On the order of the fractional Laplacian in determining the spatio-temporal evolution of a space-fractional model of cardiac electrophysiology

Space-fractional operators have been used with success in a variety of practical applications to describe transport processes in media characterised by spatial connectivity properties and high structural heterogeneity altering the classical laws of diffusion. This study provides a systematic investigation of the spatio-temporal effects of a space-fractional model in cardiac electrophysiology. We consider a simplified model of electrical pulse propagation through cardiac tissue, namely the monodomain formulation of the Beeler-Reuter cell model on insulated tissue fibres, and obtain a space-fractional modification of the model by using the spectral definition of the one-dimensional continuous fractional Laplacian. The spectral decomposition of the fractional operator allows us to develop an efficient numerical method for the space-fractional problem. Particular attention is paid to the role played by the fractional operator in determining the solution behaviour and to the identification of crucial differences between the non-fractional and the fractional cases. We find a positive linear dependence of the depolarization peak height and a power law decay of notch and dome peak amplitudes for decreasing orders of the fractional operator. Furthermore, we establish a quadratic relationship in conduction velocity, and quantify the increasingly wider action potential foot and more pronounced dispersion of action potential duration, as the fractional order is decreased. A discussion of the physiological interpretation of the presented findings is made.

Spatial model of site index based on Y-ray spectrometry and a digital elevation model for two Pinus species in Tuan Toolara State Forest, Queensland, Australia

Site index prediction models are an important aid for forest management and planning activities. This paper introduces a multiple regression model for spatially mapping and comparing site indices for two Pinus species (Pinus elliottii Engelm. and Queensland hybrid, a P. elliottii x Pinus caribaea Morelet hybrid) based on independent variables derived from two major sources: g-ray spectrometry (potassium (K), thorium (Th), and uranium (U)) and a digital elevation model (elevation, slope, curvature, hillshade, flow accumulation, and distance to streams). In addition, interpolated rainfall was tested. Species were coded as a dichotomous dummy variable; interaction effects between species and the g-ray spectrometric and geomorphologic variables were considered. The model explained up to 60% of the variance of site index and the standard error of estimate was 1.9 m. Uranium, elevation, distance to streams, thorium, and flow accumulation significantly correlate to the spatial variation of the site index of both species, and hillshade, curvature, elevation and slope accounted for the extra variability of one species over the other. The predicted site indices varied between 20.0 and 27.3 m for P. elliottii, and between 23.1 and 33.1 m for Queensland hybrid; the advantage of Queensland hybrid over P. elliottii ranged from 1.8 to 6.8 m, with the mean at 4.0 m. This compartment-based prediction and comparison study provides not only an overview of forest productivity of the whole plantation area studied but also a management tool at compartment scale.

Mathematical model of arterial stenosis

A mathematical model for pulsatile flow in a partially occluded tube is presented. The problem has applications in studying the effects of blood flow characteristics on atherosclerotic development. The model brings out the importance of the pulsatility of blood flow on separation and the stress distribution. The results obtained show fairly good agreement with the available experimental results.

Choosing a model of maternity care: decision support needs of Australian women

- BACKGROUND Access to information on the features and outcomes associated with the various models of maternity care available in Australia is vital for women's informed decision-making. This study sought to identify women's preferences for information access and decision-making involvement, as well as their priority information needs, for model of care decision-making. - METHODS A convenience sample of adult women of childbearing age in Queensland, Australia were recruited to complete an online survey assessing their model of care decision support needs. Knowledge on models of care and socio-demographic characteristics were also assessed. - RESULTS Altogether, 641 women provided usable survey data. Of these women, 26.7 percent had heard of all available models of care before starting the survey. Most women wanted access to information on models of care (90.4%) and an active role in decision-making (99.0%). Nine priority information needs were identified: cost, access to choice of mode of birth and care provider, after hours provider contact, continuity of carer in labor/birth, mobility during labor, discussion of the pros/cons of medical procedures, rates of skin-to-skin contact after birth, and availability at a preferred birth location. This information encompassed the priority needs of women across age, birth history, and insurance status subgroups. - CONCLUSIONS This study demonstrates Australian women's unmet needs for information that supports them to effectively compare available options for model of maternity care. Findings provide clear direction on what information should be prioritized and ideal channels for information access to support quality decision-making in practice.

