Here we developed a spatio-temporal bone remodeling model to simulate the action of Basic Multicelluar Units (BMUs). This model is based on two major extensions of a temporal-only bone cell population model (BCPM). First, the differentiation into mature resorbing osteoclasts and mature forming osteoblasts from their respective precursor cells was modelled as an intermittent process based on precursor cells availability. Second, the interaction between neighbouring BMUs was considered based on a “metabolic cost” argument which warrants that no new BMU will be activated in the neighbourhood of an existing BMU. With the proposed model we have simulated the phases of the remodelling process obtaining average periods similar to those found in the literature: resorption (∼22 days)—reversal (∼8 days)—formation (∼65 days)—quiescence (560–600 days) and an average BMU activation frequency of ∼1.6 BMUs/year/mm³. We further show here that the resorption and formation phases of the BMU become coordinated only by the presence of TGF-β (transforming growth factor β), i.e., a major coupling factor stored in the bone matrix. TGF-β is released through resorption so upregulating osteoclast apoptosis and accumulation of osteoblast precursors, i.e., facilitating the transition from the resorption to the formation phase at a given remodelling site. Finally, we demonstrate that this model can explain targeted bone remodelling as the BMUs are steered towards damaged bone areas in order to commence bone matrix repair.

Numerical models of bone remodelling have traditionally been used to perform in silico tests of bone loss in postmenopausal women and also to simulate the response to different drug treatments. These models simulate the menopausal oestrogen decline by altering certain signalling pathways. However, they do not consider the simultaneous effect that ageing can have on cell function and bone remodelling, and thus on bone loss. Considering ageing and oestrogen decline together is important for designing osteoporosis treatments that can selectively counteract one or the other disease mechanism. A previously developed bone cell population model was adapted to consider the effect of ageing through: (1) the decrease of TGF- $$\upbeta$$β contained in the bone matrix and (2) an increased production of sclerostin by non-skeletal cells. Oestrogen deficiency is simulated in three different ways: (a) an increase in RANKL expression, (b) a decrease in OPG production, and (c) an increase in the responsiveness of osteoclasts to RANKL. The effect of ageing was validated using the cross-sectional study of (Riggs et al. in J Bone Miner Res 19: 1945-1954, 2004) on BMD of trabecular bone of the vertebral body of men. The joint effect of ageing and oestrogen deficiency was validated using these same clinical results but in women. In ageing, the effect of the increasing production of sclerostin is more important than the decrease of TGF- $$\upbeta$$β , while the three mechanisms used to simulate the effect of oestrogen deficiency produce almost identical responses. The results show that an early menopause leads to a lower average density in the fifth decade, but after the sixth decade the average density is independent of the age at menopause. Treatment of osteoporosis with denosumab was also simulated to conclude that the drug is not very effective if started before 10 years after menopause or before age 60.