Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

An estimation of crash risks using a log-linear model and the induced exposure technique

Prevention and safety promotion programmes. Traditionally, in-depth investigations of crash risks are conducted using exposure controlled study or case-control methodology. However, these studies need either observational data for control cases or exogenous exposure data like vehicle-kilometres travel, entry flow or product of conflicting flow for a particular traffic location, or a traffic site. These data are not readily available and often require extensive data collection effort on a system-wide basis. Aim: The objective of this research is to propose an alternative methodology to investigate crash risks of a road user group in different circumstances using readily available traffic police crash data. Methods: This study employs a combination of a log-linear model and the quasi-induced exposure technique to estimate crash risks of a road user group. While the log-linear model reveals the significant interactions and thus the prevalence of crashes of a road user group under various sets of traffic, environmental and roadway factors, the quasi-induced exposure technique estimates relative exposure of that road user in the same set of explanatory variables. Therefore, the combination of these two techniques provides relative measures of crash risks under various influences of roadway, environmental and traffic conditions. The proposed methodology has been illustrated using Brisbane motorcycle crash data of five years. Results: Interpretations of results on different combination of interactive factors show that the poor conspicuity of motorcycles is a predominant cause of motorcycle crashes. Inability of other drivers to correctly judge the speed and distance of an oncoming motorcyclist is also evident in right-of-way violation motorcycle crashes at intersections. Discussion and Conclusions: The combination of a log-linear model and the induced exposure technique is a promising methodology and can be applied to better estimate crash risks of other road users. This study also highlights the importance of considering interaction effects to better understand hazardous situations. A further study on the comparison between the proposed methodology and case-control method would be useful.

On the significance of omitted variables in intersection crash modeling

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causes and contributing factors—rest upon the pursuit of numerous lines of research inquiry. The research community has focused considerable attention on analytical methods development (negative binomial models, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might logically seek to know which lines of inquiry might provide the most significant improvements in understanding crash causation and/or prediction. It is the contention of this paper that the exclusion of important variables (causal or surrogate measures of causal variables) cause omitted variable bias in model estimation and is an important and neglected line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant opportunities to better understand contributing factors and/or causes of crashes. This study examines the role of important variables (other than Average Annual Daily Traffic (AADT)) that are generally omitted from intersection crash prediction models. In addition to the geometric and traffic regulatory information of intersection, the proposed model includes many spatial factors such as local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools—representing a mix of potential environmental and human factors that are theoretically important, but rarely used. Results suggest that these variables in addition to AADT have significant explanatory power, and their exclusion leads to omitted variable bias. Provided is evidence that variable exclusion overstates the effect of minor road AADT by as much as 40% and major road AADT by 14%.

A new approach for trip generation estimation for use in traffic impact assessments

Findings from an online survey conducted by Queensland University of Technology (QUT) shows that Australia is suffering from a lack of data reflecting trip generation for use in Traffic Impact Assessments (TIAs). Current independent variables for trip generation estimation are not able to create robust outcomes as well. It is also challenging to account for the impact of the new development on public and active transport as well as the effect of trip chaining behaviour in Australian TIA studies. With this background in mind, research is being implemented by QUT to find a new approach developing a combined model of trip generation and mode choice with consideration of trip chaining effects. It is expected that the model will provide transferable outcomes as it is developed based on socio-demographic parameters. Child Care Centres within the Brisbane area have been nominated for model development. At the time, the project is in the data collection phase. Findings from the pilot survey associated with capturing trip chaining and mode choice information reveal that applying questionnaire is able to capture required information in an acceptable level. The result also reveals that several centres within an area should be surveyed in order to provide sufficient data for trip chaining and modal split analysis.

