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 \emph{in vitro} and \emph{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 \emph{in vitro} and \emph{in vivo}. This makes it possible to perform \emph{in silica} experiments more closely resembling experimental observations.Comment: Math. Biosci. Eng., 9(2), 201

Modeling and Simulation of the Effects of Cyclic Loading on Articular Cartilage Lesion Formation

We present a model of articular cartilage lesion formation to simulate the effects of cyclic loading. This model extends and modifies the reaction-diffusion-delay model by Graham et al. 2012 for the spread of a lesion formed though a single traumatic event. Our model represents "implicitly" the effects of loading, meaning through a cyclic sink term in the equations for live cells. Our model forms the basis for in silico studies of cartilage damage relevant to questions in osteoarthritis, for example, that may not be easily answered through in vivo or in vitro studies. Computational results are presented that indicate the impact of differing levels of EPO on articular cartilage lesion abatement

Selection of reference genes for normalization of quantitative real-time PCR in organ culture of the rat and rabbit intervertebral disc

<p>Abstract</p> <p>Background</p> <p>The accuracy of quantitative real-time RT-PCR (qRT-PCR) is often influenced by experimental artifacts, resulting in erroneous expression profiles of target genes. The practice of employing normalization using a reference gene significantly improves reliability and its applicability to molecular biology. However, selection of an ideal reference gene(s) is of critical importance to discern meaningful results. The aim of this study was to evaluate the stability of seven potential reference genes (Actb, GAPDH, 18S rRNA, CycA, Hprt1, Ywhaz, and Pgk1) and identify most stable gene(s) for application in tissue culture research using the rat and rabbit intervertebral disc (IVD).</p> <p>Findings</p> <p><it>In vitro</it>, four genes (Hprt1, CycA, GAPDH, and 18S rRNA) in rat IVD tissue and five genes (CycA, Hprt1, Actb, Pgk1, and Ywhaz) in rabbit IVD tissue were determined as most stable for up to 14 days in culture. Pair-wise variation analysis indicated that combination of Hprt1 and CycA in rat and the combination of Hprt1, CycA, and Actb in rabbit may most stable reference gene candidates for IVD tissue culture.</p> <p>Conclusions</p> <p>Our results indicate that Hprt1 and CycA are the most stable reference gene candidates for rat and rabbit IVD culture studies. In rabbit IVD, Actb could be an additional gene employed in conjunction with Hprt1 and CycA. Selection of optimal reference gene candidate(s) should be a pertinent exercise before employment of PCR outcome measures for biomedical research.</p