Structured population models for macrophage heterogeneity in early atherosclerosis

Thesis

Atherosclerosis is a chronic inflammatory condition of the artery wall and a leading cause of death. A particular danger is the asymptomatic nature of its early stages of development. These early stages are characterised by lipid accumulation within immune cells called monocyte-derived macrophages (MDMs). MDMs ingest extracellular lipids, sourced by low-density lipoprotein particles (LDL), and offload them onto high-density lipoprotein (HDL) particles for clearance. These interactions, together with other microenvironmental factors, generate heterogeneity in the lipid content, phenotype and spatial position of the MDMs. Understanding this heterogeneity is key to predicting which early lesions will resolve and which will persist to become life-threatening. In this thesis, we use mathematical modelling to explore how MDM heterogeneity arises and evolves in early atherosclerotic lesions.

The mathematical models we study are formulated using structured differential equations that focus on the different facets of MDM heterogeneity. In Chapter 4, we develop a new lipid-structured model in which the rate of lipid uptake by MDMs depends on their available capacity We extend this model to include phenotype resolution in Chapter 5, and spatial resolution in Chapter 6. MDM phenotype is viewed as a spectrum, ranging from inflammatory (M1) to resolving (M2) states. Spatial heterogeneity is included via a Cartesian variable that represents distance into the artery wall. In Chapter 7, we combine the models of Chapters 5 and 6 into a spatially resolved, phenotype-lipid structured model.

The model analyses, which include numerical and asymptotic solutions, show that MDM heterogeneity arises in a manner dependent on blood LDL and HDL levels. When LDL lipid dominates HDL capacity in the blood, the distributions of MDM lipid content and phenotype eventually skew towards maximal capacity and inflammatory states, respectively. MDMs deeper in the lesion exhibit greater lipid loads and more inflammatory phenotypes. When instead HDL capacity dominates in the blood, mean MDM lipid content is lower and mean MDM phenotype is resolving. MDMs deeper in the lesion exhibit greater lipid loads, but a more resolving phenotype. These results provide a framework for future model validation using single-cell RNA sequencing data, and for the numerical investigation of lipoprotein-modulating and anti-inflammatory therapies for human atherosclerotic lesions.

Authors: Chambers, KL

• DOI: 10.5287/ora-9g80zekrb
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: atherosclerosis; structured population model; macrophage; space; lipid; phenotype
• Subjects: Biology--Mathematical models