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In some special engineering circumstances, it is likely that all parameters of an uncertain automotive structure can only be treated as interval variables due to limited knowledge, but meanwhile their lower and upper bounds can just be modeled as fuzzy variables rather than as deterministic values due to ambiguous information. To handle this dual uncertainties case, a reliability-based optimization method with fuzzy-boundary interval variables is developed in this study, and it is further extended to carry out squeal instability analysis and reduction of brake involving both limited and vague information. In the proposed method, fuzzy-boundary interval variables are utilized to cope with the above dual uncertainties of structure parameters and help to build up the structure response analysis model. First, the structure responses are derived on the basis of α-cut strategy, Taylor series expansion, subinterval analysis, and central difference method. Then, with the aid of fuzzy possibility theory, a reliability analysis model of structure response is developed, which can make use of extra reliability information and thus quantify the reliability more accurately. Next, a reliability-based optimization model involving fuzzy-boundary interval variables is established by integrating the uncertain response analysis model and the reliability analysis model. Finally, the proposed method is extended to carry out automotive brake squeal instability analysis and optimization. The numerical investigations demonstrate the applicability and effectiveness of the proposed method.

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Introduction: Atherosclerosis is the main cause of many cardiovascular diseases and contributes to morbidity and mortality worldwide. The formation of macrophage-derived foam cells plays a critical role in the early stage of atherosclerosis pathogenesis. Diterpenoids found in the flowers of Callicarpa rubella Lindl., a traditional Chinese medicine, have been reported to have anti-inflammatory activity. However, little is known about the effects of these diterpenoids on macrophage foam cell formation.Methods: A macrophage-derived foam cell formation model was established by treating RAW264.7 cells with oxidized low-density lipoprotein (ox-LDL) for 24 h. Oil red O staining were used to detect the intracellular lipids. The cholesterol efflux capacity was assayed by labeling cells with 22-NBD-cholesterol. Western blots and real-time PCRs were performed to quantify protein and mRNA expressions.Results: Two diterpenoid molecules, 14α-hydroxyisopimaric acid (C069002) and isopimaric acid (C069004), extracted from the flowers of Callicarpa rubella Lindl., significantly attenuated ox-LDL-induced foam cell formation in RAW264.7 macrophages. Further investigation showed that these two diterpenoids could promote cholesterol efflux from RAW264.7 macrophages to apolipoprotein A-I or high-density lipoproteins, which was associated with upregulated expression of ATP-binding cassette A1/G1 (ABCA1/G1), liver X receptor-α (LXRα), and peroxisome proliferator-activated receptor-γ (PPARγ). Unexpectedly, the diterpenoids C069002 and C069004 failed to enhance the mRNA transcription of the ABCG1 gene in macrophage-derived foam cells induced by ox-LDL. To evaluate the effects of diterpenoids on macrophage foam cell formation and determine the underlying mechanism, two drugs (lovastatin and rosiglitazone) were used as positive controls. Although both drugs could reduce macrophage foam cell formation and promote cholesterol efflux, they each had distinctive abilities to modulate the expression of cholesterol efflux-related genes. In contrast to lovastatin, rosiglitazone showed a similar influence on the expression of cholesterol efflux-related genes (including ABCA1, LXRα, and PPARγ) as the diterpenoids regardless of the presence or absence of ox-LDL, implying a similar mechanism by which they may exert atheroprotective effects.Conclusion: Our research indicates that diterpenoids effectively inhibit ox-LDL-induced macrophage foam cell formation by promoting cholesterol efflux from macrophages via the PPARγ-LXRα-ABCA1 pathway. Further investigation of diterpenoids as potential drugs for the treatment of atherosclerosis is warranted.