A stochastic compartmental model of bone cells

Cellular dynamics play an important role in bone remodelling. The mesenchymal cells, osteoclasts, osteoblasts and osteocytes are the four types of bone cells, which mediate bone remodelling involving bone formation and resorption throughout the human life-span. A stochastic compartmental model of bone cells is formulated in the present analysis assuming these four types of cells to be in four distinct compartments. The cumulant generating function is first derived using the transition parameters for intercompartmental diffusion. Equations for the mean, variance and covariance for the number density of these cells are then derived from the partial differential equation for the cumulant generating function. The simulation results are consistent with previous experimental observations.