Effectiveness of early detection on breast cancer mortality reduction in Catalonia (Spain)

Background: At present, it is complicated to use screening trials to determine the optimal age intervals and periodicities of breast cancer early detection. Mathematical models are an alternative that has been widely used. The aim of this study was to estimate the effect of different breast cancer early detection strategies in Catalonia (Spain), in terms of breast cancer mortality reduction (MR) and years of life gained (YLG), using the stochastic models developed by Lee and Zelen (LZ). Methods: We used the LZ model to estimate the cumulative probability of death for a cohort exposed to different screening strategies after T years of follow-up. We also obtained the cumulative probability of death for a cohort with no screening. These probabilities were used to estimate the possible breast cancer MR and YLG by age, period and cohort of birth. The inputs of the model were: incidence of, mortality from and survival after breast cancer, mortality from other causes, distribution of breast cancer stages at diagnosis and sensitivity of mammography. The outputs were relative breast cancer MR and YLG. Results: Relative breast cancer MR varied from 20% for biennial exams in the 50 to 69 age interval to 30% for annual exams in the 40 to 74 age interval. When strategies differ in periodicity but not in the age interval of exams, biennial screening achieved almost 80% of the annual screening MR. In contrast to MR, the effect on YLG of extending screening from 69 to 74 years of age was smaller than the effect of extending the screening from 50 to 45 or 40 years. Conclusion: In this study we have obtained a measure of the effect of breast cancer screening in terms of mortality and years of life gained. The Lee and Zelen mathematical models have been very useful for assessing the impact of different modalities of early detection on MR and YLG in Catalonia (Spain).

Cost-effectiveness of early detection of breast cancer in Catalonia (Spain)

Background: Breast cancer (BC) causes more deaths than any other cancer among women in Catalonia. Early detection has contributed to the observed decline in BC mortality. However, there is debate on the optimal screening strategy. We performed an economic evaluation of 20 screening strategies taking into account the cost over time of screening and subsequent medical costs, including diagnostic confirmation, initial treatment, follow-up and advanced care. Methods: We used a probabilistic model to estimate the effect and costs over time of each scenario. The effect was measured as years of life (YL), quality-adjusted life years (QALY), and lives extended (LE). Costs of screening and treatment were obtained from the Early Detection Program and hospital databases of the IMAS-Hospital del Mar in Barcelona. The incremental cost-effectiveness ratio (ICER) was used to compare the relative costs and outcomes of different scenarios. Results: Strategies that start at ages 40 or 45 and end at 69 predominate when the effect is measured as YL or QALYs. Biennial strategies 50-69, 45-69 or annual 45-69, 40-69 and 40-74 were selected as cost-effective for both effect measures (YL or QALYs). The ICER increases considerably when moving from biennial to annual scenarios. Moving from no screening to biennial 50-69 years represented an ICER of 4,469€ per QALY. Conclusions: A reduced number of screening strategies have been selected for consideration by researchers, decision makers and policy planners. Mathematical models are useful to assess the impact and costs of BC screening in a specific geographical area.

Contribution of early detection and adjuvant treatments to breast cancer mortality reduction in Catalonia, Spain

Background: Reductions in breast cancer (BC) mortality in Western countries have been attributed to the use of screening mammography and adjuvant treatments. The goal of this work was to analyze the contributions of both interventions to the decrease in BC mortality between 1975 and 2008 in Catalonia. Methodology/Principal Findings: A stochastic model was used to quantify the contribution of each intervention. Age standardized BC mortality rates for calendar years 1975-2008 were estimated in four hypothetical scenarios: 1) Only screening, 2) Only adjuvant treatment, 3) Both interventions, and 4) No intervention. For the 30-69 age group, observed Catalan BC mortality rates per 100,000 women-year rose from 29.4 in 1975 to 38.3 in 1993, and afterwards continuously decreased to 23.2 in 2008. If neither of the two interventions had been used, in 2008 the estimated BC mortality would have been 43.5, which, compared to the observed BC mortality rate, indicates a 46.7% reduction. In 2008 the reduction attributable to screening was 20.4%, to adjuvant treatments was 15.8% and to both interventions 34.1%. Conclusions/Significance: Screening and adjuvant treatments similarly contributed to reducing BC mortality in Catalonia. Mathematical models have been useful to assess the impact of interventions addressed to reduce BC mortality that occurred over nearly the same periods.

