Bridging experiments, models and simulations : an integrative approach to validation in computational cardiac electrophysiology

Computational models in physiology often integrate functional and structural information from a large range of spatio-temporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and scepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace and refine animal experiments. A fundamental requirement to fulfil these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations between experiments, models and simulations in cardiac electrophysiology. We describe the processes, data and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. Validation must therefore take into account the complex interplay between models, simulations and experiments. Key points for developing strategies for validation are: 1) understanding sources of bio-variability is crucial to the comparison between simulation and experimental results; 2) robustness of techniques and tools is a pre-requisite to conducting physiological investigations using the MSE system; 3) definition and adoption of standards facilitates interoperability of experiments, models and simulations; 4) physiological validation must be understood as an iterative process that defines the specific aspects of electrophysiology the MSE system targets, and is driven by advancements in experimental and computational methods and the combination of both.

Mathematical modelling of intramembranous bone formation during fracture healing

During fracture healing, many complex and cryptic interactions occur between cells and bio-chemical molecules to bring about repair of damaged bone. In this thesis two mathematical models were developed, concerning the cellular differentiation of osteoblasts (bone forming cells) and the mineralisation of new bone tissue, allowing new insights into these processes. These models were mathematically analysed and simulated numerically, yielding results consistent with experimental data and highlighting the underlying pattern formation structure in these aspects of fracture healing.

Meta-analysis of prevalence

Meta-analysis is a method to obtain a weighted average of results from various studies. In addition to pooling effect sizes, meta-analysis can also be used to estimate disease frequencies, such as incidence and prevalence. In this article we present methods for the meta-analysis of prevalence. We discuss the logit and double arcsine transformations to stabilise the variance. We note the special situation of multiple category prevalence, and propose solutions to the problems that arise. We describe the implementation of these methods in the MetaXL software, and present a simulation study and the example of multiple sclerosis from the Global Burden of Disease 2010 project. We conclude that the double arcsine transformation is preferred over the logit, and that the MetaXL implementation of multiple category prevalence is an improvement in the methodology of the meta-analysis of prevalence.

Design, construction and evaluation of systems to predict risk in obstetrics

We present a systematic, practical approach to developing risk prediction systems, suitable for use with large databases of medical information. An important part of this approach is a novel feature selection algorithm which uses the area under the receiver operating characteristic (ROC) curve to measure the expected discriminative power of different sets of predictor variables. We describe this algorithm and use it to select variables to predict risk of a specific adverse pregnancy outcome: failure to progress in labour. Neural network, logistic regression and hierarchical Bayesian risk prediction models are constructed, all of which achieve close to the limit of performance attainable on this prediction task. We show that better prediction performance requires more discriminative clinical information rather than improved modelling techniques. It is also shown that better diagnostic criteria in clinical records would greatly assist the development of systems to predict risk in pregnancy. We present a systematic, practical approach to developing risk prediction systems, suitable for use with large databases of medical information. An important part of this approach is a novel feature selection algorithm which uses the area under the receiver operating characteristic (ROC) curve to measure the expected discriminative power of different sets of predictor variables. We describe this algorithm and use it to select variables to predict risk of a specific adverse pregnancy outcome: failure to progress in labour. Neural network, logistic regression and hierarchical Bayesian risk prediction models are constructed, all of which achieve close to the limit of performance attainable on this prediction task. We show that better prediction performance requires more discriminative clinical information rather than improved modelling techniques. It is also shown that better diagnostic criteria in clinical records would greatly assist the development of systems to predict risk in pregnancy.

Emergency department models of care in the context of care quality and cost: A systematic review

To identify current ED models of care and their impact on care quality, care effectiveness, and cost. A systematic search of key health databases (Medline, CINAHL, Cochrane, EMbase) was conducted to identify literature on ED models of care. Additionally, a focused review of the contents of 11 international and national emergency medicine, nursing and health economic journals (published between 2010 and 2013) was undertaken with snowball identification of references of the most recent and relevant papers. Articles published between 1998 and 2013 in the English language were included for initial review by three of the authors. Studies in underdeveloped countries and not addressing the objectives of the present study were excluded. Relevant details were extracted from the retrieved literature, and analysed for relevance and impact. The literature was synthesised around the study's main themes. Models described within the literature mainly focused on addressing issues at the input, throughput or output stages of ED care delivery. Models often varied to account for site specific characteristics (e.g. onsite inpatient units) or to suit staffing profiles (e.g. extended scope physiotherapist), ED geographical location (e.g. metropolitan or rural site), and patient demographic profile (e.g. paediatrics, older persons, ethnicity). Only a few studies conducted cost-effectiveness analysis of service models. Although various models of delivering emergency healthcare exist, further research is required in order to make accurate and reliable assessments of their safety, clinical effectiveness and cost-effectiveness.

