Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Hristo Kojouharov


The skeleton is a very important organ that needs to be continuously remodeled due to microdamage, changes in mechanical loading, or mineral homeostasis. The bone remodeling process is responsible for maintaining the structure and function of the skeletal system. Accumulation of microdamage that goes unrepaired within the bone matrix can lead to bone fragility and loss of mechanical properties. Evidence suggests that when microdamage is present in the bone structure, osteocyte apoptosis plays an important role in the initiation of the bone remodeling process. Osteocytes are known to release RANKL a promoter of osteoclastogenesis (bone-resorbing cells) and scelorstion an inhibitor of osteoblastogenesis (bone-forming cells). The mathematical model presented in this work studies the initiation and organization of cells within a cortical bone multicellular unit (BMU) in the presence of microdamage. We did this by extending a base model and incorporating the role of osteocytes and a signaling pathway known to regulate bone formation – Wnt canonical pathway. Equilibrium and stability analysis was performed on several simplifications of the model that indicated that osteocytes may reach their maximum density depending on the rate at which osteoblast cells undergo apoptosis or become embedded in the bone matrix. Numerical simulations were performed using MATLAB in which we study the initiation of the process in the presence of several sized microcracks. Additionally, we study age-related bone disorders and potential therapeutic targets to overcome such disorders.


Bone remodeling, Wnt canonical pathway, Osteocytes, Mathematical models


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons