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Non-Newtonian effects in a fluid-structure interaction model for atherosclerosis

El Khatib N., Genieys S., Zine A. M., Volpert V.

Journal of Technical Physics

2009

Vol. 50, no 1

55-64

The inflammatory process of atherosclerosis leads to the formation of an atheroma plaque in the blood vessel. The interaction between the blood and the plaque may have dangerous consequences such as the rupture of the plaque. This rupture exposes tissue factors to the blood flow, leading to the formation of a clot that might result in a heart attack or an ischemic stroke. The blood-plaque interaction may also produce recirculations downstream of the plaque, and these recirculations enhance the risk of clot formation. In this paper we study the blood-plaque interaction using a fluid-structure interaction model. The atheroma plaque is composed of a lipid pool and a fibrous cap and both are modeled as hyperelastic materials. The blood is supposed to be a non-Newtonian fluid with a variable viscosity modeled by the Carreau law. The parameters used in our simulations are taken from experimental data. We investigate the non-Newtonian effects on the recirculations downstream of the atheroma plaque and on the stress over the plaque. The simulations show that the Newtonian model significantly overestimates the recirculations in comparison with the non-Newtonian model. They also show that the Newtonian model slightly underestimates the stress over the plaque for usual shear rates, but that this underestimation can become significant for low shear rates.

Mechano-chemical calcium waves in systems with immobile buffers

Kaźmierczak B., Volpert V.

Archives of Mechanics

2008

Vol. 60, nr 1

3-22

We study the existence of travelling waves of the free cytosolic calcium concentration in the presence of immobile buffers. We also take into account the mechanochemical interaction. In the proof we use the a priori estimates for solutions of systems with diffusing buffers and pass to zero with their diffusion coefficients.

Modelling of convective heat explosion

Ducrot A., Volpert V.

Journal of Technical Physics

2005

Vol. 46, no 3

149-163

A strong temperature dependence of the reaction rate can result, for an exothermic chemical reaction, in heat explosion. In this work we study numerically the influence of natural convection on heat explosion. The model consists of the reaction-diffusion equation coupled with the Navier-Stokes equations under the Boussinesq approximation. A new type of heat explosion, the oscillating heat explosion is found. Critical conditions of explosion and complex nonlinear dynamics of the reaction-diffusion-convection problem are studied.