A new approach for trip generation estimation for TIA

Transport Impact Assessment (TIA) -Generally a short range transport planning activity -Assess transport impacts of new developments or expansions -Present solutions to mitigate impacts Problems with TIA Process -Private vehicles focus (i.e. Veh Trip Ends) -Proxy variables (e.g. 100sqm GFA) -Trip generation rates (e.g. VTE/proxy) -Little info/guidance on trip chaining effects -Little info/guidance on non-PV modes Requires significant professional judgment

Marginal reversible jump Markov chain Monte Carlo with application to motor unit number estimation

Motor unit number estimation (MUNE) is a method which aims to provide a quantitative indicator of progression of diseases that lead to loss of motor units, such as motor neurone disease. However the development of a reliable, repeatable and fast real-time MUNE method has proved elusive hitherto. Ridall et al. (2007) implement a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm to produce a posterior distribution for the number of motor units using a Bayesian hierarchical model that takes into account biological information about motor unit activation. However we find that the approach can be unreliable for some datasets since it can suffer from poor cross-dimensional mixing. Here we focus on improved inference by marginalising over latent variables to create the likelihood. In particular we explore how this can improve the RJMCMC mixing and investigate alternative approaches that utilise the likelihood (e.g. DIC (Spiegelhalter et al., 2002)). For this model the marginalisation is over latent variables which, for a larger number of motor units, is an intractable summation over all combinations of a set of latent binary variables whose joint sample space increases exponentially with the number of motor units. We provide a tractable and accurate approximation for this quantity and also investigate simulation approaches incorporated into RJMCMC using results of Andrieu and Roberts (2009).

Error and uncertainty of adult age estimation of the pubic symphysis in an Australian sub-population using computed tomography

After attending this presentation, attendees will gain awareness of: (1) the error and uncertainty associated with the application of the Suchey-Brooks (S-B) method of age estimation of the pubic symphysis to a contemporary Australian population; (2) the implications of sexual dimorphism and bilateral asymmetry of the pubic symphysis through preliminary geometric morphometric assessment; and (3) the value of three-dimensional (3D) autopsy data acquisition for creating forensic anthropological standards. This presentation will impact the forensic science community by demonstrating that, in the absence of demographically sound skeletal collections, post-mortem autopsy data provides an exciting platform for the construction of large contemporary ‘virtual osteological libraries’ for which forensic anthropological research can be conducted on Australian individuals. More specifically, this study assesses the applicability and accuracy of the S-B method to a contemporary adult population in Queensland, Australia, and using a geometric morphometric approach, provides an insight to the age-related degeneration of the pubic symphysis. Despite the prominent use of the Suchey-Brooks (1990) method of age estimation in forensic anthropological practice, it is subject to intrinsic limitations, with reports of differential inter-population error rates between geographical locations1-4. Australian forensic anthropology is constrained by a paucity of population specific standards due to a lack of repositories of documented skeletons. Consequently, in Australian casework proceedings, standards constructed from predominately American reference samples are applied to establish a biological profile. In the global era of terrorism and natural disasters, more specific population standards are required to improve the efficiency of medico-legal death investigation in Queensland. The sample comprises multi-slice computed tomography (MSCT) scans of the pubic symphysis (slice thickness: 0.5mm, overlap: 0.1mm) on 195 individuals of caucasian ethnicity aged 15-70 years. Volume rendering reconstruction of the symphyseal surface was conducted in Amira® (v.4.1) and quantitative analyses in Rapidform® XOS. The sample was divided into ten-year age sub-sets (eg. 15-24) with a final sub-set of 65-70 years. Error with respect to the method’s assigned means were analysed on the basis of bias (directionality of error), inaccuracy (magnitude of error) and percentage correct classification of left and right symphyseal surfaces. Morphometric variables including surface area, circumference, maximum height and width of the symphyseal surface and micro-architectural assessment of cortical and trabecular bone composition were quantified using novel automated engineering software capabilities. The results of this study demonstrated correct age classification utilizing the mean and standard deviations of each phase of the S-B method of 80.02% and 86.18% in Australian males and females, respectively. Application of the S-B method resulted in positive biases and mean inaccuracies of 7.24 (±6.56) years for individuals less than 55 years of age, compared to negative biases and mean inaccuracies of 5.89 (±3.90) years for individuals greater than 55 years of age. Statistically significant differences between chronological and S-B mean age were demonstrated in 83.33% and 50% of the six age subsets in males and females, respectively. Asymmetry of the pubic symphysis was a frequent phenomenon with 53.33% of the Queensland population exhibiting statistically significant (χ2 - p<0.01) differential phase classification of left and right surfaces of the same individual. Directionality was found in bilateral asymmetry, with the right symphyseal faces being slightly older on average and providing more accurate estimates using the S-B method5. Morphometric analysis verified these findings, with the left surface exhibiting significantly greater circumference and surface area than the right (p<0.05). Morphometric analysis demonstrated an increase in maximum height and width of the surface with age, with most significant changes (p<0.05) occurring between the 25-34 and 55-64 year age subsets. These differences may be attributed to hormonal components linked to menopause in females and a reduction in testosterone in males. Micro-architectural analysis demonstrated degradation of cortical composition with age, with differential bone resorption between the medial, ventral and dorsal surfaces of the pubic symphysis. This study recommends that the S-B method be applied with caution in medico-legal death investigations of unknown skeletal remains in Queensland. Age estimation will always be accompanied by error; therefore this study demonstrates the potential for quantitative morphometric modelling of age related changes of the pubic symphysis as a tool for methodological refinement, providing a rigor and robust assessment to remove the subjectivity associated with current pelvic aging methods.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women

