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.

Sensitivity of edge detection methods for quantifying cell migration assays

Quantitative imaging methods to analyze cell migration assays are not standardized. Here we present a suite of two–dimensional barrier assays describing the collective spreading of an initially–confined population of 3T3 fibroblast cells. To quantify the motility rate we apply two different automatic image detection methods to locate the position of the leading edge of the spreading population after 24, 48 and 72 hours. These results are compared with a manual edge detection method where we systematically vary the detection threshold. Our results indicate that the observed spreading rates are very sensitive to the choice of image analysis tools and we show that a standard measure of cell migration can vary by as much as 25% for the same experimental images depending on the details of the image analysis tools. Our results imply that it is very difficult, if not impossible, to meaningfully compare previously published measures of cell migration since previous results have been obtained using different image analysis techniques and the details of these techniques are not always reported. Using a mathematical model, we provide a physical interpretation of our edge detection results. The physical interpretation is important since edge detection algorithms alone do not specify any physical measure, or physical definition, of the leading edge of the spreading population. Our modeling indicates that variations in the image threshold parameter correspond to a consistent variation in the local cell density. This means that varying the threshold parameter is equivalent to varying the location of the leading edge in the range of approximately 1–5% of the maximum cell density.

Water absorption, permeability, and resistance to chloride-ion penetration of lightweight aggregate concrete

This paper presents an experimental study to evaluate effect of cumulative lightweight aggregate (LWA) content (including lightweight sand) in concrete [water/cement ratio (w/c) = 0.38] on its water absorption, water permeability, and resistance to chloride-ion penetration. Rapid chloride penetrability test (ASTM C 1202), rapid migration test (NT Build 492), and salt ponding test (AASHTO T 259) were conducted to evaluate the concrete resistance to chloride-ion penetration. The results were compared with those of a cement paste and a control normal weight aggregate concrete (NWAC) with the same w/c and a NWAC (w/c = 0.54) with 28-day compressive strength similar to some of the lightweight aggregate concrete (LWAC). Results indicate that although the total charge passed, migration coefficient, and diffusion coefficient of the LWAC were not significantly different from those of NWAC with the same w/c of 0.38, resistance of the LWAC to chloride penetration decreased with increase in the cumulative LWA content in the concretes. The water penetration depth under pressure and water sorptivity showed, in general, similar trends. The LWAC with only coarse LWA had similar water sorptivity, water permeability coefficient, and resistance to chloride-ion penetration compared to NWAC with similar w/c. The LWAC had lower water sorptivity, water permeability and higher resistance to chloride-ion penetration than the NWAC with similar 28-day strength but higher w/c. Both the NWAC and LWAC had lower sorptivity and higher resistance to chloride-ion penetration than the cement paste with similar w/c.

Effect of cumulative lightweight aggregate volume in concrete on its resistance to chloride-ion penetration

This paper presents an experimental study on the resistance of lightweight aggregate concretes to chloride-ion penetration in comparison to that of normal weight concrete of similar w/c. Salt ponding test (based on AASHTO T 259), rapid chloride permeability test (ASTM C 1202) and rapid migration test (NT Build 492) were carried out to evaluate the concrete resistance to the chloride-ion penetration. Results indicate that in general the resistance of the LWAC to the chloride-ion penetration was in the same order as that of NWAC of similar w/c. However, the increase in cumulative LWA volume and the incorporation of finer LWA particles led to higher charge passed, migration coefficient, and diffusion coefficient. Since the LWACs had lower 28-day compressive strength compared with that of the NWAC of similar w/c, the LWACs may have equal or better resistance to the chloride-ion penetration compared with the NWAC of equivalent strength. The trend of the resistance of concretes to chloride-ion penetration determined by the three test methods was reasonably consistent although there were some discrepancies due to different test methods.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

A retrospective cohort investigation of active range of motion within one week of open reduction and internal fixation of distal radius fractures

