Aymen Laadhari

Vesicle tumbling inhibited by inertia

Vesicles under flow constitute a model system for the study of red blood cells (RBCs) dynamics and blood rheology. In the blood circulatory system the Reynolds number (at the scale of the RBC) is not always small enough for the Stokes limit to be valid. We develop a numerical method in two dimensions based on the level set approach and solve the fluid/membrane coupling by using an adaptive finite element technique. We find that a Reynolds number of order one can destroy completely the vesicle tumbling motion obtained in the Stokes regime. We analyze in details this phenomenon and discuss some of the far reaching consequences. We suggest experimental tests on vesicles.

Mathematical modelling of active contraction in isolated cardiomyocytes

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 properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarization.

Numerical modeling of heart valves using resistive Eulerian surfaces

The goal of this work is the development and numerical implementation of a mathematical model describing the functioning of heart valves. To couple the pulsatile blood flow with a highly deformable thin structure (the valves leaflets), a resistive Eulerian surfaces framework is adopted. A lumped-parameter model helps to couple the movement of the leaflets with the blood dynamics. A reduced circulation model describes the systemic hemodynamics and provides a physiological pressure profile at the downstream boundary of the valve. The resulting model is relatively simple to describe for a healthy valve and pathological heart valve functioning while featuring an affordable computational burden. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method, and we report several numerical experiments for both two-dimensional and three-dimensional cases with the aim of illustrating its accuracy. Copyright

Eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves

We present a finite element methodology tailored for the simulation of pulsatile flow in the full aorta and sinus of Valsalva interacting with highly deformable thin leaflets. We describe an extension of the so-called Resistive Immersed Surface method. To circumvent stability issues resulting from the bad conditioning of the linear system, especially when flow and geometry become complex after the inclusion of the aorta, we use a Lagrange multiplier technique that couples the dynamics of valve and flow. A banded level set variant allows to address the singularity of the resulting linear system while featuring, in addition to the parallel implementation, higher accuracy and an affordable computational burden. High-fidelity computational geometries are built and simulations are performed under physiological conditions. Several numerical experiments illustrate the ability of the model to capture the basic fluidic phenomena in both healthy and pathological configurations. We finally examine numerically the flow dynamics in the sinus of Valsalva after Transcatheter Aortic Valve Implantation. We show numerically that flow may be subject to stagnation in the lower part of the sinuses. We highlight the far-reaching implications of this phenomenon and we hope inciting adequate studies to further investigate its potential clinical consequences. Display Omitted Hemodynamics in full aorta and aortic sinuses coupled with highly deformable valve.An exact Lagrange multiplier technique couples the dynamics of valve and flow.A damped-Newton strategy allows more stability for relatively large Reynolds numbers.Numerical examples in 2D and 3D with healthy and pathological valves.Numerical investigations pinpoint a risk of blood stagnation after TAVI.

A Three-dimensional Continuum Model of Active Contraction in Single Cardiomyocytes

We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A 3D continuum mathematical model is presented based on a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to describe the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. Some numerical tests of combined boundary conditions and ionic activations illustrate the ability of our model in reproducing key experimentally established features. Potential applications of the study for predicting pathological subcellular mechanisms affecting e.g. cardiac repolarization are discussed.

A Partial Domain Approach to Enable Aortic Flow Simulation Without Turbulent Modeling

Analysis of hemodynamics shows great potential to provide indications for the risk of cardiac malformations and is essential for diagnostic purposes in clinical applications. Computational fluid dynamics (CFD) has been established as a valuable tool for the detailed characterization of volumetric blood flow and its effects on the arterial wall. However, studies concentrating on the aortic root have to take the turbulent nature of the flow into account while no satisfactory solution for such simulations exists today. In this paper we propose to combine magnetic resonance imaging (MRI) flow acquisitions, providing excellent data in the turbulent regions while showing only limited reliability in the boundary layer, with CFD simulations which can be used to extrapolate the measured data towards the vessel wall. The solution relies on a partial domain approach, restricting the simulations to the laminar flow domain while using MRI measurements as additional boundary conditions to drive the numerical simulation. In this preliminary work we demonstrate the feasibility of the method on flow phantom measurements while comparing actually measured and simulated flow fields under straight and spiral flow regimes.