Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

A proposed validation framework for expert elicited Bayesian Networks

The popularity of Bayesian Network modelling of complex domains using expert elicitation has raised questions of how one might validate such a model given that no objective dataset exists for the model. Past attempts at delineating a set of tests for establishing confidence in an entirely expert-elicited model have focused on single types of validity stemming from individual sources of uncertainty within the model. This paper seeks to extend the frameworks proposed by earlier researchers by drawing upon other disciplines where measuring latent variables is also an issue. We demonstrate that even in cases where no data exist at all there is a broad range of validity tests that can be used to establish confidence in the validity of a Bayesian Belief Network.

Spatial and temporal clusters of Barmah Forest virus disease in Queensland, Australia

Objective To identify the spatial and temporal clusters of Barmah Forest virus (BFV) disease in Queensland in Australia, using geographical information systems (GIS) and spatial scan statistic (SaTScan). Methods We obtained BFV disease cases, population and statistical local areas boundary data from Queensland Health and Australian Bureau of Statistics respectively during 1992-2008 for Queensland. A retrospective Poisson-based analysis using SaTScan software and method was conducted in order to identify both purely spatial and space-time BFV disease high-rate clusters. A spatial cluster size of a proportion of the population and a 200km circle radius and varying time windows from 1 month to 12 months were chosen (for the space-time analysis). Results The spatial scan statistic detected a most likely significant purely spatial cluster (including 23 SLAs) and a most likely significant space-time cluster (including 24 SLAs) in approximately the same location. Significant secondary clusters were also identified from both the analyses in several locations. Conclusions This study provides evidence of the existence of statistically significant BFV disease clusters in Queensland, Australia. The study also demonstrated the relevance and applicability of SaTScan in analysing on-going surveillance data to identify clusters to facilitate the development of effective BFV disease prevention and control strategies in Queensland, Australia.

A general method to determine sampling windows for nonlinear mixed effects models with an application to population pharmacokinetic studies

Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models.

Implementing an enhanced repository statistics system for QUT ePrints

Queensland University of Technology (QUT) was one of the first universities in Australia to establish an institutional repository. Launched in November 2003, the repository (QUT ePrints) uses the EPrints open source repository software (from Southampton) and has enjoyed the benefit of an institutional deposit mandate since January 2004. Currently (April 2012), the repository holds over 36,000 records, including 17,909 open access publications with another 2,434 publications embargoed but with mediated access enabled via the ‘Request a copy’ button which is a feature of the EPrints software. At QUT, the repository is managed by the library.QUT ePrints (http://eprints.qut.edu.au) The repository is embedded into a number of other systems at QUT including the staff profile system and the University’s research information system. It has also been integrated into a number of critical processes related to Government reporting and research assessment. Internally, senior research administrators often look to the repository for information to assist with decision-making and planning. While some statistics could be drawn from the advanced search feature and the existing download statistics feature, they were rarely at the level of granularity or aggregation required. Getting the information from the ‘back end’ of the repository was very time-consuming for the Library staff. In 2011, the Library funded a project to enhance the range of statistics which would be available from the public interface of QUT ePrints. The repository team conducted a series of focus groups and individual interviews to identify and prioritise functionality requirements for a new statistics ‘dashboard’. The participants included a mix research administrators, early career researchers and senior researchers. The repository team identified a number of business criteria (eg extensible, support available, skills required etc) and then gave each a weighting. After considering all the known options available, five software packages (IRStats, ePrintsStats, AWStats, BIRT and Google Urchin/Analytics) were thoroughly evaluated against a list of 69 criteria to determine which would be most suitable. The evaluation revealed that IRStats was the best fit for our requirements. It was deemed capable of meeting 21 out of the 31 high priority criteria. Consequently, IRStats was implemented as the basis for QUT ePrints’ new statistics dashboards which were launched in Open Access Week, October 2011. Statistics dashboards are now available at four levels; whole-of-repository level, organisational unit level, individual author level and individual item level. The data available includes, cumulative total deposits, time series deposits, deposits by item type, % fulltexts, % open access, cumulative downloads, time series downloads, downloads by item type, author ranking, paper ranking (by downloads), downloader geographic location, domains, internal v external downloads, citation data (from Scopus and Web of Science), most popular search terms, non-search referring websites. The data is displayed in charts, maps and table format. The new statistics dashboards are a great success. Feedback received from staff and students has been very positive. Individual researchers have said that they have found the information to be very useful when compiling a track record. It is now very easy for senior administrators (including the Deputy Vice Chancellor-Research) to compare the full-text deposit rates (i.e. mandate compliance rates) across organisational units. This has led to increased ‘encouragement’ from Heads of School and Deans in relation to the provision of full-text versions.

Fusing loop detector and probe vehicle data to estimate travel time statistics on signalized urban networks

This article presents a methodology that integrates cumulative plots with probe vehicle data for estimation of travel time statistics (average, quartile) on urban networks. The integration reduces relative deviation among the cumulative plots so that the classical analytical procedure of defining the area between the plots as the total travel time can be applied. For quartile estimation, a slicing technique is proposed. The methodology is validated with real data from Lucerne, Switzerland and it is concluded that the travel time estimates from the proposed methodology are statistically equivalent to the observed values.

Spatial inequalities in colorectal and breast cancer survival : premature deaths and associated factors

This study examines the influence of cancer stage, distance to treatment facilities and area disadvantage on breast and colorectal cancer spatial survival inequalities. We also estimate the number of premature deaths after adjusting for cancer stage to quantify the impact of spatial survival inequalities. Population-based descriptive study of residents aged <90 years in Queensland, Australia diagnosed with primary invasive breast (25,202 females) or colorectal (14,690 males, 11,700 females) cancers during 1996-2007. Bayesian hierarchical models explored relative survival inequalities across 478 regions. Cancer stage and disadvantage explained the spatial inequalities in breast cancer survival, however spatial inequalities in colorectal cancer survival persisted after adjustment. Of the 6,019 colorectal cancer deaths within 5 years of diagnosis, 470 (8%) were associated with spatial inequalities in non-diagnostic factors, i.e. factors beyond cancer stage at diagnosis. For breast cancers, of 2,412 deaths, 170 (7%) were related to spatial inequalities in non-diagnostic factors. Quantifying premature deaths can increase incentive for action to reduce these spatial inequalities.