Ricardo Esteban Ruiz Baier

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We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical prope ...

A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined w ...

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the ...

This paper is concerned with the mathematical analysis of a coupled elliptic–parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction–diffus ...

Mathematical modeling of the human heart and its function can expand our understanding of various cardiac diseases, which remain the most common cause of death in the developed world. Like other physiological systems, the heart can be understood as a compl ...

In this paper, we are interested in the spatio-temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in t ...

We present a model for mechanical activation of the cardiac tissue depending on the evolution of the transmembrane electrical potential and certain gating/ionic variables that are available in most of electrophysiological descriptions of the cardiac membra ...

In the present paper, an optimal control problem constrained by the tridomain equations in electrocardiology is investigated. The state equations consisting in a coupled reaction-diffusion system modelling the propagation of the intracellular and extracell ...

We are interested in the development, implementation and testing of an orthotropic model for cardiac contraction based on an active strain decomposition. Our model addresses the coupling of a transversely isotropic mechanical description at the cell level, ...

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed di ...

We propose in this paper an Eulerian finite element approximation of a coupled chemical fluid-structure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an ...

A finite volume method for solving the monodomain and bidomain models for the electrical activity of myocardial tissue is presented. These models consist of a parabolic PDE and a system of a parabolic and an elliptic PDE, respectively, for certain electric ...

We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate dif ...

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection betwe ...

This paper is concerned with the study of pattern formation for an inhomogeneous Brusselator model with cross-diffusion, modeling an autocatalytic chemical reaction taking place in a three-dimensional domain. For the spatial discretization of the problem w ...

A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid desc ...

An adaptive multiresolution scheme is proposed for the numerical solution of a spatially two-dimensional model of sedimentation of suspensions of small solid particles dispersed in a viscous fluid. This model consists in a version of the Stokes equations f ...

This paper deals with the numerical approximation of the stationary two-dimensional Stokes equations, formulated in terms of vorticity, velocity and pressure, with non-standard boundary conditions. Here, by introducing a Galerkin least-squares term, we end ...

Cross-diffusion driven instabilities have gained a considerable attention in the field of population dynamics, mainly due to their ability to predict some important features in the study of spatial distribution of species in ecological systems. This paper ...

The complex phenomena underlying mechanical contraction of cardiac cells and their influence in the dynamics of ventricular contraction are extremely important in understanding the overall function of the heart. In this paper we generalize previous contrib ...

Ricardo Esteban Ruiz Baier

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Mathematical modelling of active contraction in isolated cardiomyocytes

An adaptive finite-volume method for a model of two-phase pedestrian flow

An active strain electromechanical model for cardiac tissue

Solvability analysis and numerical approximation of linearized cardiac electromechanics

Integrated Heart-Coupling multiscale and multiphysics models for the simulation of the cardiac function

Finite element and finite volume-element simulation of pseudo-ECGs and cardiac alternans

Active strain and activation models in cardiac electromechanics

Analysis of an optimal control problem for the tridomain model in cardiac electrophysiology

On some numerical aspects of an active strain model in cardiac mechanics

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Fully Eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells

A finite volume scheme for cardiac propagation in media with isotropic conductivities

Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media

Analysis of a finite volume element method for the Stokes problem

Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion

A stabilized finite volume element formulation for sedimentation-consolidation processes

A multiresolution method for the simulation of sedimentation in inclined channels

An augmented mixed finite element method for the vorticity–velocity–pressure formulation of the Stokes equations

Mathematical analysis and numerical simulation of pattern formation under cross-diffusion

Thermodynamically consistent orthotropic activation model capturing ventricular systolic wall thickening in cardiac electromechanics