Analytical model of reactive transport processes with spatially variable coefficients

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

Zebrafish as a model of Parkinson's disease

Parkinson’s disease (PD) is the second most common neurodegenerative disease among the elderly. Its etiology is unknown and no disease-modifying drugs are available. Thus, more information concerning its pathogenesis is needed. Among other genes, mutated PTEN-induced kinase 1 (PINK1) has been linked to early-onset and sporadic PD, but its mode of action is poorly understood. Most animal models of PD are based on the use of the neurotoxin 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). MPTP is metabolized to MPP+ by monoamine oxidase B (MAO B) and causes cell death of dopaminergic neurons in the substantia nigra in mammals. Zebrafish has been a widely used model organism in developmental biology, but is now emerging as a model for human diseases due to its ideal combination of properties. Zebrafish are inexpensive and easy to maintain, develop rapidly, breed in large quantities producing transparent embryos, and are readily manipulated by various methods, particularly genetic ones. In addition, zebrafish are vertebrate animals and results derived from zebrafish may be more applicable to mammals than results from invertebrate genetic models such as Drosophila melanogaster and Caenorhabditis elegans. However, the similarity cannot be taken for granted. The aim of this study was to establish and test a PD model using larval zebrafish. The developing monoaminergic neuronal systems of larval zebrafish were investigated. We identified and classified 17 catecholaminergic and 9 serotonergic neuron populations in the zebrafish brain. A 3-dimensional atlas was created to facilitate future research. Only one gene encoding MAO was found in the zebrafish genome. Zebrafish MAO showed MAO A-type substrate specificity, but non-A-non-B inhibitor specificity. Distribution of MAO in larval and adult zebrafish brains was both diffuse and distinctly cellular. Inhibition of MAO during larval development led to markedly elevated 5-hydroxytryptamine (serotonin, 5-HT) levels, which decreased the locomotion of the fish. MPTP exposure caused a transient loss of cells in specific aminergic cell populations and decreased locomotion. MPTP-induced changes could be rescued by the MAO B inhibitor deprenyl, suggesting a role for MAO in MPTP toxicity. MPP+ affected only one catecholaminergic cell population; thus, the action of MPP+ was more selective than that of MPTP. The zebrafish PINK1 gene was cloned in zebrafish, and morpholino oligonucleotides were used to suppress its expression in larval zebrafish. The functional domains and expression pattern of zebrafish PINK1 resembled those of other vertebrates, suggesting that zebrafish is a feasible model for studying PINK1. Translation inhibition resulted in cell loss of the same catecholaminergic cell populations as MPTP and MPP+. Inactivation of PINK1 sensitized larval zebrafish to subefficacious doses of MPTP, causing a decrease in locomotion and cell loss in one dopaminergic cell population. Zebrafish appears to be a feasible model for studying PD, since its aminergic systems, mode of action of MPTP, and functions of PINK1 resemble those of mammalians. However, the functions of zebrafish MAO differ from the two forms of MAO found in mammals. Future studies using zebrafish PD models should utilize the advantages specific to zebrafish, such as the ability to execute large-scale genetic or drug screens.

Model of Strangriede Cemetery during World War II when it was a holding area for Jews to be deported; Hannover Cemeteries

Digital Image

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.

Glass transition. A new approach based on cluster model of glasses

The structure of real glasses has been considered to be microheterogeneous, composed of clusters and connective tissue. Particles in the cluster are assumed to be highly correlated in positions. The tissue is considered to have a truly amorphous structure with its particles vibrating in highly anharmonic potentials. Glass transition is recognized as corresponding to the melting of clusters. A simple mathematical model has been developed which accounts for various known features associated with glass transition, such as range of glass transition temperature,T g, variation ofT g with pressure, etc. Expressions for configurational thermodynamic properties and transport properties of glass forming systems are derived from the model. The relevence and limitations of the model are also discussed.

A multi-field bio-economic model of irrigated grain-cotton farming systems.

We present a participatory modelling framework that integrates information from interviews and discussions with farmers and consultants, with dynamic bio-economic models to answer complex questions on the allocation of limited resources at the farm business level. Interviews and discussions with farmers were used to: describe the farm business; identify relevant research questions; identify potential solutions; and discuss and learn from the whole-farm simulations. The simulations are done using a whole-farm, multi-field configuration of APSIM (APSFarm). APSFarm results were validated against farmers' experience. Once the model was accepted by the participating farmers as a fair representation of their farm business, the model was used to explore changes in the tactical or strategic management of the farm and results were then discussed to identify feasible options for improvement. Here we describe the modelling framework and present an example of the application of integrative whole farm system tools to answer relevant questions from an irrigated farm business case study near Dalby (151.27E - 27.17S), Queensland, Australia. Results indicated that even though cotton crops generates more farm income per hectare a more diversified rotation with less cotton would be relatively more profitable, with no increase in risk, as a more cotton dominated traditional rotation. Results are discussed in terms of the benefits and constraints from developing and applying more integrative approaches to represent farm businesses and their management in participatory research projects with the aim of designing more profitable and sustainable irrigated farming systems.

