Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Mathematical modelling of angiogenesis and vascular adaptation

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Integration of production and financial models to analyse the financial impact of livestock diseases: a case study of Schmallenberg virus disease on British and French dairy farms

AIMS AND OBJECTIVES: The aim of the study was to investigate and compare the financial impact of Schmallenberg disease for different dairy production types in the United Kingdom and France. MATERIALS AND METHODS: Integrated production and financial models for dairy cattle were developed and applied to Schmallenberg virus (SBV) disease in a British and French context. The five main production systems that prevail in these two countries were considered. Their respective gross margins measuring the holding's profitability were calculated based on public benchmarking, literature and expert opinion data. A partial budget analysis was performed within each production model to estimate the impact of SBV in the systems modelled. Two disease scenarios were simulated: low impact and high impact. RESULTS: The model gross margin obtained per cow space and year ranged from £1014 to £1484 for the UK and from £1037 to £1890 for France depending on the production system considered. In the UK, the net SBV disease costs in £/cow space/year for an average dairy farm with 100 milking spaces were estimated between £16.3 and £51.4 in the high-impact scenario and between £8.2 and £25.9 in the low-impact scenario. For France, the net SBV disease costs in £/cow space/year ranged from £19.6 to £48.6 in the high-impact scenario and £9.7 to £22.8 in the low-impact scenario, respectively. CONCLUSION: The study illustrates how the combination of production and financial models allows assessing disease impact taking into account differing management and husbandry practices and associated price structures in the dairy sector. It supports decision-making of farmers and veterinarians who are considering disease control measures as it provides an approach to estimate baseline disease impact in common dairy production systems in the UK and France

Cost of porcine reproductive and respiratory syndrome virus at individual farm level – An economic disease model

Porcine reproductive and respiratory syndrome (PRRS) is reported to be among the diseases with the highest economic impact in modern pig production worldwide. Yet, the economic impact of the disease at farm level is not well understood as, especially in endemically infected pig herds, losses are often not obvious. It is therefore difficult for farmers and veterinarians to appraise whether control measures such as virus elimination or vaccination will be economically beneficial for their farm. Thus, aim of this study was to develop an epidemiological and economic model to determine the costs of PRRS for an individual pig farm. In a production model that simulates farm outputs, depending on farm type, farrowing rhythm or length of suckling period, an epidemiological model was integrated. In this, the impact of PRRS infection on health and productivity was estimated. Financial losses were calculated in a gross margin analysis and a partial budget analysis based on the changes in health and production parameters assumed for different PRRS disease severities. Data on the effects of endemic infection on reproductive performance, morbidity and mortality, daily weight gain, feed efficiency and treatment costs were obtained from literature and expert opinion. Nine different disease scenarios were calculated, in which a farrow-to-finish farm (1000 sows) was slightly, moderately or severely affected by PRRS, based on changes in health and production parameters, and either in breeding, in nursery and fattening or in all three stages together. Annual losses ranged from a median of € 75′724 (90% confidence interval (C.I.): € 78′885–€ 122′946), if the farm was slightly affected in nursery and fattening, to a median of € 650′090 (90% C.I. € 603′585–€ 698′379), if the farm was severely affected in all stages. Overall losses were slightly higher if breeding was affected than if nursery and fattening were affected. In a herd moderately affected in all stages, median losses in breeding were € 46′021 and € 422′387 in fattening, whereas costs were € 25′435 lower in nursery, compared with a PRRSV-negative farm. The model is a valuable decision-support tool for farmers and veterinarians if a farm is proven to be affected by PRRS (confirmed by laboratory diagnosis). The output can help to understand the need for interventions in case of significant impact on the profitability of their enterprise. The model can support veterinarians in their communication to farmers in cases where costly disease control measures are justified

From invasion to latency: intracellular noise and cell motility as key controls of the competition between resource-limited cellular populations

