Well-posedness And Asymptotic Behavior Of An Atherosclerosis Model Influenced By Reverse Cholesterol Transpor

In recent years,atherosclerotic diseases have become one of the major public health problems threatening human health.A better understanding of the mechanisms of atherosclerosis is essential to develop more effective strategies for prevention and treatment.We model the important cells and cytokines in the process of plaque formation,and analyze the well-posedness and asymptotic behavior of the corresponding atherosclerotic models.We first consider a model of atherosclerosis under the influence of low-density lipoprotein(LDL),oxidized low-density lipoprotein(ox-LDL),inflammatory immune cells and inflammatory cytokines.We investigate the simplified monotone system as α2=0,analyze the existence and stability of the fixed points of the system,and provide a biological interpretation for the stability analysis according to the initial concentration of LDL,indicating that the severity of inflammation depends on the initial concentration of ox-LDL in the intima,and this initial concentration is mainly affected by LDL particles and free radicals.Then,based on the implicit function theorem,we extend the result of α2 to the perturbation solution close to 0,and the existence of the traveling wave solution of the monotone system is proved.We then consider the well-posedness of a model of atherosclerosis with free boundaries under the influence of reverse cholesterol transport(RCT),including the modeling of LDL,HDL,endothelial cytokines,pro-inflammatory and anti-inflammatory macrophages,and foam cells.By introducing some operators and Hanzawa transform to transform the free boundary into a fixed boundary,and then simplify the system into an abstract evolution equation in Banach space.Based on the analytic semigroup theory,we prove the existence and uniqueness of the solution in Holder space.Therefore,the regional regularity requirement of corresponding problem is weakened.We further consider that only a part of foam cells are transformed into macrophages M2 with inflammatory phenotype after RCT,and the response function describing the change in the concentration of each substance is changed from the usual Holling Ⅱ type to Holling Ⅲ type.By using the contraction mapping principle and the maximum principle,we prove that the model exists a unique small radially symmetric stationary plaque for the appropriate L0 and H0,and establish a condition that guarantees their asymptotically stable behavior.Among them,the participation of HDL,which has anti-atherosclerotic effect,may bring new therapeutic methods to alleviate atherosclerotic diseases,and has a good research prospect.