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In this paper, an improved MLPG method has been introduced to simplify the algorithm and thus make it more suitable for dealing with engineering problems with complex domains. In the case of a complex domain with an irregular global boundary, it can be very hard to determine the intersections between the local sub-domains and the global boundary. The improvements of the MLPG method make the MLPG method only require the domain integrations. The intersections between local sub-domains and the global boundary as well as boundary integrations have been avoided. A rectangular problem domain and a circular problem domain with exact solutions have been studied in this paper to investigate the accuracy of the improved MLPG method. The results show that compared to the regular MLPG method, the improved MLPG method can have the same accuracy, but the improved method is much easier to deal with irregular boundaries or complex problem domains.

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Myocardial infarction is the leading cause of death and disability worldwide, and the development of new treatments can help reduce the size of myocardial infarction and prevent adverse cardiovascular events. Cardiac repair after myocardial infarction can effectively remove necrotic tissue, induce neovascularization, and ultimately replace granulation tissue. Cardiac inflammation is the primary determinant of whether beneficial cardiac repair occurs after myocardial infarction. Immune cells mediate inflammatory responses and play a dual role in injury and protection during cardiac repair. After myocardial infarction, genetic ablation or blocking of anti-inflammatory pathways is often harmful. However, enhancing endogenous anti-inflammatory pathways or blocking endogenous pro-inflammatory pathways may improve cardiac repair after myocardial infarction. A deficiency of neutrophils or monocytes does not improve overall cardiac function after myocardial infarction but worsens it and aggravates cardiac fibrosis. Several factors are critical in regulating inflammatory genes and immune cells’ phenotypes, including DNA methylation, histone modifications, and non-coding RNAs. Therefore, strict control and timely suppression of the inflammatory response, finding a balance between inflammatory cells, preventing excessive tissue degradation, and avoiding infarct expansion can effectively reduce the occurrence of adverse cardiovascular events after myocardial infarction. This article reviews the involvement of neutrophils, monocytes, macrophages, and regulatory T cells in cardiac repair after myocardial infarction. After myocardial infarction, neutrophils are the first to be recruited to the damaged site to engulf necrotic cell debris and secrete chemokines that enhance monocyte recruitment. Monocytes then infiltrate the infarct site and differentiate into macrophages and they release proteases and cytokines that are harmful to surviving myocardial cells in the pre-infarct period. As time progresses, apoptotic neutrophils are cleared, the recruitment of anti-inflammatory monocyte subsets, the polarization of macrophages toward the repair phenotype, and infiltration of regulatory T cells, which secrete anti-inflammatory factors that stimulate angiogenesis and granulation tissue formation for cardiac repair. We also explored how epigenetic modifications regulate the phenotype of inflammatory genes and immune cells to promote cardiac repair after myocardial infarction. This paper also elucidates the roles of alarmin S100A8/A9, secreted frizzled-related protein 1, and podoplanin in the inflammatory response and cardiac repair after myocardial infarction.

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