In this paper we analyse stochastic models of the competition between two resource-limited cell populations which differ in their response to nutrient availability: the resident population exhibits a switch-like response behaviour while the invading population exhibits a bistable response. We investigate how noise in the intracellular regulatory pathways and cell motility influence the fate of the incumbent and invading populations. We focus initially on a spatially homogeneous system and study in detail the role of intracellular noise. We show that in such well-mixed systems, two distinct regimes exist: In the low (intracellular) noise limit, the invader has the ability to invade the resident population, whereas in the high noise regime competition between the two populations is found to be neutral and, in accordance with neutral evolution theory, invasion is a random event. Careful examination of the system dynamics leads us to conclude that (i) even if the invader is unable to invade, the distribution of survival times, PS(t), has a fat-tail behaviour (PS(t)∼t−1) which implies that small colonies of mutants can coexist with the resident population for arbitrarily long times, and (ii) the bistable structure of the invading population increases the stability of the latent population, thus increasing their long-term likelihood of survival, by decreasing the intensity of the noise at the population level. We also examine the effects of spatial inhomogeneity. In the low noise limit we find that cell motility is positively correlated with the aggressiveness of the invader as defined by the time the invader takes to invade the resident population: the faster the invasion, the more aggressive the invader

An inner warp in the DoAr 44 T Tauri transition disk

Optical/IR images of transition disks (TDs) have revealed deep intensity decrements in the rings of HAeBes HD142527 and HD100453, that can be interpreted as shadowing from sharply tilted inner disks, such that the outer disks are directly exposed to stellar light. Here we report similar dips in SPHERE+IRDIS differential polarized imaging (DPI) of TTauri DoAr44. With a fairly axially symmetric ring in the submm radio continuum, DoAr44 is likely also a warped system. We constrain the warp geometry by comparing radiative transfer predictions with the DPI data in H band (Q_\phi(H)) and with a re-processing of archival 336GHz ALMA observations. The observed DPI shadows have coincident radio counterparts, but the intensity drops are much deeper in Q_\phi(H) (~88%), compared to the shallow drops at 336GHz (~24%). Radiative transfer predictions with an inner disk tilt of ~30+-5deg approximately account for the observations. ALMA long-baseline observations should allow the observation of the warped gas kinematics inside the cavity of DoAr44.Comment: 11 pages, 10 figures, 3 tables, accepted for publication in MNRA

Modelling the economic efficiency of using different strategies to control Porcine Reproductive & Respiratory Syndrome at herd level

PRRS is among the diseases with the highest economic impact in pig production worldwide. Different strategies have been developed and applied to combat PRRS at farm level. The broad variety of available intervention strategies makes it difficult to decide on the most cost-efficient strategy for a given farm situation, as it depends on many farm-individual factors like disease severity, prices or farm structure. Aim of this study was to create a simulation tool to estimate the cost-efficiency of different control strategies at individual farm level. Baseline is a model that estimates the costs of PRRS, based on changes in health and productivity, in a specific farm setting (e.g. farm type, herd size, type of batch farrowing). The model evaluates different intervention scenarios: depopulation/repopulation (D/R), close & roll-over (C&R), mass vaccination of sows (MS), mass vaccination of sows and vaccination of piglets (MS + piglets), improvements in internal biosecurity (BSM), and combinations of vaccinations with BSM. Data on improvement in health and productivity parameters for each intervention were obtained through literature review and from expert opinions. The economic efficiency of the different strategies was assessed over 5 years through investment appraisals: the resulting expected value (EV) indicated the most cost-effective strategy. Calculations were performed for 5 example scenarios with varying farm type (farrow-to-finish – breeding herd), disease severity (slightly – moderately – severely affected) and PRRSV detection (yes – no). The assumed herd size was 1000 sows with farm and price structure as commonly found in Germany. In a moderately affected (moderate deviations in health and productivity parameters from what could be expected in an average negative herd), unstable farrow-to-finish herd, the most cost-efficient strategies according to their median EV were C&R (€1′126′807) and MS + piglets (€ 1′114′649). In a slightly affected farrow-to-finish herd, no virus detected, the highest median EV was for MS + piglets (€ 721′745) and MS (€ 664′111). Results indicate that the expected benefits of interventions and the most efficient strategy depend on the individual farm situation, e.g. disease severity. The model provides new insights regarding the cost-efficiency of various PRRSV intervention strategies at farm level. It is a valuable tool for farmers and veterinarians to estimate expected economic consequences of an intervention for a specific farm setting and thus enables a better informed decision