both sources of errors on SI level was unlikely to be clinically significant. The impact of BG sensor errors on hour-to-hour SI variability was more pronounced. Understanding the effect of sensor and timing errors on SI allows their impact to be reduced by using the 5-95 percentile forecast range of stochastic models during glycaemic control. The performance of the model incorporating the proposed insulin kinetic parameters and secretion enhancements was validated for clinical glycaemic control and virtual trial purposes. This validation was conducted by self- and cross validation on a cohort independent to that with which the model was developed. The use of multiple stochastic models to reduce the impact of this extrinsic variability during glycaemic control was validated using virtual trials.

This thesis investigates the mechanisms underlying drug-induced arrhythmia and pro- poses a new approach for the automated analysis of the electrocardiogram (ECG). The current method of assessing the cardiac safety of new drugs in clinical trials is by the measurement and analysis of the QT interval. However, the sensitivity and specificity of the QT interval has been questioned and alternative biomarkers based on T-wave mor- phology have been proposed in the literature. The mechanisms underlying drug effects on T-wave morphology are not clearly understood. Therefore, a combined approach of for- ward cardiac modelling and inverse ECG analysis is adopted to investigate the effects of sotalol, a compound known to have pro-arrhythmic effects, on ventricular repolarisation. A computational model of sotalol and IKr, an ion channel that plays a critical role in ventricular repolarisation, was developed. This model was incorporated into a model of the human ventricular myocyte, and subsequently arranged in a 1-D fibre model of 200 cells. The model was used to assess the effect of sotalol on IKr, action potential duration and biomarkers of ventricular repolarisation derived from the simulated ECG. In parallel, an automated ECG analysis method based on machine learning, signal processing and time-frequency analysis is developed to identify a number of fiducial points in ECG waveforms so that timing intervals and a smooth T-wave segment can be extracted for morphology analysis. The approach is to train a hidden Markov model (HMM) using a data set of ECG waveforms and the corresponding expert annotations. The signal is first encoded using the undecimated wavelet transform (UWT). The UWT coefficients are used for R-peak detection, signal encoding for the HMM and a wavelet de-noising procedure. Using the Viterbi algorithm, the trained HMM is then applied to a subset of the ECG signal to infer the fiducial points for each heart beat. Furthermore, a method for deriving a confidence measure based on the trained HMM is implemented so that a level of confidence can be associated with the automated annotations. Finally, the T-wave segment is extracted from the de-noised ECG signal for morphology characterisation. This thesis contributes to the literature on automated characterisation of drug ef- fects on ventricular repolarisation in three different ways. Firstly, it investigates the mechanisms underlying the effects of drug inhibition of IKr on ventricular repolarisation as captured by the simulated ECG signal. Secondly, it shows how the combination of UWT encoding and HMM inference can be effectively used to segment 24-hour Holter ECG recordings. Evaluation of the segmentation algorithm on a clinical ECG data set demonstrates the ability of the algorithm to overcome problems associated with existing automated systems, and hence provide a more robust analysis of ECG signals. Finally, the thesis provides insight into the drug effects of sotalol on ventricular repolarisation as captured by biomarkers extracted from the surface ECG.

Cardiovascular disease is a large problem in the intensive care unit (ICU) due to its high prevalence in modern society. In the ICU, intensive monitoring is required to help diagnose cardiac and circulatory dysfunction. However, complex interactions between the patient, disease, and treatment can hide the underlying disorder. As a result, clinical staff must often rely on their skill, intuition, and experience to choose therapy, increasing variability in care and patient outcome. To simplify this clinical scenario, model-based methods have been created to track subject-specific disease and treatment dependent changes in patient condition, using only clinically available measurements. The approach has been tested in two pig studies on acute pulmonary embolism and septic shock and in a human study on surgical recovery from mitral valve replacement. The model-based method was able to track known pathophysiological changes in the subjects and identified key determinants of cardiovascular health such as cardiac preload, afterload, and contractility. These metrics, which can be otherwise difficult to determine clinically, can be used to help provide targets for goal-directed therapies to help provide deliver the optimal level of therapy to the patient. Hence, this model-based approach provides a feasible and potentially practical means of improving patient care in the ICU.