Model of Strangriede Cemetery during World War II when it was a holding area for Jews to be deported; Hannover Cemeteries

Digital Image

Constructing a new individual-based model of phosphine resistance in lesser grain borer (Rhyzopertha dominica): do we need to include two loci rather than one?

In this article, we describe and compare two individual-based models constructed to investigate how genetic factors influence the development of phosphine resistance in lesser grain borer (R. dominica). One model is based on the simplifying assumption that resistance is conferred by alleles at a single locus, while the other is based on the more realistic assumption that resistance is conferred by alleles at two separate loci. We simulated the population dynamic of R. dominica in the absence of phosphine fumigation, and under high and low dose phosphine treatments, and found important differences between the predictions of the two models in all three cases. In the absence of fumigation, starting from the same initial frequencies of genotypes, the two models tended to different stable frequencies, although both reached Hardy-Weinberg equilibrium. The one-locus model exaggerated the equilibrium proportion of strongly resistant beetles by 3.6 times, compared to the aggregated predictions of the two-locus model. Under a low dose treatment the one-locus model overestimated the proportion of strongly resistant individuals within the population and underestimated the total population numbers compared to the two-locus model. These results show the importance of basing resistance evolution models on realistic genetics and that using oversimplified one-locus models to develop pest control strategies runs the risk of not correctly identifying tactics to minimise the incidence of pest infestation.

Dietary modulation of β-catenin signalling in an experimental model of colon cancer

Colorectal cancer is among the major cancers and one of the leading causes of cancer-related deaths in Western societies. Its occurrence is strongly affected by environmental factors such as diet. Thus, for preventative strategies it is vitally important to understand the mechanisms that stimulate adenoma growth and development towards accelerated malignancy or, in contrast, attenuate them to remain in quiescence for periods as long as decades. The main objective of this study was to investigate whether diet is able to modulate β-catenin signalling related to the promotion or prevention of intestinal tumourigenesis in an animal model of colon cancer, the Min/+ mouse. A series of dietary experiments with Min/+ mice were performed where fructo-oligosaccharide inulin was used for tumour promotion and four berries, bilberry (Vaccinium myrtillus), lingonberry (Vaccinium vitis-idaea), cloudberry (Rubus chamaemorus) and white currant (Ribes x pallidum), were used for tumour prevention. The adenomas (Apc-/-) and surrounding normal-appearing mucosa (Apc+/-) were investigated separately due to their mutational and functional differences. Tumour promotive and preventive diets had opposite effects on β-catenin signalling in the adenomas that was related to the different adenoma growth effects of dietary inulin and berries. The levels of nuclear β-catenin and cyclin D1 combined with size of the adenomas in the treatment groups suggests that diets induced differences in the cancerous process. Adenomas progressing to malignant carcinomas are most likely found in the sub-groups having the highest levels of β-catenin. On the other hand, adenomas staying quiescent for a long period of time are most probably found in the cloudberry or white currant diet groups. The levels of membranous E-cadherin and β-catenin increased as the adenomas in the inulin diet group grew, which could be a result of the overall increase in the protein levels of the cell. Therefore, the increasing levels of membranous β-catenin in Min/+ mice adenomas would be undesirable, due to the simultaneous increase in oncogenic nuclear β-catenin. We propose that the decreased amount of membranous β-catenin in benign adenomas of berry groups also means a decrease in the nuclear pool of β-catenin. Tumour promotion, but not the tumour prevention, influenced β-catenin signalling already in the normal appearing mucosa. Inulin-induced tumour promotion was related to β-catenin signalling in Min/+ mice, and in WT mice changes were also visible. The preventative effects of berries in the initiation phase were not mediated by β-catenin signalling. Our results suggest that, in addition to the number, size, and growth rate of adenomatous polyps, the signalling pattern of the adenomas should be considered when evaluating preventative dietary strategies.