Document Type


Date of Degree

Summer 2019

Access Restrictions

Access restricted until 09/04/2021

Degree Name

PhD (Doctor of Philosophy)

Degree In

Applied Mathematical and Computational Sciences

First Advisor

Ayati, Bruce

Second Advisor

Mitchell, Colleen

First Committee Member

Ayati, Bruce P

Second Committee Member

Mitchell, Colleen C

Third Committee Member

Salem, Aliasger K

Fourth Committee Member

Stroyan, Keith D

Fifth Committee Member

Camillo, Victor P


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.


bone regeneration, mathematical modeling, ordinary differential equations, parameter estimation, parameter sensitivity, uncertainty quantification


xv, 286 pages


Includes bibliographical references (pages 283-286).


Copyright © 2019 Ruqiah Muhammad

Available for download on Saturday, September 04, 2021