About 15% of the world population is affected by osteoarthritis (OA), a chronic degenerative disease of the cartilage within the joint space. An estimated 39 million people are in the European Union and 20 million are in the United States. These numbers are predicted to double by 2020. Traumatic injury, disease, and chronic mechanical loading are all causes of cartilage damage. It is well established that cartilage, when damaged, has a limited intrinsic repair capacity. The regenerated tissue that does form is fibrocartilogenous in nature, and has inferior biomechanical properties. Eventually, these inferior properties lead to further degeneration, osteoarthritis and ultimately total knee replacement (TKR). There are several alternative treatment options currently in use:​ autologous chondrocyte implantation (ACI), osteochondral autograft transplantation (OATS), or microfracture.

Numerous studies have shown an increase in chondrogenic response of chondrocytes and cartilage precursor cells to mechanical stimulation in vitro. Therefore, it is reasonable to assume mechanical stimuli regulate cartilage development. Here, the goal was to evaluate how chondrogenesis and cartilage health change as a result of applying different hydrodynamic environments. In order to accomplish this, a mathematical model correlating mechanical stimuli (hydrodynamic environment) with periosteal chondrogenesis has been investigated. The main objectives of this research are:​ 1) to modify an existing mathematical model to evaluate chondrogenesis, and the maintenance and growth of cartilage over time;​ 2) to characterize the hydrodynamic environment at the tissue face in the spinner flask bioreactor and correlate the results to the modified model of chondrogenesis and cartilage growth;​ and lastly, 3) to compare the effect of mechanical stimulation on cartilage repair strategies in an in vitro culture model modified for cartilage repair whose hydrodynamic environment can be characterized accurately.

Mathematical modeling is a tool used for quantifying and simplifying the complexity of biological systems such as the numerous chemical processes occurring within tissue growth and maintenance. Furthermore, computational fluid dynamics (CFD) is a tool for quantitatively determining the hydrodynamic (fluid force) environment experienced directly by a tissue in a fluid domain. Here, we have developed a mathematical model for periosteal chondrogenesis. We have also used CFD to characterize the hydrodynamic environment of the spinner flask bioreactor that was used to induce periosteal chondrogenesis. The mathematical model uses volume fraction data acquired from histological sections. Recently, the development of contrast-enchanced nanofocus computed tomography (CE-nanoCT), a noninvasive imaging technique has been compared favorably to histology. Thus, the ,mathematical model presented here could be used in helping patients by developing and modifying rehabilitation regimes catered specifically to the status of their cartilage repair tissue.

Additionally, the volume fraction results of mechanical stimulation were compared to volume fraction data of the chondrogenic periosteal time course used for developing the mathematical model in Chapter 3. From this comparison, mechanical stimulation of periosteum by shear forces was found to stimulate chondrogenesis to the peak of its chondrocytic ECM production phase (day 21-28 in the periosteal chondrogenesis time course). This indicates that shear stress may cause differentiating cells to remain in a phase of continual cartilage formation. This conclusion of continual growth due to shear stress is further supported by the large size the samples grew to by the end of the culture period in the spinner flasks.

Developing mathematical model requires data collection from an in vitro culture in order to solve for the various parameters and constants. Therefore, in order to complete the goal and be able to evaluate more specific questions and intricacies of how hydrodynamic forces influence chondrogenesis and cartilage health and maintenance, an in vitro culture model for cartilage repair using the spinner flask bioreactor was also investigated. This in vitro model combined a spinner flask and an established integration culture model. After preliminary testing, modifications were made and further development is underway. There is still work to be done to make the final correlation between chondrogenic differentiation and changes in hydrodynamic environment. This thesis work represents a first step in accomplishing this task through investigation of different aspects of periosteal chondrogenesis and spinner flask bioreactors as well as different methods of doing so.