Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Approximation of Bayesian predictive p-values with regression ABC

In the Bayesian framework a standard approach to model criticism is to compare some function of the observed data to a reference predictive distribution. The result of the comparison can be summarized in the form of a p-value, and it's well known that computation of some kinds of Bayesian predictive p-values can be challenging. The use of regression adjustment approximate Bayesian computation (ABC) methods is explored for this task. Two problems are considered. The first is the calibration of posterior predictive p-values so that they are uniformly distributed under some reference distribution for the data. Computation is difficult because the calibration process requires repeated approximation of the posterior for different data sets under the reference distribution. The second problem considered is approximation of distributions of prior predictive p-values for the purpose of choosing weakly informative priors in the case where the model checking statistic is expensive to compute. Here the computation is difficult because of the need to repeatedly sample from a prior predictive distribution for different values of a prior hyperparameter. In both these problems we argue that high accuracy in the computations is not required, which makes fast approximations such as regression adjustment ABC very useful. We illustrate our methods with several samples.

A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.

Macro- and micronutrient disposition in an ex vivo model of extracorporeal membrane oxygenation

Background Extracorporeal membrane oxygenation (ECMO) circuits have been shown to sequester circulating blood compounds such as drugs based on their physicochemical properties. This study aimed to describe the disposition of macro- and micronutrients in simulated ECMO circuits. Methods Following baseline sampling, known quantities of macro- and micronutrients were injected post oxygenator into ex vivo ECMO circuits primed with the fresh human whole blood and maintained under standard physiologic conditions. Serial blood samples were then obtained at 1, 30 and 60 min and at 6, 12 and 24 h after the addition of nutrients, to measure the concentrations of study compounds using validated assays. Results Twenty-one samples were tested for thirty-one nutrient compounds. There were significant reductions (p < 0.05) in circuit concentrations of some amino acids [alanine (10%), arginine (95%), cysteine (14%), glutamine (25%) and isoleucine (7%)], vitamins [A (42%) and E (6%)] and glucose (42%) over 24 h. Significant increases in circuit concentrations (p < 0.05) were observed over time for many amino acids, zinc and vitamin C. There were no significant reductions in total proteins, triglycerides, total cholesterol, selenium, copper, manganese and vitamin D concentrations within the ECMO circuit over a 24-h period. No clear correlation could be established between physicochemical properties and circuit behaviour of tested nutrients. Conclusions Significant alterations in macro- and micronutrient concentrations were observed in this single-dose ex vivo circuit study. Most significantly, there is potential for circuit loss of essential amino acid isoleucine and lipid soluble vitamins (A and E) in the ECMO circuit, and the mechanisms for this need further exploration. While the reductions in glucose concentrations and an increase in other macro- and micronutrient concentrations probably reflect cellular metabolism and breakdown, the decrement in arginine and glutamine concentrations may be attributed to their enzymatic conversion to ornithine and glutamate, respectively. While the results are generally reassuring from a macronutrient perspective, prospective studies in clinical subjects are indicated to further evaluate the influence of ECMO circuit on micronutrient concentrations and clinical outcomes.

A framework for model integration and holistic modelling of socio-technical systems

This paper presents a layered framework for the purposes of integrating different Socio-Technical Systems (STS) models and perspectives into a whole-of-systems model. Holistic modelling plays a critical role in the engineering of STS due to the interplay between social and technical elements within these systems and resulting emergent behaviour. The framework decomposes STS models into components, where each component is either a static object, dynamic object or behavioural object. Based on existing literature, a classification of the different elements that make up STS, whether it be a social, technical or a natural environment element, is developed; each object can in turn be classified according to the STS elements it represents. Using the proposed framework, it is possible to systematically decompose models to an extent such that points of interface can be identified and the contextual factors required in transforming the component of one model to interface into another is obtained. Using an airport inbound passenger facilitation process as a case study socio-technical system, three different models are analysed: a Business Process Modelling Notation (BPMN) model, Hybrid Queue-based Bayesian Network (HQBN) model and an Agent Based Model (ABM). It is found that the framework enables the modeller to identify non-trivial interface points such as between the spatial interactions of an ABM and the causal reasoning of a HQBN, and between the process activity representation of a BPMN and simulated behavioural performance in a HQBN. Such a framework is a necessary enabler in order to integrate different modelling approaches in understanding and managing STS.