Very premature infants often experience high blood sugar levels as a result of incomplete metabolic development, illness, and stress. High blood sugar levels have been associated with a range of worsened outcomes and increased mortality, but debate exists as to whether high blood sugar levels are a cause of, or marker for, these worsened outcomes. Insulin can be used to lower blood sugar levels, but there is no standard protocol for its use in neonates, and the few clinical studies of insulin use in neonatal intensive care are relatively small and/or have resulted in high incidence of dangerously low blood sugar levels. Hence, there is a need for a safe and effective protocol for controlling blood sugar levels to a normal range in order that potential clinical benefits can be successfully studied in this clinical cohort. This thesis adapted a glucose-insulin model successfully used in adult intensive care for the unique physiology and situation of the very premature infant. The model aims to reflect known physiology. As such, sources and disposal of glucose and insulin within the body are examined using both published data and unique data sets from a study here in New Zealand. In addition, the absorption of glucose from milk feeds is examined. This glucose-insulin physiological model is then used alongside statistical forecasting to develop a protocol for selecting an appropriate insulin dose based on targeting of likely outcomes to a specified target normal range. The protocol is tested in silico using virtual trials, and then clinically implemented, with results showing improved performance over current clinical practice and other published studies. In particular, ~77% of blood glucose is observed within the specified target range across the cohort, and there has been no incidence of dangerously low blood glucose levels. This protocol is thus safe and effective, accounting for inter- and intra- patient variability, and thus enabling patient-specific care.

Functional hyperaemia is an important mechanism by which increased neuronal activity is matched by a rapid and regional increase in blood supply. This mechanism is facilitated by a process known as “neurovascular coupling” – the orchestrated communication system involving the cells that comprise the neurovascular unit (neurons, astrocytes and the smooth muscle and endothelial cells lining arterioles). Blood flow regulation and neurovascular coupling are altered in several pathological states including hypertension, diabetes, Alzheimer’s disease, cortical spreading depression and stroke. By adapting and extending other models found in the literature, we create, for the first time, a mathematical model of the entire neurovascular unit that is capable of simulating two separate neurovascular coupling mechanisms: a potassium- and EET-based and a NO-based mechanism. These models successfully account for several observations seen in experiment. The potassium/EET-based mechanism can achieve arteriolar dilations similar in magnitude (3%) to those observed during a 60-second neuronal activation (modelled as a release of potassium and glutamate into the synaptic cleft). This model also successfully emulates the paradoxical experimental finding that vasoconstriction follows vasodilation when the astrocytic calcium concentration (or perivascular potassium concentration) is increased further. We suggest that the interaction of the changing smooth muscle cell membrane potential and the changing potassium-dependent resting potential of the inwardly rectifying potassium channel are responsible for this effect. Furthermore, our simulations demonstrate that the arteriolar behaviour is profoundly affected by depolarization of the astrocytic cell membrane, and by changes in the rate of perivascular potassium clearance or the volume ratio between the perivascular space and astrocyte. In the modelled NO-based neurovascular coupling mechanism, NO exerts its vasodilatory effects via neuronal and endothelial cell sources. With both sources included, the model achieves a 1% dilation due to a 60-second neuronal activation. When the endothelial contribution to NO production is omitted, the arteriole is more constricted at baseline. Without the endothelial NO contribution, the arteriolar change in diameter during neuronal activity is greater (6%). We hypothesize that NO has a dual purpose in neurovascular coupling: 1) it dixxxvi rectly mediates neurovascular coupling through release by neuronal sources, and 2) it indirectly modulates the size of the neurovascular coupling response by determining the baseline tone. Our physiological models of neurovascular coupling have allowed us to replicate, and explain, some of the phenomena seen in both neurovascular coupling-oriented and clinicallyoriented experimental research. This project highlights the fact that physiological modelling can be used as a tool to understand biological processes in a way that physical experiment cannot always do, and most importantly, can help to elucidate the cellular processes that induce or accompany our most debilitating diseases.