A Quantitative Model of Early Atherosclerotic Plaques Parameterized Using In Vitro Experiments

Abstract

There are a growing number of studies that model immunological processes in the artery wall that lead to the development of atherosclerotic plaques. However, few of these models use parameters that are obtained from experimental data even though data-driven models are vital if mathematical models are to become clinically relevant. We present the development and analysis of a quantitative mathematical model for the coupled inflammatory, lipid and macrophage dynamics in early atherosclerotic plaques. Our modeling approach is similar to the biologists' experimental approach where the bigger picture of atherosclerosis is put together from many smaller observations and findings from in vitro experiments. We first develop a series of three simpler submodels which are least-squares fitted to various in vitro experimental results from the literature. Subsequently, we use these three submodels to construct a quantitative model of the development of early atherosclerotic plaques. We perform a local sensitivity analysis of the model with respect to its parameters that identifies critical parameters and processes. Further, we present a systematic analysis of the long-term outcome of the model which produces a characterization of the stability of model plaques based on the rates of recruitment of low-density lipoproteins, high-density lipoproteins and macrophages. The analysis of the model suggests that further experimental work quantifying the different fates of macrophages as a function of cholesterol load and the balance between free cholesterol and cholesterol ester inside macrophages may give valuable insight into long-term atherosclerotic plaque outcomes. This model is an important step toward models applicable in a clinical setting.

A lipid-structured model for macrophage populations in atherosclerotic plaques

“…Rates of LDL ingestion occur on the scale of minutes-to-hours whereas rates of macrophage apoptosis occur on the scale of days-to-weeks [8,38]. We assume that changes in occur over a much shorter timescale than the timescale of the cell dynamics such that changes in cell numbers M produce rapid changes in LDL particle numbers .…”

“…We assume that the LDL and HDL dynamics have a similar short timescale [38] such that the HDL dynamics are fast and we may make a quasi-steady state approximation. Setting dh dt 00 in equation (9) we deduce that:…”

“…To our knowledge, parameter values associated with atherosclerotic plaques in vivo are not currently known and may vary markedly between individuals or even plaques. Here, guided by the parameter estimates from [38], biologically plausible parameters values were chosen to simulate four different plaque states illustrated in Figure 2. The chosen values and reasoning for each state are as follows.…”

A Spatially Resolved and Quantitative Model of Early Atherosclerosis

“…Monocyte-derived macrophages are at the crux of early atherogenesis as they populate inflamed tissue, actively scavenge and ingest modified LDL, undergo controlled cell death (apoptosis) and consume other dead and dying macrophages (efferocytosis) [65,32,33,65]. Macrophages store the cholesterol from ingested LDL as intracellular free and esterified cholesterols, which are at a dynamic buffer-like equilibrium [7,8,92]. The maintenance of intracellular cholesterol balance between essential and cytotoxic limits is disrupted in plaque macrophages when there is an excess consumption of modified LDL [49] and poor access to HDL which exports intracellular free cholesterol out of cells [7,73].…”

“…The formation of early atherosclerotic plaques is modeled and quantified in a previous work by the present authors [92]. In that publication, a parameterized set of ordinary differential equations (ODEs) was developed that predicts key inflammatory and lipid processes of early atherosclerosis: LDL modification by macrophages and endothelial cells, HDL protection against LDL modification, LDL ingestion by macrophages, intracellular cholesterol cycle within macrophages, reverse cholesterol transport to HDL as well as macrophage apoptosis.…”