The internal wave field in Sau reservoir : Observation and modeling of a third vertical mode

Water withdrawal from Mediterranean reservoirs in summer is usually very high. Because of this, stratification is often continuous and far from the typical two-layered structure, favoring the excitation of higher vertical modes. The analysis of wind, temperature, and current data from Sau reservoir (Spain) shows that the third vertical mode of the internal seiche (baroclinic mode) dominated the internal wave field at the beginning of September 2003. We used a continuous stratification two-dimensional model to calculate the period and velocity distribution of the various modes of the internal seiche, and we calculated that the period of the third vertical mode is ;24 h, which coincides with the period of the dominating winds. As a result of the resonance between the third mode and the wind, the other oscillation modes were not excited during this period

Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Risk Estimates of Dengue in Travelers to Dengue Endemic Areas Using Mathematical Models

Dengue has emerged as a frequent problem in international travelers. The risk depends on destination, duration, and season of travel. However, data to quantify the true risk for travelers to acquire dengue are lacking. We used mathematical models to estimate the risk of nonimmune persons to acquire dengue when traveling to Singapore. From the force of infection, we calculated the risk of dengue dependent on duration of stay and season of arrival. Our data highlight that the risk for nonimmune travelers to acquire dengue in Singapore is substantial but varies greatly with seasons and epidemic cycles. For instance, for a traveler who stays in Singapore for 1 week during the high dengue season in 2005, the risk of acquiring dengue was 0.17%, but it was only 0.00423% during the low season in a nonepidemic year such as 2002. Risk estimates based on mathematical modeling will help the travel medicine provider give better evidence-based advice for travelers to dengue endemic countries.

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.

Participatory Surveillance and Mathematical Models in Epidemiologic Research: Successes and Challenges

Theoretical epidemiology aims to understand the dynamics of diseases in populations and communities. Biological and behavioral processes are abstracted into mathematical formulations which aim to reproduce epidemiological observations. In this thesis a new system for the self-reporting of syndromic data — Influenzanet — is introduced and assessed. The system is currently being extended to address greater challenges of monitoring the health and well-being of tropical communities.(...)

Mathematical models of influenza A virus infection : from intracellular replication to virus growth in cell populations

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2015

Case studies and mathematical models of ecological speciation. 1. Cichlids in a crater lake.

A recent study of a pair of sympatric species of cichlids in Lake Apoyo in Nicaragua is viewed as providing probably one of the most convincing examples of sympatric speciation to date. Here, we describe and study a stochastic, individual-based, explicit genetic model tailored for this cichlid system. Our results show that relatively rapid (<20,000 generations) colonization of a new ecological niche and (sympatric or parapatric) speciation via local adaptation and divergence in habitat and mating preferences are theoretically plausible if: (i) the number of loci underlying the traits controlling local adaptation, and habitat and mating preferences is small; (ii) the strength of selection for local adaptation is intermediate; (iii) the carrying capacity of the population is intermediate; and (iv) the effects of the loci influencing nonrandom mating are strong. We discuss patterns and timescales of ecological speciation identified by our model, and we highlight important parameters and features that need to be studied empirically to provide information that can be used to improve the biological realism and power of mathematical models of ecological speciation.

Three mathematical models for bucking-to-order

Abstract

The role of surface vertical mixing in phytoplankton distribution in a stratified reservoir

We investigated convection caused by surface cooling and mixing attributable to wind shear stress and their roles as agents for the transport of phytoplankton cells in the water column by carrying out two daily surveys during the stratified period of the Sau reservoir. Green algae, diatoms, and cryptophyceae were the dominant phytoplankton communities during the surveys carried out in the middle (July) and end (September) of the stratified period. We show that a system with a linear stratification and that is subject to weak surface forcing, with weak winds , < 4 m S (-1) and low energy dissipation rate values of the order of 1028 m2 s23 or lower, enables the formation of thin phytoplankton layers. These layers quickly disappear when water parcels mix because there is a medium external forcing (convection) induced by the night surface cooling, which is characterized by energy dissipation rates on the order of , 5x10(-8)m2s(-3). During both surveys the wind generated internal waves during the entire diurnal cycle. During the day, and because of the weak winds, phytoplankton layers rise in the water column up to a depth determined by both solar heating and internal waves. In contrast, during the night phytoplankton mixes down to a depth determined by both convection and internal waves. These internal waves, together with the wind-driven current generated at the surface, seem to be the agents responsible for the horizontal transport of phytoplankton across the reservoir.

The seasonal evolution of high vertical–mode internal waves in a deep reservoir

The causal mechanism and seasonal evolution of the internal wave field in a deep, warm, monomictic reservoirare examined through the analysis of field observations and numerical techniques. The study period extends fromthe onset of thermal stratification in the spring until midsummer in 2005. During this time, wind forcing wasperiodic, with a period of 24 h (typical of land–sea breezes), and the thermal structure in the lake wascharacterized by the presence of a shallow surface layer overlying a thick metalimnion, typical of small to mediumsized reservoirs with deep outtakes. Basin-scale internal seiches of high vertical mode (ranging from mode V3 toV5) were observed in the metalimnion. The structure of the dominant modes of oscillation changed asstratification evolved on seasonal timescales, but in all cases, their periods were close to that of the local windforcing (i.e., 24 h), suggesting a resonant response. Nonresonant oscillatory modes of type V1 and V2 becamedominant after large frontal events, which disrupted the diurnal periodicity of the wind forcing

Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

The present study aimed to determine the volumetric shrinkage rate of bean (Phaseolus vulgaris L.) seeds during air-drying under different conditions of air, temperature and relative humidity, and to adjust several mathematical models to the empiric values observed, and select the one that best represents the phenomenon. Six mathematical models were adjusted to the experimental values to represent the phenomenon. It was determined the degree of adjustment of each model from the value of the coefficient of determination, the behavior of the distribution of the residuals, and the magnitude of the average relative and estimated errors. The rate of volumetric shrinkage that occurred in bean seeds during drying is between 25 and 37%. It basically depends on the final moisture content, regardless of the air conditions during drying. The Modified Bala & Woods' model best represented the process.

Application of mathematical models for the prediction of adsorption isotherms in solid mixture for mango powder refreshment

Solid mixtures for refreshment are already totally integrated to the Brazilian consumers' daily routine, because of their quick preparation method, yield and reasonable price - quite lower if compared to 'ready-to-drink' products or products for prompt consumption, what makes them economically more accessible to low-income populations. Within such a context, the aim of this work was to evaluate the physicochemical and mineral composition, as well as the hygroscopic behavior of four different brands of solid mixture for mango refreshment. The BET, GAB, Oswim and Henderson mathematical models were built through the adjustment of experimental data to the isotherms of adsorption. Results from the physiochemical evaluation showed that the solid mixtures for refreshments are considerable sources of ascorbic acid and reductor sugar; and regarding mineral compounds, they are significant sources of calcium, sodium and potassium. It was also verified that the solid mixtures for refreshments of the four studied brands are considered highly hygroscopic.