Lumbar spine diseases have caught much social attention during the past decades due to their impacts on our living quality, and it is generally accepted that the functional adaptation of bone is a significant factor for the prevention and surgical treatment of spine disorders.

In this thesis, a methodology frame was postulated and a simulation algorithm developed. The motivations for developing this methodology frame include:​

• Loading histories to which a bone structure is subjected could be mapped to daily physical activities.
• Whole inventory of loading histories should be considered while relating the bone adaptive remodeling process with mechanical stimuli.
• Biological subjects should be dealt with individually, associated with the available information from a specific subject.
• Comprehensive mathematical models, which can handle all the information contained in loading histories, and finite element models, corresponding to the mathematical models, should be developed for the exploration of the bone remodeling phenomenon.

In the algorithm, loading histories were described as stochastic processes. The feasibility of the algorithm was confirmed by applying stochastic loading histories on two and three-dimensional finite element models of simplified spine structures.

As an application, the algorithm was used to evaluate the biomechanical environment for inter-vertebral fusion as well as the associated risks of device/graft subsidence. With the capability provided by the algorithm, the effects of bone adaptive remodeling on the fusion environment and the risks of device/graft subsidence were considered simultaneously. With the flexibility imbedded in the methodology frame, not only the effects of the contributing factors, but also the interactions among the factors were examined.

The simulation results indicated that bone density in adjacent vertebrae and contact area between device/graft and vertebrae are the factors contributing the most to prevent device/graft subsidence and to increase the structural stiffness reached by intervertebral fusion. The effect of bone adaptive remodeling is a statistically significant factor for reducing the risk of device/graft subsidence. W hether the condition immediately after instrumentation is the worst-case scenario for mechanical strength and stiffness of the instrumented spine structure depends on the initial condition of the tested factors, such as initial bone density distribution, contact area, and the capability of bone growth.