Exact series solutions of reactive transport models with general initial conditions

Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

Extending genetic linkage analysis to diffusion tensor images to map single gene effects on brain fiber architecture

We extended genetic linkage analysis - an analysis widely used in quantitative genetics - to 3D images to analyze single gene effects on brain fiber architecture. We collected 4 Tesla diffusion tensor images (DTI) and genotype data from 258 healthy adult twins and their non-twin siblings. After high-dimensional fluid registration, at each voxel we estimated the genetic linkage between the single nucleotide polymorphism (SNP), Val66Met (dbSNP number rs6265), of the BDNF gene (brain-derived neurotrophic factor) with fractional anisotropy (FA) derived from each subject's DTI scan, by fitting structural equation models (SEM) from quantitative genetics. We also examined how image filtering affects the effect sizes for genetic linkage by examining how the overall significance of voxelwise effects varied with respect to full width at half maximum (FWHM) of the Gaussian smoothing applied to the FA images. Raw FA maps with no smoothing yielded the greatest sensitivity to detect gene effects, when corrected for multiple comparisons using the false discovery rate (FDR) procedure. The BDNF polymorphism significantly contributed to the variation in FA in the posterior cingulate gyrus, where it accounted for around 90-95% of the total variance in FA. Our study generated the first maps to visualize the effect of the BDNF gene on brain fiber integrity, suggesting that common genetic variants may strongly determine white matter integrity.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Linear models for endocytic transformations from live cell imaging

Endocytosis is the process by which cells internalise molecules including nutrient proteins from the extracellular media. In one form, macropinocytosis, the membrane at the cell surface ruffles and folds over to give rise to an internalised vesicle. Negatively charged phospholipids within the membrane called phosphoinositides then undergo a series of transformations that are critical for the correct trafficking of the vesicle within the cell, and which are often pirated by pathogens such as Salmonella. Advanced fluorescent video microscopy imaging now allows the detailed observation and quantification of these events in live cells over time. Here we use these observations as a basis for building differential equation models of the transformations. An initial investigation of these interactions was modelled with reaction rates proportional to the sum of the concentrations of the individual constituents. A first order linear system for the concentrations results. The structure of the system enables analytical expressions to be obtained and the problem becomes one of determining the reaction rates which generate the observed data plots. We present results with reaction rates which capture the general behaviour of the reactions so that we now have a complete mathematical model of phosphoinositide transformations that fits the experimental observations. Some excellent fits are obtained with modulated exponential functions; however, these are not solutions of the linear system. The question arises as to how the model may be modified to obtain a system whose solution provides a more accurate fit.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Genetics of brain fiber architecture and intellectual performance

The study is the first to analyze genetic and environmental factors that affect brain fiber architecture and its genetic linkage with cognitive function. We assessed white matter integrity voxelwise using diffusion tensor imaging at high magnetic field (4 Tesla), in 92 identical and fraternal twins. White matter integrity, quantified using fractional anisotropy (FA), was used to fit structural equation models (SEM) at each point in the brain, generating three-dimensional maps of heritability. We visualized the anatomical profile of correlations between white matter integrity and full-scale, verbal, and performance intelligence quotients (FIQ, VIQ, and PIQ). White matter integrity (FA) was under strong genetic control and was highly heritable in bilateral frontal (a 2 = 0.55, p = 0.04, left; a 2 = 0.74, p = 0.006, right), bilateral parietal (a 2 = 0.85, p < 0.001, left; a 2 = 0.84, p < 0.001, right), and left occipital (a 2 = 0.76, p = 0.003) lobes, and was correlated with FIQ and PIQ in the cingulum, optic radiations, superior fronto- occipital fasciculus, internal capsule, callosal isthmus, and the corona radiata (p = 0.04 for FIQ and p = 0.01 for PIQ, corrected for multiple comparisons). In a cross-trait mapping approach, common genetic factors mediated the correlation between IQ and white matter integrity, suggesting a common physiological mechanism for both, and common genetic determination. These genetic brain maps reveal heritable aspects of white matter integrity and should expedite the discovery of single-nucleotide polymorphisms affecting fiber connectivity and cognition.

Air pollution and fasting blood glucose: A longitudinal study in China

Limited studies have examined the associations between air pollutants [particles with diameters of 10um or less (PM10), sulfur dioxide (SO2), and nitrogen dioxide (NO2)] and fasting blood glucose (FBG). We collected data for 27,685 participants who were followed during 2006 and 2008. Generalized Estimating Equation models were used to examine the effects of air pollutants on FBG while controlling for potential confounders. We found that increased exposure to NO2, SO2 and PM10 was significantly associated with increased FBG levels in single pollutant models (p<0.001). For exposure to 4 days’ average of concentrations, a 100 µg/m3 increase in SO2, NO2, and PM10 was associated with 0.17 mmol/L (95%CI: 0.15–0.19), 0.53 mmol/L (95%CI: 0.42–0.65), and 0.11 mmol/L (95%CI: 0.07–0.15) increase in FBG, respectively. In the multi-pollutant models, the effects of SO2 were enhanced, while the effects of NO2 and PM10 were alleviated. The effects of air pollutants on FBG were stronger in female, elderly, and overweight people than in male, young and underweight people. In conclusion, the findings suggest that air pollution increases the levels of FBG. Vulnerable people should pay more attention on highly polluted days to prevent air pollution-related health issues.