Distal radius fractures stabilized by open reduction internal fixation (ORIF) have become increasingly common. There is currently no consensus on the optimal time to commence range of motion (ROM) exercises post-ORIF. A retrospective cohort review was conducted over a five-year period to compare wrist and forearm range of motion outcomes and number of therapy sessions between patients who commenced active ROM exercises within the first seven days and from day eight onward following ORIF of distal radius fractures. One hundred and twenty-one patient cases were identified. Clinical data, active ROM at initial and discharge therapy assessments, fracture type, surgical approaches, and number of therapy sessions attended were recorded. One hundred and seven (88.4%) cases had complete datasets. The early active ROM group (n = 37) commenced ROM a mean (SD) of 4.27 (1.8) days post-ORIF. The comparator group (n = 70) commenced ROM exercises 24.3 (13.6) days post-ORIF. No significant differences were identified between groups in ROM at initial or discharge assessments, or therapy sessions attended. The results from this study indicate that patients who commenced active ROM exercises an average of 24 days after surgery achieved comparable ROM outcomes with similar number of therapy sessions to those who commenced ROM exercises within the first week.

β-Actin—an unsuitable internal control for RT-PCR

Despite reports confirming cell-cycle dependent gene expression and a number of studies describing specific circumstances in which β-actin is also regulated, the mRNA for β-actin remains a widely used housekeeping gene internal control. Utilizing differential reverse transcriptase-polymerase chain reaction (RT-PCR), we report here the dose-dependent inhibition of β-actin by matrigel. This was detected by comparison to the very moderate inhibition of the target gene, membrane type-1 matrix metalloproteinase (MT1-MMP), with results independently confirmed by similar findings on MT1-MMP expression using competitive RT-PCR. Furthermore, RT-PCR of the housekeeping gene 18 Svedberg Units (S) rRNA demonstrated excellent consistency, reproducibility and non-regulation by a matrigel treatment. We conclude that β-actin is highly regulated by matrigel and therefore unsuitable as an internal control in this treatment. Hence, these findings suggest that researchers have a responsibility to ensure that the housekeeping gene of choice is not regulated in their specific application, as such regulation may dramatically affect the accuracy of their results. This study reinforces the necessity for minimally regulated housekeeping genes such as 18S rRNA, and the superiority of competitive templates as internal controls for quantitative applications of RT-PCR.

Introduction : the anthropology of migration

This introduction to the volume places the study of migration within the wider processes of social change and the complex actions of class, gender and ethnicity that are integrated into the experience of displacement. It argues that the articles in this volume contribute important new ethnographic and theoretical analyses to our knowledge and understanding of the constraints and the opportunities provided by cultural diversity in several societies by elaborating upon recent advances made in conceptualisations of migrancy. It places particular emphasis on developing phenomenological approaches to migration studies which incorporate the lived experience of migrants into any analysis. It also suggests that redressing the neglect of this area of study in Australia has the possibility of generating informed interruptions into the current political shift towards divisive public debates on immigration and cultural pluralism.

Generate : Youth Culture and Migration Heritage in Western Sydney

Executive Summary This report is the first in-depth exploration of identity and popular culture among Middle Eastern and Asian youth. It documents preliminary research findings on the contribution of Middle Eastern and Asian youth to Sydney’s cultural life and migration heritage. While young people from these communities, the largest migrant communities in NSW, are often negatively portrayed, this research has focused on their social practices of cultural invention, opening up new and creative means of mobilising cultural difference. These young people’s cultural negotiations between migrant family background and the wider society require real engagement with difference and provide rich resources for invigorating the multicultural fabric of the nation. Their repertoire of cultural skills and their involvement in different cultural worlds are often viewed as evidence of not ‘belonging’ to the mainstream or dominant culture. However, the results of our research reveal that the ‘in-betweenness’ of these young people often enables them to move easily between different social and cultural groupings, embracing cultural diversity as inherent and integral to their everyday experience, that is, ‘normal’ to urban life. In this report, we document the changing nature of friendship networks and family relations, the particular meanings and uses of different languages and expressions, and the patterns of consumption of Middle Eastern and Asian youth. In these everyday activities these young people contribute to a changing migration heritage and are redefining what it means to be Australian.

