An energy-based technique for the development of a mechanobiological growth model of vertebrae

Mechanobiological growth is the biological process whereby bone growth is modulated by mechanical loading. The goal of this study is to develop an energy-based mechanobiological bone growth model. Mechanobiological procedures basically include mechanosensing and mechanoregulation. This study represented the mechanosensing as a mathematical model combining energy and mechanical-triggered deformation. The mechanoregulation was modelled as a mathematical form integrated distortion and dilatation energy. Mechanobiological growth model was developed from those two procedures and represented as a function of distortion and dilatation stresses. The model was tested by using finite element model of a thoracic vertebra (T7) for simulating one-year growth procedure under multi-axial loads. The simulation results presented the retarded and stimulated growth under compression and tension. Shear stress increased the growth rate with 20%–40%. This model agreed with experimental study of growth and published numerical growth simulation of human vertebrae as well as mechanobiology theory. This model allows simulating vertebral growth under multi-direction loads.