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.

A burning issue : fashion and sun protection

The 'dick' tog, a briefs-style male swimsuit as it is colloquially referred to, is linked to Australia's national identity with overtly masculine bronzed 'Aussie' bodies clothed in this iconic apparel. However, the reality is, our hunger for worshiping the sun and the addiction to a beach culture is tempered by the pragmatic need to cover up and wear neck-to-knee, or more apt, head-to-toe sun protective clothing. Australia, in particular the state of Queensland, has one of the highest rates of skin cancer in the world; nevertheless, even after wide-ranging public programs for sun safety awareness many people still continue to wear designs that provide minimal sun protection. This paper will examine issues surrounding fashion and sun safe clothing. It will be proposed that in order to have effective community adoption of sun safe practices it is critical to understand the important role that fashion plays in determining sun protective behaviour.

A randomised controlled trial of a theory-based intervention to improve sun protective behaviour in adolescents ('you can still be HOT in the shade') : study protocol

Background: Most skin cancers are preventable by encouraging consistent use of sun protective behaviour. In Australia, adolescents have high levels of knowledge and awareness of the risks of skin cancer but exhibit significantly lower sun protection behaviours than adults. There is limited research aimed at understanding why people do or do not engage in sun protective behaviour, and an associated absence of theory-based interventions to improve sun safe behaviour. This paper presents the study protocol for a school-based intervention which aims to improve the sun safe behaviour of adolescents. Methods/design: Approximately 400 adolescents (aged 12-17 years) will be recruited through Queensland, Australia public and private schools and randomized to the intervention (n = 200) or 'wait-list' control group (n = 200). The intervention focuses on encouraging supportive sun protective attitudes and beliefs, fostering perceptions of normative support for sun protection behaviour, and increasing perceptions of control/self-efficacy over using sun protection. It will be delivered during three × one hour sessions over a three week period from a trained facilitator during class time. Data will be collected one week pre-intervention (Time 1), and at one week (Time 2) and four weeks (Time 3) post-intervention. Primary outcomes are intentions to sun protect and sun protection behaviour. Secondary outcomes include attitudes toward performing sun protective behaviours (i.e., attitudes), perceptions of normative support to sun protect (i.e., subjective norms, group norms, and image norms), and perceived control over performing sun protective behaviours (i.e., perceived behavioural control). Discussion: The study will provide valuable information about the effectiveness of the intervention in improving the sun protective behaviour of adolescents.

Application of an appearance-based intervention to improve sun protection outcomes of outdoor workers in Queensland, Australia