Lean body mass (LBM) and muscle mass remains difficult to quantify in large epidemiological studies due to non-availability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n= 2220; 36% females; age 18-79 y) representing a wide range of body mass index (14-44 kg/m2) participated in this study. Their LBM including ALST was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height and weight explained > 90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of SFTs) increased the explained variation by 5-8% in the fully adjusted models predicting LBM and ALST. More complex equations using all the above anthropometric variables could predict the DXA measured LBM and ALST accurately as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively) as well as good agreement by Bland Altman analyses. These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition.

Traffic state estimation from partial Bluetooth and volume observations : case study in the Brisbane metropolitan area

The application of the Bluetooth (BT) technology to transportation has been enabling researchers to make accurate travel time observations, in freeway and arterial roads. The Bluetooth traffic data are generally incomplete, for they only relate to those vehicles that are equipped with Bluetooth devices, and that are detected by the Bluetooth sensors of the road network. The fraction of detected vehicles versus the total number of transiting vehicles is often referred to as Bluetooth Penetration Rate (BTPR). The aim of this study is to precisely define the spatio-temporal relationship between the quantities that become available through the partial, noisy BT observations; and the hidden variables that describe the actual dynamics of vehicular traffic. To do so, we propose to incorporate a multi- class traffic model into a Sequential Montecarlo Estimation algorithm. Our framework has been applied for the empirical travel time investigations into the Brisbane Metropolitan region.

Development and validation of anthropometric prediction equations for estimation of body fat in Indonesian men

Body composition of 292 males aged between 18 and 65 years was measured using the deuterium oxide dilution technique. Participants were divided into development (n=146) and cross-validation (n=146) groups. Stature, body weight, skinfold thickness at eight sites, girth at five sites, and bone breadth at four sites were measured and body mass index (BMI), waist-to-hip ratio (WHR), and waist-to-stature ratio (WSR) calculated. Equations were developed using multiple regression analyses with skinfolds, breadth and girth measures, BMI, and other indices as independent variables and percentage body fat (%BF) determined from deuterium dilution technique as the reference. All equations were then tested in the cross-validation group. Results from the reference method were also compared with existing prediction equations by Durnin and Womersley (1974), Davidson et al (2011), and Gurrici et al (1998). The proposed prediction equations were valid in our cross-validation samples with r=0.77- 0.86, bias 0.2-0.5%, and pure error 2.8-3.6%. The strongest was generated from skinfolds with r=0.83, SEE 3.7%, and AIC 377.2. The Durnin and Womersley (1974) and Davidson et al (2011) equations significantly (p<0.001) underestimated %BF by 1.0 and 6.9% respectively, whereas the Gurrici et al (1998) equation significantly (p<0.001) overestimated %BF by 3.3% in our cross-validation samples compared to the reference. Results suggest that the proposed prediction equations are useful in the estimation of %BF in Indonesian men.

