Comparative analysis of carrying capacity indices for the central Aegean Islands

The tourist industry is one of the most important economic activities in Greece. The country receives over 14 million visitors per year. In an era where tourism is one of the fastest growing sectors of the developing countries the competition with existing tourism destinations, such as Greece, will intensify. Greece has enjoyed increasing numbers and revenues from tourism due to the unique environment both natural and man-made making it a high profile tourist destination. However, it is already clear, that the uncontrolled growth of the industry can bring serious environmental and social problems, leading to a decline in the quality of tourist product and services provided. Such negative effects can be controlled and reduced using environmental and tourism indices to estimate the impact of tourism and other businesses on the environment. The purpose of this paper is to apply the principles of coastal environmental management for the Islands in the central Aegean Sea islands via the carrying capacity assessment methodology in order to develop environmental performance indicators necessary for formulating a novel sustainable development policy proposal for Greek tourism.peer-reviewe

Mathematical analysis of a model for the growth of the bovine corpus luteum

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2).\ud \ud In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system.\ud \ud We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, p5. We find that weak (low p5) or strong (high p5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of p5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

A proliferation saturation index to predict radiation response and personalize radiotherapy fractionation

BACKGROUND: Although altered protocols that challenge conventional radiation fractionation have been tested in prospective clinical trials, we still have limited understanding of how to select the most appropriate fractionation schedule for individual patients. Currently, the prescription of definitive radiotherapy is based on the primary site and stage, without regard to patient-specific tumor or host factors that may influence outcome. We hypothesize that the proportion of radiosensitive proliferating cells is dependent on the saturation of the tumor carrying capacity. This may serve as a prognostic factor for personalized radiotherapy (RT) fractionation. METHODS: We introduce a proliferation saturation index (PSI), which is defined as the ratio of tumor volume to the host-influenced tumor carrying capacity. Carrying capacity is as a conceptual measure of the maximum volume that can be supported by the current tumor environment including oxygen and nutrient availability, immune surveillance and acidity. PSI is estimated from two temporally separated routine pre-radiotherapy computed tomography scans and a deterministic logistic tumor growth model. We introduce the patient-specific pre-treatment PSI into a model of tumor growth and radiotherapy response, and fit the model to retrospective data of four non-small cell lung cancer patients treated exclusively with standard fractionation. We then simulate both a clinical trial hyperfractionation protocol and daily fractionations, with equal biologically effective dose, to compare tumor volume reduction as a function of pretreatment PSI. RESULTS: With tumor doubling time and radiosensitivity assumed constant across patients, a patient-specific pretreatment PSI is sufficient to fit individual patient response data (R(2) = 0.98). PSI varies greatly between patients (coefficient of variation >128 %) and correlates inversely with radiotherapy response. For this study, our simulations suggest that only patients with intermediate PSI (0.45–0.9) are likely to truly benefit from hyperfractionation. For up to 20 % uncertainties in tumor growth rate, radiosensitivity, and noise in radiological data, the absolute estimation error of pretreatment PSI is <10 % for more than 75 % of patients. CONCLUSIONS: Routine radiological images can be used to calculate individual PSI, which may serve as a prognostic factor for radiation response. This provides a new paradigm and rationale to select personalized RT dose-fractionation

Modeling of dynamic cerebrovascular reactivity to spontaneous and externally induced CO2 fluctuations in the human brain using BOLD-fMRI

In this work, we investigate the regional characteristics of the dynamic interactions between arterial CO2 and BOLD (dynamic cerebrovascular reactivity - dCVR) during normal breathing and hypercapnic, externally induced step CO2 challenges. To obtain dCVR curves at each voxel, we use a custom set of basis functions based on the Laguerre and gamma basis sets. This allows us to obtain robust dCVR estimates both in larger regions of interest (ROIs), as well as in individual voxels. We also implement classification schemes to identify brain regions with similar dCVR characteristics. Our results reveal considerable variability of dCVR across different brain regions, as well as during different experimental conditions (normal breathing and hypercapnic challenges), suggesting a differential response of cerebral vasculature to spontaneous CO2 fluctuations and larger, externally induced CO2 changes that are possibly associated with the underlying differences in mean arterial CO2 levels. The clustering results suggest that anatomically distinct brain regions are characterized by different dCVR curves that in some cases do not exhibit the standard, positive valued curves that have been previously reported. They also reveal a consistent set of dCVR cluster shapes for resting and forcing conditions, which exhibit different distribution patterns across brain voxels

Constraining N2O emissions since 1940 using firn air isotope measurements in both hemispheres

N2O is currently the third most important anthropogenic greenhouse gas in terms of radiative forcing and its atmospheric mole fraction is rising steadily. To quantify the growth rate and its causes over the past decades, we performed a multi-site reconstruction of the atmospheric N2O mole fraction and isotopic composition using new and previously published firn air data collected from Greenland and Antarctica in combination with a firn diffusion and densification model. The multi-site reconstruction showed that while the global mean N2O mole fraction increased from (290±1)nmolmol-1 in 1940 to (322±1)nmolmol-1 in 2008, the isotopic composition of atmospheric N2O decreased by (-2.2±0.2)% for δ15Nav, (-1.0±0.3)% for δ18O, (-1.3±0.6)% for δ15Nα, and (-2.8±0.6)% for δ15Nβ over the same period. The detailed temporal evolution of the mole fraction and isotopic composition derived from the firn air model was then used in a two-box atmospheric model (comprising a stratospheric box and a tropospheric box) to infer changes in the isotopic source signature over time. The precise value of the source strength depends on the choice of the N2O lifetime, which we choose to fix at 123 years. The average isotopic composition over the investigated period is δ15Nav Combining double low line (-7.6±0.8)% (vs. air-N2), δ18O Combining double low line (32.2±0.2)% (vs. Vienna Standard Mean Ocean Water-VSMOW) for δ18O, δ15Nα Combining double low line (-3.0±1.9)% and δ15Nβ Combining double low line (-11.7±2.3)%. δ15Nav, and δ15Nβ show some temporal variability, while for the other signatures the error bars of the reconstruction are too large to retrieve reliable temporal changes. Possible processes that may explain trends in 15N are discussed. The 15N site preference (Combining double low line δ15Nα-δ15Nβ) provides evidence of a shift in emissions from denitrification to nitrification, although the uncertainty envelopes are large

Modelling Stochastic and Deterministic Behaviours in Virus Infection Dynamics

Many human infections with viruses such as human immunodeficiency virus type 1 (HIV--1) are characterized by low numbers of founder viruses for which the random effects and discrete nature of populations have a strong effect on the dynamics, e.g., extinction versus spread. It remains to be established whether HIV transmission is a stochastic process on the whole. In this study, we consider the simplest (so-called, 'consensus') virus dynamics model and develop a computational methodology for building an equivalent stochastic model based on Markov Chain accounting for random interactions between the components. The model is used to study the evolution of the probability densities for the virus and target cell populations. It predicts the probability of infection spread as a function of the number of the transmitted viruses. A hybrid algorithm is suggested to compute efficiently the dynamics in state space domain characterized by a mix of small and large species densities

Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years