Outdoor workers are exposed to high levels of ultraviolet radiation (UVR) and may thus be at greater risk to experience UVR-related health effects such as skin cancer, sun burn, and cataracts. A number of intervention trials (n=14) have aimed to improve outdoor workers’ work-related sun protection cognitions and behaviours. Only one study however has reported the use of UV-photography as part of a multi-component intervention. This study was performed in the USA and showed long-term (12 months) improvements in work-related sun protection behaviours. Intervention effects of the other studies have varied greatly, depending on the population studied, intervention applied, and measurement of effect. Previous studies have not assessed whether: - Interventions are similarly effective for workers in stringent and less stringent policy organisations; - Policy effect is translated into workers’ leisure time protection; - Implemented interventions are effective in the long-term; - The facial UV-photograph technique is effective in Australian male outdoor workers without a large additional intervention package, and; - Such interventions will also affect workers’ leisure time sun-related cognitions and behaviours. Therefore, the present Protection of Outdoor Workers from Environmental Radiation [POWER]-study aimed to fill these gaps and had the objectives of: a) assessing outdoor workers’ sun-related cognitions and behaviours at work and during leisure time in stringent and less stringent sun protection policy environments; b) assessing the effect of an appearance-based intervention on workers’ risk perceptions, intentions and behaviours over time; c) assessing whether the intervention was equally effective within the two policy settings; and d) assessing the immediate post-intervention effect. Effectiveness was described in terms of changes in sun-related risk perceptions and intentions (as these factors were shown to be main precursors of behaviour change in many health promotion theories) and behaviour. The study purposefully selected and recruited two organisations with a large outdoor worker contingent in Queensland, Australia within a 40 kilometre radius of Brisbane. The two organisations differed in the stringency of implementation and reinforcement of their organisational sun protection policy. Data were collected from 154 male predominantly Australian born outdoor workers with an average age of 37 years and predominantly medium to fair skin (83%). Sun-related cognitions and behaviours of workers were assessed using self-report questionnaires at baseline and six to twelve months later. Variation in follow-up time was due to a time difference in the recruitment of the two organisations. Participants within each organisation were assigned to an intervention or control group. The intervention group participants received a one-off personalised Skin Cancer Risk Assessment Tool [SCRAT]-letter and a facial UV-photograph with detailed verbal information. This was followed by an immediate post-intervention questionnaire within three months of the start of the study. The control group only received the baseline and follow-up questionnaire. Data were analysed using a variety of techniques including: descriptive analyses, parametric and non-parametric tests, and generalised estimating equations. A 15% proportional difference observed was deemed of clinical significance, with the addition of reported statistical significance (p<0.05) where applicable. Objective 1: Assess and compare the current sun-related risk perceptions, intentions, behaviours, and policy awareness of outdoor workers in stringent and less stringent sun protection policy settings. Workers within the two organisations (stringent n=89 and less stringent n=65) were similar in their knowledge about skin cancer, self efficacy, attitudes, and social norms regarding sun protection at work and during leisure time. Participants were predominantly in favour of sun protection. Results highlighted that compared to workers in a less stringent policy organisation working for an organisation with stringent sun protection policies and practices resulted in more desirable sun protection intentions (less willing to tan p=0.03) ; actual behaviours at work (sufficient use of upper and lower body protection, headgear, and sunglasses (p<0.001 for all comparisons), and greater policy awareness (awareness of repercussions if Personal Protective Equipment (PPE) was not used, p<0.001)). However the effect of the work-related sun protection policy was found not to extend to leisure time sun protection. Objective 2: Compare changes in sun-related risk perceptions, intentions, and behaviours between the intervention and control group. The effect of the intervention was minimal and mainly resulted in a clinically significant reduction in work-related self-perceived risk of developing skin cancer in the intervention compared to the control group (16% and 32% for intervention and control group, respectively estimated their risk higher compared to other outdoor workers: , p=0.11). No other clinical significant effects were observed at 12 months follow-up. Objective 3: Assess whether the intervention was equally effective in the stringent sun protection policy organisation and the less stringent sun protection policy organisation. The appearance-based intervention resulted in a clinically significant improvement in the stringent policy intervention group participants’ intention to protect from the sun at work (workplace*time interaction, p=0.01). In addition to a reduction in their willingness to tan both at work (will tan at baseline: 17% and 61%, p=0.06, at follow-up: 54% and 33%, p=0.07, stringent and less stringent policy intervention group respectively. The workplace*time interaction was significant p<0.001) and during leisure time (will tan at baseline: 42% and 78%, p=0.01, at follow-up: 50% and 63%, p=0.43, stringent and less stringent policy intervention group respectively. The workplace*time interaction was significant p=0.01) over the course of the study compared to the less stringent policy intervention group. However, no changes in actual sun protection behaviours were found. Objective 4: Examine the effect of the intervention on level of alarm and concern regarding the health of the skin as well as sun protection behaviours in both organisations. The immediate post-intervention results showed that the stringent policy organisation participants indicated to be less alarmed (p=0.04) and concerned (p<0.01) about the health of their skin and less likely to show the facial UV-photograph to others (family p=0.03) compared to the less stringent policy participants. A clinically significantly larger proportion of participants from the stringent policy organisation reported they worried more about skin cancer (65%) and skin freckling (43%) compared to those in the less stringent policy organisation (46%,and 23% respectively , after seeing the UV-photograph). In summary the results of this study suggest that the having a stringent work-related sun protection policy was significantly related to for work-time sun protection practices, but did not extend to leisure time sun protection. This could reflect the insufficient level of sun protection found in the general Australian population during leisure time. Alternatively, reactance caused by being restricted in personal decisions through work-time policy could have contributed to lower leisure time sun protection. Finally, other factors could have also contributed to the less than optimal leisure time sun protection behaviours reported, such as unmeasured personal or cultural barriers. All these factors combined may have lead to reduced willingness to take proper preventive action during leisure time exposure. The intervention did not result in any measurable difference between the intervention and control groups in sun protection behaviours in this population, potentially due to the long lag time between the implementation of the intervention and assessment at 12-months follow-up. In addition, high levels of sun protection behaviours were found at baseline (ceiling effect) which left little room for improvement. Further, this study did not assess sunscreen use, which was the predominant behaviour assessed in previous effective appearance-based interventions trials. Additionally, previous trials were mainly conducted in female populations, whilst the POWER-study’s population was all male. The observed immediate post-intervention result could be due to more emphasis being placed on sun protection and risks related to sun exposure in the stringent policy organisation. Therefore participants from the stringent policy organisation could have been more aware of harmful effects of UVR and hence, by knowing that they usually protect adequately, not be as alarmed or concerned as the participants from the less stringent policy organisation. In conclusion, a facial UV-photograph and SCRAT-letter information alone may not achieve large changes in sun-related cognitions and behaviour, especially of assessed 6-12 months after the intervention was implemented and in workers who are already quite well protected. Differences found between workers in the present study appear to be more attributable to organisational policy. However, against a background of organisational policy, this intervention may be a useful addition to sun-related workplace health and safety programs. The study findings have been interpreted while respecting a number of limitations. These have included non-random allocation of participants due to pre-organised allocation of participants to study group in one organisation and difficulty in separating participants from either study group. Due to the transient nature of the outdoor worker population, only 105 of 154 workers available at baseline could be reached for follow-up. (attrition rate=32%). In addition the discrepancy in the time to follow-up assessment between the two organisations was a limitation of the current study. Given the caveats of this research, the following recommendations were made for future research: - Consensus should be reached to define "outdoor worker" in terms of time spent outside at work as well as in the way sun protection behaviours are measured and reported. - Future studies should implement and assess the value of the facial UV-photographs in a wide range of outdoor worker organisations and countries. - More timely and frequent follow-up assessments should be implemented in intervention studies to determine the intervention effect and to identify the best timing of booster sessions to optimise results. - Future research should continue to aim to target outdoor workers’ leisure time cognitions and behaviours and improve these if possible. Overall, policy appears to be an important factor in workers’ compliance with work-time use of sun protection. Given the evidence generated by this research, organisations employing outdoor workers should consider stringent implementation and reinforcement of a sun protection policy. Finally, more research is needed to improve ways to generate desirable behaviour in this population during leisure time.

