Bone tissue is known to adapt to a stress change with some time delay. In vivo experimental studies were conducted for measuring the effects of mechanical loading on bone remodelling. In parallel, numerous models were developed for simulating the long-term bone response to various physical activities. However, most of models neglected the delay of bone response and they were not fully identified with corresponding experimental measurement. The purpose of this work was to develop a model describing the delay between stress change and cortical bone response.

A mathematical model was developed, accounting for the delays for bone response to stress. For in vivo experiment, 80 female Wistar rats (9-week old) were randomly divided into a running and a control group. First group regimen consisted of treadmill running program: 1 hr. per day, 6 days a week during first 15 weeks (treadmill speed 1.6 km/h). At week 15, the running group rats were returned to normal activity (sedentary state in cages), during last 15 weeks. Rats of the control group were subjected to normal activity for each period. At week 0, 3, 7, 15 (end of running period), 16, 18, 22 and 30 (end of experiment), 5 rats of each group were sacrificed for measuring the bone relative density via micro-hardness measurement on the left tibia (60 points per tibia).

Bone density of running group increased asymptotically during the first 15 weeks. An abrupt decrease of density occurred when rats returned to sedentary state at week 15. The densification rate is ten times lower than the rate whereas bone formation delay (13 days) is greater than bone resorption delay (1 day). These delays were related to the delays of bone cells activities with mineralisation process in reaction to physical activities.