Effects of temporal changes in PTHrP and Ihh expressions on bone growth, studied by a theoretical model

The rate of bone growth reduces in response to both short-term daily mechanical loading and irradiation therapy. The nature of these interventions and their distinct temporal effects suggest different mechanisms. Yet, both mechanical loading and irradiation therapy have been associated with changes in PTHrP. The question rises to what extent the observed effects can be assigned to the PTHrP-Ihh control system, which is probably the most important mechanism for regulating bone growth. This chapter addresses this question using a theoretical model in which bone growth is only controlled by the growth factors PTHrP, Ihh and VEGF.To study the effects of mechanical loading on bone growth, first the expressions of PTHrP and Ihh by growth-plate chondrocytes in response to compressive loading are monitored. They decrease to 18% (PTHrP) and 44% (Ihh) of control levels. These values are used throughout the chapter to simulate both mechanical loading and irradiation therapy. Simulations of daily loading periods reveal load-dependent variations in growth rate, without significant structural changes to the growth plate. Structural adaptation starts when multiple hours of loading are applied daily, therewith further reducing the growth rate. When twelve hours of activity are applied each day, a circadian growth-rhythm emerges. In simulations of irradiation therapy, it takes almost ten weeks to recover from structural changes that are initiated during a one-week irradiation period. During this time the growth rate remains reduced and a bone-length difference develops which persists till adulthood. These effects concur with experimental data. Therefore, it is concluded that a system with only PTHrP, Ihh and VEGF is sufficient to capture effects of temporal variations in growth factor expressions on bone growth. The most interesting insight from this study is that two effects with different time-constants determine the responses. The first one is the direct effect of these growth factors on the rates of proliferation and hypertrophy. The second one, acting on a longer time-scale, relates to the structural changes in the tissue, secondary to sustained changes in growth-factor expressions.