Saddle-Node Bifurcation in Macrophage Proliferation Determines Atherosclerotic Plaque Stability

Atherosclerotic plaques are fatty deposits in arterial walls and a major cause of heart attacks and strokes. Macrophage proliferation triggers plaque growth and instability, but the exact conditions that cause stable plaques to become unstable remain unclear. To provide an insight into the conditions for this transition, we apply bifurcation analysis to the lipid-structured atherosclerosis model proposed by Chambers et al. (Bull Math Biol 86(8):104, 2024). Our main contribution is that the reduced dynamics of the system remain meaningful even beyond previously identified limits of validity. Furthermore, along with numerical bifurcation methods, the use of fast-slow analysis, combined with Fenichels theory, identifies a saddle-node bifurcation at infinity. A sharp threshold exists where macrophage proliferation balances emigration. Below this balance, the system stabilises in a biologically reasonable state; contrary to above it, macrophage numbers and lipid load grow unboundedly, triggering instability and runaway inflammation. Trends in determinant and eigenvalues also support this threshold. Parameter scans and heatmaps demonstrate that increased proliferation or reduced emigration enhances the number of macrophages and the lipid content of the necrotic core. Efferocytosis rate modulates downstream severity but does not shift the primary threshold. These findings reconcile conflicting results on macrophage proliferation, demonstrating that it is protective when emigration sufficiently balances this process. In other words, co-targeting reduced macrophage proliferation and enhanced emigration could help maintain plaque stability and reduce the risk of acute cardiovascular events. While this remains a theoretical recommendation, it offers a potential therapeutic strategy that authorises further investigation in experimental and clinical settings.