  Macrophages in atherosclerotic lesions exhibit a spectrum of behaviours or
phenotypes. The phenotypic distribution of monocyte-derived macrophages (MDMs),
its correlation with MDM lipid content, and relation to blood lipoprotein
densities are not well understood. Of particular interest is the balance
between low density lipoproteins (LDL) and high density lipoproteins (HDL),
which carry bad and good cholesterol respectively. To address these issues, we
have developed a mathematical model for early atherosclerosis in which the MDM
population is structured by phenotype and lipid content. The model admits a
simpler, closed subsystem whose analysis shows how lesion composition becomes
more pathological as the blood density of LDL increases relative to the HDL
capacity. We use asymptotic analysis to derive a power-law relationship between
MDM phenotype and lipid content at steady-state. This relationship enables us
to understand why, for example, lipid-laden MDMs have a more inflammatory
phenotype than lipid-poor MDMs when blood LDL lipid density greatly exceeds HDL
capacity. We show further that the MDM phenotype distribution always attains a
local maximum, while the lipid content distribution may be unimodal, adopt a
quasi-uniform profile or decrease monotonically. Pathological lesions exhibit a
local maximum in both the phenotype and lipid content MDM distributions, with
the maximum at an inflammatory phenotype and near the lipid content capacity
respectively. These results illustrate how macrophage heterogeneity arises in
early atherosclerosis and provide a framework for future model validation
through comparison with single-cell RNA sequencing data.
