Atherosclerosis Initiation Modeled as an Inflammatory Process

Abstract

Abstract. In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one-and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL concentrations correspond to a bistable system and can lead to a travelling wave propagation corresponding to a chronic inflammatory reaction. In this case the disease development depends on the initial condition. If the concentration of monocytes in the intima is sufficiently high, which can be caused by an inflammation related to other factors, then the development of atherosclerosis can start. Otherwise, the system returns to the stable disease free equilibrium. High ox-LDL concentrations correspond to a monostable system and even a small perturbation of the non inflammatory case leads to a travelling wave propagation which corresponds to a chronic inflammatory response.

Reaction–diffusion model of atherosclerosis development

“…At large LDL concentrations, even a small perturbation of the non inflammatory state leads to the chronic inflammatory reaction (El Khatib et al 2007). We suggested in El Khatib et al (2007) that inflammation propagates in the intima as a reaction-diffusion wave. In the case of intermediate LDL concentrations, where a threshold occurs, there are two stable equilibria.…”

“…But in the present study, the range of possible values of α 1 is limited by the qualitative behavior of the model: it is necessary that α 1 > βγ α 2 0.095 for the 1D limiting model to exhibit the monostable behavior (see El Khatib et al 2007), and it is necessary that α 1 < β 1 τ 1 = 1 for g to be an increasing function of A. In the present simulations, the value α 1 = 0.6 was chosen.…”

“…In our previous work, we have developed a simplified model of the reactions arising in the arterial intima (El Khatib et al 2007). The model represents a reaction-diffusion system in one space dimension:…”

“…The form of the functions f (A) and g(A) is chosen so that in the approximation of thin domain h → 0 we obtain the 1D model of El Khatib et al (2007):…”

“…The former takes into account the monocyte recruitment through nonlinear boundary conditions, the latter includes a nonlinear production term in the equation. In some cases, the limiting passage from 2D to 1D as the width goes to zero can be justified (El Khatib et al 2007). This is not proved for travelling waves.…”