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Disclosing donation decisions : the role of organ donor prototypes in an extended theory of planned behaviour

This study explored the role of donor prototype evaluations (perceptions of the typical organ donor) in organ donation communication decisions using an extended theory of planned behaviour (TPB) model. The model incorporated attitude, subjective norm, perceived behavioural control, moral norm, self-identity, and donor prototype evaluations to predict intentions to record consent on an organ donor register and discuss the organ donation decision with significant others. Participants completed surveys assessing the extended TPB constructs related to registering (n = 359) and discussing (n = 282). Results supported a role for donor prototype evaluations in predicting discussing intentions only. Both extended TPB structural equation models were a good fit to the data, accounting for 74 and 76% of the variance in registering and discussing intentions, respectively. Participants’ self-reported discussing behaviour (but not registering behaviour given low numbers of behavioural performers) was assessed 4 weeks later, with discussing intention as the only significant predictor of behaviour (Nagelkerke R2 = 0.11). These findings highlight the impact of people's perceptions of a typical donor on their decisions to discuss their organ donation preference, assisting our understanding of the factors influencing individuals' communication processes in efforts to bridge the gap between organ supply and demand.

The relationship between particulate air pollution and emergency hospital visits for hypertension in Beijing, China

BACKGROUND: A number of epidemiological studies have examined the adverse effect of air pollution on mortality and morbidity. Also, several studies have investigated the associations between air pollution and specific-cause diseases including arrhythmia, myocardial infarction, and heart failure. However, little is known about the relationship between air pollution and the onset of hypertension. OBJECTIVE: To explore the risk effect of particulate matter air pollution on the emergency hospital visits (EHVs) for hypertension in Beijing, China. METHODS: We gathered data on daily EHVs for hypertension, fine particulate matter less than 2.5 microm in aerodynamic diameter (PM(2.5)), particulate matter less than 10 microm in aerodynamic diameter (PM(10)), sulfur dioxide, and nitrogen dioxide in Beijing, China during 2007. A time-stratified case-crossover design with distributed lag model was used to evaluate associations between ambient air pollutants and hypertension. Daily mean temperature and relative humidity were controlled in all models. RESULTS: There were 1,491 EHVs for hypertension during the study period. In single pollutant models, an increase in 10 microg/m(3) in PM(2.5) and PM(10) was associated with EHVs for hypertension with odds ratios (overall effect of five days) of 1.084 (95% confidence interval (CI): 1.028, 1.139) and 1.060% (95% CI: 1.020, 1.101), respectively. CONCLUSION: Elevated levels of ambient particulate matters are associated with an increase in EHVs for hypertension in Beijing, China.

Molecular dynamics studies of the effects of branching characteristics on the crystalline structure of polyethylene

Molecular dynamics simulations were carried out on single chain models of linear low-density polyethylene in vacuum to study the effects of branch length, branch content, and branch distribution on the polymer’s crystalline structure at 300 K. The trans/gauche (t/g) ratios of the backbones of the modeled molecules were calculated and utilized to characterize their degree of crystallinity. The results show that the t/g ratio decreases with increasing branch content regardless of branch length and branch distribution, indicating that branch content is the key molecular parameter that controls the degree of crystallinity. Although t/g ratios of the models with the same branch content vary, they are of secondary importance. However, our data suggests that branch distribution (regular or random) has a significant effect on the degree of crystallinity for models containing 10 hexyl branches/1,000 backbone carbons. The fractions of branches that resided in the equilibrium crystalline structures of the models were also calculated. On average, 9.8% and 2.5% of the branches were found in the crystallites of the molecules with ethyl and hexyl branches while C13 NMR experiments showed that the respective probabilities of branch inclusion for ethyl and hexyl branches are 10% and 6% [Hosoda et al., Polymer 1990, 31, 1999–2005]. However, the degree of branch inclusion seems to be insensitive to the branch content and branch distribution.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Collective motion of dimers

We consider a discrete agent-based model on a one-dimensional lattice and a two-dimensional square lattice, where each agent is a dimer occupying two sites. Agents move by vacating one occupied site in favor of a nearest-neighbor site and obey either a strict simple exclusion rule or a weaker constraint that permits partial overlaps between dimers. Using indicator variables and careful probability arguments, a discrete-time master equation for these processes is derived systematically within a mean-field approximation. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy of the dimer population are obtained. In addition, we show that multiple species of interacting subpopulations give rise to advection-diffusion equations. Averaged discrete simulation data compares very well with the solution to the continuum partial differential equation models. Since many cell types are elongated rather than circular, this work offers insight into population-level behavior of collective cellular motion.

