The goal of this project is to advance the understanding of tendon disease and injury through the design and validation of a new model of tendon injury. Controlled, mechanically-induced traction injury was created in rat Achilles’ tendons with a tensioning apparatus through a minimally invasive surgical approach. Tendons were tensioned to subailure loads. Assessments of damage to tendons included gross morphology, evaluation of biomechanical of load strain curves, histopathology under light microscopy (H&E), collagen fibril structure and disruption under scanning electron microscopy, and immunohistochemical study of MMP-13 expression under confocal laser microscopy. Tendon injuries were found to be more severe with respect to loads placed upon them. Differences between treatment groups were identified subjectively in microscopic appearance (H&E), in collagen fibril organization (SEM), and in MMP-13 expression. However, analysis of the numerical data did not provide definitive evidence that this model for acute tendon injury is consistent and repeatable.

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Microbial biofilms are defined as clusters of microbial cells living in self-produced extracellular polymeric substances (EPS), which always attached to various kinds of surfaces. In this thesis, we studied several mathematical models of biofilm in the human body and marble environment. Some related background of biofilm growth and some basic existing numerical models were introduced in the first chapter. In the first project, we introduced how biofilm affects the local oxygen concentration near the neutrophil cells in the human body with three one-dimensional reaction-diffusion models from different geometries. In nature, microbial biofilm development can be observed on almost all kinds of stone monuments and can also be associated with the problem of monument conservation. In the second part of my research, we built the deliquescence models for biofilm growth environment in the first model and added biomass into consideration in the second one. Also, we analyzed the stability of the equilibria. In the third part, we applied the weather data collected from the weather station on the roof of the Jefferson Memorial to the deliquescence model with biofilm. Furthermore, compared the simulation result for biofilm growth in cold and warm weathers. In the last part of this thesis, we analyzed the biofilm activity with support vector regression. The machine learning model we obtained can be used to find the growth trends of biofilm for any pair of temperature and relative humidity data. / Mathematics