Unified user experience model enabling a more comprehensive understanding of emotional experience design

Design deals with improving the lives of people. As such interactions with products, interfaces, and systems should facilitate not only usable and practical concerns but also mediate emotionally meaningful experiences. This paper presents an integrated and comprehensive model of experience, labeled 'Unified User Experience Model', covering the most prominent perspectives from across the design field. It is intended to support designers from different disciplines to consider the complexity of user experience. The vision of the model is to support both the analysis of existing products, interfaces, and systems, as well as the development of new designs that take into account this complexity. In essence, we hope the model can enable designers to develop more marketable, appropriate, and enhanced products to improve experiences and ultimately the lives of people.

Conformational Spread in the Flagellar Motor Switch: A Model Study

The reliable response to weak biological signals requires that they be amplified with fidelity. In E. coli, the flagellar motors that control swimming can switch direction in response to very small changes in the concentration of the signaling protein CheY-P, but how this works is not well understood. A recently proposed allosteric model based on cooperative conformational spread in a ring of identical protomers seems promising as it is able to qualitatively reproduce switching, locked state behavior and Hill coefficient values measured for the rotary motor. In this paper we undertook a comprehensive simulation study to analyze the behavior of this model in detail and made predictions on three experimentally observable quantities: switch time distribution, locked state interval distribution, Hill coefficient of the switch response. We parameterized the model using experimental measurements, finding excellent agreement with published data on motor behavior. Analysis of the simulated switching dynamics revealed a mechanism for chemotactic ultrasensitivity, in which cooperativity is indispensable for realizing both coherent switching and effective amplification. These results showed how cells can combine elements of analog and digital control to produce switches that are simultaneously sensitive and reliable. © 2012 Ma et al.

Adaptable interface model for intuitively learnable interfaces : an approach to address diversity in older users' capabilities

This study started with the aim to develop an approach that will help designers create interfaces that are more intuitive for older adults to use. Two objectives were set for this study: 1) to investigate one of the possible strategies for developing intuitive interfaces for older people, and; 2) to investigate factors that could interfere with intuitive use. This paper briefly presents the outcome of the two experiments and how it has lead to the development of an adaptable interface design model that will help designers develop interfaces that are intuitive to learn and, over time, intuitive to use for users with diverse technology prior experience and cognitive abilities.

A simulation model of the within-host dynamics of Plasmodium vivax infection

Background The benign reputation of Plasmodium vivax is at odds with the burden and severity of the disease. This reputation, combined with restricted in vitro techniques, has slowed efforts to gain an understanding of the parasite biology and interaction with its human host. Methods A simulation model of the within-host dynamics of P. vivax infection is described, incorporating distinctive characteristics of the parasite such as the preferential invasion of reticulocytes and hypnozoite production. The developed model is fitted using digitized time-series’ from historic neurosyphilis studies, and subsequently validated against summary statistics from a larger study of the same population. The Chesson relapse pattern was used to demonstrate the impact of released hypnozoites. Results The typical pattern for dynamics of the parasite population is a rapid exponential increase in the first 10 days, followed by a gradual decline. Gametocyte counts follow a similar trend, but are approximately two orders of magnitude lower. The model predicts that, on average, an infected naïve host in the absence of treatment becomes infectious 7.9 days post patency and is infectious for a mean of 34.4 days. In the absence of treatment, the effect of hypnozoite release was not apparent as newly released parasites were obscured by the existing infection. Conclusions The results from the model provides useful insights into the dynamics of P. vivax infection in human hosts, in particular the timing of host infectiousness and the role of the hypnozoite in perpetuating infection.

