A new dynamic model for non-viral multi-treatment gene delivery systems for bone regeneration: parameter extraction, estimation, and sensitivity

In this thesis we develop new mathematical models, using dynamical systems, to represent localized gene delivery of bone morphogenetic protein 2 into bone marrow-derived mesenchymal stem cells and rat calvarial defects. We examine two approaches, using pDNA or cmRNA treatments, respectively, towards the production of calcium deposition and bone regeneration in in vitro and in vivo experiments. We first review the relevant scientific literature and survey existing mathematical representations for similar treatment approaches. We then motivate and develop our new models and determine model parameters from literature, heuristic approaches, and estimation using sparse data. We next conduct a qualitative analysis using dynamical systems theory. Due to the nature of the parameter estimation, it was important that we obtain local and global sensitivity analyses of model outputs to changes in model inputs. Finally we compared results from different treatment protocols. Our model suggests that cmRNA treatments may perform better than pDNA treatments towards bone fracture healing. This work is intended to be a foundation for predictive models of non-viral local gene delivery systems.