A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

Motorway crash duration and its determinants: Do durations vary across motorways?

Traffic congestion has been a growing issue in many metropolitan areas during recent years, which necessitates the identification of its key contributors and development of sustainable strategies to help decrease its adverse impacts on traffic networks. Road incidents generally and crashes specifically have been acknowledged as the cause of a large proportion of travel delays in urban areas and account for 25% to 60% of traffic congestion on motorways. Identifying the critical determinants of travel delays has been of significant importance to the incident management systems which constantly collect and store the incident duration data. This study investigates the individual and simultaneous differential effects of the relevant determinants on motorway crash duration probabilities. In particular, it applies parametric Accelerated Failure Time (AFT) hazard-based models to develop in-depth insights into how the crash-specific characteristic and the associated temporal and infrastructural determinants impact the duration. AFT models with both fixed and random parameters have been calibrated on one year of traffic crash records from two major Australian motorways in South East Queensland and the differential effects of determinants on crash survival functions have been studied on these two motorways individually. A comprehensive spectrum of commonly used parametric fixed parameter AFT models, including generalized gamma and generalized F families, have been compared to random parameter AFT structures in terms of goodness of fit to the duration data and as a result, the random parameter Weibull AFT model has been selected as the most appropriate model. Significant determinants of motorway crash duration included traffic diversion requirement, crash injury type, number and type of vehicles involved in a crash, day of week and time of day, towing support requirement and damage to the infrastructure. A major finding of this research is that the motorways under study are significantly different in terms of crash durations; such that motorway exhibits durations that are on average 19% shorter compared to the durations on motorway. The differential effects of explanatory variables on crash durations are also different on the two motorways. The detailed presented analysis confirms that, looking at the motorway network as a whole, neglecting the individual differences between roads, can lead to erroneous interpretations of duration and inefficient strategies for mitigating travel delays along a particular motorway.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

Influences of Allee effects in the spreading of malignant tumours

A recent study by Korolev et al. [Nat. Rev. Cancer, 14:371–379, 2014] evidences that the Allee effect—in its strong form, the requirement of a minimum density for cell growth—is important in the spreading of cancerous tumours. We present one of the first mathematical models of tumour invasion that incorporates the Allee effect. Based on analysis of the existence of travelling wave solutions to this model, we argue that it is an improvement on previous models of its kind. We show that, with the strong Allee effect, the model admits biologically relevant travelling wave solutions, with well-defined edges. Furthermore, we uncover an experimentally observed biphasic relationship between the invasion speed of the tumour and the background extracellular matrix density.

Mathematical modelling of human corneal oxygenation and cell kinetics in corneal epithelial wound healing

Healthy transparent cornea depends upon the regulation of fluid, nutrient and oxygen transport through the tissue to sustain cell metabolism and other critical processes for normal functioning. This research considers the corneal geometry and investigates oxygen distribution using a two-dimensional Monod kinetic model, showing that previous studies make assumptions that lead to predictions of near-anoxic levels of oxygen tension in the limbal regions of the cornea. It also considers the comparison of experimental spatial and temporal data with the predictions of novel mathematical models with respect to distributed mitotic rates during corneal epithelial wound healing.

Genome-wide association study of prostate cancer-specific survival

BACKGROUND: Unnecessary intervention and overtreatment of indolent disease are common challenges in clinical management of prostate cancer. Improved tools to distinguish lethal from indolent disease are critical. METHODS: We performed a genome-wide survival analysis of cause-specific death in 24,023 prostate cancer patients (3,513 disease-specific deaths) from the PRACTICAL and BPC3 consortia. Top findings were assessed for replication in a Norwegian cohort (CONOR). RESULTS: We observed no significant association between genetic variants and prostate cancer survival. CONCLUSIONS: Common genetic variants with large impact on prostate cancer survival were not observed in this study. IMPACT: Future studies should be designed for identification of rare variants with large effect sizes or common variants with small effect sizes.