Cold and heat waves in the United States

Extreme cold and heat waves, characterised by a number of cold or hot days in succession, place a strain on people’s cardiovascular and respiratory systems. The increase in deaths due to these waves may be greater than that predicted by extreme temperatures alone. We examined cold and heat waves in 99 US cities for 14 years (1987–2000) and investigated how the risk of death depended on the temperature threshold used to define a wave, and a wave’s timing, duration and intensity. We defined cold and heat waves using temperatures above and below cold and heat thresholds for two or more days. We tried five cold thresholds using the first to fifth percentiles of temperature, and five heat thresholds using the ninety-fifth to ninety-ninth percentiles. The extra wave effects were estimated using a two-stage model to ensure that their effects were estimated after removing the general effects of temperature. The increases in deaths associated with cold waves were generally small and not statistically significant, and there was even evidence of a decreased risk during the coldest waves. Heat waves generally increased the risk of death, particularly for the hottest heat threshold. Cold waves of a colder intensity or longer duration were not more dangerous. Cold waves earlier in the cool season were more dangerous, as were heat waves earlier in the warm season. In general there was no increased risk of death during cold waves above the known increased risk associated with cold temperatures. Cold or heat waves earlier in the cool or warm season may be more dangerous because of a build up in the susceptible pool or a lack of preparedness for cold or hot temperatures.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Investigating mothers' decisions about their child's sun-protective behaviour using the Theory of Planned Behaviour

This study tested the utility of the Theory of Planned Behaviour (TPB) to predict mothers’ decisions to ensure their child engages in sun-protective behaviours. Mothers (N = 162) of children aged four or five years completed standard TPB items (attitude, subjective norm, perceived behavioural control, intention) and additional variables of role construction, mothers’ own sun safe behaviour, planning and past behaviour. One week later, participants (N = 116) reported their behaviour. Results found support for the TPB constructs, role construction, past behaviour and the mediating role of planning. These findings can inform strategies to prevent skin cancer.

Personalised electronic messages to improve sun protection in young adults

The incidence of all skin cancers, including melanoma, continues to rise. It is well known that ultraviolet (UV) radiation is the main environmental risk factor for skin cancer, and excessive exposure at a young age increases the risk of developing skin cancer. The aim of this study was to determine the acceptability and feasibility of delivering sun protection messages via electronic media such as short message services (SMS) to people 18-40 years, and explore factors associated with their acceptability. Overall, 80% of participants agreed that they would like to receive some form of sun protection advice; of these, 20% prefer to receive it via SMS and 42% via email. Willingness to receive electronic messages about the UV index was associated with being unsure about whether a suntanned person would look healthy and greater use of sun protection in the past. Careful attention to message framing and timing of message delivery and focus on short-term effects of sun exposure such as sunburn and skin ageing should increase the acceptability of such messages to young people. We conclude that sun protection messages delivered to young adults via electronic media appear feasible and acceptable.

