2. Atherosclerosis
We studied the bifurcation for a highly nonlinear and highly coupled free boundary PDE system describing the growth of arterial plaque. The model involves high density lipoprotein cholestrols (HDL), low density lipoprotein cholestrols (LDL), macrophage cells and foam cells. As shown in the upper left figure, we consider the cross section of an artery. There are plaque region and blood flow region, with the interface separating these two regions being a free boundary. Finite branches of symmetry-breaking stationary solutions were established for the model. Moreover, we showed that the first bifurcation point for the system corresponds to the mode n=1, which would result in the solution pattern shown in the upper right figure. As some arterial plaque is often accumulated more on one side of the artery, our bifurcation result can help to understand this phenomenon.
Journal papers
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X. E. Zhao and B. Hu, “Bifurcation for a free boundary problem modeling a small arterial plaque”, Journal of Differential Equations, 2021. [ DOI | arxiv ]
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X. E. Zhao and B. Hu, “On the first bifurcation point for a free boundary problem modeling a small arterial plaque”, Mathematical Methods in the Applied Sciences, 2022. [ DOI | arxiv ]