Model-based analysis and optimization of bioreactor for hematopoietic stem cell cultivation

One of the problems to be solved in attaining the full potentials of hematopoietic stem cell (HSC) applications is the limited availability of the cells. Growing HSCs in a bioreactor offers an alternative solution to this problem. Besides, it also offers the advantages of eliminating labour intensive process as well as the possible contamination involved in the periodic nutrient replenishments in the traditional T-flask stem cell cultivation. In spite of this, the optimization of HSC cultivation in a bioreactor has been barely explored. This manuscript discusses the development of a mathematical model to describe the dynamics in nutrient distribution and cell concentration of an ex vivo HSC cultivation in a microchannel perfusion bioreactor. The model was further used to optimize the cultivation by proposing three alternative feeding strategies in order to prevent the occurrence of nutrient limitation in the bioreactor. The evaluation of these strategies, the periodic step change increase in the inlet oxygen concentration, the periodic step change increase in the media inflow, and the feedback control of media inflow, shows that these strategies can successfully improve the cell yield of the bioreactor. In general, the developed model is useful for the design and optimization of bioreactor operation.

Identifying risk factors and protective factors for venous leg ulcer recurrence using a theoretical approach : a longitudinal study

Background The high recurrence rate of chronic venous leg ulcers has a significant impact on an individual’s quality of life and healthcare costs. Objectives This study aimed to identify risk and protective factors for recurrence of venous leg ulcers using a theoretical approach by applying a framework of self and family management of chronic conditions to underpin the study. Design Secondary analysis of combined data collected from three previous prospective longitudinal studies. Setting The contributing studies’ participants were recruited from two metropolitan hospital outpatient wound clinics and three community-based wound clinics. Participants Data were available on a sample of 250 adults, with a leg ulcer of primarily venous aetiology, who were followed after ulcer healing for a median follow-up time of 17 months after healing (range: 3 to 36 months). Methods Data from the three studies were combined. The original participant data were collected through medical records and self-reported questionnaires upon healing and every 3 months thereafter. A Cox proportion-hazards regression analysis was undertaken to determine the influential factors on leg ulcer recurrence based on the proposed conceptual framework. Results The median time to recurrence was 42 weeks (95% CI 31.9–52.0), with an incidence of 22% (54 of 250 participants) recurrence within three months of healing, 39% (91 of 235 participants) for those who were followed for six months, 57% (111 of 193) by 12 months, 73% (53 of 72) by two years and 78% (41 of 52) of those who were followed up for three years. A Cox proportional-hazards regression model revealed that the risk factors for recurrence included a history of deep vein thrombosis (HR 1.7, 95% CI 1.07–2.67, p=0.024), history of multiple previous leg ulcers (HR 4.4, 95% CI 1.84–10.5, p=0.001), and longer duration (in weeks) of previous ulcer (HR 1.01, 95% CI 1.003–1.01, p<0.001); while the protective factors were elevating legs for at least 30 minutes per day (HR 0.33, 95% CI 0.19–0.56, p<0.001), higher levels of self-efficacy (HR 0.95, 95% CI 0.92–0.99, p=0.016), and walking around for at least three hours/day (HR 0.66, 95% CI 0.44–0.98, p=0.040). Conclusions Results from this study provide a comprehensive examination of risk and protective factors associated with leg ulcer recurrence based on the chronic disease self and family management framework. These results in turn provide essential steps towards developing and testing interventions to promote optimal prevention strategies for venous leg ulcer recurrence.

Development and parameterization of a rain- and fire-driven model for exploring elephant effects in African savannas

We describe the development and parameterization of a grid-based model of African savanna vegetation processes. The model was developed with the objective of exploring elephant effects on the diversity of savanna species and structure, and in this formulation concentrates on the relative cover of grass and woody plants, the vertical structure of the woody plant community, and the distribution of these over space. Grid cells are linked by seed dispersal and fire, and environmental variability is included in the form of stochastic rainfall and fire events. The model was parameterized from an extensive review of the African savanna literature; when available, parameter values varied widely. The most plausible set of parameters produced long-term coexistence between woody plants and grass, with the tree-grass balance being more sensitive to changes in parameters influencing demographic processes and drought incidence and response, while less sensitive to fire regime. There was considerable diversity in the woody structure of savanna systems within the range of uncertainty in tree growth rate parameters. Thus, given the paucity of height growth data regarding woody plant species in southern African savannas, managers of natural areas should be cognizant of different tree species growth and damage response attributes when considering whether to act on perceived elephant threats to vegetation. © 2007 Springer Science+Business Media B.V.