Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Model-driven process configuration of enterprise systems

The configuration of comprehensive enterprise systems to meet the specific requirements of an organisation up to today is consuming significant resources. The results of failing or delayed enterprise system implementation projects are severe and may even threaten the organisation’s existence. One of the main drivers for implementing comprehensive enterprise systems is to streamline business processes. However, an intuitive conceptual support for business process configuration is insufficiently addressed by enterprise system vendors and inadequately researched in academia. This paper presents a model-driven approach to target this problem and proposes several configuration patterns that describe generic patterns of configuration alternatives, in order to understand what situations can occur during business process configuration. Based on these configuration patterns, a configuration notation is introduced that allows for visually highlighting configuration alternatives. Finally, we will sketch how configurable Event Driven Process Chains and the configuration of business processes can be supported using relational databases.

Modelling surface and shallow groundwater interactions in an ungauged subtropical coastal catchment using the SWAT model, Elimbah Creek, southeast Queensland, Australia

The study presented here applies the highly parameterised semi-distributed U.S. Department of Agriculture Soil and Water Assessment Tool (SWAT) to an Australian subtropical catchment. SWAT has been applied to numerous catchments worldwide and is considered to be a useful tool that is under ongoing development with contributions coming from different research groups in different parts of the world. In a preliminary run the SWAT model application for the Elimbah Creek catchment has estimated water yield for the catchment and has quantified the different sources. For the modelling period of April 1999 to September 2009 the results show that the main sources of water in Elimbah Creek are total surface runoff and lateral flow (65%). Base-flow contributes 36% to the total runoff. On a seasonal basis modelling results show a shift in the source of water contributing to Elimbah Creek from surface runoff and lateral flow during intense summer storms to base-flow conditions during dry months. Further calibration and validation of these results will confirm that SWAT provides an alternative to Australian water balance models.

Towards a compendium of process technologies : the jBPT library for process model analysis

This paper presents the idea of a compendium of process technologies, i.e., a concise but comprehensive collection of techniques for process model analysis that support research on the design, execution, and evaluation of processes. The idea originated from observations on the evolution of process-related research disciplines. Based on these observations, we derive design goals for a compendium. Then, we present the jBPT library, which addresses these goals by means of an implementation of common analysis techniques in an open source codebase.

A new model to study healing of a complex femur fracture with concurrent soft tissue injury in sheep

High energy bone fractures resulting from impact trauma are often accompanied by subcutaneous soft tissue injuries, even if the skin remains intact. There is evidence that such closed soft tissue injuries affect the healing of bone fractures, and vice versa. Despite this knowledge, most impact trauma studies in animals have focussed on bone fractures or soft tissue trauma in isolation. However, given the simultaneous impact on both tissues a better understanding of the interaction between these two injuries is necessary to optimise clinical treatment. The aim of this study was therefore to develop a new experimental model and characterise, for the first time, the healing of a complex fracture with concurrent closed soft tissue trauma in sheep. A pendulum impact device was designed to deliver a defined and standardised impact to the distal thigh of sheep, causing a reproducible contusion injury to the subcutaneous soft tissues. In a subsequent procedure, a reproducible femoral butterfly fracture (AO C3-type) was created at the sheep’s femur, which was initially stabilised for 5 days by an external fixator construct to allow for soft tissue swelling to recede, and ultimately in a bridging construct using locking plates. The combined injuries were applied to twelve sheep and the healing observed for four or eight weeks (six animals per group) until sacrifice. The pendulum impact led to a moderate to severe circumferential soft tissue injury with significant bruising, haematomas and partial muscle disruptions. Posttraumatic measurements showed elevated intra-compartmental pressure and circulatory tissue breakdown markers, with recovery to normal, pre-injury values within four days. Clinically, no neurovascular deficiencies were observed. Bi-weekly radiological analysis of the healing fractures showed progressive callus healing over time, with the average number of callus bridges increasing from 0.4 at two weeks to 4.2 at eight weeks. Biomechanical testing after sacrifice showed increasing torsional stiffness between four and eight weeks healing time from 10% to 100%, and increasing ultimate torsional strength from 10% to 64% (relative to the contralateral control limb). Our results demonstrate the robust healing of a complex femur fracture in the presence of a severe soft tissue contusion injury in sheep and demonstrate the establishment of a clinically relevant experimental model, for research aimed at improving the treatment of bone fractures accompanied by closed soft tissue injuries.

