With the aging population, bone implants, as the key medical devices in orthopedic surgery, have captured great interest of the scientific and medical communities. An ideal bone implant should form a stable composite with the host bone, restore the original mechanical support and load transfers in the bone tissue, slow down bone degradation and reduce the risk of fractures in patients. However, bone tissue is an adaptive system that undergoes structural evolution in response to the mechanical stimulus, which means that the formation and the long-term stability of the bone-implant composite postoperatively heavily depend on the mechanical environment constructed by the bone implant, placing higher demands on implant designs. Therefore, the study of bone remodeling algorithm under mechanical stimulus and its application in predicting bone remodeling induced by the mechanical environment of orthopedic implants holds significant scientific and clinical value for bone implants design.

Firstly, this thesis proposed a bone structure prediction algorithm that coupled physiological stochastic features into conventional topology optimization, and predicted the trabecular structure of the proximal femur under two physiological conditions: the adult healthy bone and the elderly osteoporotic bone. In addition, a mechanical boundary condition on femur based on 13 daily activities was established to reproduce the mechanical stimuli driving the trabecular bone evolution. The results showed that: (1) Coupling physiological stochastic characteristics into the topology optimization algorithm resulted in a bone density distribution closer to real bone. (2) Compared with the adoption of the adult physiological feature, the introduction of the elderly physiological feature in the prediction model led to the degeneration of bone morphological parameters, including trabecular thickness and trabecular spacing, which was more consistent with the bone structural deterioration in clinical data. (3) The introduction of physiological stochastic features did not undermine the convergence of the topology optimization algorithm but instead led to a more uniform distribution of strain energy density in the bone tissue, which was closer to the goal of actual bone evolution. (4) The boundary condition based on the 13 daily activities reproduced the mechanical environment of the proximal femur well in the two-dimensional model. Porous patterns and trabecular trajectories similar to those of the real bones can be realized without the adoption of extra constraints, such as the perimeter constraints and local density constraints.

Secondly, this thesis explored the factors that affect the mechano-regulated bone ingrowth in porous fusion cages, including the internal mechanical environment of the porous cages and the global stiffness of the porous cage. A third lumbar finite element model was established for the in silico fusion surgery. The bone remodeling algorithm based on design space optimization and topology optimization was used to simulate the osseointegration process of the third lumbar with different cages. At the same time, the mechanical boundary condition of the third lumbar was calculated using the inverse Wolff's law approach. The results showed that: (1) The boundary condition obtained by the inverse Wolff's law approach for the third lumbar resulted in similar bone density distribution to real bones, indicating the feasibility of the obtained boundary condition. (2) The cage with higher global stiffness had excellent initial mechanical stability, but failed to provide sufficient mechanical stimulus on bone tissue in porous space, resulting in poor bone ingrowth. The cage of low global stiffness led to more bone ingrowth, but its mechanical stability was relatively low, which increased the risk of implant failure. (3) The strain-enhanced cage combined the strengths of both, providing additional mechanical stimulus on bone tissue while maintaining relatively low cage’s compliance, resulting in more bone formation and optimal mechanical stability simultaneously. It is possible to guide bone ingrowth and promote bone-implant integration via designing the internal mechanical environment of the scaffolds, while ensuring global rigidity of bone cage for initial mechanical stability.

Then, this thesis proposed a vertebral fusion cage based on twist metamaterials to achieve improved bone bridging by designing the internal mechanical environment of the cage. In addition, an immune-regulated bone regeneration model was used to simulate the osteogenesis process during the early postoperative stage. The design space optimization-topology optimization based bone remodeling algorithm was applied to simulate the long-term mechano-regulated postoperative fusion process. The results showed that: (1) Twist metamaterials constructed cell pathways in the direction of bone bridging formation via the unique structural design, resulting in higher immune-regulated bone growth. (2) Twist metamaterials generated a shear driving force on the bone tissue in the direction of depth via the unique displacement mode of struts, providing continuous mechanical stimulus for bone bridging. (3) Twist metamaterials efficiently utilized bone mass to achieve intervertebral bone bridging without excessively undermining the microstructure of the host bone. (4) Instead of most researches that focus on the apparent properties of metamaterials, this thesis suggested that the distinctive displacement modes within metamaterials could be intentionally engineered to create a mechanical environment that directed bone growth, which provided more degrees of freedom in the design of porous bone scaffolds.

Finally, this thesis developed the time-dependent topology optimization method and applied it in the design of bone cement injection protocols in vertebroplasty. Compared with the ‘passive’, ‘trial-and-error approach’ design approach of bone implants, this thesis aimed to achieve intentional ‘active’ design of the bone cement protocol. Via establishing the relationship between bone formation in future and the bone cement distribution, the optimized bone cement protocol for highest bone preservation was obtained via the time-dependent topology optimization. The mechanical stimulus reference value in the bone mechanostat model was predicted using an iterative method. The results showed that: (1) The bone cement injection protocol designed using the time-dependent topology optimization method had a positive effect on maintaining long-term bone mass in elderly people. (2) Compared with the control group and the uniform bone cement group, the axial stiffness of the augmented vertebral body in optimized group was higher. (3) The bone cement distribution obtained via the topology optimization for maximum cement stiffness, although provided highest mechanical stability, caused significant bone loss due to its severe stress shielding effect.