Palaeolithic Populations and Waves of Advance

The wave-of-advance model has been previously applied to Neolithic human range expansions, yielding good agreement to the speeds inferred from archaeological data. Here, we apply it for the first time to Palaeolithic human expansions by using reproduction and mobility parameters appropriate to hunter-gatherers (instead of the corresponding values for preindustrial farmers). The order of magnitude of the predicted speed is in agreement with that implied by the AMS radiocarbon dating of the lateglacial human recolonization of northern Europe (14.2–12.5 kyr BP). We argue that this makes it implausible for climate change to have limited the speed of the recolonization front. It is pointed out that a similar value for the speed can be tentatively inferred from the archaeological data on the expansion of modern humans into the Levant and Europe (42–36 kyr BP)

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length ξ and a large critical temperature, T c, appropriate for some high-T c materials. The BCS gap, T c, ξ and specific heat C s(T c) as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below T c in p and d waves.

Roll waves evolution in high gradient channels to a non-Newtonian rheology

The criteria for the occurrence of roll wave phenomenon in the supercritical and turbulent Newtonian and non-Newtonian flows from the engineering point of view was analyzed. Imposing a constant discharge at the upstream of the canal and superposing a small perturbation, it was observed that roll waves can be developed more easily for small wave numbers and for high cohesions. Moreover, from the mathematical model used, it was demonstrated that the numerical viscosity was 10 times the physical viscosity.

Water waves generated by local disturbance: Serre's model validity

Water waves generated by landslides were long menace in certain localities and the study of this phenomenon were carried out at an accelerated rate in the last decades. Nevertheless, the phase of wave creation was found to be very complex. As such, a numerical model based on Boussinesq equations was used to describe water waves generated by local disturbance. This numerical model takes in account the vertical acceleration of the particles and considers higher orders derivate terms previously neglected by Boussinesq, so that in the generation zone, this model can support high relative amplitude of waves.

Nonlinear dynamics of short traveling capillary-gravity waves

We establish a Green-Nagdhi model equation for capillary-gravity waves in (2+1) dimensions. Through the derivation of an asymptotic equation governing short-wave dynamics, we show that this system possesses (1 + 1) traveling-wave solutions for almost all the values of the Bond number θ (the special case θ=1/3 is not studied). These waves become singular when their amplitude is larger than a threshold value, related to the velocity of the wave. The limit angle at the crest is then calculated. The stability of a wave train is also studied via a Benjamin-Feir modulational analysis. ©2005 The American Physical Society.

Optimal Boussinesq model for shallow-water waves interacting with a microstructure

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential theory model and of a family of reduced Boussinesq systems parametrized by a free parameter that is the depth at which the velocity is evaluated. We obtain explicit expressions for the coefficients of the resulting effective Korteweg-de Vries (KdV) equations. We show that it is possible to choose the free parameter of the reduced model so as to match the KdV limits of the full and reduced models. Hence the reduced model is optimal regarding the embedded linear weakly dispersive and weakly nonlinear characteristics of the underlying physical problem, which has a microstructure. We also discuss the impact of the rough bottom on the effective wave propagation. In particular, nonlinearity is enhanced and we can distinguish two regimes depending on the period of the bottom where the dispersion is either enhanced or reduced compared to the flat bottom case. © 2007 The American Physical Society.

Application of the dynamic models to the detection of imperfections in plate Structures

This paper is part of a set of publications related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. The first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment, particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection of the first class of imperfections, i.e. cracks and it is the object of the present paper. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With this group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally, in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present and a numerical application has been shown.

Modern mathematical methods and models; a book of experimental text materials.

v. 1. Multicomponent methods.--v. 2. Mathematical models.

A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

Modelling solute transport in structured soils: Performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals, and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO3-, Cl-, PO43-) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed tone-way ANOVA, p < 0.001) indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale. (C) 2001 Elsevier Science Ltd. All rights reserved.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Mathematical modelling of supercritical CO2 extraction of volatile oils from aromatic plants

The modelling of the experimental data of the extraction of the volatile oil from six aromatic plants (coriander, fennel, savoury, winter savoury, cotton lavender and thyme) was performed using five mathematical models, based on differential mass balances. In all cases the extraction was internal diffusion controlled and the internal mass transfer coefficienty (k(s)) have been found to change with pressure, temperature and particle size. For fennel, savoury and cotton lavender, the external mass transfer and the equilibrium phase also influenced the second extraction period, since k(s) changed with the tested flow rates. In general, the axial dispersion coefficient could be neglected for the conditions studied, since Peclet numbers were high. On the other hand, the solute-matrix interaction had to be considered in order to ensure a satisfactory description of the experimental data.