Quantifying alterations in cell migration : tracking fluorescently-tagged migrating cells by FACs and live-imaging

Cell migration is fundamental to many different physiological processes including embryonic development, inflammation and wound healing. Given the range and importance cell migration plays a number of assays have been developed to measure different aspects of cell migration. Here we describe two different methods to analyze cell migration. The first method analyzes the migration of fluorescently tagged cells using Boyden chambers and FACs and the second looks at migration properties using time-lapse microscopy.

Help-seeking strategies of victim/survivors of human trafficking involving partner migration

Victim/survivors of human trafficking involving partner migration employ diverse help-seeking strategies, both formal and informal, to exit their exploitative situations. Drawing on primary research conducted by Lyneham and Richards (forthcoming), the authors highlight the importance of educating the community and professionals from a wide range of sectors—including health, mental health, child protection, social welfare, social work, domestic violence, migration, legal and law enforcement services—about human trafficking and the help-seeking strategies of victims/survivors in order to support them to leave exploitative situations. Enhancing Australia’s knowledge of victim/survivors’ help-seeking strategies will better inform government and community responses to this crime, improve detection and identification of human trafficking matters and subsequent referral to appropriate victim services.

Predicting the fatigue life of internal fracture fixation plates

Failures of fracture fixation plates, often related to fatigue fractures of the implants, have been reported (Banovetz et al, 1996). While metallurgical defects can usually be excluded, many of these fractures can be explained with the biomechanical situation. This study investigated the biomechanics of two clinical cases, both of which used a 14-hole locking compression plate. In the first case, a titanium plate was used in a rigid configuration with 12 screws resulting in plate breakage after 7 weeks (Sommer et al, 2003). In the second case, a stainless steel plate, which endured the entire healing process, was used in a flexible application with only 6 screws.

Vascular remodeling in the internal mammary artery graft and association with in situ endothelin-1 and receptor expression

BACKGROUND: The vasoconstricting peptide endothelin-1 (ET-1) has been associated with atherosclerotic cardiovascular disease, vascular smooth muscle cell (VSMC) growth stimulation, and intimal thickening. ET-1 binds 2 receptor subtypes, endothelin A and B, and the ETA receptor mediates vasoconstriction and VSMC growth. This study aims to quantitatively assess arterial remodeling variables and compare them with changes in ET-1, ETA, and ETB expression in the internal mammary artery (IMA). METHODS AND RESULTS: Specimens from 55 coronary artery disease (CAD) patients (45 men, 10 women; mean age 65 years) and 14 control IMA specimens (from 7 men and 7 women; mean age 45 years) were collected. IMA cross sections were assessed by histochemical and immunohistochemical staining methods to quantify the levels of medionecrosis, fibrosis, VSMC growth, ET-1, ETA, ETB, and macrophage infiltration. The percentage area of medionecrosis in the patients was almost double that in the controls (31.85+/-14.52% versus 17.10+/-9.96%, P=0.0006). Total and type 1 collagen was significantly increased compared with controls (65.8+/-18.3% versus 33.7+/-13.7%, P=0.07, and 14.2+/-10.0% versus 4.8+/-2.8%, P=0.01, respectively). Despite ACE and/or statin therapy, ET-1 expression and cell cycling were significantly elevated in the patient IMAs relative to the controls (46.27+/-18.46 versus 8.56+/-8.42, P=0.0001, and 37.29+/-12.88 versus 11.06+/-8.18, P=0.0001, respectively). ETA and ETB staining was elevated in the patient vessels (46.88+/-11.52% versus 18.58+/-7.65%, P=0.0001, and 42.98+/-7.08% versus 34.73+/-5.20%, P=0.0067, respectively). A mild presence of macrophages was noted in all sections. CONCLUSIONS: Elevated distribution of collagen indicative of fibrosis coupled with increased cell cycling and high levels of ET-1 and ETA expression in the absence of chronic inflammation suggests altered IMA VSMC regulation is fundamental to the remodeling process.