  The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol
ratio has been shown a high correlation with the cardiovascular risk
assessment. Is it possible to quantify the correlation mathematically? In this
paper, we develop a bifurcation analysis for a mathematical model of the plaque
formation with a free boundary in the early stage of atherosclerosis. This
bifurcation analysis, to the ratio of LDL/HDL, is based on the explicit
formulation of radially symmetric steady-state solutions. By performing the
perturbation analysis to these solutions, we establish the existence of
bifurcation branches and derive a theoretical condition that a bifurcation
occurs for different modes. Then we also analyze the stability of radially
symmetric steady-state solutions and conduct numerical simulations to verify
all the theoretical results.
