All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 65 Next

Displaying 1281 – 1300 of 1854

Showing per page

Optimized Schwarz coupling of Bidomain and Monodomain models in electrocardiology

Luca Gerardo-Giorda, Mauro Perego, Alessandro Veneziani (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents...

Optimized Schwarz coupling of Bidomain and Monodomain models in electrocardiology

Luca Gerardo-Giorda, Mauro Perego, Alessandro Veneziani (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents...

Optimized Schwarz Methods for the Bidomain system in electrocardiology

Luca Gerardo-Giorda, Mauro Perego (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in...

Oscillation and global attractivity in a discrete survival red blood cells model

I. Kubiaczyk, S. H. Saker (2003)

Applicationes Mathematicae

We consider the discrete survival red blood cells model (*) N n + 1 - N ₙ = - δ ₙ N ₙ + P ₙ e - a N n - k , where δₙ and Pₙ are positive sequences. In the autonomous case we show that (*) has a unique positive steady state N*, we establish some sufficient conditions for oscillation of all positive solutions about N*, and when k = 1 we give a sufficient condition for N* to be globally asymptotically stable. In the nonatonomous case, assuming that there exists a positive solution Nₙ*, we present necessary and sufficient conditions for oscillation...

Oxygen exchange between multiple capillaries and living tissues: An homogenisation study

Andro Mikelić, Mario Primicerio (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.

Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE

E. Grenier, V. Louvet, P. Vigneaux (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases...

Parameter Identification of a Fed-Batch Cultivation of S. Cerevisiae using Genetic Algorithms

Angelova, Maria, Tzonkov, Stoyan, Pencheva, Tania (2010)

Serdica Journal of Computing

Fermentation processes as objects of modelling and high-quality control are characterized with interdependence and time-varying of process variables that lead to non-linear models with a very complex structure. This is why the conventional optimization methods cannot lead to a satisfied solution. As an alternative, genetic algorithms, like the stochastic global optimization method, can be applied to overcome these limitations. The application of genetic algorithms is a precondition for robustness...

Parametric inference for mixed models defined by stochastic differential equations

Sophie Donnet, Adeline Samson (2008)

ESAIM: Probability and Statistics

Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed. This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants. A tuned...

Particle Dynamics Methods of Blood Flow Simulations

A. Tosenberger, V. Salnikov, N. Bessonov, E. Babushkina, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

Various particle methods are widely used to model dynamics of complex media. In this work molecular dynamics and dissipative particles dynamics are applied to model blood flows composed of plasma and erythrocytes. The properties of the homogeneous particle fluid are studied. Capillary flows with erythrocytes are investigated.

Past, Present and Future of Brain Stimulation

J. Modolo, R. Edwards, J. Campagnaud, B. Bhattacharya, A. Beuter (2010)

Mathematical Modelling of Natural Phenomena

Recent technological advances including brain imaging (higher resolution in space and time), miniaturization of integrated circuits (nanotechnologies), and acceleration of computation speed (Moore’s Law), combined with interpenetration between neuroscience, mathematics, and physics have led to the development of more biologically plausible computational models and novel therapeutic strategies. Today, mathematical models of irreversible medical conditions...

Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources

S. Genieys, V. Volpert, P. Auger (2010)

Mathematical Modelling of Natural Phenomena

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.

Currently displaying 1281 – 1300 of 1854