Estimation of biodiesel properties from chemical composition – An artificial neural network (ANN) approach

Biodiesel, produced from renewable feedstock represents a more sustainable source of energy and will therefore play a significant role in providing the energy requirements for transportation in the near future. Chemically, all biodiesels are fatty acid methyl esters (FAME), produced from raw vegetable oil and animal fat. However, clear differences in chemical structure are apparent from one feedstock to the next in terms of chain length, degree of unsaturation, number of double bonds and double bond configuration-which all determine the fuel properties of biodiesel. In this study, prediction models were developed to estimate kinematic viscosity of biodiesel using an Artificial Neural Network (ANN) modelling technique. While developing the model, 27 parameters based on chemical composition commonly found in biodiesel were used as the input variables and kinematic viscosity of biodiesel was used as output variable. Necessary data to develop and simulate the network were collected from more than 120 published peer reviewed papers. The Neural Networks Toolbox of MatLab R2012a software was used to train, validate and simulate the ANN model on a personal computer. The network architecture and learning algorithm were optimised following a trial and error method to obtain the best prediction of the kinematic viscosity. The predictive performance of the model was determined by calculating the coefficient of determination (R2), root mean squared (RMS) and maximum average error percentage (MAEP) between predicted and experimental results. This study found high predictive accuracy of the ANN in predicting fuel properties of biodiesel and has demonstrated the ability of the ANN model to find a meaningful relationship between biodiesel chemical composition and fuel properties. Therefore the model developed in this study can be a useful tool to accurately predict biodiesel fuel properties instead of undertaking costly and time consuming experimental tests.

Distribution harmonic state estimation based on a modified PSO considering parameters uncertainty

This paper presents a new algorithm based on a Modified Particle Swarm Optimization (MPSO) to estimate the harmonic state variables in a distribution networks. The proposed algorithm performs the estimation for both amplitude and phase of each injection harmonic currents by minimizing the error between the measured values from Phasor Measurement Units (PMUs) and the values computed from the estimated parameters during the estimation process. The proposed algorithm can take into account the uncertainty of the harmonic pseudo measurement and the tolerance in the line impedances of the network as well as the uncertainty of the Distributed Generators (DGs) such as Wind Turbines (WTs). The main features of the proposed MPSO algorithm are usage of a primary and secondary PSO loop and applying the mutation function. The simulation results on 34-bus IEEE radial and a 70-bus realistic radial test networks are presented. The results demonstrate that the speed and the accuracy of the proposed Distribution Harmonic State Estimation (DHSE) algorithm are very excellent compared to the algorithms such as Weight Least Square (WLS), Genetic Algorithm (GA), original PSO, and Honey Bees Mating Optimization (HBMO).

A novel algorithm based on honey bee mating optimization for distribution harmonic state estimation including distributed generators

This paper presents a new algorithm based on honey-bee mating optimization (HBMO) to estimate harmonic state variables in distribution networks including distributed generators (DGs). The proposed algorithm performs estimation for both amplitude and phase of each harmonics by minimizing the error between the measured values from phasor measurement units (PMUs) and the values computed from the estimated parameters during the estimation process. Simulation results on two distribution test system are presented to demonstrate that the speed and accuracy of proposed distribution harmonic state estimation (DHSE) algorithm is extremely effective and efficient in comparison with the conventional algorithms such as weight least square (WLS), genetic algorithm (GA) and tabu search (TS).

Distribution harmonic state estimation based on a hybrid PSO and SA algorithm considering parameters uncertainty

This paper presents a new algorithm based on a Hybrid Particle Swarm Optimization (PSO) and Simulated Annealing (SA) called PSO-SA to estimate harmonic state variables in distribution networks. The proposed algorithm performs estimation for both amplitude and phase of each harmonic currents injection by minimizing the error between the measured values from Phasor Measurement Units (PMUs) and the values computed from the estimated parameters during the estimation process. The proposed algorithm can take into account the uncertainty of the harmonic pseudo measurement and the tolerance in the line impedances of the network as well as uncertainty of the Distributed Generators (DGs) such as Wind Turbines (WT). The main feature of proposed PSO-SA algorithm is to reach quickly around the global optimum by PSO with enabling a mutation function and then to find that optimum by SA searching algorithm. Simulation results on IEEE 34 bus radial and a realistic 70-bus radial test networks are presented to demonstrate the speed and accuracy of proposed Distribution Harmonic State Estimation (DHSE) algorithm is extremely effective and efficient in comparison with the conventional algorithms such as Weight Least Square (WLS), Genetic Algorithm (GA), original PSO and Honey Bees Mating Optimization (HBMO) algorithm.