Understanding causal relationships between the built and social environment, health and associated behaviours and risk factors

Introduction: Built environment interventions designed to reduce non-communicable diseases and health inequity, complement urban planning agendas focused on creating more ‘liveable’, compact, pedestrian-friendly, less automobile dependent and more socially inclusive cities.However, what constitutes a ‘liveable’ community is not well defined. Moreover, there appears to be a gap between the concept and delivery of ‘liveable’ communities. The recently funded NHMRC Centre of Research Excellence (CRE) in Healthy Liveable Communities established in early 2014, has defined ‘liveability’ from a social determinants of health perspective. Using purpose-designed multilevel longitudinal data sets, it addresses five themes that address key evidence-base gaps for building healthy and liveable communities. The CRE in Healthy Liveable Communities seeks to generate and exchange new knowledge about: 1) measurement of policy-relevant built environment features associated with leading non-communicable disease risk factors (physical activity, obesity) and health outcomes (cardiovascular disease, diabetes) and mental health; 2) causal relationships and thresholds for built environment interventions using data from longitudinal studies and natural experiments; 3) thresholds for built environment interventions; 4) economic benefits of built environment interventions designed to influence health and wellbeing outcomes; and 5) factors, tools, and interventions that facilitate the translation of research into policy and practice. This evidence is critical to inform future policy and practice in health, land use, and transport planning. Moreover, to ensure policy-relevance and facilitate research translation, the CRE in Healthy Liveable Communities builds upon ongoing, and has established new, multi-sector collaborations with national and state policy-makers and practitioners. The symposium will commence with a brief introduction to embed the research within an Australian health and urban planning context, as well as providing an overall outline of the CRE in Healthy Liveable Communities, its structure and team. Next, an overview of the five research themes will be presented. Following these presentations, the Discussant will consider the implications of the research and opportunities for translation and knowledge exchange. Theme 2 will establish whether and to what extent the neighbourhood environment (built and social) is causally related to physical and mental health and associated behaviours and risk factors. In particular, research conducted as part of this theme will use data from large-scale, longitudinal-multilevel studies (HABITAT, RESIDE, AusDiab) to examine relationships that meet causality criteria via statistical methods such as longitudinal mixed-effect and fixed-effect models, multilevel and structural equation models; analyse data on residential preferences to investigate confounding due to neighbourhood self-selection and to use measurement and analysis tools such as propensity score matching and ‘within-person’ change modelling to address confounding; analyse data about individual-level factors that might confound, mediate or modify relationships between the neighbourhood environment and health and well-being (e.g., psychosocial factors, knowledge, perceptions, attitudes, functional status), and; analyse data on both objective neighbourhood characteristics and residents’ perceptions of these objective features to more accurately assess the relative contribution of objective and perceptual factors to outcomes such as health and well-being, physical activity, active transport, obesity, and sedentary behaviour. At the completion of the Theme 2, we will have demonstrated and applied statistical methods appropriate for determining causality and generated evidence about causal relationships between the neighbourhood environment, health, and related outcomes. This will provide planners and policy makers with a more robust (valid and reliable) basis on which to design healthy communities.

Genetic effects on the cerebellar role in working memory: Same brain, different genes?

Over the past several years, evidence has accumulated showing that the cerebellum plays a significant role in cognitive function. Here we show, in a large genetically informative twin sample (n= 430; aged 16-30. years), that the cerebellum is strongly, and reliably (n=30 rescans), activated during an n-back working memory task, particularly lobules I-IV, VIIa Crus I and II, IX and the vermis. Monozygotic twin correlations for cerebellar activation were generally much larger than dizygotic twin correlations, consistent with genetic influences. Structural equation models showed that up to 65% of the variance in cerebellar activation during working memory is genetic (averaging 34% across significant voxels), most prominently in the lobules VI, and VIIa Crus I, with the remaining variance explained by unique/unshared environmental factors. Heritability estimates for brain activation in the cerebellum agree with those found for working memory activation in the cerebral cortex, even though cerebellar cyto-architecture differs substantially. Phenotypic correlations between BOLD percent signal change in cerebrum and cerebellum were low, and bivariate modeling indicated that genetic influences on the cerebellum are at least partly specific to the cerebellum. Activation on the voxel-level correlated very weakly with cerebellar gray matter volume, suggesting specific genetic influences on the BOLD signal. Heritable signals identified here should facilitate discovery of genetic polymorphisms influencing cerebellar function through genome-wide association studies, to elucidate the genetic liability to brain disorders affecting the cerebellum.