A novel mathematical model identifies potential factors regulating bone apposition

Regulatory Perspectives in Pharmacometric Models of Osteoporosis

Osteoporosis is a disorder of the bones in which they are weakened to the extent that they become more prone to fracture. There are various forms of osteoporosis: some of them are induced by drugs, and others occur as a chronic progressive disorder as an individual gets older. As the median age of the population rises across the world, the chronic form of the bone disease is drawing attention as an important worldwide health issue. Developing new treatments for osteoporosis and comparing them with existing treatments are complicated processes due to current acceptance by regulatory authorities of bone mineral density (BMD) and fracture risk as clinical end points, which require clinical trials to be large, prolonged, and expensive to determine clinically significant impacts in BMD and fracture risk. Moreover, changes in BMD and fracture risk are not always correlated, with some clinical trials showing BMD improvement without a reduction in fractures. More recently, bone turnover markers specific to bone formation and resorption have been recognized that reflect bone physiology at a cellular level. These bone turnover markers change faster than BMD and fracture risk, and mathematically linking the biomarkers via a computational model to BMD and/or fracture risk may help in predicting BMD and fracture risk changes over time during the progression of a disease or when under treatment. Here, we discuss important concepts of bone physiology, osteoporosis, treatment options, mathematical modeling of osteoporosis, and the use of these models by the pharmaceutical industry and the Food and Drug Administration.

The role of osteocytes in targeted bone remodeling: a mathematical model

Until recently many studies of bone remodeling at the cellular level have focused on the behavior of mature osteoblasts and osteoclasts, and their respective precursor cells, with the role of osteocytes and bone lining cells left largely unexplored. This is particularly true with respect to the mathematical modeling of bone remodeling. However, there is increasing evidence that osteocytes play important roles in the cycle of targeted bone remodeling, in serving as a significant source of RANKL to support osteoclastogenesis, and in secreting the bone formation inhibitor sclerostin. Moreover, there is also increasing interest in sclerostin, an osteocyte-secreted bone formation inhibitor, and its role in regulating local response to changes in the bone microenvironment. Here we develop a cell population model of bone remodeling that includes the role of osteocytes, sclerostin, and allows for the possibility of RANKL expression by osteocyte cell populations. We have aimed to give a simple, yet still tractable, model that remains faithful to the underlying system based on the known literature. This model extends and complements many of the existing mathematical models for bone remodeling, but can be used to explore aspects of the process of bone remodeling that were previously beyond the scope of prior modeling work. Through numerical simulations we demonstrate that our model can be used to explore theoretically many of the qualitative features of the role of osteocytes in bone biology as presented in recent literature.

Towards a new spatial representation of bone remodeling

Irregular bone remodeling is associated with a number of bone diseases such as osteoporosis and multiple myeloma. Computational and mathematical modeling can aid in therapy and treatment as well as understanding fundamental biology. Different approaches to modeling give insight into different aspects of a phenomena so it is useful to have an arsenal of various computational and mathematical models. Here we develop a mathematical representation of bone remodeling that can effectively describe many aspects of the complicated geometries and spatial behavior observed. There is a sharp interface between bone and marrow regions. Also the surface of bone moves in and out, i.e. in the normal direction, due to remodeling. Based on these observations we employ the use of a level-set function to represent the spatial behavior of remodeling. We elaborate on a temporal model for osteoclast and osteoblast population dynamics to determine the change in bone mass which influences how the interface between bone and marrow changes. We exhibit simulations based on our computational model that show the motion of the interface between bone and marrow as a consequence of bone remodeling. The simulations show that it is possible to capture spatial behavior of bone remodeling in complicated geometries as they occur in vitro and in vivo. By employing the level set approach it is possible to develop computational and mathematical representations of the spatial behavior of bone remodeling. By including in this formalism further details, such as more complex cytokine interactions and accurate parameter values, it is possible to obtain simulations of phenomena related to bone remodeling with spatial behavior much as in vitro and in vivo. This makes it possible to perform in silica experiments more closely resembling experimental observations.

Short-time survival and engraftment of bone marrow stromal cells in an ectopic model of bone regeneration

In tissue-engineered applications bone marrow stromal cells (BMSCs) are combined with scaffolds to target bone regeneration; animal models have been devised and the cells' long-term engraftment has been widely studied. However, in regenerated bone, the cell number is severely reduced with respect to the initially seeded BMSCs. This reflects the natural low cellularity of bone but underlines the selectivity of the differentiation processes. In this respect, we evaluated the short-term survival of BMSCs, transduced with the luciferase gene, after implantation of cell-seeded scaffolds in a nude mouse model. Cell proliferation/survival was assessed by bioluminescence imaging: light production was decreased by 30% on the first day, reaching a 50% loss within 48 h. Less than 5% of the initial signal remained after 2 months in vivo. Apoptotic BMSCs were detected within the first 2 days of implantation. Interestingly, the initial frequency of clonogenic progenitors matched the percentage of in vivo surviving cells. Cytokines and inflammation may contribute to the apoptotic onset at the implant milieu. However, preculturing cells with tumor necrosis factor alpha enhanced survival, allowing detection of 8.1% of the seeded BMSCs 2 months after implantation. Thus culturing conditions may reduce the apoptotic overload of seeded osteoprogenitors, strengthening the constructs' osteogenic potential.