Comparison of ultrafine particle release from hardcopy devices in emission test chambers and office rooms

The release of ultrafine particles (UFP) from laser printers and office equipment was analyzed using a particle counter (FMPS; Fast Mobility Particle Sizer) with a high time resolution, as well as the appropriate mathematical models. Measurements were carried out in a 1 m³ chamber, a 24 m³ chamber and an office. The time-dependent emission rates were calculated for these environments using a deconvolution model, after which the total amount of emitted particles was calculated. The total amounts of released particles were found to be independent of the environmental parameters and therefore, in principle, they were appropriate for the comparison of different printers. On the basis of the time-dependent emission rates, “initial burst” emitters and constant emitters could also be distinguished. In the case of an “initial burst” emitter, the comparison to other devices is generally affected by strong variations between individual measurements. When conducting exposure assessments for UFP in an office, the spatial distribution of the particles also had to be considered. In this work, the spatial distribution was predicted on a case by case basis, using CFD simulation.

A quasi stationary approach to drying kinetics of cylindrical food particulates in a heat pump asisted fluid bed dryer

Experiments were undertaken to study drying kinetics of moist cylindrical shaped food particulates during fluidised bed drying. Cylindrical particles were prepared from Green beans with three different length:diameter ratios, 3:1, 2:1 and 1:1. A batch fluidised bed dryer connected to a heat pump system was used for the experimentation. A Heat pump and fluid bed combination was used to increase overall energy efficiency and achieve higher drying rates. Drying kinetics, were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50o C. Numerous mathematical models can be used to calculate drying kinetics ranging from analytical models with simplified assumptions to empirical models built by regression using experimental data. Empirical models are commonly used for various food materials due to their simpler approach. However problems in accuracy, limits the applications of empirical models. Some limitations of empirical models could be reduced by using semi-empirical models based on heat and mass transfer of the drying operation. One such method is the quasi-stationary approach. In this study, a modified quasi-stationary approach was used to model drying kinetics of the cylindrical food particles at three drying temperatures.

Constraints on the complete optimization of human motion

In sport and exercise biomechanics, forward dynamics analyses or simulations have frequently been used in attempts to establish optimal techniques for performance of a wide range of motor activities. However, the accuracy and validity of these simulations is largely dependent on the complexity of the mathematical model used to represent the neuromusculoskeletal system. It could be argued that complex mathematical models are superior to simple mathematical models as they enable basic mechanical insights to be made and individual-specific optimal movement solutions to be identified. Contrary to some claims in the literature, however, we suggest that it is currently not possible to identify the complete optimal solution for a given motor activity. For a complete optimization of human motion, dynamical systems theory implies that mathematical models must incorporate a much wider range of organismic, environmental and task constraints. These ideas encapsulate why sports medicine specialists need to adopt more individualized clinical assessment procedures in interpreting why performers' movement patterns may differ.

A model to predict hypovigilance during a monotonous task

The driving task requires sustained attention during prolonged periods, and can be performed in highly predictable or repetitive environments. Such conditions could create drowsiness or hypovigilance and impair the ability to react to critical events. Identifying vigilance decrement in monotonous conditions has been a major subject of research, but no research to date has attempted to predict this vigilance decrement. This pilot study aims to show that vigilance decrements due to monotonous tasks can be predicted through mathematical modelling. A short vigilance task sensitive to short periods of lapses of vigilance called Sustained Attention to Response Task is used to assess participants’ performance. This task models the driver’s ability to cope with unpredicted events by performing the expected action. A Hidden Markov Model (HMM) is proposed to predict participants’ hypovigilance. Driver’s vigilance evolution is modelled as a hidden state and is correlated to an observable variable: the participant’s reactions time. This experiment shows that the monotony of the task can lead to an important vigilance decline in less than five minutes. This impairment can be predicted four minutes in advance with an 86% accuracy using HMMs. This experiment showed that mathematical models such as HMM can efficiently predict hypovigilance through surrogate measures. The presented model could result in the development of an in-vehicle device that detects driver hypovigilance in advance and warn the driver accordingly, thus offering the potential to enhance road safety and prevent road crashes.