A Combined Process Algebraic and Stochastic Approach to Bone Remodeling

In adult life the bone is continuously being resorbed and renewed. Here we present a stochastic model of the homeostatic nature of bone remodeling, where osteoclasts perform bone resorption which is equally balanced by bone formation performed by osteoblasts. The stochastic model is embedded in a process-algebraic specification based on the Shape Calculus, which provides an ef- fective multiscale description of the process. Our model considers increasing dimensionality from RANKL molecular signaling to osteoclast/osteoblast stochastic dynamics within a basic multicel- lular unit (BMU) to bone mass formation. We show that after a micro-fracture the simulated bone remodeling dynamics is timescale consistent with the biological process. Our combined methodol- ogy provides a first effective stochastic model of the bone remodeling framework which could be used to test healthy and pathological conditions.