Shape parametrization of the time-dependent geometry of the heart for steady fluid dynamical analysis.
Simulation of electrophysiological waves with an unstructured finite element method
Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.
Simulation of Electrophysiological Waves with an Unstructured Finite Element Method
Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is investigated using a test case with re-entrant waves.
Steady state in a biological system: global asymptotic stability
A suitable Liapunov function is constructed for proving that the unique critical point of a non-linear system of ordinary differential equations, considered in a well determined polyhedron , is globally asymptotically stable in . The analytic problem arises from an investigation concerning a steady state in a particular macromolecular system: the visual system represented by the pigment rhodopsin in the presence of light.
Synchronization of cardiorhythm by weak external forcing.
Testing for periodicity in signals: An application to detect partial upper airway obstruction during sleep.
The Effect of Bacteria on Epidermal Wound Healing
Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an...
The power-law formalism as a tool for modeling hormonal systems.
Three models of non periodic fibrous materials obtained by homogenization
Thymic presentation of autoantigens and the efficiency of negative selection.
Time delays in proliferation and apoptosis for solid avascular tumour
The role of time delays in solid avascular tumour growth is considered. The model is formulated in terms of a reaction-diffusion equation and mass conservation law. Two main processes are taken into account-proliferation and apoptosis. We introduce time delay first in underlying apoptosis only and then in both processes. In the absence of necrosis the model reduces to one ordinary differential equation with one discrete delay which describes the changes of tumour radius. Basic properties of the...
Two periodic solutions of neutral difference equations modelling physiological processes.
Линейная трансверсально неоднородная модель улитки с высокой частотной избирательностью