This mathematical modeling study provides a theoretical framework demonstrating how arterial geometry and antioxidant levels influence the initiation of atherosclerosis as an inflammatory instability.
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Hypothesis-generating for atherogenesis mechanisms; leaves open clinical translation pending experimental validation.
This paper presents a linear, asymptotic stability analysis for a reaction-diffusion-convection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved, giving conditions on system parameters guaranteeing stability of the health state, and a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation.
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Ibragimov et al. (2010) studied this question.
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