Objective To propose a topology-optimized design method for bone plates that effectively reduces stress concentration and improves bone healing compared with traditional topology-optimized method.Methods Based on the load constraints of a bone plate in a broken bone-splint system,an improved topology optimization method based on the load path was used to optimize the design of the bone plate structure.Subsequently,a bone regeneration simulation model based on bias strain was used to simulate the transverse fracture of the tibial tuberosity,and the force state,fixation stability,and healing performance of the optimized plate were evaluated based on data from the bone regeneration process.Results Using the optimized bone plate based on the load path optimization method,the maximum stresses of the bone plate were 55.68 MPa and 42.23 MPa at volume fractions f=0.55 and 0.65,respectively,which were reduced by 32.96％and 29.95％,respectively,compared with the optimized bone plate using the traditional topology optimization method.The average elastic moduli of the callus after the bone-healing process were 1 439.47 MPa and 1 355.71 MPa,respectively.These values were 145.86％and 131.06％higher than those of traditional bone plates,respectively.Conclusions In this study,the proposed improved topology optimization method based on the load path was used to optimize bone-plate structures.Compared to the bone plate obtained using the traditional topology optimization method,the optimized bone plate was more uniformly loaded and safer.The bone-healing performance was significantly improved compared to the traditional bone plate.These results provide a new method for the optimal design of internal fixation implants for fractures.

Objective To study distributions of stiffness and stress of each component in internal fixation system for long bone fractures composed of fractured bones (including callus) and bone plates,and propose a method for determining bending stiffness of fracture internal fixation implants. Methods Based on the linear bending theory and composite beam theory, the mechanical model of femoral shaft internal fracture fixing system composed of fractured bones and bone plate was constructed and verified with the finite element model based on artificial femur CT data. The relationship between stress and stiffness of the internal fixation system for long bone fractures was established. Results The three stages (slow-rapid-steady growth) for variation of fractured bone bending stiffness with callus elastic modulus obtained by calculation and analysis were consistent with the three stages of actual bone healing process, which proved accuracy of the theoretical calculation method. Changing patterns for the neutral axis position of internal fracture fixing system composed of fractured bones and bone plate were further obtained, namely, the neutral axis position was close to (away from) the central axis of bone plate when stiffness of bone plate increased (decreased). According to the stress required for fracture healing (0.72-0.80 MPa), the reasonable range for bending stiffness of bone plate was 0.99-4.20 kN·mm2. Conclusions When elastic modulus of the callus was 0.037.00 GPa, bending stiffness of the fractured bones increased rapidly, which was at the stage of bone bridge formation. When elastic modulus of the callus was above 7 GPa, the callus tended to mature. Based on the femur model in this study, when thickness of bone plate was 3.6-6.0 mm and elastic modulus of fractured bones was 3.013.5 GPa, the entire fractured bone section could be effectively stimulated. In this study, when bending stiffness of bone plate was 0.99-4.20 kN·mm2 during the generation stage of bone bridge, it was conducive to bone healing.

Internal fixator is usually adopted in the treatment of bone fractures. In order to achieve anatomical reduction and effective fixation of fractures, the placement of internal fixators should comply with the biology force line of the bone and adapt to the specific anatomical morphological characteristics of the cortical bone. In order to investigate the distribution characteristics and formation regularity of biology force line and cortical thickness of human bone, three-dimensional model of proximal femur is established by using three-dimensional reconstruction technique in this paper. The normal physiological stress distribution of proximal femur is obtained by finite element analysis under three kinds of behavior conditions: one-legged stance, abduction and adduction. The structural topology optimization method is applied to simulate the cortex of the proximal femur under the combined action of three kinds of behavior conditions, and the anatomic morphological characteristics of the proximal femur are compared. The distribution trend of biology force line of proximal femur and the characteristics of cortex are analyzed. The results show that the biology force lines of bone structure and the morphological characteristics of cortex depend on the load of human activities. The distribution trend of biology force line is related to the direction of trabecular bone and the ridge trend and firmness of cortex when bone is loaded physiologically. The proposed analytical method provides a solution to determine the biology force line of bone and the distribution characteristics of cortex. The conclusions obtained may guide the reasonable placement of internal fixator components of fracture.