Vitamin D intake, sun exposure and 25-hydroxy vitamin D status in Peritoneal dialysis (PD) and Haemodialysis (HD) patients

Inadequate vitamin D levels have been linked to bone disease but more recently have been associated with wider health implications. Limited studies suggest a high prevalence of Vitamin D deficiency in dialysis patients, although evidence is lacking on whether this is due to dietary restrictions, limited mobility and time outdoors or a combination of these. The aim of this study was to assess the contributions of diet, supplements and sunlight exposure to serum Vitamin D (25(OH)D) levels in dialysis patients. Cross-sectional data were obtained from 30 PD (Mean±SD age 56.9±16.2 y; n=13 male) and 22 HD (Mean±SD age 65.4±14.0 y; n=18 male) patients between 2009 and 2010. Serum 25(OH)D was measured and oral vitamin D intake estimated through a food-frequency-questionnaire and quantifying inactive supplementation. Sunlight exposure was assessed using a validated questionnaire. Prevalence of inadequate/insufficient vitamin D differed between dialysis modality (31% and 43% insufficient (<50nmol/L); 4% and 34% deficient (<25nmol/L) in HD and PD patients respectively (p=0.002)). In HD patients, there was a significant correlation between diet plus supplemental vitamin D intake and 25(OH)D (ρ=0.84, p<0.001). Results suggest a higher frequency of 25(OH)D inadequacy/deficiency in PD compared to HD patients. No other relationships between intake, sun exposure and 25(OH)D were seen. This could reflect limitations of the study design or the importance of other factors such as age, ethnicity and sun protection as interactions in the analysis. Understanding these factors is important given Vitamin D’s emerging status as a biomarker of systemic ill health.

Identifying critical sun-protective beliefs among Australian adults

We investigated critical beliefs to target in interventions aimed at improving sun-protective behaviours of Australian adults, a population at risk for skin cancer. Participants (N = 816) completed a Theory of Planned Behaviour belief-based questionnaire and a 1-week follow-up of sun-protective behaviour. A range of behavioural, normative and control beliefs correlated with sun-protective behaviour, with no and only minimal differences observed in correlations between beliefs and behaviour by gender and age, respectively. A range of key beliefs made independent contributions to behaviour; however, the behavioural belief about being less likely to tan (β = 0.09); normative belief about friends (β = 0.20); and control beliefs about forgetfulness (β = −0.14), inconvenience (β = −0.17), knowing I will be in the sun for a long time (β = 0.16) and more fashionable sun-protective clothing (β = 0.13) were significant critical beliefs guiding people’s sun-protective behaviour. Our study fills a gap in the literature by investigating an at-risk population for skin cancer and using an established theoretical framework to identify critical beliefs that guide Australian adults’ decisions to sun protect. Attention to these critical beliefs will assist health campaigns and interventions aimed at combating the increasing rates of skin cancer for adults.

Assessing the impacts of lifetime sun exposure on skin damage and skin aging using a non-invasive method

Background: Ultraviolet radiation exposure during an individuals' lifetime is a known risk factor for the development of skin cancer. However, less evidence is available on assessing the relationship between lifetime sun exposure and skin damage and skin aging. Objectives: This study aims to assess the relationship between lifetime sun exposure and skin damage and skin aging using a non-invasive measure of exposure. Methods: We recruited 180 participants (73 males, 107 females) aged 18-83 years. Digital imaging of skin hyper-pigmentation (skin damage) and skin wrinkling (skin aging) on the facial region was measured. Lifetime sun exposure (presented as hours) was calculated from the participants' age multiplied by the estimated annual time outdoors for each year of life. We analyzed the effects of lifetime sun exposure on skin damage and skin aging. We adjust for the influence of age, sex, occupation, history of skin cancer, eye color, hair color, and skin color. Results: There were non-linear relationships between lifetime sun exposure and skin damage and skin aging. Younger participant's skin is much more sensitive to sun exposure than those who were over 50 years of age. As such, there were negative interactions between lifetime sun exposure and age. Age had linear effects on skin damage and skin aging. Conclusion: The data presented showed that self reported lifetime sun exposure was positively associated with skin damage and skin aging, in particular, the younger people. Future health promotion for sun exposure needs to pay attention to this group for skin cancer prevention messaging. (C) 2012 Elsevier B.V. All rights reserved.

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.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Sun, sea, sex, sand and soap

A recent issue of Young People Now (November 1995) mentioned the new (UK) Channel 4 television soap opera Hollyoaks by Phil Redmond, which raises the issue of the role of ‘soaps’ in the daily lives of young people. Australian soaps are especially popular in Britain and of interest to those who work with young people, because they have a high proportion of youthful looking actors and actresses and frequently depict scenes involving young people and apparent ‘real’ teenage dilemmas.