A microscopic simulation model to estimate Bus Rapid Transit (BRT) station service capacity with mixed stopping and non-stopping bus operation

Bus Rapid Transit (BRT) station is the interface between passenger and service. The station is crucial to line operation as it is typically the only location where buses can pass each other. Congestion may occur here when buses maneuvering into and out of the platform lane interfere with bus flow, or when a queue of buses forms upstream of the platform lane blocking the passing lane. However, some systems include operation where express buses pass the critical station, resulting in a proportion of non stopping buses. It is important to understand the operation of the critical busway station under this type of operation, as it affects busway line capacity. This study uses micro simulation to treat the BRT station operation and to analyze the relationship between station Limit state bus capacity (B_ls), Total Bus Capacity (B_ttl). First, the simulation model is developed for Limit state scenario and then a mathematical model is defined, calibrated for a specified range of controlled scenarios of mean and coefficient of variation of dwell time. Thereafter, the proposed B_ls model is extended to consider non stopping buses and B_ttlmodel is defined. The proposed models provides better understanding to the BRT line capacity and is useful for transit authorities for designing better BRT operation.

Conceptual model linking knowledge management with organisational performance

Better management of knowledge assets has the potential to improve business processes and increase productivity. This fact has led to considerable interest in recent years in the knowledge management (KM) phenomenon, and in the main dimensions that can impact on its application in construction. However, a lack of a systematic way of assessing KM initia-tives’ contribution towards achieving organisational business objectives is evident. This paper describes the first stage of a research project intended to develop, and empirically test, a KM input-process-output framework comprising unique and well-defined theoretical constructs representing the KM process and its internal and external determinants in the context of con-struction. The paper presents the underlying principles used in operationally defining each construct through the use of extant KM literature. The KM process itself is explicitly mod-elled via a number of clearly articulated phases that ultimately lead to knowledge utilisation and capitalisation, which in turn adds value or otherwise to meeting defined business objec-tives. The main objective of the model is to reduce the impact of subjectivity in assessing the contribution made by KM practices and initiatives toward achieving performance improvements.

Numerical techniques for simulating a fractional mathematical model of 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 the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is 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 the 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 Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

Using a maturity model to move student engagement practices beyond the generational approach

This paper proposes that the generational approach to conceptualising first year student learning behaviour, while it has made a very useful contribution to understanding that behaviour, can be expanded upon. The generational approach has an explicit focus on student behaviour and it is suggested that a capability maturity model interpretation may provide a complementary extension of that as it allows an assessment of institutional capability to initiate, plan, manage and evaluate institutional student engagement practices. The development of a Student Engagement, Success and Retention Maturity Model (SESR-MM) is discussed along with Australasian FYE generational data and Australian SESR-MM data.

The place of higher education institutions in assessing student engagement, success and retention : a maturity model to guide practice

The perennial issues of student engagement, success and retention in higher education continue to attract attention as the salience of teaching and learning funding and performance measures has increased. This paper addresses the question of the responsibility or place of higher education institutions (HEIs) for initiating, planning, managing and evaluating their student engagement, success and retention programs and strategies. An evaluation of the current situation indicates the need for a sophisticated approach to assessing the ability of HEIs to proactively design programs and practices that enhance student engagement. An approach—the Student Engagement Success and Retention Maturity Model (SESR-MM)—is proposed and its development, current status, and relationship with and possible use in benchmarking are discussed.

A finite element model of seat cushion indentation with a soft tissue human occupant model

Effective digital human model (DHM) simulation of automotive driver packaging ergonomics, safety and comfort depends on accurate modelling of occupant posture, which is strongly related to the mechanical interaction between human body soft tissue and flexible seat components. This paper presents a finite-element study simulating the deflection of seat cushion foam and supportive seat structures, as well as human buttock and thigh soft tissue when seated. The three-dimensional data used for modelling thigh and buttock geometry were taken on one 95th percentile male subject, representing the bivariate percentiles of the combined hip breadth (seated) and buttock-to-knee length distributions of a selected Australian and US population. A thigh-buttock surface shell based on this data was generated for the analytic model. A 6mm neoprene layer was offset from the shell to account for the compression of body tissue expected through sitting in a seat. The thigh-buttock model is therefore made of two layers, covering thin to moderate thigh and buttock proportions, but not more fleshy sizes. To replicate the effects of skin and fat, the neoprene rubber layer was modelled as a hyperelastic material with viscoelastic behaviour in a Neo-Hookean material model. Finite element (FE) analysis was performed in ANSYS V13 WB (Canonsburg, USA). It is hypothesized that the presented FE simulation delivers a valid result, compared to a standard SAE physical test and the real phenomenon of human-seat indentation. The analytical model is based on the CAD assembly of a Ford Territory seat. The optimized seat frame, suspension and foam pad CAD data were transformed and meshed into FE models and indented by the two layer, soft surface human FE model. Converging results with the least computational effort were achieved for a bonded connection between cushion and seat base as well as cushion and suspension, no separation between neoprene and indenter shell and a frictional connection between cushion pad and neoprene. The result is compared to a previous simulation of an indentation with a hard shell human finite-element model of equal geometry, and to the physical indentation result, which is approached with very high fidelity. We conclude that (a) SAE composite buttock form indentation of a suspended seat cushion can be validly simulated in a FE model of merely similar geometry, but using a two-layer hard/soft structure. (b) Human-seat indentation of a suspended seat cushion can be validly simulated with a simplified human buttock-thigh model for a selected anthropomorphism.