The Cellular Dynamics of Bone Remodeling: a Mathematical Model

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nonlinear PDE
time delay
bone remodeling
bone multicellular units
cellular dynamics

The mechanical properties of vertebrate bone are largely determined by a processwhich involves the complex interplay of three different cell types. This process is called bone remodelingand occurs asynchronously at multiple sites in the mature skeleton. The cells involvedare bone resorbing osteoclasts, bone matrix producing osteoblasts, and mechanosensing osteocytes.These cells communicate with each other by means of autocrine and paracrine signaling factors andoperate in complex entities, the so-called bone multicellular units (BMUs). To investigate the BMUdynamics in silico, we develop a novel mathematical model resulting in a system of nonlinear partialdifferential equations (PDEs) with time delays. The model describes the osteoblast and osteoclastpopulations together with the dynamics of the key messenger molecule RANKL and its decoy receptorOPG. Scaling theory is used to address parameter sensitivity and predict the emergence ofpathological remodeling regimes. The model is studied numerically in one and two space dimensionsusing finite difference schemes in space and explicit delay equation solvers in time. The computationalresults are in agreement with in vivo observations and provide new insights into the role ofthe RANKL/OPG pathway in the spatial regulation of bone remodeling.

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Ryser, M., Komarova, S., & Nigam, N. (2010). The cellular dynamics of bone remodeling: A mathematical model. SIAM Journal on Applied Mathematics, 70(6), 1899-1921. doi:10.1137/090746094