[Structural design and evaluation of bone remodeling effect of fracture internal fixation implants with time-varying stiffness].

The stiffness of an ideal fracture internal fixation implant should have a time-varying performance, so that the fracture can generate reasonable mechanical stimulation at different healing stages, and biodegradable materials meet this performance. A topology optimization design method for composite structures of fracture internal fixation implants with time-varying stiffness is proposed, considering the time-dependent degradation process of materials. Using relative density and degradation residual rate to describe the distribution and degradation state of two materials with different degradation rates and elastic modulus, a coupled mathematical model of degradation simulation mechanical analysis was established. Biomaterial composite structures were designed based on variable density method to exhibit time-varying stiffness characteristics. Taking the bone plate used for the treatment of tibial fractures as an example, a composite structure bone plate with time-varying stiffness characteristics was designed using the proposed method. The optimization results showed that material 1 with high stiffness formed a columnar support structure, while material 2 with low stiffness was distributed at the degradation boundary and inside. Using a bone remodeling simulation model, the optimized bone plates were evaluated. After 11 months of remodeling, the average elastic modulus of callus using degradable time-varying stiffness plates, titanium alloy plates, and stainless steel plates were 8 634 MPa, 8 521 MPa, and 8 412 MPa, respectively, indicating that the use of degradable time-varying stiffness plates would result in better remodeling effects on the callus.

Topology optimization of embracing fixator considering bone remodeling to mitigate stress shielding effect.

The embracing fixator is one of the widely used internal fixation implants for bone fracture treatment. However, the stress shielding effect, a stress imbalance between the implant and bone caused by the mismatch in mechanical properties between them, is a significant and critical issue that may lead to treatment failure. Thus, it is of great importance to design the implant with an appropriate stiffness which can mitigate the stress shielding effect and provide the most favorable mechanical environment for bone healing and remodeling. To this end, a time-dependent topology optimization algorithm considering bone remodeling is proposed to optimize an embracing fixator used in the tibia fracture treatment. The change of callus density over time is simulated based on a bone remodeling model, and the callus density after a period of bone remodeling is selected to be the design objective to maximize. The design constraints include volume and the compliance of the whole fixation system. Meanwhile, the influence of the constraints on the regularity of material distribution of the optimized result is also studied. Besides, to test the effectiveness of the consideration of the bone remodeling in the embracing fixator design, a topology optimization concerning the minimization of the compliance of the entire system is also performed to make a comparison. Finally, the safety performance of optimized results considering bone remodeling is also verified by static analysis.

Biomechanical evaluation of a healed acetabulum with internal fixators: finite element analysis.

BACKGROUND: Treatment of complicated acetabular fracture with internal fixation usually has high risk of failure because of unbefitting fixation. However, evaluation of the biomechanical effect of internal fixation under physiological loading for fracture healing is still generally rarely performed. The purpose of this study is to analyze the biomechanical characteristics of a healed acetabulum with designed internal fixators under gait and to explore the biomechanical relationship between the healed bone and the internal fixator. METHODS: A patient-specific finite element model of whole pelvis with designed internal fixators was constructed based on the tomographic digital images, in which the spring element was used to simulate the main ligaments of the pelvis. And the finite element analysis under both the combination loading of different phases and the individual loading of each phase during the gait cycle was carried out. The displacement, von Mises stress, and strain energy of both the healed bone and the fixation were calculated to evaluate the biomechanical characteristics of the healed pelvis. RESULTS: Under the combination loading of gait, the maximum difference of displacement between the left hip bone with serious injury and the right hip bone with minor injury is 0.122 mm, and the maximum stress of the left and right hemi-pelvis is 115.5 MPa and 124.28 MPa, respectively. Moreover, the differences of average stress between the bone and internal fixators are in the range of 2.3-13.7 MPa. During the eight phases of gait, the stress distribution of the left and right hip bone is similar. Meanwhile, based on the acetabular three-column theory, the strain energy ratio of the central column is relatively large in stance phases, while the anterior column and posterior column of the acetabular three-column increase in swing phases. CONCLUSIONS: The acetabular internal fixators designed by according to the anatomical feature of the acetabulum are integrated into the normal physiological stress conduction of the pelvis. The design and placement of the acetabular internal fixation conforming to the biomechanical characteristics of the bone is beneficial to the anatomical reduction and effective fixation of the fracture, especially for complex acetabular fracture.

The optimal design of 3D-printed lattice bone plate by considering fracture healing mechanism.

The biomechanical stimulus is the most important factor for fracture healing and mainly determined by the structural stiffness of bone plate. Currently, the materials commonly used in bone plates are stainless steel and titanium, which often lead to stress shielding effects because of their higher elastic modulus compared with the bone. This article suggests an optimal design method of lattice bone plate based on fracture healing theory. First, the mechanical regulation model with deviatoric strain is established to simulate the tissue differentiation process during fracture healing process. The ratio of the average elastic modulus of callus at the 120th day to the elastic modulus of mature bone is used to characterize the fracture healing rate. Second, the optimal elastic modulus of the design domain is obtained by the optimization mathematical model with the maximum fracture healing rate. Then, the design domain is filled with microstructures, the porosity of which is adjusted to make it possible that the equivalent elastic modulus is equal to the optimized value. And the finite element analysis of the bone plate with microstructure is executed. Finally, the designed lattice bone plates are manufactured through 3D printing, and the mechanical test is carried out. The simulation results indicate that the fracture healing rate is maximum when the elastic modulus of material in design domain is 38 GPa under the constraints of fixation stability. And both the finite element analysis and experiment results show that the designed lattice bone plate meet the strength requirements of fracture internal fixation implants.

[Study on the characteristics of biology force line of proximal femur based on structural topology optimization].

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.