Design and validation of a mathematical model to describe macrophage dynamics in wound healing

Tony Yu

doi:10.17918/etd-6080

Macrophages have been shown to play an essential role in regulating the foreign body response, and understanding and modulating the macrophage dynamics in wound healing could potentially help overcome their ability to impair biomaterial performance. However, in vivo animal studies are often utilized to study the macrophage dynamics, which are costly and time consuming. Although there have been previous models that describe the macrophage behavior and the foreign body response, many of the parameters of these models were not based on experiments and are not physiologically relevant to macrophage biology. Therefore, there is a need to develop a model that can help predict the in vivo foreign body response in wound healing based on in vitro and/or in vivo experiments. In this study, a mathematical model was developed to describe the macrophage dynamics (M0, M1, and M2) in normal wound healing based on cell viability and flow cytometry experiments of unactivated and polarized macrophages cultured in vitro. The ordinary differential equations that describe the macrophage populations take into consideration the polarization, transition, and proliferation of surviving macrophages within each population, resulting in an accurate description of macrophage biology. This mathematical model was then applied to describe macrophage dyanmics an in vivo study of the macrophage response to implanted biomaterials, which have often been described as chronic wounds. Gelatin hydrogels, crosslinked to different extents, were used as model biomaterials. The hydrogels were characterized for properties including mechanical stiffness, degradation, swelling, and crosslinking density, and were implanted subcutaneously in C57BL/6 mice for 3 day, 10 days, and 3 weeks. H&E, Masson's trichrome, and immunohistochemistry were performed on these samples to quantify the thickness of the fibrous capsule and the relative proportions of different macrophage populations. The mathematical model was able to describe the macrophage profiles that were consistent with normal wound healing. In this model, an initial inflammatory response was observed, followed by an accumulation of M2 macrophages over time. The implanted hydrogels imposed a chronic inflammation throughout the study with a constant infiltration of M1 macrophages. The M2 macrophages behaved in a similar manner to that of normal wound healing, with a slow and gradual accumulation of M2 macrophages over time. The M1:M2 ratio indicated a dominant M1 phenotype at the early time point. At the later time point, a ratio of 1 indicated an even distribution of M1 and M2 macrophages. Correlation analyses showed that the M2 macrophages were strongly correlated with fibrous capsule thickness. Thus, the mathematical model developed here can be used to increase our understanding of macrophage dynamics in wound healing and response to biomaterials.

Design and validation of a mathematical model to describe macrophage dynamics in wound healing

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Design and validation of a mathematical model to describe macrophage dynamics in wound healing

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