Modeling, analysis and simulation of macrophage activation post-myocardial infarction

Background: Left ventricle (LV) remodeling is the key part after myocardial infarction (MI). Adverse LV remodeling can cause congestive heart failure, and the outcome is determined by, most notably, classical activation macrophage (M1) and alternative activation macrophage (M2). Due to lack of complete sets of experimental data, building a mathematical model for macrophage activation is usually a difficult task.

Methods: In this study, we proposed three strategies to mathematically model the interaction of M1 and M2. First, we investigated a conceptual dynamic network to model the cellular interaction between M1 and M2. The population of M1 and M2 were determined by the interaction strength among the particles of M1 or M2. This population based model is aim to analyze the effects of the interaction strength at cellular level. Second, we employed ordinary differential equations (ODEs) to represent the population of M1 and M2 (cell density) by molecular interactions with a mechanism-based method. A mechanism-based model was supported by the experimental data from literature search and validated by the experimental data. Third, we established one combined model based on replicator dynamics to describe the process of macrophage activation at two different levels. Finally, we also analyzed the stability conditions by Lyapunov theory. The stability conditions of different models were demonstrated through simulated systems.

Results: We established a mechanism-based mathematical model for macrophage activation and evaluated the model with population measurement. Our stability analysis gave the condition on interaction strength and could be used as a useful tool to predict the responses of specific cellular populations. The mechanism-based mathematical model offered a powerful tool to understand the macrophage activation during LV remodeling. The combined model gave a better way to analyze the macrophage activation at different levels.

Conclusions: In this dissertation, we studied two types of macrophage activation process at the cellular level in order to investigate game dynamics in large population with discrete generations. We compared the different strategies that a single individual will compete or cooperate with the individuals around it. Furthermore, ODEs model can quantify the dynamic interactions and temporal changes of the regulatory factors. The model was established using our own experimental data and validated by the experimental data from literatures. Finally, the replicator dynamic based combined model can give better understanding about the relationship between the interaction strength and stability of the biological system.