Mathematical Model of Targeted Bone Remodeling

Abstract

In this thesis stability analysis of the mathematical models for osteoporotic and osteomyelitic bone turnover is checked. The study of diseases in silico has been becoming very popular because of its rapid outcomes. This study is also beneficial from economical point of view. Several diseases have been investigated through mathematical modeling like cancer, chronic kidney diseases, liver disorders etc. Osteoporosis and osteomyelitis are very common bone disorders having different incident causes. Osteoporosis occurs due to several factors like age, estrogen deficiency or an imbalance in bone remodeling process, while osteomyelitis is caused by a bacterium called Staphylococcus aureus, a type of staph bacteria. We examined the expository signaling among the bone cells named as osteoclast and osteoblast. Main functioning of osteoblasts is bone formation while osteoclasts are bone removal cells. Mathematical frame works for both pathologies comprising of the communication between osteoclasts and osteoblasts have been presented to exhibit the conditions for stability in normal and dysregulated bone turnover. The percentage ratios of the population of osteoblast/osteoclast have been determined via numerical simulations. The remedial upshots of targeting both osteomyelitic and osteoporotic cells participating in such processes are examined. This work not only studies the dynamics of osteoporotic and osteomyelitic bone turnover but also exemplifies how therapeutic approaches might be inspected via such computational methodologies. This thesis is divided into five chapters. First chapter is about the introduction of bone biology, second chapter is comprised of the existing literature of different mathematical models of bone remodeling. Chapter 3 is based on our main results. Discussions, open problems and references are provided in chapter 4 and 5 respectively.