We investigate the remodeling process of trabecular bone inside a human vertebral body using a stochastic lattice model, in which the ability of living bone to adapt to mechanical stimuli is incorporated. Our simulations show the emergence of a networklike structure similar to real trabecular bone. With time, the bone volume fraction reaches a steady state. The microstructure, however, coarsens with a typical length in the system following a power law. The simulation results suggest that a coarsening of the trabecular structure should occur as a natural aging phenomenon, not related to disease.